Vibration based structural damage detection in flexural members using multi-criteria approach

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Abstract

This paper uses dynamic computer simulation techniques to develop and apply a procedure using non-destructive methods for damage assessment in beams and plates, which are important flexural members in building and bridge structures. In addition to changes in natural frequencies, this multi-criteria procedure incorporates two methods, called the modal flexibility and the modal strain energy method, which are based on the vibration characteristics of the structure. Using the results from modal analysis, algorithms based on flexibility and strain energy changes before and after damage are obtained and used as the indices for the assessment of the status of the structural health. The objective is to evaluate the feasibility of the proposed multi-criteria method to identify and localise single and multiple damages in numerical models of flexural members having different boundary conditions. The application of the approach is demonstrated through two sets of numerical simulation studies on beam and plate structures with nine damage scenarios in each. Results show that the proposed multi-criteria method incorporating modal flexibility and modal strain energy method is effective in multiple damage assessment in beam and plate structures.

Introduction

Civil infrastructures such as bridges, buildings are normally designed to have long life spans. Changes in load characteristics, deterioration with age, environmental influences and random actions may cause local or global damage to structures. Continuous health monitoring of structures will enable the early identification of distress and allow appropriate retrofitting to prevent potential sudden structural failures. In recently times, structural health monitoring (SHM) has attracted much attention in both research and development. SHM defined by Housner et al. [1] refers to the use of in-situ, continuous or regular (routine) measurement and analyses of key structural and environmental parameters under operating conditions, for the purpose of warning impending abnormal states or accidents at an early stage to avoid casualties as well as giving maintenance and rehabilitation advice. SHM encompasses both local and global methods of damage identification [2]. In the local case, the assessment of the state of a structure is done either by direct visual inspection or using experimental techniques such as acoustic emission, ultrasonic, magnetic particle inspection, radiography and eddy current. A characteristic of all these techniques is that their application requires a prior localisation of the damaged zones. The limitations of the local methodologies can be overcome by using vibration-based (VB) methods, which give a global damage assessment. Health monitoring techniques based on processing vibration measurements basically handle two types of characteristics: the structural parameters (mass, stiffness, damping) and the modal parameters (modal frequencies, associated damping values and mode shapes). As the dynamic characteristics of a structure, namely natural frequencies and mode shapes are known to be functions of its stiffness and mass distribution, variations in modal frequencies and mode shapes can be an effective indication of structural deterioration. Deterioration of a structure results in a reduction of its stiffness which causes the change in its dynamics characteristics. Thus, damage state of a structure can be inferred from the changes in its vibration characteristics [3]. Usually four different levels of damage identification are discriminated [4]: damage detection (Level 1), damage localisation (Level 2), damage quantification (Level 3), and predication of the acceptable load level and of the remaining service life of the damaged structure (Level 4). The amount of literature is quite large for a single damage scenario, but limited for multiple damage cases. Also existing methods are limited in scope and may not be useful in several realistic situations. It is observed that changes in natural frequencies alone may not provide enough information for integrity monitoring. It is common to have more than one damage case giving a similar frequency-change characteristic ensemble. In case of symmetric structures, the changes in natural frequency due to damage at two symmetric locations are exactly the same. Alternatively, no changes in the mode shapes could be detected if the mode had a node point at the location of damage [5]. There is thus a need for a more comprehensive method of damage assessment in structures.

Fast computers and sophisticated finite element programs have enabled the possibility of analysing hitherto intractable problems in structural engineering while simplifying the analyses of other problems. This paper uses dynamic computer simulation techniques to develop and apply two non-destructive damage detection methods for damage assessment in beams and plates which are both important flexural members in buildings and bridges. These methods called the modal flexibility method and the modal strain energy method, which are based on the dynamic characteristics of natural frequencies and mode shapes and their variations with the state of the health of the structure. The objective is to evaluate the feasibility of the proposed methods to identify and localise single and multiple damages in numerical models of the flexural members with different boundary conditions. The application of the approach is demonstrated through two sets of numerical simulation studies on beam and plate structures with nine damage scenarios in each case. Results show the procedure incorporating the modal flexibility and modal strain energy methods is effective in the multiple damage assessment of beam and plate structures.

Section snippets

Recent studies on VB damage identification

A number of methodologies have been found recently in the literature to identify, locate and estimate the severity of damage in structures using numerical simulation. Lee et al. summarise the features applied for damage detection algorithms utilising vibration properties as shown in Table 1. It is noticed that those methods utilising mode shapes are the most developed in terms of displaying the ability to identify, locate and estimate the severity of damage [6]. The modal flexibility and modal

Modal flexibility matrix

The modal flexibility matrix includes the influence of both the mode shapes and the natural frequencies. It is defined as the accumulation of the contributions from all available mode shapes and corresponding natural frequencies. The modal flexibility matrix associated with the referenced degrees of freedom can be established from Eq. (1) found in Huth et al. [13].[F]=[φ][1/ω2][φ]Twhere [F] is the modal flexibility matrix; [φ] is the mass normalised modal vectors; and [1/ω2] is a diagonal

Method

As a single damage indicator is not reliable, especially in the case of multiple damages, a damage multi-criteria approach which incorporates (1) change of frequency Δf, (2) change of flexibility matrix ΔF and (3) modal strain energy based damage index βi is used in the damage assessment of beam and plate structures. Initial beam and plate-like structures are first defined and developed as finite element (FE) models and their modal responses are obtained using the FE software package SAP2000.

Results and discussions

The natural frequencies of the first five modes of the beams and plates before and after damage in nine scenarios obtained from the results of the FE analysis are shown in Table 6, Table 7, Table 8. Percentage changes in the natural frequencies between the undamaged and damages conditions are listed within brackets in Table 7, Table 8. It can be observed that in general the presence of damage in flexural members causes a small decrease in the natural frequencies in all damage cases, with very

Conclusions

This paper uses dynamic computer simulation techniques to develop and apply a multi-criteria based non-destructive damage detection methodology for beam and plate structures which are important flexural members. The proposed procedure involves two damage detection methods (1) modal flexibility matrix and (2) modal strain energy based damage index, in addition to change in natural frequencies, all of which are evaluated from the results of free vibration analysis of the damaged and healthy

Acknowledgements

This research forms part of a continuing study of structural health monitoring of structures conducted in Queensland University of Technology. H.W. Shih is supported by a Queensland University of Technology Postgraduate Research Award.

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