VIBRATION-BASED DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES UTILISING ARTIFICIAL NEURAL NETWORKS

Ulrike Dackermann, Jianchun Li, Bijan Samali, Fook Choon Choi & Keith Crews

University of Technology Sydney Centre for Built Infrastructure Research, Faculty of Engineering,

NSW 2007 Australia

udacker@eng.uts.edu.au KEYWORDS: Damage identification, artificial neural network, neural network ensemble, structural

health monitoring, modal strain energy, damage index method, timber structure ABSTRACT Vibration-based damage identification methods utilise the abnormality in dynamic characteristics of a structure to detect defects. Dynamic characteristics can be time histories, frequency response functions, natural frequencies, mode shapes and modal strain energies. As damage occurs in a structure the dynamic characteristics change and can therefore be used to identify the defects. This paper presents an overview of a project, which aims to detect structural damage by examining a variety of dynamic characteristics. Artificial neural networks are used to identify pattern changes due to damage and thereby estimate locations and severities of damage. A neural network ensemble is used to fuse the network outcomes of the individual dynamic parameters and an overall damage prediction is obtained. In detail, the procedure presented utilises changes in modal strain energies to detect damage in a timber beam. Finite element models of timber beams, inflicted with several types of damage, are created. Damage index values, which are based on modal strain energies, are calculated from the numerical models and used as input pattern for training and testing of neural networks. To incorporate real life issues with limited sensors, cubic spline techniques are adopted to reconstruct finer mode shapes and thereby improve the damage identification. INTRODUCTION From the early days of Australia’s colonisation, many timber bridges were constructed. Australia supplied the settlers with an untouched natural resource of timber, which provided material of strength, size and durability. As the colonies expanded, and the need to transport people and commodities increased, many innovations in timber bridge technology were developed and widely implemented. In the early 1950’s, however, timber bridge construction ceased due to advent of modern materials, like steel or reinforced concrete, and timber appeared to have lost the appeal to designers and those managing the road networks. The timber bridge assets were neglected over decades and became first a problem during the 1970s through the high cost of maintenance (Walter 1996). In 2003, the Department of Transport and Regional Services (DoTaRS) estimated that there are 29,000 timber bridges in Australia, of which one third are older than 50 years. About half of the 29,000 timber bridges are in use on heavy vehicle routes and are rated as not being in good condition (DoTaRS 2003). As it is economically not possible to replace all of the aged timber bridges, structural health monitoring and condition assessment is necessary to ensure the reliability of the aged structures and the safety of the public. Most of the current methods of structural integrity assessment for timber bridges are through destructive and semi-destructive means, like resistance drilling, probing or coring. Some non-destructive techniques have been developed over the past decades. Most of them, however, are localised methods, which are based, for instance, on visual inspection, stress wave, ultrasonic or radiography. But when these local methods are applied to large timber structures, they are very time consuming and costly.

