Frequency response function based damage identification using principal component analysis and pattern recognition technique

Highlights

• The proposed method does not require eigenvalue analysis and optimization process.

• The method can identify light damage with good accuracy with noise polluted data.

• PCA is done for subsets separately hence main features are extracted precisely.

• It is noted that method is able to detect multiple faults.

• Networks trained with summation FRFs were better than the individual networks.

Abstract

Pattern recognition is a promising approach for the identification of structural damage using measured dynamic data. Much of the research on pattern recognition has employed artificial neural networks (ANNs) and genetic algorithms as systematic ways of matching pattern features. The selection of a damage-sensitive and noise-insensitive pattern feature is important for all structural damage identification methods. Accordingly, a neural networks-based damage detection method using frequency response function (FRF) data is presented in this paper. This method can effectively consider uncertainties of measured data from which training patterns are generated.

The proposed method reduces the dimension of the initial FRF data and transforms it into new damage indices and employs an ANN method for the actual damage localization and quantification using recognized damage patterns from the algorithm. In civil engineering applications, the measurement of dynamic response under field conditions always contains noise components from environmental factors. In order to evaluate the performance of the proposed strategy with noise polluted data, noise contaminated measurements are also introduced to the proposed algorithm. ANNs with optimal architecture give minimum training and testing errors and provide precise damage detection results. In order to maximize damage detection results, the optimal architecture of ANN is identified by defining the number of hidden layers and the number of neurons per hidden layer by a trial and error method. In real testing, the number of measurement points and the measurement locations to obtain the structure response are critical for damage detection. Therefore, optimal sensor placement to improve damage identification is also investigated herein.

A finite element model of a two storey framed structure is used to train the neural network. It shows accurate performance and gives low error with simulated and noise-contaminated data for single and multiple damage cases. As a result, the proposed method can be used for structural health monitoring and damage detection, particularly for cases where the measurement data is very large. Furthermore, it is suggested that an optimal ANN architecture can detect damage occurrence with good accuracy and can provide damage quantification with reasonable accuracy under varying levels of damage.

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.