a review of uncertainty in flight vehicle structural damage monitoring, diagnosis and control:...

Progress in Aerospace Sciences 46 (2010) 247–273

Contents lists available at ScienceDirect

Progress in Aerospace Sciences

0376-04

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/paerosci

A review of uncertainty in flight vehicle structural damage monitoring,diagnosis and control: Challenges and opportunities

Israel Lopez, Nesrin Sarigul-Klijn n

Mechanical and Aerospace Engineering, Space Engineering Research and Graduate Program, University of California at Davis, Davis, CA 95616-5294, USA

a r t i c l e i n f o

Available online 11 May 2010

Keywords:

Structural health monitoring

Flight vehicles

Uncertainties

Diagnostics

Control

21/$ - see front matter & 2010 Elsevier Ltd. A

016/j.paerosci.2010.03.003

esponding author. Tel.: +1 530 752 0682; fax

ail address: [email protected] (N. Sar

a b s t r a c t

This paper presents a comprehensive review of uncertainties involved in flight vehicle structural

damage monitoring, diagnosis, prognosis and control. Uncertainties can cause infeasibilities, false

diagnosis and very imprecise prognosis if not correctly taken into account. The purpose of this paper is

to review existing methods that have been developed to address the problem of uncertainty in the area

of damage sensing, diagnosis, prognosis and control in flight vehicles. The mathematical and statistical

methods in analyzing uncertainty are first presented and compared. Then, the different sources and

perspectives of uncertainties in the damage assessment process are presented and classified. Following

this, diagnosis and prognosis methods are reviewed. Final review section covers the control of damaged

structure under uncertainty. In each section and in the concluding remarks section the research

challenges in the field of flight vehicle structural damage sensing, diagnosis and prognosis methods as

well as control under uncertainty are identified and promising new ideas are discussed.

& 2010 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

2. Uncertainty analysis methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

2.1. Probability theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

2.2. Fuzzy sets (possibility) theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

2.3. Dempster–Shafer (D–S) evidence theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

2.4. Comparison of methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

3. Sources of uncertainty in flight vehicle structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

3.1. Complex structural dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

3.2. Environment and operational effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

3.3. Sensor uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257

4. Fault and damage diagnosis methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

4.1. Data pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

4.2. Feature extraction and selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

4.3. Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

4.4. Data fusion and decision-making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

5. Prognosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

6. Control sytems under uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

7. Concluding remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

ll rights reserved.

: +1 530 752 4158.

igul-Klijn).

1. Introduction

In today’s modern society, the availability, reliability and high-performance of flight vehicles are increasingly more demanding.The flight transportation systems are a major source of network

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mailto:[email protected]

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Nomenclature

AI artificial intelligenceANN artificial neural networkARMA autoregressive moving averageARX autoregressive with exogenous inputBNs Bayesian networksDOF degree of freedomD–S Dempster–Shafer evidence theoryFA factor analysisFDI fault detection and identificationFDD fault detection and diagnosisFDIR fault detection, identification, and reconfigurationFTCS fault tolerant control systemHUMS health usage monitoring systemsICA independent component analysiskNN k-nearest neighborLDA linear discriminant analysisLLE local linear embeddingLTSA local tangent space analysisMDS multidimensional scalingMDOF multi-degree of freedomMVU maximum variance unfoldingMLP multilayer perceptron neural networkNNs neural networksPDF probability distribution functionRF random forestsPZT piezoelectricPCA principal component analysisRUL remaining useful lifeROC receiver operating characteristic

SHM structural health monitoringSVD singular value decompositionSVM support vector machineUAV unmanned aerial vehiclePðAÞ probability of event A

Y finite set or frame of discernmentpðAÞ probability distribution of event AA not A; negation of A

PosðUÞ possibility measureNec Uð Þ necessity measure| empty set[,\ set theoretic union and intersectionA set membership� set summation8x for all x valuesm(x) degree of membership function for value x

A0 support of triangular fuzzy numberaA 0,1½ � fuzzy membership valueAa fuzzy membership support at resolution level am Uð Þ basic belief assignment, BBAC¼ 2Y set of all of subsets of YBel Að Þ belief measure of event A

Pl Að Þ plausibility measure of event A

Ek evidenceX measurement matrixY transformed data matrixL Uð Þ likelihood functionHA hypothesis of event A

t Uð Þ damage threshold functionC classifiero class label (classification type)

I. Lopez, N. Sarigul-Klijn / Progress in Aerospace Sciences 46 (2010) 247–273248

support for every-day life and economic stability. The impact thataircraft and aerospace industry has had on our lives and worldeconomy is very pronounced. As such, the aerospace industrycontinues at the forefront of engineering research and develop-ment technologies. An ever-constant objective in all technologicalinnovations is the maintenance of highly reliable and safetransportation systems, but as complexity of components andsystems increases, and continuous deterioration of current aircraftexists due to aging, the risk of system faults and failures increases.Technologies addressing these safety and performance issues arerapidly evolving. Recent developments in sensing technology,signal processing, controllers and their systematic integration have

Fig. 1. Diagnostic and damage tolerant

attractive potential for resolving numerous issues related to aircraftdiagnostics, prognostics and control, such as maintenance optimi-zation, improved performance, extended life of structures andoverall safety improvement. Fig. 1 presents a general architecturerepresenting the integration of flight vehicle structural damageassessment and control. Automated structural health monitoringand diagnostics based on advanced technologies will alleviateservice and in-flight damage problems. Accordingly, controlsystems are required with the capability of compensating forcritical and unpredictable system dynamics changes caused bydamage or failures, and maintainability of the same or, at a veryminimum, a safe level of performance of the controlled aircraft.

control process of flight vehicles.

I. Lopez, N. Sarigul-Klijn / Progress in Aerospace Sciences 46 (2010) 247–273 249

The primary goals of any structural damage monitoring andassessment system are to ensure reliability and safety and tominimize life-cycle cost of the structure in question. Damageassessment has applications in the majority of engineeringstructures and mechanical systems ranging from aerospacesystems to manufacturing equipment. As a result, a multitude ofdifferent approaches appear in the literature to address theproblem of damage assessment. Some recent reviews providevaluable categorization of existing structural heath managementmethods [1–9]. Multiple structural health monitoring (SHM) anddiagnostic technologies have been developed and applied tonumerical simulations and scaled structural experiments. How-ever, the transition from research to practice has been rather slowwith the exception of the rotating machinery industry. Successfulapplications of rotating machinery damage diagnosis and prog-nosis exist because extensive training data are available, and moreimportantly, the damage location and damage types as well asoperational and environmental conditions are often well known apriori and do not vary significantly [10].

One major reason for the slow-progress in applying diagnostictechnologies to real-world structures is the existence ofuncertainty in every step of the damage assessment process.Early works in the area of damage estimation focused on directapplication of physics-based system identification techniques,such as estimation of system stiffness matrix and/or modalparameters [1]. These conventional damage estimationapproaches deal with deterministic models where all theparameters are considered identifiable and uncertainties are notdirectly accounted for, which make it rather difficult to evaluatehow reliable the estimated damage index is. Along with thestudies in deterministic damage assessment, consideration ofuncertainties has received more attention in recent years,particularly in data-based damage assessment methods.Data-driven methods rely on previous system measurements fortraining and assessment of the current system health state.Although data-driven methods are great for indicating thepresence of damage, damage assessment results obtained fromdata-driven methods are generally more simplistic and lackinformation with regard to the nature of the damage. More recentworks [3,7,9,10] have attempted finding a balance betweenphysics-based and data-driven methods to maximize theinformation and confidence levels of the damage diagnosis. Increasein confidence in damage diagnosis is directly proportional to theuncertainty level considered.

In applications of structural diagnostic systems, uncertaintymay take the form of component and/or system variability,environmental and operational conditions, data acquisition errorsand data interrogation errors, to name a few. Uncertainty, in plainwords, is lack of certainty. In more detail, uncertainty is a stateof limited knowledge where it is impossible to exactly describeexisting state or future outcome(s) [11]. In cases where uncertaintycannot be fully described via deterministic or random approaches,also known as aleatory uncertainty, then uncertainty is categorizedas epistemic, which deals with lack-of-knowledge of quantitiesor processes of the system or the environment. Many applicationsof uncertainty analysis in damage assessment have assumed analeatory model when the uncertainty is of epistemic nature.Legitimate reasons can be leveled for reducing epistemicuncertainties to aleatory uncertainties. Consequently, selectingand developing an uncertainty model can sometimes be more of anart than a science. The systematic consideration of uncertainties isas important as having the appropriate structural system model,especially during model validation where the total error betweenphysical observation and model prediction must be characterized.

The scope of this paper is to provide an analysis of the sourcesof uncertainties in flight vehicle structural damage assessment,

present different methods of describing the uncertainties and givea detailed literature review on existing approaches that addressthe problem of uncertainty. Following these introductory re-marks, the next section presents theoretical formulation methodsfor analysis of uncertainties. The section after this covers thealternative approaches that exist in the literature for addressinguncertainties at each step of the structural damage diagnosis andprognosis processes. The final review section covers control ofdamaged systems under uncertainties. After these reviews, thechallenges and future research directions are presented in theconcluding remarks section.

2. Uncertainty analysis methods

Propositions of future events are neither true nor false, butpotentially either; hence, their truth value is undetermined. Theproblem of ‘‘truth’’ status is not limited to future events only. Theuncertainty covers all cases where a decision cannot be reached inclassifying as either completely true or completely false. The focusof this paper is on dealing with flight vehicle structural damageunder uncertainty. The diagnostic accuracy and confidence levelof a damage assessment technique are adversely affected by theinherent system, environment and data interrogation uncertain-ties. From the risk assessment community, two types ofuncertainties have been identified, aleatory and epistemic [12].Aleatory uncertainty refers to the inherent variation associatedwith the physical system under question and its environment, andit is not due to a lack of knowledge and cannot be reduced. In theliterature, aleatory uncertainty is also known as variability,irreducible uncertainty, stochastic or random uncertainty. Epis-temic uncertainty refers to the lack of knowledge or incompleteinformation of the system and its environment. In the literature,epistemic uncertainty is also known as subjective uncertainty,state of knowledge uncertainty or reducible uncertainty. The mainareas of research in uncertainty can be organized as probability-based methods; possibility-based methods; set–theoreticalmethods; evaluation and measures; and epistemologicalconcepts—verifiability, validation, and usability [12,13]. In orderto describe and quantify different types of uncertainties withinthe flight vehicle structural damage analysis, we will focus on theprimary uncertainty analysis methods known as: (1) probabilitytheory; (2) fuzzy set or possibility theory and (3) evidence theory.

2.1. Probability theory

In the probabilistic approach, uncertainties are characterizedby the probabilities associated with the events. The probabilitycan be represented by the frequency of occurrence, if sufficientdata are available, from which a probability distribution isgenerated for statistical analysis. Probabilistic analysis is themost widely used method for characterizing uncertainty, whichcould be due to stochastic disturbances, such as noise, variabilityconditions and risk considerations. Uncertainty can be modeledusing either discrete or continuous probability distributions. Ingeneral, there are three approaches to calculate the probabilityof event A. Classical probability: P(A)¼k/n, where k is the numberof elementary events involved in A and n is the total number ofelementary events. Frequency approach: P(A)¼m/n, where n isthe number of repeated times of the experiment and m is the totalnumber of times A happens. Subjective determination (Bayesian)approach: P(A)¼the value given by priors or experts [14]. It isusually used for random events that cannot be repeated in largequantity. Any probability measure P(U) on a finite set Y can be

Fig. 2. Example membership function, m in fuzzy sets theory.


uniquely determined by a probability distribution function

p : Y- 0,1½ � ð1Þ

from the formula given below

PðAÞ ¼XYAA

pðyÞ ð2Þ

2.2. Fuzzy sets (possibility) theory

Fuzzy sets theory allows uncertainty modeling when trainingor historical data are not available for analysis. Fuzzy theoryfacilitates uncertainty analysis where the uncertainty arises fromlack of knowledge or ‘‘fuzziness’’ rather than randomness alone.Fuzzy sets theory was introduced by Zadeh [15] as a means tomodel the uncertainty of natural language, which developed thenotion of partial-truths or fuzzy form of determining if an elementis a member of a set or not. Classical set theory allows for ‘‘crisp’’membership, while on the other hand, fuzzy theory allows forgradual degree membership. This approach has been used toanalyze uncertainty associated with incomplete and subjectiveinformation in engineering design and analysis. The reader shouldnote that in this paper, the possibility theory is assumed to be apart of the fuzzy theory. Zadeh used fuzzy sets as a basis forpossibility since a proposition that associates an uncertainparameter to a fuzzy set induces a possibility distribution forthis quantity, which provides information about the values thatthis quantity can assume. Given the universal set Y, thepossibility is defined on S and it is a set function with values in[0,1]. A possibility measure, Pos, is characterized by the property

Pos [iA I

Ai

� �¼ sup

iA IPosðAiÞ ð3Þ

for any value of subsets of Y defined by an arbitrary index set I; itis semi-continuous from below. A necessity measure, Nec, ischaracterized by the following property:

Nec \iA I

Ai

� �¼ inf

iA INecðAiÞ ð4Þ

for any family of subsets of Y; it is semi-continuous from above.Possibility theory satisfies the following conditions:

Posð|Þ ¼ 0, PosðYÞ ¼ 1 ð5Þ

PosðV [WÞ ¼maxðPosðVÞ, PosðWÞÞ ð6Þ

where V and W are two non-intersecting sets involved in Y.The essential difference between possibility theory and

probability theory is that the probability sum of all non-intersecting events in probability theory is 1, while it may notbe 1 in possibility theory. Furthermore, possibility theory may beviewed as a special branch of imprecise probabilities, in whichfocal elements are always nested [13,14]. This makes possibilitytheory naturally suited for representing evidence in fuzzy sets,since a-cuts of fuzzy sets are also nested. The imprecision inprobabilities and utilities is modeled in fuzzy sets throughmembership functions defined on the sets of possible probabil-ities and utilities [13]. The theory of fuzzy sets aims to modelambiguity by assigning a degree of membership m(x), between 0and 1, see Fig. 2. The parameter x is represented as a triangularfuzzy number with support A0. The wider the support of themembership function, the higher the uncertainty. The fuzzy setthat contains all elements with a membership of aA[0,1] andabove is called the a-cut of the membership function. At aresolution level of a, it will have support of Aa. The higher thevalue of a, the higher the confidence in the parameter.