Vibration-based techniques are global methods and are able to assess the condition of the entire structure. A technique to test the remaining strength of timber bridges based on the dynamic characteristics of the bridge was developed by the University of Technology, Sydney in collaboration with the Institute of Public Works Engineering Australia and 14 New South Wales councils. With this technique, councils can prioritise bridge maintenance and rehabilitation and place appropriate load limits on bridges. They can monitor deterioration rates and predict intervention timeframes at a cost of 15-20 % of traditional load testing (DoTaRS 2003). Besides the determination of the structural strength, vibration-based techniques are also capable of determining the actual location and extent of the damage. Over the past two decades, many vibration-based damage identification methods have been developed. These techniques, which examine changes in the dynamic characteristics of a structure, eventually reduce to some form of pattern recognition problem. Comprehensive literature reviews on modal-based damage detection methods were published by Doebling et al. (1996) and Carden & Fanning (2004). Among various vibration-based damage detection approaches a particularly promising method is the damage index method. It is based on changes in modal strain energy before and after damage and has successfully been used in some applications. Several modifications of the algorithm have been developed and verified by analytical and experimental studies (Stubbs, Kim & Farrar 1995, Stubbs & Park 1996, Kim & Stubbs 2002 and Choi et al. 2007). The method, however, faces some critical issues due to complex nature of structures, uncertainties and limited measurements when it is applied to real life civil engineering structures. In recent years, the use of Artificial Neural Networks (ANNs) in structural damage detection gained much attention. ANNs are artificial intelligence that simulate the operation of the human brain. Once trained, they are capable of learning, i.e. pattern recognition and classification. These characteristics make ANNs powerful complementary tools in vibrational damage identification. With applying ANNs for damage detection, traditional methods can be greatly improved. Several researchers used ANNs in combination with vibration-based damage detection techniques (Gutierrez, Ferregut & Osegueda 1996, Marwala 2000, Loh & Yeh 2000, Suresh et al. 2004, Kao & Hung 2005 and Xu & Humar 2005). In this paper, authors present a robust and reliable procedure that accurately determines the location and severity of single damage in a timber beam. The damage index method in combination with ANNs is used to identify defects. The approach of neural network ensembles is utilised to respect individual characteristics of mode separated damage indices and to consider the varying importance of different modes. PROJECT OVERVIEW The objective of this project is to develop a damage detection procedure for timber structures, which is suitable for assessing the condition of real structures in the field. It can incorporate conditions of real life testing, like limited number of sensor arrays, measurement noise, humidity variations or incomplete data sets. The developed method will be able to determine the existence, location and severity of single as well as multiple damage. A variety of vibrational quantities can be used to identify and evaluate the damage. Vibrational quantities are, for instance, time histories obtained from ambient or controlled vibrations, frequency response functions, natural frequencies, mode shapes, damping ratios or modal strain energies. The selected vibrational quantities will individually be processed for inputs to ANNs for damage detection. An ANN ensemble will then be used to fuse results from individual damage detection and produce more reliable and accurate results. In this way, the benefits of each vibrational parameter are used to its best and an artificial intelligence will result in damage prediction. This paper presents the first stage of this study, namely, a numerical study where the damage index method in conjunction with neural network techniques is applied to a finite element timber beam model to identify the location and extent of single damage.

DAMAGE INDEX METHOD The damage index method was firstly introduced by Stubbs, Kim & Topole in 1992. This method utilises the relative differences in modal strain energy of a structure before and after damage to identify defects. A mode shape stores an amount of strain energy in a particular structural load path. When damage occurs, the modal strain energy in that load path alters due to the high sensitivity of the frequency and shape of that mode. The strain energy in a Bernoulli-Euler beam associated with a particular mode shape ‘φi’ is calculated from

( )L

2i i

0

1U EI (x) dx2

′′= φ∫

(1)

where EI is the flexural rigidity of the beam and ‘φi″’ the curvature of mode shape ‘φi’. By subdividing the Euler-Bernoulli beam into N elements, the modal strain energy associated with the jth element of the ith mode is given by

( ) ( )2ij ij

j

1U EI (x) dx2

′′= φ∫

(2)

The fractional energy of the jth element, denoted as ‘Fij’, is therefore

( ) ( )

( )

2ij

ij jij L

2ii

0

1 EI (x) dx2U

F U 1 EI (x) dx

2

′′φ

= =′′φ

∫

∫(3)

By assuming that the fraction of modal energy is the same for damaged* and undamaged structures it is found that

( ) ( )

( )

( ) ( )

( )

22 * *i ij j

j jL L 22 * *

i i0 0

1 1EI (x) dx EI (x) dx2 2

1 1EI (x) dx EI (x) dx2 2

′′ ′′φ φ

=′′ ′′φ φ

∫ ∫

∫ ∫(4)

Rearranging equation (4), the so-called damage index ‘βij’ of mode i and member j is obtained from

( )( )

( ) ( )

( ) ( )

