Frequency response function based damage identification using principal component analysis and pattern recognition technique
Introduction
Structural health monitoring is an active area of research and practice in recent years. Damage diagnosis, including damage identification, damage localization and damage severity estimation, is a key issue of structural health monitoring [1]. Among different damage identification methods, vibration-based damage identification methods are considered to be very attractive as they can provide rapid and global evaluation of large structures. As a result, there has been a large volume of research, extending over the last three decades, devoted to vibration-based methods for damage identification in structures. The basis of these methods is that changes in the physical properties of a structure, especially loss of stiffness caused by cracking and other damage, result in measurable changes to the modal properties (frequencies, mode shapes and damping).
Although there are many methods available for damage identification such as those based on natural frequency changes, mode shape changes, mode shape curvature changes, dynamically measured flexibility, modal strain energy, artificial neural networks (ANNs) and frequency response functions (FRFs), most of them have their own positive and negative attributes. As an example, the advantages of using natural frequencies are easy implementation and relatively low cost. However, the feasibility of damage localization using changes in natural frequencies is limited due to the following reasons: (i) damage which creates low frequency changes requires very precise measurements [2], (ii) significant damage may cause very small changes in natural frequencies particularly for larger structures and these small changes may be undetected due to measurement errors, (iii) inability to distinguish damage at symmetrical locations in a symmetric structure and (iv) natural frequencies are easily affected by environmental changes such as temperature or humidity fluctuations. Hence, the use of natural frequencies alone in damage identification can lead to unrealistic predictions [3].
In order to overcome these difficulties, research efforts have focused on the use of mode shapes [4], [5], [6] and mode shape derivatives [7] as changes in them are more sensitive to local damage than changes in natural frequencies [8]. However, measured mode shapes are affected by environmental effects, the number of sensors and their locations, all of which can influence the accuracy of the damage identification procedure [9]. Accordingly, the modal strain energy method has been widely investigated for damage identification and condition assessment of structures because both damage location and magnitude can be determined by this method. However, the identification of light damage is still problematic [10]. Another drawback is the sensitivity of noise from ambient loads or inconsistent sensor positions, especially in the quantification of damage [11]. Further, Patjawit and Worsak [12] proposed a global flexibility index and their method was validated by laboratory tests and a field test on an existing highway bridge.
One of the soft computing techniques, neural networks have been utilized increasingly for damage identification due to their excellent pattern recognition, auto-association, self-organization, self- learning and non-linear modeling capability [13], [14], [15], [16], [17]. ANN-based methods can operate on a finite element (FE) model of the structure or on real measurement data and a neural network approach can be used to identify faults in the tested structure [18]. Usage of neural networks for damage identification has a number of attractive advantages. ANNs are sensitive to errors and insensitive to measurement noise, and they can also automate the fault diagnosis procedure, once the network is trained [19]. However, an ANN usually requires enormous computational effort especially when structures with many degrees of freedom are assessed. Due to this reason, most applications of ANN for damage identification are limited to small structures with limited number of degrees of freedom.
The use of FRFs which are usually the most compact form of data obtained from vibration tests of structures seems very promising for damage identification in recent years as utilizing FRFs to form a damage indicator has several advantages. FRFs require a small number of sensors and in situ measurements are straight forward [20]. Therefore, among all the dynamic responses, the FRF is one of the easiest to obtain in real time. Measured FRF data are usually obtained from vibrational testing. Hence these data provide information of structural dynamic behavior much of which would have been lost in using modal analysis data. Researchers have developed damage identification algorithms that use either direct FRF measurements [21] or their derivatives such as FRF curvatures [22], FRF differences [19] or compressed FRFs [23]. However, FRF approaches have many obstacles such as the large size and complexity of FRF data. Furthermore, FRFs are very sensitive to measurement noise and environmental fluctuations, which may lead to inaccurate damage identification and condition assessment [24].
Extensive literature exists on the subject of damage identification using modal parameters as well as frequency- or time-domain responses [25], [26], [27]. Furukawa et al. [25] presented a structural damage identification method using uncertain FRFs. Their method improved the identification accuracy in cases where a large amount of noise makes deterministic identifications fail. Using only a subset of vectors from the full set of FRFs for a few frequencies was suggested by Hwang and Kim [26]. A new neural network-based strategy was proposed and developed by Xu et al. [27] for the direct identification of structural parameters from the forced vibration time domain responses of the structure. Their method can be used for real-time structural health monitoring as eigenvalue analysis and direct optimization search process were not involved.