The membership function is cut horizontally at a finite numberof a-levels between 0 and 1. For each a-level of the parameter, the

model is run to determine the minimum and maximum possiblevalues of the output. This information is then directly used toconstruct the corresponding fuzziness (membership function) ofthe output, which is used as a measure of uncertainty. Furtherdetails on fuzzy sets are provided in References [15,16].

2.3. Dempster–Shafer (D–S) evidence theory

Dempster–Shafer’s evidence theory [17,18] relies on theconcept that information of a given problem can be inherentlyimprecise. Hence, the bound result that consists of both beliefvalues, the lower bound of probability and, plausibility, upperbound of probability, is presented. Unlike possibility or fuzzy setand probability theory, in evidence theory there is no need tomake an assumption or approximation for the imprecise informa-tion. Epistemic plausibility can be represented in evidence theoryvia belief functions, where the degrees of belief may or may nothave mathematical properties of probabilities. In comparisonto probability theory, instead of using probability distributionsto capture system uncertainties, a belief function is used torepresent a degree of belief. Probability values are assigned to setsof possibilities rather than a single event. The basic entity in theD–S theory is a set of exclusive and exhaustive hypotheses aboutsome problem domain. It is called the frame of discernment,denoted as Y. Given a universal set or frame of discernment Y,then a basic belief assignment (BBA) is a function m:C-[0,1],where C is the set of all subsets of Y and the power set of Y isC¼2Y. The function m can be interpreted as distributing belief toeach of element in C, with the following criteria satisfied:XAAC

mðAÞ ¼ 1 ð7Þ

mð|Þ ¼ 0 ð8Þ

In evidence theory, we do not assign any degree of belief to theempty proposition | and we ignore the possibility for an uncertainparameter to be allocated outside the frame of discernment. Thus,the element A is assigned as a basic belief number m(A) describingthe degree of belief that is committed exclusively to A. Note that asituation of total ignorance is characterized by m(Y)¼1. The totalevidence that is attributed to A is the sum of all probabilitynumbers assigned to A and its subsets

BelðAÞ ¼X8E:EDA

mðEÞ ð9Þ

Given that we have n number of information sources affectingdecision-making, then each information source Si will contributeby assigning its beliefs over Y. The assignment function of eachsource is denoted by mi. Thus, according to the observations ofinformation source, the probability that the safest value isindicated by the evidence interval becomes

BeliðAÞ,PliðAÞ� �

ð10Þ


The above interval reduces to a single point in the case ofBayesian belief function (BBF). The lower bound of the evidenceinterval is the belief function, which amounts for all the evidenceEk that supports the selection of A

BeliðAÞ ¼X

Ek DA

miðEkÞ ð11Þ

The upper bound of the evidence interval is the plausibilityfunction, which accounts for all the observations that do not ruleout the selection A

PliðAÞ ¼ 1�BeliðAÞ ¼ 1�X

Ek\Aa|

miðEkÞ ð12Þ

Because of uncertainty, the degree of belief for selecting choiceA and the degree of belief for a negation of deciding for A do nothave to sum up to 1. Given two independent belief functions overthe same frame of discernment, Dempster’s rule gives a way forcombining BBA structures

mi �mj

� �ðAÞ ¼

PEk\Ek0 ¼ AmiðEkÞmjðEk0 Þ

1�P

Ek\Ek0 ¼ |miðEkÞmjðEk0 Þð13Þ

The denominator of (13) is a conflict of information given byindependent information sources. Dempster’s rule disregardsevery contradiction by normalizing with the complementarydegree of contradiction because it is designed to use consistentopinions from multiple sources as much as possible [18]. For n

Fig. 4. Uncertainty sources a

Fig. 3. Relationship among main classes of uncertainty measures.

mass functions m1, m2,y,mn, the combined mass function andmeasure of contradiction are given by

mðAÞ ¼ m1 �m2 � . . .�mnð ÞðAÞ

¼1

1�C

X\N

i ¼ 1Ei ¼ A

m1ðE1Þm2ðE2Þ. . .mnðEnÞ ð14Þ

C ¼X

\Ni ¼ 1

Ei ¼ |

m1ðE1Þm2ðE2Þ � � �mnðEnÞ40 ð15Þ

The D–S theory has become an important tool for dealing withuncertainty. Recent advancements in the D–S theory are bestcovered in a book by Yager et al. [18].

2.4. Comparison of methods

The diagram shown in Fig. 3 illustrates the relationship amongthe main classes of uncertainty theories. The flight vehicleuncertainty sources and uncertainty quantification strategies aredepicted in Fig. 4 based on the characteristics of the sourceinformation. Given complete knowledge, flight structure damageuncertainties are aleatory uncertainties, but they can be epistemicuncertainties, when insufficient data and/or lack of knowledgeexist to construct probability distribution. Due to space limitation,the well established theories of uncertainty in the D–S theory, thefuzzy sets theory, and other fuzzy theory variations areintroduced only in their basic forms. The various properties ofthese basic forms and the associated conditional forms arediscussed in [13–18]. Due to the broad concept of uncertainty,this research area and its engineering applications are still in itsinfancy.

In general, the probability theory formalizes uncertainty whensufficient information is available. A central assumption of theBayesian theory is that uncertainty should always be measuredby a single probability measure and values should always bemeasured by a precise utility function, which is called theBayesian dogma of precision [13]. Alternative formalisms inuncertainty analysis have been motivated by the fact that thedogma of precision is mistaken in addressing non-randomuncertainties. Imprecision, indeterminacy, vagueness and indeci-sion are incompatible with individual probabilistic expressions.

nd analysis approaches.


The Bayesian approach assesses precise prior probabilities ofparameters and combines these to output precise posteriorprobabilities, even when there is very little prior information,which may render unreliable and irrational results. Alternativeformalisms, such as the D–S theory, give explicit notation toconfidence measures, also known as imprecise probabilities,where lower and upper probabilities are generated. In general,lower probability is taken as the minimum certainty at which youare willing to make a specific decision, and upper probability isthe maximum certainty at which you are willing to make aspecific decision. From the standpoint of the D–S theory

pðyÞ ¼mðfygÞ ð16Þ

for all yAY. Probability measures are the point where belief andplausibility measures coincide.

Admission of imprecision in probabilities is needed to reflectthe amount of information on which they are based. In terms oftime-constraint situations, assessment of precise probabilitiesmight be impractical due to lack of time or computational ability,or because of the level of system complexity. In other words, forpartial data, partial answers should be given. The D–S theoryhandles both the uncertainty and imprecision contained in datadue to the belief and plausibility functions, which can be seen asan interval enclosing imprecise probability. The D–S theory doesnot pretend to provide full answers to probabilistic data, butrather provides partial answers by estimating how much theevidence supports the truth of a hypothesis, instead of estimatinghow close the hypothesis is to being true. But, greater generality isneeded because the class of belief functions in the D–S theory isnot large enough to model all reasonable types of uncertainty.Furthermore, Dempster’s rule of combination, which is central tocombining evidence and updating probabilities, has limitationswhen dealing with highly conflictive data sources, which renderthe rule unreliable [14]. While imprecise probability approachescan construct mathematical theories that exhibit desirableproperties in terms of imprecision and ignorance analysis, theutility or practicality of such approaches depends on how wellthey account for the origin of imprecision or ignorance, and howwell they can integrate new evidence or information. Given thatinterval probabilities are generated as outputs, how do theseintervals convey information for inference and decision-makingprocesses?

In terms of damage assessment, the fuzzy sets theory can alsohave problems when dealing with pattern recognition. Forexample, assume we have a normal and a faulty operatingcondition. If a given pattern is far away from the normal operatingclass, it will have a small membership value according to thisclass, and consequently, it will have a bigger membership tofaulty class. But if in addition, this pattern is far from both classes,it will be wrongly assigned to second class instead of beingrejected, which could be a rejection class. In other words, fuzzysets can only deal with vagueness and not necessarily impreci-sion. Ambiguity is only one potential source of imprecision inprobabilities and, unlike other sources of imprecision, it can beeliminated through careful elicitation [13]. Critics of fuzzy sets

Table 1Axioms of probability, fuzzy-set (possibility), and evidence theories.

Probability theory Possibility theory

P(Y)¼1 Posð|Þ ¼ 0, PosðYÞ ¼ 1

P(A)Z08AAS 8 A,BAS if ADB, then PosðAÞrPosðBÞ

8Ai , iA I, Ai disjoint P [Ii ¼ 1Ai

� �¼P

iA IPðAiÞ 8Ai , iA I, Ai disjoint P [Ii ¼ 1Ai

� �¼max

iA IPosðAið

argue that the membership functions that are chosen to modelambiguous probability judgments seem both arbitrary andinappropriately precise and that no clear interpretation of themembership function has been established [13,14]. The assess-ment of fuzzy sets requires substantial input from a user, whichmight render its usage closer to that of expert systems.

The multiple uncertainty management paradigms producedifferent numerical responses and with different limitations,which makes the choice clearly not arbitrary. Thus, the choice ofuncertainty analysis approach depends on the nature of theproblem and the expertise of the user. In the case of insufficientinformation and no-conflicting evidence, the possibility theory isa suitable method to quantify uncertainty. If conflicting informa-tion exists, the evidence theory should be used instead. Evidencetheory is the general theory to represent uncertainty and includesthe possibility and probability theories. Table 1 compares theuncertainty theories in terms of their axioms. Probability theorycan handle uncertainty contained in data, but it cannot treat theimprecision. Fuzzy sets theory can handle the vagueness typeimprecision by replacing the additive axiom in probability theorywith the weaker monotonicity axiom.

There have been relatively few reports of experiments todirectly compare methods to combine probabilistic informationunder imprecision with the D–S, fuzzy sets and Bayesian theories.Several comparison papers based on simulation data or assumedsituations [19–25] have concluded that differences in perfor-mance were for the latter evidence combination approaches, butno definite advantage exists among the algorithms apart from thewell known, such as that Bayesian is better fitted for precise priorprobabilities and that it is sensitive to parameter errors andimprecision. The Bayesian theory is best suited for applicationswhere there is no ignorance and conditioning is easily obtainablethrough probabilistic representation and prior odds are available.The Dempster–Shafer theory, and other similar imprecise prob-ability approaches, is more appropriate where uncertainty cannotbe assigned precise probability to a proposition and conditioningeffects are difficult or impossible to measure separately, and priorodds are not pertinent.

3. Sources of uncertainty in flight vehicle structures

Flight vehicle structures differ from any other engineeringsystems in terms of primarily their dynamic environment [26],see Fig. 5. In flight vehicle structural terms, diagnostics is thedetection and quantification of damage; prognostics occur whengiven damage assessment estimation of useful life remaining and/or performance life remaining until full failure is determined. Inorder to conduct diagnosis and prognosis several steps arerequired. Diagnostics is to investigate or analyze the cause ornature of a condition, situation or problem, whereas prognosis isto know before, to calculate or predict the future as a result ofrational study and analysis of available pertinent data [27]. Ingeneral, a diagnostic system consists of data acquisition system,signal processing, feature extraction and selection, physical

D–S evidence theory

mð|Þ ¼ 0, mðYÞ ¼ 1

8 A,BAmðYÞ if ADB, then mðAÞrmðBÞ

ÞÞ 8 Ai , iA I, gðUÞ of subsets of Y if sequence is monotonic, thenlimi-1

gðAiÞ ¼ g limi-1ðAiÞ

Bel Að ÞþBel A�

r1Pl Að ÞþPl A�

Z1

Fig. 5. Aeronautical and space vehicles and their design environment within the atmosphere and beyond.


models and knowledge base of damage when possible, which maybe derived from expert knowledge, such as historical data, referto Fig. 6. Decision making is made by comparing the extractedfeature information with the knowledge base, essentiallybecoming a pattern recognition method. For degradationanalysis and prognosis, performance and degradation predictivemodels, which could be derived from time-series analysismethods, probability theory and/or artificial intelligenceapproaches, are required to forecast when the structuralperformance will decrease to an unacceptable level. In the areasof damage assessment and prognosis, information gatheringand decision making processes are plagued by imperfectcommunication channels, in other words noise and ignorance,which have been improved via enhanced signal and sensingcapabilities, additional data mining techniques and addingdiagnostic system redundancy. Fig. 6 shows the general processdescribing diagnostics and prognostics. However, diagnosticimprovements can be time-consuming, complex and expensiveto apply in real flight vehicles due to limited sensory system,environmental factors, among others. In any case, uncertaintyquantification is required in order to understand the capabilitiesand limitations of the diagnostic and prognostic system at hand.The following sections present the issue and application ofuncertainty analysis to the flight vehicle structural damageassessment and prognosis problem.

3.1. Complex structural dynamics

The demand for expansion of the performance envelope ofmobility structures, such as ever increasing speeds, has generatedsignificant advances in the development of lighter, more flexible,

and consequently, more complex and nonlinear structuralsystems. At the same time, higher-fidelity models with fastersolution methods and algorithms have been developed for manyapplications resulting in reduced simulation and cycle times.However, for complex structural systems, the computationaladvances still fall short for many reasons. Furthermore, thepotential of modeling and simulation to understand the innatesystem behavior under unforeseen damage scenarios becomeshighly inefficient. Recently, Worden et al. [8] presented a reviewof nonlinear dynamics applications to structural health monitor-ing. The uncertainties of models of complex systems are muchgreater than for simple systems. Models are simplifications ofsystem descriptions, which allow one to use incomplete informa-tion about the system, and as such, if high definition ofinformation is not necessary, one is allowed to suppress orreduced the order of the mode without loss of model accuracy.The concept of uncertainty is therefore connected with complex-ity and information. This review classifies nonlinear techniquesfor structural heath monitoring (SHM) into three main categories:(i) nonlinear indicator functions; (ii) nonlinear dynamical systemstheory and (iii) nonlinear system identification. The authorsacknowledge that this work is not intended as another nonlineardynamics review in SHM, but to bring forth the importance andchallenges nonlinear response has in generating uncertainty inthe decision-making process during damage assessment.