L2 2*i i

j j 0ij * L 22 *

j i ij 0

(x) dx (x) dxEI

EI (x) dx (x) dx

′′ ′′φ φ

β = =′′ ′′φ φ

∫ ∫

∫ ∫(5)

Here it is assumed that the flexural rigidity EI of the damaged and undamaged modes are constant over the entire length of the beam. To establish a comparative basis for different modes, the damage index ‘βij’ is transformed into the standard normal space and the normalised damage index ‘Zij’ is calculated from ij ij

ijij

Z β

β

β −μ=

σ (6)

with ‘μβij’ being the mean and ‘σβij’ the standard deviation of the ‘βij’ values for all j elements. Positive ‘Zij’ values indicate the possibility of damage and can therefore be utilised to locate the defects. The estimation of the damage severity for element j can be formulated by equation

ijij

1 1α = −β

(7)

with ‘α ij’ being the severity estimator.

ARTIFICIAL INTELLIGENCE Artificial neural networks (ANNs) are artificial intelligence originally developed as a methodology for emulating the biology of the human brain. The biological network consists of small cellular units called neurons, which are massively interconnected by nerve fibres. A neuron receives biological stimuli (input signals) from adjacent neurons, processes the signals and forwards them to other neighbouring neurons. A key property of the neural system is the ability to modify their responses as a result of exposure to external signals, which occur through changes in the strength of the interconnections and is called learning (Bishop 1994). Artificial Neural Networks ANNs mimic biological networks and consist of weighted interconnected neurons, arranged in sets of input, hidden and output layer. The neurons are weighted by an adjustable variable (weight) and offset by a constant (bias). The layers are linked by transfer functions. A key property of ANNs is the capability of learning, i.e. pattern recognition and classification. ANNs can be regarded as nonlinear mathematical functions that map a set of input variables ‘pi’ (i = 1, 2 ... d) to a set of output variables ‘ak’ (k = 1, 2 ... r) (Bishop 1994). Once the networks are trained, they are capable of pattern recognition and classification. In damage detection, the most commonly used networks are feed-forward multi-layer neural network. The outputs of these networks are given as m d

k kj ji i j0 k0j 1 i 1

a (p) w f w p b b= =

⎛ ⎞= + +⎜ ⎟

⎝ ⎠∑ ∑ (8)

where ‘pi’ are the input variables, ‘wkj’ and ‘wji’ the interconnection weights, ‘bj0’ and ‘bk0’ the bias parameters, ‘f’ the transfer function, ‘d’ the number of input units and ‘m’ the number of hidden layer. The transfer function ‘f’ can be linear or non-linear. The weights and biases in the hidden layers are iteratively varied in order to move the network outputs closer to the targets. This process is called learning or training.

Fig. 1 Feed-forward multi-layer neural network ensemble.

Individual Network

Network 2

Network n

Network Ensemble

Network Ensemble

Output

ak2

akn

a

. . .

. . .

