a mode-shape-based fault detection

8/2/2019 A Mode-Shape-Based Fault Detection

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A Mode-Shape-Based Fault DetectionMethodology for Cantilever Beams

By

CH.THIRUPATHI.REDDY


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OBJECTIVE

This report presents a OVERVIEW of the

physical principles behind the modeling of

vibrating structures such as cantilever beams

(the natural model of a wing).

It also reviews two different classes of fault

detection techniques and proposes a

particular detection method for cracks in

wings, which is amenable to formal

verification


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INTRODUCTION

Detection methods based on strain sensors makeuse of data collected during the operation of thestructure under analysis.

In the particular case of an airplane wing, thestrain data is collected while the wing vibrates asa result of an external stimulus, usually anexternal sinusoidal load.

The data is then processed to extract parametersthat characterize a mathematical model of thewings response to the load, which are ultimatelycompared to the ideal parameters of the wing.


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The simplest mathematical model of a vibrating

wing is a cantilever beam. This model is readily

available in the literature for undamaged beams.As will be shown in the sequel, the model of a

vibrating cantilever is a fourth-order partial

differential equation. The derivation of this equation of motion (EOM)

using dynamical equilibrium concepts has been

included. in the report to introduce the basic

concepts needed for fault detection (such as mode

shape functions) and to introduce a new system-

theoretical view of the cantilever which is

amenable for dynamical simulation


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Several methods are available to extract themodels parameters from experimental data andto detect faults (if present).

The detection methods can be broadly classifiedinto frequency-based methods and mode-shape-based methods. Both types of methods are

reviewed in this report, which also presents adetection algorithm that is amenable to formalverification.

It is important to remark that most of the analysis

is based on the theory of statics and dynamics ofstructures developed in [24]. Additionally, all thenumerical examples are based on data providedin [5].


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Basic Concepts from Mechanics of

Materials This section summarizes the basic concepts from mechanics of

materials presented in .

The goal is to provide common background and terminology to supportthe analysis of the

vibrating cantilever presented in the next section. It is important toremark that all the

figures in this section were also taken from [3].

2.1 Normal Stress and Strain

Consider the prismatic bar shown in Figure 1 (left). A prismatic bar is astraight structural

member having the same cross section throughout its length [3].When it is subject

to an axial force P normal to its cross section, its length increases from Lto L + . For an

isotropic bar, the elongation per unit length or normal strain, , iscomputed as

a mode-shape-based fault detection

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