The increasing development and demand for lighter and morecomplex structures has considerably shifted structural analysistoward a limited applicability of linear approximations. Instructural dynamics, typical sources of nonlinear phenomenaare material properties, energy dissipation such as damping,boundary conditions, and structural geometry [26]. When astructure is damaged, nonlinearities are likely to increase or

Fig. 6. Damage diagnosis and prognosis process.


arise: fatigue cracks, loose joints, friction, impacting components,increased flexibility, among others. Research developments innonlinear dynamical systems have resulted in increasing applica-tions that take advantage of nonlinear phenomena to designdamage detection systems. Sarigul-Klijn et al. [28] presented asmart health monitoring approach tailored for in flight complexdynamics environments using acoustic and vibration sensors dataand their fusion.

Nonlinear instabilities experienced by many engineeringsystems and the resulting aperiodic motions have been studied.Numerous works [28–30] using damaged and buckled beamshave been published in which chaotic motions are studied tounderstand the fractal characteristics of strange attractors viaPoincare maps. In related work, the changes in the geometricalfeatures of an attractor associated with the structural responsehave been studied in the considered system. Recently, progresshas been made by using chaotic excitation and attractor analysisto detect damage in structures [29]. The approach is validatedthrough experiments with a cantilever beam. By tailoring thechaotic excitation, these studies have shown that differences inresponse attractors can be used to identify structural damage. Toaccommodate for uncertainty, a baseline of healthy attractors, thedamage attractors are identified. In addition, statistical processcontrol is used to create and track the nonlinear cross-predictionerror (NCPE) as the structure changes from healthy to increasinglydamaged. Harrison et al. [31] presented a comparative studyamong NCPE, chaotic amplification of attractor distortion (CAAD),Holder exponent, attractor continuity map, and the simple rootmean square (RMS) statistic. This study was performed on acomposite unmanned aerial vehicle (UAV) wing using fibre-bragggrating sensors. Due to the time-scale of experiments, environ-ment effects and measurement systematic errors are part of thepresented analysis. Results of this work demonstrate that CAADand Holder exponent identify damage in all test cases, while theNCPE and continuity measures based on attractor analysis andRMS features fail at detecting the damage. Adams and Nataraju[32] presented a nonlinear dynamical systems framework forstructural diagnosis and prognosis based on lower dimensionaldamage manifolds and normal form simplifications. However, theexperimental results demonstrated were rather limited and no

clear identification and assessment of damage was made based onthe proposed nonlinear approach. Many other nonlinear dynami-cal systems approaches, such as Lyapunov exponents, local andglobal bifurcation, have been studied for SHM [27,29]. Kerschenet al. [29] presented a review of nonlinear system identificationmethods. The authors concluded that due to the highly indivi-dualistic nature of nonlinear systems, no general analysis methodis applicable to all systems in all instances. For nonlinear systems,analytical description is rarely possible. Hence, there is a greatneed to develop a robust and less model dependent approach ofdamage diagnosis in a complex nonlinear dynamic system [27].

Structural damage management systems based on systemidentification approaches can be broadly classified into thefollowing three categories: (a) nonparametric identificationapproaches and (b) parametric identification approaches. Non-parametric techniques attempt to identify the functional repre-sentation of the structure without any priori assumptions of themodel’s structure. Nonparametric models are described by curves,functional relationships, such as neural networks, and tables.Nonparametric analysis methods applied to the area of damageassessment are transient analysis, frequency response, correlationanalysis, time-frequency analysis, spectral analysis, and black boxmodeling. Frequency domain methods have been widely studiedfor SHM applications and they suffer from the fact that they arelimited to linear systems. Worden et al. [8] presented a surveycontaining multiple applications of correlation and spectralanalysis in the area of nonlinear dynamics in structural healthmonitoring. Correlation and spectral analysis can detect presenceof nonlinear response, and cannot handle non-monotonic natureof many nonlinear systems. Fassois and Sakellariou [2] presenteda paper on time-series methods for fault detection and identifica-tion. Uncertainties are naturally taken into account using time-series methods since they are data based rather than physicsbased. Time-series nonparametric nonlinear system identificationfor damage assessment includes spectral models, Hilbert trans-form, Huang–Hilbert transform, and stochastic subspace identi-fication, among others [8,29,33]. Frequency-domain nonlinearsystem identification methods include Volterra–Wiener series,nonlinear normal mode (NNMs), and higher order spectra [29]. Inthe last decade, time-frequency analysis has been shown to be an


effective tool in studying nonlinear phenomena, especiallydamage characteristics. As its name states, time-frequencyanalysis blends the frequency and time-domain methods to offer‘‘continuous’’ snapshots of nonlinear and non-stationary systemdynamics. Multiple reviews of the analysis of damage assessmentof nonlinear and non-stationary via time-frequency methods areavailable [4–6,34]. Readers should note that the authors organizewavelet approaches as part of the time-frequency domain.Analytical approaches for time-frequency analysis include, butare not limited to, Gabor transform, Wigner–Ville distribution,Haar wavelet, short time Fourier transform (STFT), Choi–Williamsdistribution, and multiple wavelet analysis methods [5,6]. Thenonparametric approach can have general applicability withoutrestriction on the system input excitation and can effectivelymodel structural nonlinearity.

Neural network (NNs) approaches for SHM relies on estimatingthe outputs and residuals of the system response. Neural networkapproaches include multi-layer perceptrons, self-organizingmaps, radial basis function networks, support vector machines,Hopfield networks, oscillatory networks, etc. NNs can be used toapproximate any nonlinear relationship with suitable weighingfactors and architecture. Very important to damage assessmentapplications is the attractive property of self-learning ability,which makes it suitable for pattern recognition applications.Given the lack of comparative studies of NNs, Markou and Singh[35] present a guide to enable proper selection of neural networkapproach for its desired application. This review presents acomprehensive survey of neural network approaches for noveltydetection. Several studies have considered uncertainty in applica-tion of artificial neural network (ANN) [36–42]. The noiserejection learning method proposed by Matsouka [43] has beena popular method of considering uncertainties in ANN applica-tions. In the noise rejection method, certain amounts of noise areapplied to the training data to consider either modeling ormeasurement error. Bakhary et al. [36] studied the uncertaintygenerated from errors in the finite element model and noises inthe measurement data. The statistical approach applied to theANN assumes normal distribution and generated a probability ofdamage existence by comparing model probabilities generatedusing the Monte Carlo simulation. ANNs do not quantify theuncertainty involved in a process event, instead, they are used tofilter out uncertainty. Patton et al. [37] developed a neuralnetwork approach for multi-input and multi-output nonlineardynamic system where residual analysis is used to detect andlocalize faults. Work by Patton demonstrates that NNs areexcellent for nonlinear systems, but with moderate noisetolerance, extensive training sessions during design, compleximplementation, and requires a large amount of computation.Recently, Yang et al. [44] presented a neural network approach fordiagnosis of complex dynamic systems based on multi-sensor andmulti-domain knowledge fusion (MSMDK). By using the MSMDKmodel, fault decision uncertainty was reduced by making full usof the sensor information and system knowledge. Yang proposedthe use of the Dempster–Shafer evidence theory to reduce theconflict of different evidences by defining the preference weight.The proposed approach was demonstrated via an experiment ofthe diagnosis of a helicopter autopilot. Neural networks methodsrely on a trained network, and during monitoring, the changes ofthe structure are identified. Primary strengths of ANNs are itsapplication to problems with robustness, complex nonlinearsystems and on-line identification. However, the non-uniquenessof the neural network models of the dynamics of systems is amajor impediment in matching physical behavior with a changein neural network parameters. Although NNs are very effective inidentifying nonlinear relationships, the reliability of the damageassessment remains questionable due to the errors in the input

modal parameters. Model updating would improve the modelingaccuracy, but the applicability of this process is rather limited dueto complexity of real structures. Taking modeling errors intoaccount, the NN approach effectively detects damage on experi-mental data, but with difficult applicability to large structuralsystems such as flight vehicles. The multiple publications on theuse of NNs for damage diagnosis have demonstrated the benefitsof using this analytical tool especially for nonlinear complexstructural systems.

The problem of parametric model identification using dynamicdata is a promising area in various engineering applications due toits applications when structures are time-varying. In practice, it isnot possible to fully capture the dynamic characteristics of astructure via high fidelity simulation models due to incomplete-ness in parameter and model uncertainty. Much attention hasbeen devoted to the identification of mass-stiffness and modalparameters of linear systems under stationary input excitation.The linearity and stationary assumption is valid only in small-amplitude inputs (relative) and when Gaussian noise analysis isapplicable. Methods based on least squares and Kalman filter[45–47] have been proposed to estimate dynamics properties suchas stiffness, mass, natural frequencies, modal damping, and modeshapes of multi-degree of freedom (MDOF) systems. In practice,stationarity is not always applicable, and nonstationarity analysis isrequired. For the identification of time-varying structures and theirvariations due to damage, time domain analyses have been usedextensively, in particular, the methods of least-square estimation,extended and regular Kalman filters, adaptive recursive leastsquares (RLS) with constant or varying forgetting factor and/ormatrix [47]. The commonly used technique is the application of aforgetting factor, which can be constant or varying. The drawbackof a constant forgetting factor is that if the forgetting factor is small,it has a better capability of tracking parametric variation, but it isvery sensitive to measurement noises. But if the forgetting factor istoo big, its tracking capability is compromised. The application offorget matrix, in other words an individual factor per varyingparameter, attempts to isolate each parameter and its variationfrom the rest of the system, which allows for detection andlocalization of damage. Furthermore, Smyth and Wu [46] and Yanget al. [47] show that the direct and simultaneous identification ofstiffness and mass parameters requires the acceleration, velocityand displacement measurements, which are rarely all obtainable oravailable. Likewise, if displacement and velocity responses arederived through integration of acceleration response, significanterrors will result. These approaches can identify and track time-varying system parameters; however, they are not very efficientwhen non-Gaussian uncertainties are involved and require theavailability of all DOF and state responses. Additional nonlinearsystem identification approaches discussed in the literature includethe nonlinear autoregressive moving average with exogenous input(NARMAX) which is a generalization of the ARMA time-seriesmodels [29].

In order to properly describe the uncertainties arising frommeasurement noise, modeling error, data incompleteness, statis-tical methodologies based on Bayesian probabilistic inferencehave been developed. The advantage of Bayesian approach is thatit follows directly from the probability axioms and there are noad-hoc assumptions that lead to loss of information. Multipleworks have been presented in the use of Bayesian inference toidentify and update the uncertainties in model parameters andmodel selection [45]. Model identification and selection for bothlinear and nonlinear dynamic models have been studied in thecase of measured input and outputs and for the case of outputonly measurements [48]. Katafygiotis and Yuen [49] present astatistical model updating methodology based on modal identi-fication method. This study was limited with training data since it


was based on benchmark study. When noise was included, theresults showed multiple false-positive damage locations. Yuenet al. [50,51] presented a Bayesian approach for damage detectionusing output measurements only. The method presented does notmake any assumptions about stationarity of input excitation andsignal noise content, but it was limited to a numerical example.Muto et al. [52] and Kerschen et al. [53] applied Bayesianinference and Markov Chain Monte Carlo (MCMC) to identifythe unknown probability distribution, which captures theuncertainty of a parametric model and as a goodness-of-fit modelcomparison. These works have been based on the quantitativeexpression of model parsimony, also known as Ockham’s razor,which states that effective simpler models are to be preferredover unnecessarily complicated models. The reason for this is thatcomplicated models will tend to over-fit data and result in poorfuture prediction performance. In addition, most of these studieshave only been demonstrated with numerical and experimentalmodels that have limited degrees of freedom.

State estimation and system identification of nonlinearstructures with non-Gaussian uncertainties can be applied.However, this technique is computationally expensive and toreduce this expense, significant experience is required to developa simplified model that captures the necessary system dynamics.Through comparative analysis, Ching et al. [45] demonstrate thatGaussian-based estimation and identification algorithms, such asKalman filter, are only reliable for models that are almost linearon the time scale of the updating intervals, and when applied toreal structural data, their applicability and reliability is question-able. This study demonstrates the need for time-varying models,model selection, and proper uncertainty quantification. Stateestimation for general nonlinear dynamical systems is an activeresearch area in engineering, especially in signal processingapplications. The developments on parametric and model identi-fication algorithms based on stochastic analysis are applicable tonon-Gaussian and nonlinear systems, but have not yet had asignificant impact on damage diagnosis of complex engineeringstructures.

The uncertainties associated with structural model predictionshave a significant impact on the decision-making process instructural health monitoring. System identification based onupdating finite element models using system response data ischallenging and computationally expensive, however the largenumber of uncertain parameters associated with these modelsmakes the inverse problem extremely ill-conditioned. In addition,non-Gaussian estimation capability is required in order toproperly capture the uncertainty probability distribution. Directcalculation of the probability density function of the modelparameters allows for quantification of the uncertainties of theparameter estimates. As stated by Ockhams’ razor, simplifiedmodels are required, but with appropriate model selection. In realworld applications, complicated models would require a largenumber of sensors and its data processing would be computa-tionally expensive.

While significant work has been done to understand thestructural damage under external excitations, little work has beendone to understand damage characteristics under complexloading conditions, such as aeroelastic phenomena. Wang et al.[54] studied the aeroelastic characteristics of a cantileveredcomposite panel. This paper investigated the effects edge crackgrowth and location has on flutter and divergence speeds. Thecrack damage was assumed to remain open; thus negating thenonlinear phenomena. This qualitative analysis demonstratesthe multiple difficulties involved when considering complexstructural and loading conditions.