p1 p2 p3

pd pd-1 pd-2

…

Input Layer First

Hidden Layer Second

Hidden LayerOutput Layer

Network 1 ak

1

Network Output

In supervised learning, the training algorithm is provided with a set of examples (the training set) { } { } { }1 1 2 2 q qp , t , p , t ,..., p , t (9) where ‘pq’ is an input to the unit and ‘tq’ is the corresponding correct output, also referred to as target. As the inputs are applied to the network, the network outputs are compared to the targets. The training algorithm is then used to adjust the weights and bias of the unit in order to move the network outputs closer to the targets. The circled illustration of Error! Reference source not found. shows the schematic model of a multi-layer feed-forward neural network. Neural Networks Ensemble Many real-world problems are too large and too complex to be solved by a single monolithic system. A composite system consisting of several subsystems can reduce the total complexity of the system while solving a difficult problem satisfactorily (Xin & Yong 1998). Neural network ensembles, developed by Hansen & Salamon (1990), are learning paradigms where a collection of neural networks is trained simultaneously for the same task (Sollich & Krogh 1996). First, each network in the ensemble is trained individually and then the outputs of each of the networks ‘ae’ (e = 1, 2 ... n) are combined to produce the ensemble output ‘a’. Through assembling a number of neural networks, the generalization ability of a neural network system can significantly be improved (Zhou, Wu & Tang 2002). Generally, the single networks can be generated either by varying the design of the networks (i.e. different architecture, transfer functions, training algorithms) or by training the individual networks with different training sets. The latter is applied in this project. A model of a neural network ensemble is also shown in Error! Reference source not found.. DAMAGE IDENTIFICATION Methodology This paper presents a vibration-based method to identify defects in timber structures. Damage is identified by artificial neural networks, which utilise damage index values as input patterns. The neural network ensemble approach is used to fuse damage detection outputs from individual modes. The rationale is that the inputs (damage index) separated into individual modes contain distinguishable pattern which is better for individual ANN training and combined information of all modes produce more reliable results. By complementing the damage index method with artificial intelligence that is capable of pattern recognition, issues regarding uncertainty, coarse sensor arrays, incomplete data sets and false positive damage identifications can be overcome. Firstly, mode shape vectors are obtained by solving the eigenvalue problem of the given structure. Real life issues regarding limited sensor arrays are incorporated by reducing the number of sampling points. The cubic spline interpolation technique is adopted to reconstruct mode shapes in finer mode coordinates which dictates the accuracy of damage location exercise. Secondly, from the identified mode shapes the modal strain energy based damage index values ‘Zij’ and ‘αij’ are derived. Thirdly, two sets of individual neural networks are trained with modally separated damage index values to determine the location and the severity of damage, respectively. Finally, the outcomes of the individual networks are fused with a network ensemble and an overall damage prediction is obtained. Numerical Model A numerical model of a timber beam with the dimensions of 45 mm by 90 mm by 4,500 mm was created using the finite element analysis package ANSYS (2005a). The beam is assumed to be of radiata pine timber with a modulus of elasticity of 12,196 N/mm2, a Poisson’s ratio of 0.3 and a density of 500 kg/m3. The element type used is SOLID45, which is a 3 dimensional structural solid defined by eight nodes having 3 degrees of freedom at each node. The cross-section is modelled with 20 elements across the height and 4 elements along the width. A division into 201 nodes and 200 elements in the longitudinal direction of the model was adopted in accordance with previous sensitivity studies undertaken by Choi (2007). The support conditions are set as pin-pin. Fig. 2 depicts a model of the timber beam.

Fig. 2 Finite element modelling of a pin-pin supported timber beam.

Seven different damage locations with spacings of 562.5 mm (1/8th of the span length) are considered. The locations are denoted as 1, 2, 3, 4, 5, 6 and 7, and are shown in Fig. 2. For each of these locations five different damage severities, termed as extra light (‘XL’), light (‘L’), medium (‘M’), severe (‘S’) and extra severe (‘XS’) are investigated, generating a total of 35 different damage cases. All the inflicted damage are 45 mm in length (1 % of the total span length) and 9 mm, 18 mm, 27 mm, 36 mm and 45 mm in height (10 %, 20 %, 30 %, 40 % and 50 % of the beam height). This corresponds to 27.1 %, 48.8 %, 65.7 %, 78.4 % and 87.5 % of loss of the moment of inertia. Damage is modelled by rectangular openings from the soffit of the beam along the span length. A medium size damage is depicted in Fig. 3.

Fig. 3 Finite element modelling of medium size damage (27 mm x 45 mm).