Combination of ANN, principal component analysis (PCA) and FRFs has been applied by Samali et al. [28], Dackermann et al. [29] and Li et al. [30] to obtain accurate damage identification results for data polluted up to 10% noise. Outcome of individual networks and hierarchical network ensemble approach were compared each other and it was found that network ensemble was efficient in accurate damage detection. However, their method was not tested with multiple damage scenarios and three dimensional structures. In addition, accuracy of light damage identification was affected by high noise levels. ANN, PCA and FRFs for damage identification have been applied by Ni et al. [23] and Zang and Imregun [31]. For satisfactory evaluation of damage in their methods, it was necessary to distribute sufficient sensors along the structure. Furthermore, as the reliability of the measured data was a major issue for accurate damage identification it was necessary to carefully select the measurement points. Damage-induced small abnormalities must be included in the measured FRF shapes to successfully locate damage from the method proposed by Liu et al. [32]. Measurements at a number of points on the structure were required to achieve successful damage identification results.
The damage identification method proposed by Nozarian and Esfandiari [33] was successful only at higher excitation frequencies. Bakhary et al. [34] presented an approach to detect small structural damage by using ANNs progressively. It used the substructure technique together with a two-stage ANN to detect the location and extent of the damage. By using their approach, the location and severity of low level structural damage were detected. Mehrjoo et al. [35] presented a method for estimating the damage intensities of joints in truss bridge structures using a back-propagation (BP) based neural network. However, only numerical examples on truss bridges were presented to demonstrate the accuracy and efficiency of their method. But when the damage was too small, their methodology could not detect it in the presence of modeling and measurement uncertainties. A Bayesian probabilistic approach based on ANN approach utilizing dynamic data was proposed by Yuen and Lam [36]. The method was only validated for a two dimensional structure. The three stage ANN method based on FRF data was proposed by Bandara et al. [37]. Their method has the characteristics of high calculation efficiency, small calculation error and is suitable for damage identification in large and complex structures.
As most of the methods have advantages and disadvantages, it will be beneficial to combine these methods to utilize their individual advantages. This paper presents a new approach to detect local structural damage by combining ANNs and FRFs to overcome the problems associated with large size data and measurement noise by incorporating those with PCA. To demonstrate the efficiency and reliability of this proposed method, a two storey framed structure is considered with single and multiple damage cases under different damage locations and severities.
Section snippets
Methodology
There are two approaches for damage identification; the first one is an inverse problem and the second one is a pattern recognition problem. The inverse problem usually adopts a finite element (FE) model of the structure and changes in the measured data of the physical structure are matched to changes in the developed FE model [38]. The second approach is based on the measured data of the structure of interest and damage classes (type, severity, location) are assigned by a pattern recognition
Illustrative example
FE modeling of the two-storey-framed structure is carried out in the first stage of the study. The objective of the FE modeling is to create a model that represents, as closely as possible, the laboratory structure in a previous study by Ulrike Dackermann [18]. In that project, the two-storey-framed structure was manufactured in the University of Technology, Sydney (UTS) Metal Workshop to experimentally validate the proposed damage identification method of Ulrike Dackermann. The two storey
Damage identification with noise polluted data
In reality, measured signals are degraded by various sources of noise. It is therefore necessary to examine the performance of the proposed method in the presence of noise. To do so, White Gaussian noise was added to the acceleration data obtained from transient analysis. In this study, measurement noise is assumed to be normally distributed with zero mean and specific variance. Noise-to-signal-ratios used in this study are 1%, 3%, 5% and 10% which create four different noise levels. FRFs
Conclusions
This paper presents an innovative procedure to accurately locate and quantify damage by combining FRFs, ANNs and PCA. The method can treat single and multiple damage scenarios and noise levels up to 10% and computational time is reduced. As demonstrated in the damage identification formulation, the proposed method requires FRF information of the healthy or undamaged structure, as well as FRF data extracted from the damaged structure. FRFs of the undamaged situation are necessary for damage
Acknowledgments
The first author would like to thank the Queensland University of Technology for providing the financial support to conduct this study at the School of Civil Engineering & Built Environment, Queensland University of Technology. All the assistance provided by the supervisors is gratefully appreciated. Furthermore, the authors would like to acknowledge the research work of U. Dackermann, J. Li and B. Samali who established the optimal sensor placements.
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