Furthermore, as pointed out by Worden et al. [8] nonlinearresponse contains non-uniqueness ability, meaning that system

responses will not vary monotonically. Therefore, the monotoni-city of the structure in question needs to be well understood ifrequired for damage assessment. As a result, complex systemdynamics often generates significant epistemic uncertainty indamage assessment since understanding and predicting responseof nonlinear systems – even when undamaged – is a verychallenging task. The stronger the nonlinear response is, thebigger the lack-of-knowledge becomes. As stated in Worden et al.,with the exception of the Holder exponent example, all applica-tions of nonlinear dynamics to SHM have been made at thenumerical and laboratory scaled experiments where systemvariability and system complexity uncertainties are well con-trolled and limited. Furthermore, Kerschen et al. [29] point outthat most nonlinear approaches assume a deterministic nature,and the degree of uncertainty is rarely quantified, and thefollowing fundamental questions need to be properly addressed:(1) Are the experiments and simulations consistent statisticallyspeaking? (2) What is the degree of confidence associated withthe first answer? and (3) If additional datasets are available, byhow much does the confidence increase? Nonlinearity and systemcomplexity is a type of uncertainty where there is not enoughinformation, in other words it is an epistemic uncertainty.

3.2. Environment and operational effects

In practice, engineering structures are exposed to varyingoperational or forced and environmental or natural conditions. Inthe structural health monitoring area, it has been widelyrecognized that changes in structural response and/or behaviorattributed to damage is difficult to discriminate from those due toenvironmental and operational effects. As such, understanding ofthe structural system condition is knowledge-limited makinguncertain the validity of the applied diagnostic and prognostictechnique. In addition, the often non-stationary nature ofenvironmental and operational conditions, such as wind, traffic,temperature, and humidity, makes data normalization difficult.The difficulty that arises from separating environmental andoperational variations from structural damage is that damage-features are sensitive to both scenarios.

Considerable research efforts have been made to investigatethe separability and/or filtering of environmental variability fromstructural changes due to damage. Sohn [55] published a reviewof the effects of environmental and operational variability onstructural health monitoring. In this survey, data normalization isdetermined as the primary path for filtering the unwanted effectsof operational and environmental conditions. In civil engineeringstructures, numerous studies [55,56] have been performed todetermine the variability of modal properties of the civiltransportation and structural systems in consideration of differentenvironmental factors. The natural variability of the eigenfre-quencies of bridges has been approximately determined to vary5–10% over a 24-hour period. Sohn et al. [56] proposed a linearadaptive model to discriminate the changes of modal parametersdue to temperature changes from those caused by structuraldamage. Peeters et al. [57] proposed a methodology to detectdamage in the presence of varying environmental conditionsusing ARX models and confidence intervals. Other researchershave also studied the effects of varying operational conditions[55,56].

Most of the work in accounting for environmental andoperational effects during damage assessment has been donevia a data normalization scheme. Data normalization requires aknowledge basis or training at all the normal conditions of thestructure in question. Data normalization methods include neuralnetworks, dimensional reduction, novelty detection, principal


component application, and regression modeling, among others[55,58]. Balmes et al. [59] proposed a nonparametric basedapproach on residual associated with a subspace identificationalgorithm. In this study, temperature effects are accounted for bymerging reference datasets recorded at unknown temperatures.To deal with the uncertainties associated with varying environ-mental conditions, Sohn et al. [56] proposed an outlier analysisapproach based on a neural network trained with results of anonlinear principal component analysis (NPCA) that determinesthe distribution of certain identified structural parameters over anundetermined number of environmental factors. Koo et al. [60]proposed an impedance-based SHM technique combining atemperature compensation technique and outlier analysis. Thecompensation technique is based on a cross-correlation coeffi-cient with an effective frequency shift, which is defined as thefrequency shift causing the concurrent impedance data to havethe maximum correlation with the reference-impedance data.Lopez and Sarigul-Klijn [58] presented a comparative study oflinear and nonlinear dimensional reduction techniques to normal-ize modal data of a deteriorating cantilever beam model undertemperature variations and artificial noise. The study demon-strates the importance of dimensionality reduction techniquesprior to proper classification of damage or undamaged data.Manson et al. [61] studied the damage detection of compositepanels under changing conditions of humidity and temperature.In this study, the analysis was based on Lamb waves, PCA pre-processing and outlier analysis. Piezoelectric (PZT) sensors used togenerate Lamb waves can be used as both exciter and sensoryreceiver, which provides the very important benefit of having thecapability of controlling the input excitation. Results of this studydemonstrate that damage-sensitive features are more sensitive totemperature in comparison to humidity, and emphasize the needfor normalization data which covers all normal operations of‘damage-free’ structures. Raghavan and Cesnik [62] presented theuse of the pulse-echo approach of guided-waves to study damagedetection at elevated temperature for space applications. Indenta-tion damage detection was possible at temperatures up to 80 1C,and thru-hole damage was achievable at all temperatures, 20 1Cto 150 oC. In this study, a search for temperature insensitivematerial properties and a simple signal similarity differenceapproach was used to perform an outlier analysis.

Environmental factors can also have a significant effect theboundary conditions of the structure. Lew [63] presented the useof feedback control to enhance the sensitivity of naturalfrequencies to structural damage, while minimizing the sensitiv-ity due to uncertain boundary conditions. This study, however,assumes that the primary structure has or allows for a secondarystructure (up to 20% of primary mass) to act as passive controller,disregards any effects the vibration control would have on thestructural performance, and does not take noise content intoaccount. Moyo and Brownjohn [64] presented the use ofBox–Jenkins modeling to assess and separate the effects ofoperational anomalies, such as traffic, accidents and maintenance,from permanent effects originating from damage on a bridge.In this study, temporary structural response anomalies, i.e.operational changes, were identified as separate from permanentchanges, i.e. damage.

3.3. Sensor uncertainty

In the process of damage assessment, a very critical commu-nication component is the sensor unit and network chosen anddesigned for the monitored structure. The information providedby the sensory system must be assessed under a completeunderstanding of the principles governing the operation of the

sensor and its physical and spatial limitations. Sensors impreci-sion and uncertainty is an inherent property because they aresubject to noise, which is a generic term encompassing impreciseand/or unwanted behavior. The occurrence of sensor noise is dueto poor understanding of the principles governing the sensorbehavior, a lack of understanding of the environment, changingenvironmental and/or operational conditions, and toleranceswithin the sensor, among others. Note to the reader, this sectiondoes not deal with the typical filtering, such as windowing andsampling rate, of the signal in order to remove noise. Due to itsuncertain nature, sensor data must be validated for damageassessment since high fidelity is required. Sensing uncertaintymay arise from non-permitted deviations due to sensing device,transducer, signal processor, and communication interface, whichmay appear mainly as bias, drift, complete failure and precisiondegradation.

Sensor or instrument fault detection and identification (IFDI)has been studied by numerous researchers in multiple areas.Mehranboud et al. [65] offers a detailed review on the applicationof Kalman filters, parity relation, PCA, artificial neural networks(ANN) and Bayesian belief networks (BBN) to detect and identifyfaults in sensors. Mehranboud’s work is based on BBNs for dealingwith uncertain knowledge on the reliability of sensors. In thiscontext, the sensor becomes the structure under question forhealth monitoring. Furthermore, it is recognized that simulta-neous IFDI and structural damage assessment should beperformed; thus, quantifying and incorporating sensor uncer-tainty into the overall SHM process. Often times, redundancy isincluded in sensor network design to make sure that sensor datais available even when discrete sensor failures occur. Friswell andInman [66] presented sensor validation methods based on modalfiltering as well as PCA residual analysis given the case of dataredundancy. For modal filtering, the analysis assumes lowuncertainty in the modal parameters. In a follow-up work,Abdelghani and Friswell [67] presented a residual analysismethod for the localization of faulty sensors for additive andmultiplicative faults in sensors. The damage localization is basedon a correlation index; however, the correlation index fails atproviding sensor fault magnitude. Thus; the deciding if sensor isfaulty depends on user’s threshold or experience. Kerschen et al.[68] makes use of PCA for sensor fault detection, isolation andcorrection. The procedure was experimentally evaluated using abeam under linear and nonlinear behavior. Very importantly,Kerschen identifies that work needs to be done in separatingsensor faults from structural damage.

Ibarguengoytia et al. [69] presents an algorithm for sensorvalidation in real-time environments. The algorithm is basedon Bayesian networks and was applied to temperature sensorsfrom a combined cycle gas turbine for sensor fault diagnosis.A hierarchical process is applied where one Bayesian network isapplied for detection and a separate one for faulty sensor isolation.Mengshoel et al. [70] applied Bayesian networks for sensorvalidation and diagnosis to an electrical power system of aerospacevehicles. Dai et al. [71] proposed an adaptive distributedcoordination framework for handling sensor uncertainty. Thisapproach is based on multi-agent systems and rough set theory,an extension of set theory and similar to fuzzy theory. Theframework offers a hierarchical approach to handle multiple typesof sensor uncertainties via data fusion techniques; however,demonstration of such framework was not provided. Goebel [72]studied fuzzy logic to achieve sensor validation by expressing aconfidence for a given measurement based upon an expectedvalue, the system state, the environmental conditions, sensorreliability, and physical limitations of the system. In this work,uncertainty management is achieved via validation of sensorreadings, sensor fusion, and sensor diagnosis. Sensor validation


and fusion are addressed by probabilistic, fuzzy and neuralnetworks, while sensor diagnosis was addressed via fuzzy theory.Guo et al. [73] proposed a framework for sensor validation inclassification problems based on evidence theory. The proposedevaluation framework is applied to a target classification ofmoving vehicles using acoustic, seismic, and infrared sensors.

Significant progress has been achieved in addressing sensorplacement in the area of SHM. Because sensor placement isessentially an optimization problem and not an uncertaintyproblem, only a few sensor placement papers address the issueof sensor related uncertainty for structural damage applications.Guratzsch and Mahadevan [74] proposes a methodology forsensor placement optimization for SHM under uncertainty. Thismethodology was numerically evaluated using stochastic finiteelement models to generate random uncertainty levels. Optimalsensor placement was derived from probabilistic and reliability-optimization analysis of model responses. Guratzsch points outthat his proposed approach is computationally expensive due tothe optimization of stochastic finite element models. In addition,the study provides optimal sensor placement but no validationwith experiments. For further information, Staszweski andWorden [75] present an overview of optimal sensor placementmethods for damage detection applications.

When dense sensor networks are utilized, wireless commu-nication becomes attractive since electrical wiring is practicallyeliminated or centralized. A promising research area is that of‘smart’ sensors. Nagayama [76] studied the application of smartsensors in SHM. Smart sensors are designed with the followingcapabilities: signal pre-processing, such as measurement ofmultiple physical quantities and data compression; low- or self-power feature; and self-organizing collaborative capability.Giurgiutiu et al. [77] present a brief review and application ofembedded piezoelectric transducers (PZT) in which acts as both asensor and an actuator. The sensor-actuator approach enhancesthe control over the damage-sensitive feature being extractedfrom acquired signals. In this study, it is identified that work isstill required to account for operational and environmentalvariations in order to reduce uncertainty affecting the damagediagnosis. For practical implementation of smart sensors, severalchallenges, such as data loss, time synchronization errors,scalability, sensitivity, communication range, and power limita-tions, must be overcome.

4. Fault and damage diagnosis methods

Uncertainty has been defined as an information gap where adifference exists between the amount of information required toperform the task at hand and the amount of information alreadypossessed. As such, uncertainty becomes a limitation on under-standing and intelligence. Information gathering for knowledgediscovery, in this case structural health state, can be performedvia mathematical and non-mathematical methodologies, and theycan be either by deduction or induction. Given the discovery taskof damage assessment and the user’s experience/knowledge, theuser will analyze system response data and design appropriate‘mining’ tools for automatic knowledge extraction; thus perform-ing data mining. The following paragraphs cover the area ofinformation gathering for structural health monitoring underuncertainty in terms of feature extraction, classification, and datafusion.

In general, the process of data mining and knowledgediscovery consists of the following steps: (1) description ofdiscovery task; (2) data collection; (3) data pre-processing; (4)data mining and (5) situational assessment and decision-making.Step (1) depends on the user knowledge of the structure at hand,

its environment, and user experience. Due to the fact that theknowledge can be subjective and uncertain, the initial descriptionof the problem definition contains uncertainty as well. In the datacollection step it is difficult to determine which original datashould be collected. For many applications, data collectionbecomes a balancing job between collecting limited data at alower overall cost and limited information, or collecting allpossible data but with significant increase in cost, data manage-ment, and possibly conflicting information. The collection ofnecessary data is not always known because the properties and‘location’ of the knowledge is unforeseeable.

4.1. Data pre-processing

Different pre-processing techniques for handling measure-ment error, noisy data, and data transformation and compressionexist. Multiple reviews concerning the application of advance-ments in signal processing to damaged structural response havebeen published, as reported in [2,4,5,7,8,78,79]. Most signalprocessing techniques for damage detection rely on Fourieranalysis for time-invariant stationary problems, and time-variantmethods, such as wavelets, time-frequency and time-seriesanalyses. Staszewski [78,79] has written multiple review papersdiscussing the usage of time-variant analysis in damage assess-ment. Time-frequency methods include, but are not limited toshort time Fourier transform (STFT), Wigner–Ville distribution(WVD), Choi–Williams distribution (CWD), among others. Stas-zewski states that the major difference between each time-frequency method is the way that it handles the problem ofuncertainty. Staszewski [5] and Taha et al. [6] present a review ofwavelet analysis for damage assessment. Wavelets serve as time-varying analysis tools suitable for decomposition, compressionand feature selection. Well known wavelet methods includecontinuous, discrete, and multi-resolution wavelets. Wavelets arealso subject to the uncertainty principle. In the case of wavelets,Staszewski marks the difference between time-frequency repre-sentations and time-scale representations, i.e. wavelets. Animportant usage of time-variant methods is its application tononlinear and non-stationary signal response analysis.