Using the modal analysis module in ANSYS, the first five flexural modes, with their corresponding natural frequencies and mass normalised mode shapes are obtained. To incorporate real life problems with limited sensor arrays, the mode shape vectors are reduced from 201 data points to 9 data points, representing 9 measurement sensors. Subsequently, the mode shape vectors are reconstructed from 9 to 41 data points, utilising cubic spline interpolation techniques, in order to improve the damage identification results. By correlating the mode shape curvature vectors of the undamaged beam to those of the different damaged beams the damage index values ‘Zij’ and ‘αij’ are determined following the procedure outlined above. Artificial Neural Network Model Two ensembles of supervised feed-forward multi-layer neural networks are designed to identify damage. The modal strain energy based damage indices ‘Zij’ and ‘αij’ are utilised, respectively, as input pattern to the two network ensembles, determining the location and the severity of damage. First, individual neural networks are trained with the mode specific damage indices ‘Zij’ and ‘αij’, respectively. Then, the outcomes of each of the two network sets are combined in a neural network ensemble and a final damage prediction is obtained. The individual neural networks comprise of an input layer with 41 nodes, representing the 41 data points of the damage indices, three hidden layers with 30, 20 and 10 nodes and one single node output layer estimating the location or the severity of the damage. The network ensembles are designed with 5 input nodes, which are the outputs of the 5 individual networks, three hidden layer of 7, 5, and 3 nodes and one output node estimating the damage location or severity. The transfer functions used are hyperbolic tangent sigmoid functions. Training is performed utilising the back-propagation conjugate gradient descent algorithm. The input data is divided into three sets; a training, a validation and a testing set. While the network adjusts its weight from the training samples, its performance is supervised utilising the validation set to avoid overfitting. The network training stops when the error of the validation set increases while the error of the training set still decreases, which is the point when the generalisation ability of the network is lost and overfitting occurs. The data set of 35 samples is divided into 25 for training and 5 each for validation and testing. The design and operation of all neural networks is performed with the software Alyuda NeuroIntelligence version 2.2 from Alyuda Research Inc.

90 mm

45 mm

27 mm

90 mm

4,500 mm 562.5 mm

1 2 3 4 5 6 7

RESULTS AND DISCUSSION Damage Index Values The damage index values ‘Zij’ and ‘αij’, which indicate the possibility and extent of damage, are the first intermediate results as inputs for the developed ANNs. Exemplarily, Fig. 4 (a) illustrates the location indicator ‘Zij’ derived from mode 1 of a beam that is damaged at location 4. In the figure, the x-axis shows the length of the beam with the damage locations 1 to 7 and the y-axis the damage index. The actual damage location is indicated by a vertical line. As mentioned earlier, the damage index method inherits some problems. Firstly, if damage is located at a node point of a mode shape it cannot be detected. The severity estimator ‘αij’ does not give any indication of the damage extent. For the damage localisation using damage index ‘Zij’, possible false damage indications can occur, as presented in Fig. 4 (b), where ‘Zij’ is obtained from mode 4 of a beam damaged at mid-span. Secondly, if only a limited number of measurement data is available, false positive damage indications occur in a couple of damage cases. This phenomenon is shown in Fig. 4 (c), which displays ‘Zij’ derived from mode 3 of a beam damaged at location 3. Here, besides the correct damage location, a false indication at location 2 is visible. Thirdly, damage index method slightly misplaces damage where it is close to the supports for all modes, when only a few measurement points are available. This is presented in Fig. 4 (d) for ‘Zij’ derived from mode 2 of a beam damaged at location 1.

(a)

(b)

(c)

(d)

Fig. 4 ‘Zij’ values derived from (a) mode 1 (beam damaged at location 4), (b) mode 4 (beam damaged at location 4), (c) mode 3 (beam damaged at location 3) and (d) mode 2 (beam damaged at location 1). When the damage index method is used alone to detect defects, damage may falsely be identified, as outlined above. By utilising neural network techniques, with its ability to recognise patterns, the damage identification process can be improved and critical issues overcome. Individual Neural Network Outcomes Individual neural networks are trained with mode separated damage index values to identify damage. The damage index ‘Zij’ is utilised to determine the location of the damage and the damage index ‘αij’ to estimate the damage severity. The individual networks that are trained to localise the defects, precisely determine the locations of all damage cases. The networks trained to estimate the severity of damage, however, give many false predictions, which are displayed in Fig. 5 (a) to (e). In the figures, the x-axis displays the 35 damage cases sorted by their severities (SXL to SXS) and their locations (L1 to L7). The y-axis represents the normalised error, which is defined as Enorm(d) = (Td-Od)/Smax, where ‘d’ is the damage case, ‘Td’, the target value of ‘d’, ‘Od’ the network output value of ‘d’ and ‘Smax’ the maximum severity. The marked error band around the 0 % error axis indicates the area in which the network estimations must fall into in order to correctly quantify the damage. Here the error band ranges from −12 % to +12 % normalised error. In the figures it can be seen that the outcomes of the individual neural network largely vary. Although the damage cases of the networks trained with mode 3 and mode 5 derivatives are all quantified correctly, many misidentifications occurred for the networks of mode 1, mode 2 and mode 4. Misquantifications of the networks of mode 2 and mode 4 occur at the node points of the modes, i.e. location 4 for mode 2 and locations 2, 4 and 6 for mode 4. Also damage in extra light damage cases are wrongly identified for mode 2 and mode 4 networks.

(a) Neural network outcomes to quantify damage trained with ‘αij’ derived from mode 1

(b) Neural network outcomes to quantify damage trained with ‘αij’ derived from mode 2

(c) Neural network outcomes to quantify damage trained with ‘αij’ derived from mode 3

(d) Neural network outcomes to quantify damage trained with ‘αij’ derived from mode 4

(e) Neural network outcomes to quantify damage trained with ‘αij’ derived from mode 5

Fig. 5 Individual neural network outcomes trained with ‘αij’ damage indices derived from

(a) mode 1 to (e) mode 5 to estimate the damage severity.

Based only on the outcomes of the individual networks to produce a final damage prediction is problematic as their damage estimations are not reliable, nor accurate. Therefore, an intelligent fusion of the network predictions is necessary, which is achieved in this project with a neural network ensemble. Neural Network Ensemble Outcomes Neural network ensembles are created that combine outcomes of the individual networks and give a final prediction on the damage state. The outcomes of the neural network ensembles, which determine the location and the severity of the damage, respectively, are illustrated in Error! Reference source not found. (a) and (b). From the figures it can be seen that the locations and the severities of all damage cases are eventually identified correctly. These outcomes show that the developed damage identification procedure is capable of overcoming issues of the damage index method. It is precise, reliable and robust in the identification of damage.

(a) Neural network ensemble outcomes to locate damage trained with ‘Zij’

(b) Neural network ensemble outcomes to quantify damage trained with ‘αij’

Fig. 6 Neural network ensemble outcomes trained with (a) ‘Zij’ damage indices to

locate damage and (b) ‘αij’ damage indices to quantify damage. CONCLUSION This paper presents a vibration-based method for damage identification in timber structures. The damage index method, which is based on changes in modal strain energies before and after damage, in conjunction with neural network techniques is utilised to determine the location and the severity of damage. The developed method considers real life testing issues such as limited number of sensors by using cubic spline techniques to improve the accuracy of damage identification. Numerical models of timber beams, damaged at various locations with different severity levels, are modelled with a finite element program. Individual neural networks corresponding to individual modes are created to take advantage of clear patterns of modally separated damage index for training efficiency. Neural network ensembles then fuse the outcomes of the individual networks and a final damage prediction is obtained. The results of the damage detection procedure show that the developed method is precise and reliable in the identification of the defects and that it is capable of overcoming issues of the damage index method.

ACKNOWLEDGEMENTS The authors wish to thank the Centre for Built Infrastructure Research (CBIR), Faculty of Engineering, University of Technology, Sydney (UTS) for supporting this project. Alyuda Research Inc. is gratefully acknowledged for providing us with a free copy of their Alyuda NeuroIntelligence software. REFERENCES Bishop, C.M. (1994), 'Neural Networks and their Applications', Review of Scientific Instruments, Vol. 65,

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