In general, time history response from sensors can be analyzedas is or can be transformed to the frequency or time-frequencydomain. Fassois and Sakellariou [2] presented a review of time-series methods for fault detection. Fassois argues that for linearsystems there is little information loss between time andfrequency domains. Further feature extraction, such as modalproperties from frequency response data, inevitably results in lossof information since the tails of data range are usually discardedand it is contaminated by error propagation. Time-series analysisuses statistical tools for developing mathematical models describ-ing one or more measured stochastic signals and analyzing theirobserved and future behavior. Furthermore, Fassois states thattime-series methods account for uncertainty since they are data-driven based rather than physics based. But it must be alsorecognized that uncertainties are present and need be quantifiedeven for data-driven methods, and that statistical methods are notalways sufficient to account for and quantify the relateduncertainties.

4.2. Feature extraction and selection

Subsequent to data pre-processing is the data mining process,whose main purpose is to discover the hidden knowledge andpatterns within data, which may be applied for informationmanagement, optimization purposes, decision support, andprocess control. Critical to the objectives of data mining is the


generation of quality data, which facilitates the decision-makingin the assessment of structural health. Given large sets of datawith multiple features, there exists significant amount ofredundancy or unnecessary features which reduces the effective-ness, accuracy, and understandability of the data mining results.As such, data compression and dimensional reduction techniquesmay be utilized to reduce the size of datasets [58]. One mustunderstand that uncertainties will arise from the way data istruncated and compressed during the removal of unnecessarydata features, feature extraction, feature selection and noisecleansing. Uncertainties are inevitable, but they can and should besystematically addressed and accounted for. In general, datamining must be performed in order to facilitate the decision-making process of classification. The performance of the classifierdepends on the interrelationship between datasets, number offeatures, and classifier complexity. Increasing number of data anddimensions results in what is known as ‘‘curse of dimensionality’’,which leads to the ‘‘peaking phenomenon’’ in classifier design[80]. In other words, more data does not necessarily mean moreinformation due to the dependency and correlation of manymultidimensional datasets. Jain et al. [81] states that increasingnumber of features may in fact degrade the performance of aclassifier if the number of training samples that are used to designthe classifier is small relative to the number of features.

Due to the complexity and high dimensionality of dynamicresponse data, the simple binary classification (detection case) ofstructural health into damaged or undamaged categories is notalways clear. To perform binary classification, a pattern needs tobe identified among signal features. In real-world data, thesepatterns are scattered in high-dimensional and very oftennonlinear subspaces.

Dimensional reduction simplifies the pattern representationand reduces the computational effort required from classifiers[82]. Dimensionality reduction can be defined as follows. Given ameasurement matrix XARMxD consisting of M data vectors and D

features, dimensional reduction techniques transform dataset

Fig. 7. Taxonomy of dimensio

X into a new data set YARMxd, where doD, with minimal loss ofdata geometry. Fig. 7 shows taxonomy of techniques for dimen-sional reduction, where the main distinction is made betweenlinear and nonlinear methods. Fig. 8 shows the taxonomy ofdimensional reduction methods [80–85].

The best known feature extractor is the principal componentanalysis (PCA) or Karhunen–Loeve expansion that computes them largest eigenvectors of the d� d covariance matrix of the n

d-dimensional patterns. PCA has been used as feature extractor,selector, data compressor and data clustering technique. Othermethods, like nonlinear-PCA, KPCA, factor analysis (FA), projectionpursuit, neural network based mappings, among other nonlinearmapping techniques have been used for feature extraction andclustering in damage assessment studies [3,7,9,35,78,79,83]. Lopezet al. [82] presented a comparative study of dimensional reductionmethods for damage detection applied to an aeroacoustic experi-ment. Results of this study demonstrate that nonlinear dimensionalreduction techniques can be more effective than PCA in clusteranalysis for damage detection, but not consistently and PCA tendsto be more robust to lack of excitation. In the reviewed literature,limited studies have been published in using nonlinear dimen-sional reduction methods for SHM research.

Feature reduction can also be achieved via selection of featuresbased on theoretical and/or practical engineering knowledge. Theproblem of feature selection is defined as follows: given a set of d

features, select a subset of size m that leads to the smallestclassification error. Feature selection methods that have beenapplied in SHM include branch-and-bound search, sequentialforward selection (SFS), and sequential backward selection (SBS),[81]. Other works include similarity based feature selectionmethods. Mitra et al. [84] present an unsupervised featureselection using feature similarity and a brief review of featureselection methods. A more detailed explanation and review ofthese methods can be found in [81–85].

In general, different dimensional reduction and selectionapproaches will generate different feature spaces, and consequently

nal reduction techniques.

Fig. 8. Taxonomy of classifier techniques.


result in different concept spaces and discovering differentknowledge spaces. Feature extraction and selection is critical inthe area of damage assessment. In general, these data miningtechniques are based on methodologies of machine learning, patternrecognition, and statistical analysis. Given that the user is not clearon the properties of the damage knowledge that is of interest, theadoption of mining algorithms will be uncertain. The aim ofapplying data mining techniques in diagnostics is to provide theuser with novel, useful knowledge, which can be easily understoodand evaluated in order to make decisions quickly and precisely. Insystem diagnostics, it is desired and necessary to properly induceand reduce the acquired knowledge, and describe it in a way thatcan be easily understood and classified. Given that data mining hasbeen performed, the next step is that of evaluation and explanationof discovered knowledge, in our case damage assessment. One majorproblem in knowledge explanation is to account and describethe uncertainties in qualitative concepts and how to implement theuncertainty transformation from quantitative data to qualitativeconcepts. Therefore, there are uncertainties not only in the processof data mining, but also in the discovered structural health stateknowledge.

4.3. Classification

Classification is the most fundamental and most significantactivity in SHM research activities. Classification is applied todescribe the known data classes or models of concepts, so as toclassify the objects with unknown class index by the knownmodels/classes. As a supervised or unsupervised learning method,classification contains uncertainties. Complex classifiers are neededwhen the object to be classified is adjacent to two classes, or lies inthe overlap region of multiple classes. In addition, if insufficienttraining is performed, the learning result will probably not be

reflective of the overall structure of the data set, and therefore, willnot categorize the damage state correctly. Therefore for new data,there will be a lot of uncertain problems in its classification. Manyclassification approaches have been used and proposed forclassification of SHM data, such as similarity metrics, decision treeinduction, Bayesian-based classification, neural networks, geneticalgorithms, fuzzy set classifiers, etc. [81–85]. The most general andbest performing classification in the damage assessment process isvia direct statistical analysis. Most of the initial work in diagnosticsfocused in applying statistical analyses, as reported and/orreviewed in [2,3,4,9,10,56,78,79,85–90].

Given a set of vectors x¼ x1,x2,. . .,xnð Þwith d extracted features,the decision-making process is pattern recognition. It is basedon assigning these vectors to one of the possible classesx¼ o1,o2,. . .,oCð Þ. A decision rule partitions the measurementspace into C regions Oi, i¼1,2,y, C. Each region may be made up ofmultiple overlapping regions. The boundaries between the regionsare the decision boundaries or decision surfaces. In terms ofdamage diagnosis, the overlap of these regions, in other wordshealth states, are the highest proportions of misclassifications orfalse diagnosis. In general, two decision-boundary methods exist inclassification. The first assumes knowledge of the underlying class-conditional probability density function. In many situations thiswill be unknown and must be approximated. The second approachdevelops decision rules that use the data to estimate decisionboundaries directly, without explicit calculation of the probabilitydensity functions. Consider the binary hypothesis testing problemwhere a sequence of independent identically distributed damageindex vectors are observed, then the likelihood ratio test (LRT)function is denoted as

Ymk ¼ 1

LðXkÞ4HD

oHU

tðmÞ ð17Þ


where HD denotes the damage state, HU the undamaged state, andt(N) is a predefined (if prior information exists) damage threshold.

A major issue in damage classification is that many classifica-tion algorithms assume that for training, class labels, i.e.information on each class, are available, but in practical damageassessment applications, labels of damaged data are not availableunless destructive testing is performed. As a result, directapplication of supervised classification approaches is not alwayspossible. Fig. 8 shows the taxonomy of classification methods[80–85]. Clustering methods aim at finding groups in data viafeature similarity. Although clusters are important in patternrecognition, because in SHM we are interested in classes withlabels, clustering will not be covered in this paper. Structuralclassifiers are used for building classifier ensembles. Structuralclassifiers are usually described in graph, network, or membershipterminology. Structural classifiers are becoming important andcontinuously growing as the demand for more robust and moreaccurate classification decisions are required. In particular,classifier combination is highly justified as the next logical stepin increasing decision knowledge. Comparing classifier combina-tion to feature extraction, prior to extracting the most informativefeatures, data is integrated as a single set, and then transformed toa lower dimension. Given that we can combine multipleclassifiers, the next logical step will be to select the most effectiveclassifier set. In the following paragraphs, we explore the multipleapplications of classification methods in SHM.

Neural networks (NNs) have been extensively applied for featureextraction and classification of structural health data. Zang andImregun [42] performed structural damage detection via artificialneural networks (ANNs) compressed by PCA. The integration ofANNs with PCA allowed for reduction in FRF data, i.e. reduction ofcomputational expense, without loss of accuracy. The author statesthat pattern recognition and system identification are complemen-tary; thus, indicating that methodologies should be fused formaximization of damage knowledge. Niu et al. [92] presented acomparison study of classifiers for fault diagnosis of a motor usingmulti-type signals. The study used the following classifiers forcomparison: support vector machines (SVMs), linear discriminantanalysis (LDA), k-Nearest Neighbors (kNN), random forests (RF), andadaptive resonance theory-Kohonen neural network (ART-KNN). Thestudy demonstrates that individual classifier performance is highlydependent on the damage scenario (binary to m-ary classification).Critiques of NNs point out that this approach conceals importantinformation, such as data statistics, from the user and tend to becomputationally expensive. Jain et al. [81] states that despite theseissues, NNs do offer several advantages, such as unified approachesfor feature extraction and classification, and flexible procedures forfinding good, moderately nonlinear solutions.

One of the most interesting developments in classifier design isthe introduction of the support vector machine (SVM). Cao [93]used SVMs to develop a framework of probabilistic uncertaintymodeling and reliability analysis and compared them to the MonteCarlo simulation method, and first and second order reliabilitymethods. In this work, uncertainties due to system lack-of-knowledge and human induced factors were studied as randomvariables with normal distributions. Using SVMS, accurate resultsrelative to Monte Carlo simulation method were obtained withmuch less training data. Das et al. [94] used one-class SVMs basedon time-frequency information for damage assessment of compo-site panels. One-class SVMs are useful for outlier detection whendata is not available on damaged states. Das points out that furtherresearch is necessary in order to increase robustness of classifier inthe presence of material and experimental uncertainties.

In diagnostic systems, knowledge from domain-specific expertsis usually inexact and reasoning on knowledge is thereforeimprecise. Thus, measures of uncertainties in knowledge and

reasoning are required for classification and decision-making toprovide more robust damage assessment results. As statedpreviously, commonly used uncertainty measures are probability,fuzzy member functions and belief functions. The performances ofstatistical pattern recognition methods depend on the priorknowledge, which is often imperfect and incomplete. Probabilitytheory can handle the uncertainty contained in the data, but itcannot treat the imprecision. The imperfect knowledge can beaddressed by the use of belief- and/or evidence-based methods.The problem of uncertainty in classification for damage assessmentcan be addressed by a continuous learning in order to addinformation carried by each new classified pattern to the databaseor prior knowledge.

Fuzzy sets classifiers assign degrees of membership in severalclasses to each input pattern. Fuzzy sets theory was introduced byZadeh to solve the problem of data imperfection. Ramu andJohnson [95] integrated ANNs and fuzzy logic to treat uncertaintiesrelated to damage assessment of composites. They point out thatappropriate network construction is extremely heuristic andlaborious. Altunok et al. [96] presented a damage patternrecognition approach based on fuzzy set theory. The proposedmethod does not assume any special statistical assumptions anddoes not require finite element modeling and was tested on anexperimental model steel bridge. One drawback to this method isthat damage quantification is as accurate as the number of setschosen, which can be insufficient or rough. Lei et al. [97] presenteda clustering technique based on fuzzy c-means (FCM), PCA andcompensation distance technique for rotating machinery. Thefeatures selected for clustering analysis are based on thecharacteristics of statistical-moments. Pierce et. al [98] appliedmultilayer perceptron neural network (MLP) classifiers to adamage detection problem within a framework of an intervalarithmetic-based information-gap technique. The inclusion ofinterval analysis allowed the assessment of robustness of trainedclassifiers to uncertainty. DeSimio et al. [99] studied the effects ofuncertainty via statistical classification in decision-making for SHMsystems. Loose bolt damage assessment was performed on acomposite thermal protection panel. Feature selection via sequen-tial forward greedy approach developed is discussed and applied.Uncertainty analysis was limited to defining rejection criteria forclassification of anomalous data, so when uncertainty is high andlabeling is not clear, data is discarded. The latter approach relies onsignificant training data being available. Altunok et al. [100]presented the use of possibility distributions to quantify healthyand unknown events, in other words outlier detection, to theAmerican Society of Civil Engineers (ASCE) benchmark problem. Byapplying possibility theory, the authors observe intervals withoutassuming any particular probability distribution. Chandrashekharand Ganguli [101] proposed a fuzzy logic system for damagedetection and isolation in beam structures with uncertainty. Tahaand Lucero [102] applied fuzzy sets to develop a damage metriccombined with Bayesian updating scheme. Da Silva et al. [103]demonstrated an approach to vibration-based damage classifica-tion via fuzzy sets. Pawar and Ganguli [104] developed a geneticfuzzy system and applied it for damage detection in beams andhelicopter rotor blades. The genetic algorithm facilitated theselection time and optimality of fuzzy sets. Application of fuzzysets and possibility theories has also been applied to faultdiagnostic systems, such as satellite fault diagnosis [105], androtating machinery fault diagnosis [106].

Structural design problems have been investigated via fuzzylogic and evidence theory by multiple researchers, such asNikolaidis et al. [22], Mourelatos and Zhou [107], Bae et al.[108,109], Yang and Kim [110], to handle imprecise datasituations arising from structural complexity. In particular,evidence theory has been used by multiple researchers for data


fusion applications. Bao et al. [111] employed the D–S theory tocombine evidence individual damage basic probability assess-ments from multi-sensory data. Such combination improved thedamage assessment results in comparison to individual sensordamage assessment results. Guo and Zhang [112] used the D–Stheory to identify multiple damage locations of a structure. Theymade use of Yager’s weighted Dempster–Shafer (D–S) evidencetheory approach to address the fact that different sources havedifferent levels of importance and/or reliability. Li et al. [113] usedthe Shannon entropy to measure the uncertainty of the evidenceand presented a weighted and selective fusion method by usingan artificial neural network combined with the D–S evidencetheory and Shannon entropy. Basir and Yuan [114] performedengine fault diagnosis based on multi-sensor information fusionusing the D–S theory. In particular, they focused on the combiningschemes for evidence sources to address conflictive information.Denoeux [115] developed an adaptive neural network classifierbased on the D–S theory. Denoeux points out that the D–S theoryis suitable for classifier combination, since it yields robustdecisions procedures to changes in environment and possiblesensor failures. Parikh et al. [116] made use of the D–S theory andpredictive rates for combining classifiers in a case study ofthermostatic valve faults in a diesel engine cooling system. Byusing the D–S theory based approach, the authors were able toproperly classify multiple engine conditions. Results from themultiple classification comparison studies demonstrate the needfor classifier combination or fusion schemes since it can beunpredictable which classifier will be the most effective on a case-by-case basis. Classifier combination aims at integrating thebenefits of individual classifiers to maximize performancerobustness; thus, reducing uncertainty in the classificationoutputs [80,83,117].

Through the analysis and review of classification and cluster-ing algorithms, the following problems and challenges have beenidentified:

(1)
Individual classes of clusters might be linear, spherical,nested, or some arbitrary form. Hence, classifiers need to beable to detect clusters and form decision boundaries witharbitrary shape, size and density;
(2)
almost all classifiers contain tuning parameters, such asnumber of neighbors, cluster number, noise threshold, etc.In real applications, the selection of these tuning parametersis extremely difficult to obtain unless significant priorknowledge exists;
(3)
while classifiers are mainly confined to low-dimensionaldatasets, structural response features can exist in thethousands. As such, dimensional reduction techniques mustbe integrated with the classifier in order for classifiers to dealwith high-dimensional problems;
(4)
for some diagnostic applications, damage assessment needs tobe processed on-line, which makes it computationallyexpensive when dealing with large datasets;
(5)
in real applications, sensor data contains large quantities ofnoise and outliers or abnormal data, which makes it moredifficult for classifiers to assess damage. Therefore, it isnecessary to detect and isolate ‘bad’ data by creating outlieror rejection classes; and
(6)
classifier robustness needs to be addressed. Classificationcombination schemes should be used to maximize accuracyrecognition and the overall performance of the classifier.
Although significant research has been done in developingmethods and tools for data mining and knowledge discovery, suchas recursive analysis, discriminative analysis, genetic algorithm,

neural networks, multidimensional data analysis, there is still alarge gap between the performance of the existing methods andthe expectation and requirements desired for diagnostics. Data-driven methodologies can only provide part of the informationrequired to develop effective diagnostic systems. To maximizeknowledge discovery, data-driven techniques must be fused withphysics-based models of the structure under analysis.

4.4. Data fusion and decision-making

Due to uncertainty and imprecise nature of data acquisitionand processing, individual informational data sources must beappropriately integrated and validated. To maximize diagnosticperformance, data must be processed and contextually filtered toextract valuable relevant information. In terms of diagnostics,data fusion can be used at the feature and decision levels. Datafusion can be used to combine information from a multi-sensorarrangement to validate signals and extract damage-sensitivefeatures. System sensory data is generally processed to extractdamage signature features, which can then be mapped todifferent health condition states. In the multi-sensory approach,individual sensory data may be classified and contribute a uniqueset of classifications represented by a measure of belief orprobability, which can be numerical or of symbolic nature. Therepresentation as numerical classification degrees lead to aquantification of its uncertainty content or incompleteness. Dueto the less than unity classification, classified features whencombined, provide a better estimate of the true diagnostic state.In terms of decision-level data fusion, the main task of data fusionis to combine information from several sources to make a betterdecision compared to decisions based on a single data source. Thegoal of data fusion is to reduce imprecision and uncertainty byincreasing information completeness [20].

Various techniques exist for performing data fusion. Todiscriminate between feature-level and decision-level data fusion,we will focus on ensemble classifiers as the main feature-leveldata fusion approach, and inference engines as the decision-leveldata fusion approaches. Fig. 9 shows sample architecture for datafusion based on the distinction between feature-level anddecision-level fusion. The final goal of condition monitoring anddiagnostics is to make diagnostic decision under uncertainty andimpreciseness. To distinguish between inference and decisions,we use the following definitions. Inference is the process ofdrawing conclusions from premises or evidence, and decision isthe process of choosing an action. As stated in Walley [13],inference is more theoretical and impersonal, while decision is amore practical and specialized activity since it has practicalconsequences and it requires consideration of these consequencesand their values. Inference engines include Bayesian networks,Dempster–Shafer’s evidence theory, fuzzy sets, amongst others.Inference systems combine evidence to assess probabilities orpossibilities of relevant events, in our case damage states. Fig. 10

Kuncheva [80] defines these outputs in four categories:

�
Type 1—abstract level: each classifier Ci produces a class labelLj. At this level, there is no information about the certainty ofthe obtained labels (condition), nor are any alternative labelssuggested; � Type 2—rank level: each classifier Ci produces alternative class
labels Lj ranked in order of plausibility of being the correctlabel;
� Type 3—measurement level: each classifier Ci produces a
d-dimensional vector, [ci,1,y,ci,d] consisting of values ci,j

representing the support for the hypothesis that the givenmeasurement comes from class oj and

Fig. 9. Architecture of multi-source and multi-classifier information fusion.

Fig. 10. Prognosis encompasses the concept of estimating the remaining useful life (RUL) of a component or system. Given this information; user or control system may be

capable to proactively adapt its usage or mission to complete mission goals and/or extend RUL.


�
Type 4—oracle level: the output of classifier Ci for a givenmeasurement is only known to be either correct (value¼1) orwrong (value¼1). The oracle output is artificial since it canonly be applied to a labeled data set. So, for a given labeleddataset, the classification of correct or wrong pertains tohaving the correct label on the data vector.
To this we add an intermediate classifier output:Type 3.5: imprecise level: each classifier Ci produces a

d-dimensional vector, ½fci,l,ci,1g,. . .,fci,d,ci,dg� consisting of valuesci,j and ci,j representing the lower and upper probabilistic support,respectively, for the hypothesis that the given measurementcomes from class oj. the inclusion of this level is to acknowledgethe existence of imprecise probabilities as outputs from inferenceengines, such as Dempster–Shafer approach.

The possible ways of combining the outputs of multipleclassifiers or information sources in data fusion depends on whattype of information is extracted from the individual classifiers.Some of the well known classifier combinations are product rule,sum rule, majority vote, Naive Bayes combination, Singular ValueDecomposition (SVD), neural networks, adaptive weighting,bagging and boosting [80]. Jain et al. [81] provides a review ofclassifier combination schemes and their selection process. Bloch[19] presented a classification of numerical fusion operators with

respect to their behavior in terms of severity or indulgence. Anumber of researchers have reviewed the multi-sensor fusionalgorithms, arquitectures and application to diagnostic systems.Kutcheva’s book on combined classifiers offers a great review ofmultiple classifier fusion approaches. Hall and Llinas [20] haveedited an informative handbook of multi-sensor data fusion. Luoet al. [21] reviewed the multi-sensor fusion and integrationfocusing in sensor technology development and varying applica-tions, such as robotics, biomedical and equipment monitoring.Byington and Garga [118] addressed false alarms originating fromfaulty sensor performance, transient operating conditions,improper damage indicator selection and logic by performingfeature-level and decision-level data fusion. Vachtsevanos et al.[119] provides an overview of data fusion applications infault diagnostics and prognostics. The majority of data fusionworks in diagnostics has focused on the Bayesian approach[10,13,14,19,44,72,81,90,93,120]. Basir and Yuan [114] performedengine diagnostics based on the D–S evidence theory withdecision-making rules. Fan and Zuo [121,122] conducted a twopart study using fuzzy membership functions and conflictfactor in conjunction with the D–S evidence theory to performgearbox fault diagnosis. The proposed method was used toresolve conflicting information from multi-source informationby embodying uncertainty and expert’s subjective knowledgein decision-making. Li et al. [113] developed a weighted and


selective diagnostic fusion approach by combining artificialneural networks, D–S evidence theory and entropy information.Additional works adopting the D–S evidence theory as a primarydata fusion technique in diagnostics has been used in multipleworks [121–126]. Data fusion studies comparing D–S evidencetheory, Bayesian probability fuzzy sets, etc. have been performed[20–25]. Nikolaidis et al. [22] compared Bayesian theory andpossibility theory in terms of fuzzy sets to study reliabilityassessment for designing against catastrophic failure. The mainconclusion was that both methods are useful when used inparallel since big discrepancies between their results might be anindication that design analysis problems exist. Osegueda et al.[127] enhanced probabilistic data fusion with the D–S evidencetheory in testing structural integrity of aerospace structuralcomponents. One problem that needs considerable attention isthat of performing multi-sensor data fusion under impreciseinformation. Multi-sensor fusion often requires exact informationabout the sensed environment, but in real situations, informationabout the sensed environment is often imprecise and scarce.Soundappan et al. [24] compared evidence theory and Bayesiantheory to model uncertainty and assess the safety of a systemwhen information is of interval type. Because the study wasperformed for interval probability bounds, the performance wasbiased toward the evidence theory since it focuses on dealingwith imprecise probabilities. Given that interval gap are relativelysmall, then Bayesian theory, as it is well known, will provide abetter decision result.

Given that diagnostic decision problems relate to uncertainevents, it is generally acceptable that quantification of expertopinions about the occurrence of these events should be in termsof probabilities or related concepts [13]. An expert systemconsists of two parts, as given by the following equation

Expert system¼ knowledge baseþ inference engine ð18Þ

The knowledge base consists of the domain-specific knowl-edge of the problem, and the inference engine, as previouslydescribed, processes the acquired data and encodes it according tothe knowledge base. An inference engine also improves theknowledge in light of new information, and thus, facilitateslearning. Expert systems are designed to act as consultants byreplacing or enhancing domain-specific human knowledge. Typesof expert systems can be classified into diagnostic trees,rule-based systems, fuzzy logic, certainty factors (CF), rough sets,Bayesian networks, and probabilistic logic [13,14]. Procedures fordealing with uncertainty and imprecision are essential require-ments for expert systems. In situations where uncertainty,imprecision, and contradictory information exists, the usage ofopinions elicited from domain-specific expert systems is a way ofcomplementing such lack or imprecision of information.

Generation of expert opinions can be done qualitatively orquantitatively. In the quantitative form, the expert may provide

Fig. 11. F-22 flight vehicle contr

opinions as numeric according to the uncertainty theory that will beused to represent available information. In the qualitative form, theexperts express opinions in a natural way deferring the use ofnumeric representation. For example, an expert diagnostic systemmight require the faulty features or symptoms, operational informa-tion, and other relevant context information, and would utilize thisinformation to search the knowledge base to determine thecorresponding diagnostic condition. An expert system does not onlymanage large quantities of data and sources, but it also manipulatesthe information, such that the result is intelligent and has significancein order to respond to questions that are not completely specified. Forfurther details on expert systems refer to [13,14,20].

The end goal for aggregating information is to generatediagnostic decisions by assessing the uncertainty levels an utilityinformation. The decision problem can be decomposed by specify-ing a set of possible actions or outcomes, and assessment of theavailable information supporting each outcome. The decisionprocess determines preferences between actions, reduces the setof actions from which you must choose, or may result in therequirement of acquiring additional information. Multiple worksrelated to decision-making under uncertainty have been publishedrecently with some application to machinery and aircraft diag-nostics [3,7,25,106,119,128–133]. The overall trend in aircraftstructure and overall system diagnostics is the emulation ofnatural intelligence by incorporating declarative actions involvingexpert decision-making, incorporation of system modeling, andcompleteness in contextual information identification.

5. Prognosis

Damage prognosis is defined as the estimate of an engineeredsystem’s remaining useful life [27], see Fig. 11. In the literature,damage prognosis is tightly associated or also known as failureprognostics, predictive prognostics, time-to-failure analysis,condition-based prognostics, probability of reliable operation,etc. A reliable prognostic system is needed and required in orderto predict the damage deterioration in structures. Prognosticsmust make use of historical data, when available, and availableknowledge. Common to any prognostic system is the incompleteand imprecise knowledge about the observed data and system,especially in the failure space. In mechanical systems, prognosticshave received increasing attention, especially in the areas ofrotating machinery and aircraft systems. Unlike electrical faults,mechanical faults, not including impact structural damage, tendto deteriorate slowly, which allows for monitoring to assessdegradation and estimate remaining useful operational life.

In comparison to damage identification, in the area of damageprognosis, few experimental validation articles have been writtento date [27,119]. The reason for this lack of attention may beattributed to the difficulty in predicting future states if the current

ol surfaces and parameters.


state is uncertain. Multiple review papers have been writtendedicated to the topic of prognosis and most of them focus onproposing prognostic architectures [119,134]. Farrar and Lieven[27] presented a review of structural damage prognosis. In thisreview, the following key areas are defined as the main challengestowards the successful development of damage prognosis: (1)development and integration of hardware technology areas, suchas measurement/processing/telemetry; (2) development of de-terministic and probabilistic predictive modeling capabilities; and(3) quantification of uncertainty in diagnostic and prognosticpredictions. Jardine et al. [3] provided an overview of machinerydiagnostics and prognostics implementing condition-based main-tenance (CBM). Jardine provides a good review of model-basedand data-driven techniques in prognostics. Heng et al. [10]presented a review of rotating machinery prognostics. Theauthors state that difficulty in prognosis is due to the inherentstructural and operational complexities of real-life systems,which cannot be determined with absolute certainty and mustbe addressed via assumptions and simplifications. Artificialintelligence (AI) techniques have also been considered byresearchers [119,125,129,135]. Most of the prognostic AI techni-ques have been based on ANNs [38] and information fusionmethods. Roemer et al. [136] presented an assessment of data andknowledge fusion strategies for prognostics and health manage-ment. Chelidze and Cusumano [137] presented a dynamicalsystems approach for failure prognosis. The algorithm was basedon a multi-step-time scale analysis of changes in the dynamics ofthe hierarchical system and applied to a battery dischargeapplication. Niu and Yang [138] discussed the use of data-driventechniques with the D–S evidence theory fusion to investigateprognosis via a multi-step-time scale analysis. Hess et al.[139,140] presented a review paper focusing on the challenges,issues and lessons learned. In the paper, it is stated that one of themajor challenges is the development of prognostic methods thatare ‘‘truly capable of handling real-world uncertainties–as theworld is not deterministic.’’ Engel et al. [141] presented a reviewpaper discussing the critical issues concerning the prediction ofremaining life. The key issue, according to Engel, is the treatmentof uncertainty in the prognosis problem. A second conclusion wasthat the variance of the remaining life decreases as damageincreases. The analysis of remaining life was performed using theBayesian theory analysis with known priors. Engel provided thefollowing useful research challenges and research recommenda-tions in the area of prognostics:

�
Features need to be found or created that are especiallydesigned for prognostics. The features that are ’optimal’ fordamage assessment, may not be the same as those forprognosis; � development and application of methods that can bound the
uncertainty in prognosis in lieu of well characterized PDFs.Prognosis decisions are better performed on the basis ofbounds of confidence intervals rather than exact remaininguseful life. In other words, imprecise probabilities for prog-nosis;
� research studies are needed in regards to the convergence
rates of accuracy and uncertainty as a function of remaininguseful life and
� development of a fusion testbed for prognostic methods.
Again, data fusion algorithms can be exploited to find asynergistic solution.

Complementing the latter points, Schwabacher [142] publisheda review paper of artificial intelligence for prognostics. Someconclusions from the review paper include: (1) prognostics is

extremely difficult; (2) prognostics of complex systems remainsinfantile; (3) verification and validation (V&V) is a majorchallenge in prognostics and (4) once remaining useful life isestimated further study is necessary to determine what effects ithas on the system.

Although, numerous efforts have been made in developingeffective prognosis frameworks, we are still not aware of anydeployed prognostic system on complex engineering system.Journal publications in the topic of prognostics have been basedon experimental prototypes or simulations. Prognostics of com-plex engineering systems remain an area with much neededresearch. Component-level prognostics must be extended tosystem-level prognostic decisions based on the relationship ofthe system components to the system functionality. Aside fromthe difficulty in assessing remaining useful life, the availablereviews in the area of prognostics all share one thing in common,which is the need to effectively account for uncertainties whenmaking prognostic predictions. Future health predictions areinevitably uncertain, and as such, prognostic requirements mustbe well understood prior to making and validating prognosticpredictions.

6. Control sytems under uncertainty

This section presents major research developments of moderncontrol systems designed to tackle the challenging problem ofuncertainties in the form of flight vehicles avionics fault orstructural damage. Control systems ensure the stability of avehicular system and allow for a predefined performance undersafe and normal operation. However, the more the system isunder operation, especially in extreme environments, the morethe vehicle is subject to structural damage and faults. Fig. 11shows the control surfaces on the F-22 aircraft and keyparameters. Several mid-flight accidents have occurred in whichcontrol surfaces of the aircraft become damaged or disabled.Losing control of its surfaces causes an aircraft to have diminishedperformance, lose stability, and possibly crash due to completeloss of control. In addition, as the vehicle design increases inautonomy, its design complexity is subject to increased prob-ability of faults. Given that design redundancy is exceeded, aconventional feedback control system may result in unsatisfac-tory performance, which may lead to system instability. Underdistress events, such as faults and structural damage, it isdesirable to design a control system capable of ensuring nominalperformance, or at the very least, safe performance, when takinginto account the occurrence of faults. New generations of flightvehicles will be designed to achieve mission completion withincreased efficiency, safety, and security. Safe and reliableoperation of flight vehicles relies on the following key points[143–145]: (i) flight control must be robust against flight vehicleand environmental uncertainties and disturbances, respectively;(ii) an efficient system must be capable of monitoring the healthstatus of the flight vehicle and (iii) an adaptable guidance systemsubjected on fault or damage occurrence must be capable ofgenerating an appropriate flight trajectory despite flight perfor-mance degradation.

Since the usage of damage, fault and failure are usedfrequently and interchangeably in the literature, we providesome basic definitions: (a) fault: an unpermitted deviations of atleast one characteristic property or variable of the system fromacceptable-usual-standard behavior; (b) failure: permanent inter-ruption of the system ability to perform a required function underoperating conditions(c) damage: changes introduced into asystem that adversely affects its current or future performance[143–145].


Based on the latter definitions, a fault corresponds to anabnormal behavior of the system, which may not affect theperformance of the system, but may eventually lead to failure.Similarly, damage may not affect the performance of the system,but increases the risk in the occurrence of failures. Faults andstructural damage may be small or hidden, and therefore difficultto detect and estimate. On aircraft, common sources of failures areactuator and sensor faults. Actuators are used to deflect controlsurfaces and to actuate other mechanisms. Sensor faults occurwhen the measurement data deviates from the real physicalmeasured process by more than the noise uncertainty. Structuraldamage in aircraft corresponds to scenarios where missing pieces,which includes holes, of aircraft exist, such as perforated controlsurfaces or missing wing parts.

Multiple approaches exist for fault or damage aircraft controlaccommodation and a few have been successfully demonstratedduring real flight tests. Unfortunately, multiple terminologieshave also been used, such as ‘‘reconfigurable,’’ ‘‘adaptable,’’ ‘‘fault-tolerant,’’ and ‘‘robust.’’ This review makes mention of allapproaches that are relevant to control augmentation underuncertainty given the occurrence of damage and/or faults.Over the past few decades, the need for safer and more reliableaircraft control systems has drawn significant research efforts,and it is well documented in multiple review publications[128,143,144,146,147,132–134], and books [145,148,149]. Inparallel, significant effort has gone into the development of faultand damage diagnostic systems capable of detecting, locating,isolating, identifying, and/or assessing the characteristics of thefault or damage. Appropriate techniques and solutions for thesetasks are known as fault detection and isolation (FDI) and failure/damage detection and diagnosis (FDD). Control systems devel-oped to accommodate component failures automatically are oftenknown as fault tolerant control systems (FTCS), see Fig. 12.Aircraft flight control has motivated research in FTCS with thegoal of providing ‘‘self-repairing’’ capability in order to ensuresafe-landing and/or mission completion in the event of severeaircraft faults [144]. In terms of flying performance, sensorfailures can be handled by using sensor redundancy. However,actuator and control surface failure or damage to airframedegrades flying qualities and thus requires immediate action topreserve the aircraft’s integrity, which is the primary objective inwriting this paper.

In general, FTCS are classified as passive (PFTCS) and active(AFTCS). In PFTCS, the controller is fixed and designed to be robustagainst a class of presumed faults. Several control approaches can

Fig. 12. Fault tolerant control (FTC) with

automatically deal with ‘‘minor’’ faults or damages very effi-ciently. In robust control, the control loop is unchanged at all inresponse to a fault since it is assumed that robustness ofcontroller can account for different minor fault cases withoutany change; therefore, robust systems work without FDI.Furthermore, relatively low-levels of system uncertainty can beaccommodated via robust control approaches [143,144,150].Unfortunately, if a robust control system is designed to accom-modate increasing types of faults, the performance is oftendisappointing. AFTCS react to the system component failures byactively reconfiguring control actions so that the stability andacceptable performance of the entire system can be maintained.One type of control approaches is referred as adaptive control forwhich the controller becomes modifiable given a change insystem characteristics, such as fault occurrence, but it does notexplicitly implement FDI [143]. Adaptive control approachescontinuously adapt to any changes in the plant system. Adaptivecontrollers have been shown to perform well under slow andsmall parameter changes, but such performance has not beenadaquate given severe and sudden faults. Fault accommodation isanother type of FTCS and similar to adaptive control, but it isbased on an explicit diagnosis of the fault. In fault accommodationapproaches, control system parameters are adjusted according tofault types. However, the structure of the controller remainsunchanged, which makes it incapable of dealing with severefaults. Predictive control techniques also provide fault-toleranceby performing trajectory optimization on a model of the plant.Unfortunately, predictive controllers require significant comput-ing resources, but nevertheless, predictive control is one of themost powerful methods known for the control of nonlinearsystems.

The development of artificial intelligence (AI) involves thecriteria of autonomy in machine systems that are capable ofmaking decisions under changing circumstances. Intelligent-based methods based on neural networks and fuzzy logic hasalso received attention in terms of FTCS. These methods can beapplied to nonlinear systems [151]. The learning capabilities ofthese methods make it possible for the controller to adjustaccording to the changes the plant has undergone due to fault ordamage. Consideration of complexity in control of nonlinearsystems has led to the development of intelligent control theory[151,152] that enhances the degree of adaptation, learningand autonomy. Intelligent control uses artificial intelligence(AI) soft computing approaches, such as neural networks,Bayesian probability, fuzzy logic, machine learning, evolutionary

supervision and expert system input.


computation, generic algorithms, and reinforcement learning,among others [152–157]. Intelligent approaches have also givenway to supervision systems, or knowledge based systems (KBSs)which introduce different forms of inference rules, selection logicand system management into FTCS. Supervision systems deter-mine the most appropriate action to be taken, such as controllerstate and structure adaptation, according to the present conditionand commands [158]. As such, the supervision system mustdetermine if the fault or damage are significant such that itrequires controller changes. In this manner, the controller evolvesover time, successively improving its performance and adaptingto its environment. The primary difference from conventionalapproaches is that intelligent control techniques are motivated bythe functionality of intelligent biological systems, either in howthey perform the control task or in how they provide aninnovative solution to another problem that can be adapted tosolve a control problem [152].

Numerous studies have been conducted on the use of expertsystems in failure detection and identification and to superviseand control various processes. The idea behind expert control is toreduce the engineering effort in using feedback control bysupporting several of the functions that are traditionallyperformed by control system users, such as pilots. Therefore, anexpert control system represents a system with a higher degree ofautomation, specifically decision-making, compared to othercontrol systems. Other key concepts of intelligent controllersinclude planning systems [159]. A control system integrated withan expert system may consist of an FDD or FDI sub-system. Themultiple sub-systems would be coordinated by an expert system,which may decide what algorithms to use and what decisionsneed to be made, such as performance adjustments [157]. In anexpert system, domain-specific knowledge is explicitly repre-sented by a combination of rules-of-thumb heuristics andknowledge-based theoretical understanding. In other words, theexpert system consists of a rule base and an inference engine.The inference engine, such as Fuzzy and Dempster–Shafer, is analgorithm that draws conclusions based on the data and the rulebase. Applications of expert systems to aircraft control and FDDare described in [151,160–163]. Central to intelligent control is toenable a wider class of problems to be solved by reducing thea priori uncertainty to the point where satisfactory solutions cabbe obtained on-line.

By addressing a broader class of problems, intelligentapproaches can overcome the limitations of a fixed control design,especially under significant complexity or uncertainty. Similar toFTCS approaches, intelligent control approaches attempt to treatthe problem of uncertainty through on-line means. By adjustingitself to accommodate new situations, such as faults and failures,the control system parameters can be adjusted to achieve somedesired performance objective. An adaptive intelligent controlsystem will attempt to adapt the behavior of the plant changes,and if the dynamical characteristics of the plant vary considerablyover its operating envelope, then the control system will berequired to adapt to and/or constrain the operational envelopeand mission objectives. In general, the processes of adaptationand learning in intelligent control systems are complementary.Adaptive controls can accommodate slowly time-varyingdynamics and novel situations, but are often inefficient forproblems involving significant variation in the nonlineardynamics. On the other hand, learning approaches are wellequipped to accommodate poorly modeled nonlinear dynamicalbehavior, such as damage, but are not well suited for time-varyingdynamics. Common to most intelligent and expert system controlapproaches is the difficulty in their application to reasoning whentime is limited, i.e. when quick decisions are required, such as inemergency control scenarios. The lack of satisfactory formal

techniques for studying the stability of intelligent control systemsis a major drawback.

Failure Detection, Identification and Reconfiguration (FDIR)control approaches integrate the capability of rapidly detectingflight-critical failures and reconfigure the control system to assurestability and performance of the flight control [144,151]. Thefocus of FDIR relies primarily on failure accommodation andcontrol adaptation with a secondary focus on failure assessment,which leaves a significant gap in terms of failure knowledge.Typically, reconfigurable control systems assume pseudo-perfectknowledge of FDD. Most FDI and FDD techniques have beendeveloped as diagnostic and monitoring tools. Integration of FDIand reconfigurable control (RC) needs to be well addressed withfull interaction between these two research areas. Many FDDalgorithms do not consider the closed-loop operation of thesystem and many FTCS methods assume the availability of perfectfault estimates from the FDD scheme. Such lack of interconnec-tion increases uncertainty levels which clearly decreases anyguarantees that a satisfactory post-fault performance, or evenstability, can be maintained by such a scheme. Impreciseinformation from the FDD can be incorrectly interpreted andapplied by the FTCS, which might lead to instabilities andcomplete loss of stability of the aircraft.

AFTCS usually contains an FDD module, which informs theseriousness of the fault, failure or damage. Such information maybe passed onto a supervision module to decide to reconfigure theflight guidance, navigation and control (GN&C) system. UnderAFTCS, two types of FDD schemes exist: passive-FDD and active-FDD. Passive-FDD wait until fault or failure occurs, whereasactive-FDD will artificially excite the aircraft by flying health-check maneuvers or by generating test signals in the sensor-actuator network. Numerous papers consider integrated FTCSand FDD. Such approaches are considered in [146,149,150,162,164–167]. However, these integrated methods do not considermodel uncertainty and are usually developed by means of directlyinterconnecting an FTCS to an FDD approach, which again, payslittle attention to possible imprecision in the FDD information.Additionally, reliability of FDD techniques is not guaranteed. Toachieve acceptable reliability a FDD system needs to be robustagainst external disturbances, model uncertainties and sensornoise or faults. In general, FDD systems must overcome theproblem of balancing minimization of false alarms with sufficientsensitivity to assess faults or damage, also know as the receiveroperating characteristic (ROC), which in signal detection theory isapplied to graphically distinguish true positive rate from falsepositive rate [145,174]. FDD systems may experience significantperformance reduction if system uncertainties are not properlyconsidered.

In general, at time of fault or damage occurrence, informationis limited in terms of input/output measurements from thesystem that are available for the FDD approach. As such, time-delay exists between occurrence and fault diagnostics, whichresults in initial information imprecision with larger uncertainty,and diagnostic accuracy increases as time elapses. In practice, it isunlikely to have error-free and no time-delay estimation andidentification when abrupt plant changes occur. In adaptivesystem and state estimation, accelerating mechanisms, such asadaptive forgetting factors [168], can be used to obtain post-faultparameters quickly. Therefore, a FTCS should be able to handleuncertainty not only in normal operation but also during FDDoperation and perform satisfactorily. In addition, the vehicledynamics is never represented with high fidelity when usinglinear dynamical models. Therefore, nonlinear modeling techni-ques are often applied to represent the system dynamics. But as itis often the case, nonlinear models are derived to approximate aparticular system behavior. For all modeling approximations,


uncertainty is increased due to the truncations introduced byelimination of higher order terms in formulations.

Uncertainty in control problems arises from insufficientknowledge about the system and its environment in whichit operates. Multiple control system have been developedto achieve stability and predetermined levels of performanceunder unexpected changes in the system characteristics due tofaults and/or damages. In modern aircraft, control systems needto be designed to guarantee robustness under uncertain flightenvelope. Varying flight conditions effect various parameters ofan aircraft system. In control studies, model and parameteruncertainties are often referred to as unstructured and structureduncertainties, respectively [168]. Herzallah [169] presented asurvey of uncertainty in control systems focusing primarily onprobabilistic techniques for modeling neural networks andprovide brief mention of multiple-model approaches. Zang et al.[170] provide a review of the needs and opportunities foruncertainty-based multidisciplinary design methods for aero-space vehicles. The review also gives a survey of uncertainty incontrol systems.

A typical control design under uncertainty is known asbounded uncertainty design and analysis [171]. In robust controltheory of aircraft systems, a particular flight envelope is presentedas uncertainty with predefined bounds. Linear Fractional Trans-formations (LFTs) is a framework in classical uncertaintyformulation methods used to address robust control problems.Special cases of LFTs are norm-bounded and polytopic uncertain-ties [171,172]. LFTs framework provides a mechanism toconstruct a dynamic system with varying parameters. Belcastroet al. [172] used LFT models to represent parametric systemuncertainty and applied them to simulations of an F-16 controlupset prevention and recovery system. Comparison to other LFTapproaches was also made. Recognizing that faults and/or damagemay occur randomly, some works [169,171] have proposed astochastic approach to the stability analysis of some AFTCSemploying FDD schemes. Another issue is that uncertaintymodeling is usually limited to linear plant models, sinceuncertainty propagation through nonlinear models would notobey Gaussian distributions of error signals. In terms of uncertainsystems, these have been traditionally controlled using the theoryof stochastic adaptive control [143]. Uncertainty analysis of thestability of feedback systems with parameter and modeluncertainties has been typically defined in terms of probabilitydensity functions, also referred to as probability of stability [173].Via sensitivity analysis, the probabilistic parametric uncertaintiesare used to assess the system stability. Mahmoud [174] studiedthe second moment stability of AFTCSs with norm boundedparameter uncertainties in noisy environments. Mahmoud alsoprovides a brief review of stochastic stability approaches forAFTCSs. Parameter uncertainties were assumed to be unknownyet bounded having norm bounded structure. Qu et al. [175]studied the design of a Lyapunov-based AFTCS for the stabilityand robustness of an uncertain nonlinear system with sensorfailures.

Yang et al. [176] presented a control system switching schemeto integrate FDI and FTCS and applied it to a class of uncertainnonlinear systems. The approach assumes that all possible faultmodels are known a priori and that the selected controllers coverthe stabilization for all fault conditions. Zhang et al. [177] alsopresented an FDI and FTCS integration approach. Variablestructure control (VSC) with sliding mode, a type of robustcontrol based on a switching feedback function, has been appliedto flight control systems with plant uncertainties [178]. Jafarovand Tasaltin [179] presented a robust sliding mode control for theuncertain MIMO F-18 aircraft model. Khammash et al. [180]studied aircraft longitudinal control under weight and center of

gravity uncertainty. Center of mass properties and its effects oncontrol are important because asymmetry might result fromdamaged aircraft [181]. Ganguli et al. [182] has presented FDIintegration with a Control Upset Prevention and Recovery System(CUPRSys) with measurement error handling capability. Thesimulated vehicle in this study was the NASA LaRC’s ARIES(Airborne Research Integrated Experiments System) aircraft.Damage was simulated by using reduced control surfaceaerodynamic look-up values.

Patel et al. [183] applied the L1 adaptive controller to a MIMOunstable UAV with accommodation to actuator failures and pitchbreak uncertainty, which was used to model uncertain aero-dynamics. Comparison to model reference adaptive control(MRAC) architecture, the L1 adaptive controller improved thetransient command tracking with increased robustness to time-delay. Hallouzi and Verhaegen [184] presented a FTCS systembased on subspace predictive control. The approach is based onusing a subspace predictor to continuously adapt after a fault hasoccurred in a closed-loop setting based on past input–output data.The developed FTCS approach was applied to a simulated Boeing-747 with actuator faults.

Niemann and Stoustrup [150] performed a performancecomparative study in terms of integrating and not-integratingthe FDI in FTCS systems with model uncertainties. Resultsdemonstrated that when model was free uncertainty, optimalfunctionality was obtained in both cases. However, in theuncertain case, optimal functionality could be obtained byseparate designs of robust controller and FDI. For systems withsignificant uncertainties, there is a fundamental trade-offbetween performance of the control loop and the performanceof the FDI.

Tolani et al. [185] provided a comprehensive decision andcontrol strategy integrating probabilistic robust control, damagemitigating control, health and usage monitoring systems (HUMS),and discrete event supervisory decision and control. The approachis based on a two-tier hierarchical architecture with one level forcontinuous-varying control and a second level for discrete-anomalous decision and control. The proposed approach wastested and validated on rotorcraft simulation testbed.

Kwong et al. [158] developed a fuzzy model reference learningcontroller (FMRLC) used to reconfigure the nominal controller ofan F-16 aircraft to compensate for actuator failures with andwithout explicit information about the failure. The fuzzy adaptiveapproach was developed as performance adaptive in the sensethat it attempted to recover the best possible performancedepending on the type of failure that occurred. Rong et al.[186,187] developed a sequential adaptive fuzzy inference controlstrategy for aircraft landing under the failures of stuck controlsurfaces. Hassan [161] attempted to use the Dempster–Shafertheory of evidence as an expert system for information fusion andcontrol of a time-varying nonlinear process. This work lacksignificant control application results.

Control design requires characterization of parameter andmodel form uncertainties. But it requires information from abroad range of disciplines, such as aeroelasticity [188]. Conven-tional robust control approaches rely on norm-bounded uncer-tainties in analysis and design, but little work has been done inincorporating probabilistic uncertainties into robust controldesign and analysis processes. Specific needs in terms of controlsystems of aerospace vehicles were outlined in Zang et al. [170]and are stated as follows: (1) Characterize the uncertainties insensors and actuators; (2) Characterize uncertainties in thecontrol design models obtained by using system identificationtechniques.

Several successful flight tests with health management andcontrol systems have been performed over the past few years.


Hunt and Hebden [189] presented the validation of the SHMsystem for the Eurofighter Typhoon. In the late 1990 s, the NASAF-15 aircraft with the Self Repairing Flight Control System,achieved failure and damage tolerance through an indirectadaptive reconfigurable control architecture and used an explicitFDI system to perform on-line damage and fault detection andestimation using hypothesis testing techniques associated with abank of Kalman filters [153]. A series of flight tests using analternative indirect adaptive control architecture demonstrated aso called Self Designing Controller applied to a fault scenariocorresponding to the landing of an F-16 with a simulated missingelevon [183]. The Reconfigurable Systems and Tailless FighterAircraft (RESTORE) program used a combined dynamic inversioncontrol law in an explicit model following framework. A neuralnetwork was used for on-line learning of selected aircraftparameters and incorporated in the feedback linearization loops[183]. Flight tests of the US Air Force’s Integrated AdaptiveGuidance and Control program were made for the Boeing X-40 A[149]. A number of flight tests of reconfigurable control systemswere carried out as part of the Defense Advanced ResearchProjects Agency (DARPA) Software Enabled Control program ontwo unmanned aerial vehicles (UAVs), namely the Boeing T-33and Boeing X-45 UAVs [149]. NASA Langley Research Center isalso actively involved in developing and testing reconfigurablesystems for the new generation of re-entry vehicles, commercialaircraft and small UAVs [149,153,183]. Several recovery systemsand technologies were developed as part of the Aviation Safetyprogram. High risk flight tests were conducted utilizing adynamically scaled transport aircraft that has been developed atthe NASA Langley Research Center as part of the AirborneSubscale Transport Aircraft Research testbed [183,190]. TheNASA/Boeing X-36 Tailless Fighter Agility Research Aircraftprogram successfully demonstrated the tailless fighter designusing advanced technologies to improve the maneuverability andsurvivability of possible future fighter aircraft. At the end of 2004and beginning of 2005, the US Air Force and Boeing Companyconducted a flight test of a modified MK-82 weapon at Eglin AirForce Base, which was controlled with a direct adaptive modelreference flight control system that is capable of learning on-linesome aerodynamics parameters with a neural network algorithmsimilar to the one used in the RESTORE program [144,183].Rockwell Collins developed and demonstrated an adaptive-baseddamage tolerant control system, called Automatic SupervisoryAdaptive Control (ASAC), during flight tests of an in-flightdamaged subscale F/A-18 UAV. Battle damage was simulated byin-flight ejection of ailerons and incurring up to 60% wing-loss.The flight test also demonstrated fully autonomous takeoff andlanding using GPS reference only [191].

7. Concluding remarks

In this paper, we reviewed issues and challenges facing thediagnostics, prognostics and controls research area in terms of theassociated uncertainties. Statistical pattern recognition techni-ques can be very useful and extremely effective for clearly definedtypes of problems, but their effectiveness is very much limited bythe quality and representation of the data from which it is trained.Emerging developments in data mining techniques have extendedthe capabilities of statistical pattern recognition and machinelearning approaches. With the developments in technologyhardware also come with increases in databases volume; there-fore, in order to separate the ‘bad’ data from the ‘good’ data, datamining techniques are necessary and very important tools in thearea of health management. Data-driven techniques are alsodependent on the quality and representation of the training data.

Model selection, feature extraction, feature selection, and classi-fication remain critical components that need to be welladdressed and optimized under imprecise information anduncertainties. To reduce uncertainty in the diagnosis and prog-nosis processes, knowledge must be maximized via integration ofvarious information sources.

In probabilistic theory, the Bayesian framework is used forinference in which probabilities are identified with degrees ofbelief. Methods based on probability theory can be very useful,but in general, they cannot deal well with imprecise data. ABayesian approach requires the user to make strong assumptionsabout the credibility of the experts to estimate the likelihood ofthe available evidence. The results obtained via the Bayesianapproach yield a single estimate of probability, which facilitatesthe decision-making of the monitoring system or user.

Non-probabilistic methods, such as fuzzy sets and theDempster–Shafer theory, have been used to overcome theproblem of imprecise data. One major advantage of fuzzy sets orevidence theory is that these methods do not require moreassumptions beyond what is already available. In the case of theD–S theory, the results yield maximum and minimum bounds ofthe probability of failure of a system, which can help in thedecision-making processes of collecting further data, continuingoperation, evaluation of health state, and prognostics prediction.Fuzzy sets and D–S methods suffer from not always being clearlyinterpretable, and their integration to reliable probabilistic resultsis not always clear. These ‘‘non-traditional’’ uncertainty analysisapproaches have the advantage of being capable of dealing withproblems when lack of information exists, and when subjectiveinfluences must be considered. Decision-making is usually basedon the bounds of the confidence interval for each available choice.Therefore, the interval or membership methods that can bounduncertainties in diagnostic and prognostic decisions are prefer-able in many situations to the well-characterized PDFs obtainedvia probabilistic approach.

The non-probabilistic and probabilistic approaches should notbe treated as competing methodologies, but more as comple-mentary techniques. These contrasting techniques should be usedin parallel in order to build and analyze diagnostic and prognosticmodels with maximum usage of available information. Forexample, we recommend that the belief and plausibility bound-aries of the D–S theory are integrated with the single probabilityresults found via the Bayesian theory. When a large gap existsbetween belief and plausibility boundaries, then more informa-tion should be collected, and the Bayesian theory would facilitatethe decision-making process. In addition, due to the complexity ofengineering systems, vagueness generally increases with increas-ing functional hierarchical levels, and the applicability of pureprobabilistic approaches diminishes and interval or membershipapproaches become more suitable.

The world we live in is not deterministic. Physics-basedmodels can only be used up to a certain accuracy. Even ifwe had all the time to collect and re-collect data on a givensystem, it would be impossible to collect all the informationneeded to predict all possible phenomena. As such, data-driventechniques have clear limitations as well. No single method iscapable of being the best solution in all situations; therefore, thestrengths of multiple methods must be integrated intelligentlyinto the appropriate flight vehicle damage management systems.In health management research, we aim at making general-izations and predictions of current and future system states basedon the past, and as such, we engage in inductive reasoning andinference. In order to address the issue of uncertainty, contextualinformation, knowledge, and experience must be well incorpo-rated into the flight vehicle structural health management andcontrol system.


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a review of uncertainty in flight vehicle structural damage monitoring, diagnosis and control:...

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