Damage identification in civil engineering structures utilizing PCA-compressed residual frequency response functions and neural network ensembles

STRUCTURAL CONTROL AND HEALTH MONITORING

Struct. Control Health Monit. (2009) Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/stc.369

Damage identification in civil engineering structures utilizing PCA-compressed residual frequency response functions and neural network ensembles Jianchun Li1, Ulrike Dackermann1,,y, You-Lin Xu2 and Bijan Samali1 1

Centre for Built Infrastructure Research, Faculty of Engineering and Information Technology, University of Technology Sydney, NSW 2007, Australia 2 Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

SUMMARY This paper presents a non-destructive, global, vibration-based damage identification method that utilizes damage pattern changes in frequency response functions (FRFs) and artificial neural networks (ANNs) to identify defects. To extract damage features and to obtain suitable input parameters for ANNs, principal component analysis (PCA) techniques are applied. Residual FRFs, which are the differences in the FRF data from the intact and the damaged structure, are compressed to a few principal components and fed to ANNs to estimate the locations and severities of structural damage. A hierarchy of neural network ensembles is created to take advantage of individual information from sensor signals. To simulate fieldtesting conditions, white Gaussian noise is added to the numerical data and a noise sensitivity study is conducted to investigate the robustness of the developed damage detection technique to noise. Both numerical and experimental results of simply supported steel beam structures have been used to demonstrate effectiveness and reliability of the proposed method. Copyright r 2009 John Wiley & Sons, Ltd. KEY WORDS:

damage identification; artificial neural network; neural network ensemble; structural health monitoring; frequency response functions; principal component analysis

1. INTRODUCTION It is inevitable for civil engineering structures to continuously accumulate damage during their service life in which damage may be caused by various sources including harsh environmental conditions, ageing materials, overloading or inadequate maintenance. In order to prolong the service life of the structures and to prevent catastrophic failures, early and reliable damage

*Correspondence to: Ulrike Dackermann, Faculty of Engineering and Information Technology, University of Technology Sydney, CB02.03.03D, PO Box 123, Broadway, NSW 2007, Australia. y E-mail: [email protected]

Copyright r 2009 John Wiley & Sons, Ltd.

Received 23 July 2009 Revised 18 September 2009 Accepted 26 October 2009

J. LI ET AL.

assessment is critically important. In civil engineering practices, current non-destructive damage detection methods are based, for instance, on visual inspection, stress wave, ultrasonic, X-ray, acoustics or radiography. Most of these methods, however, are restricted to local observations in a limited area and rely on a presumption of likely damage in the targeted areas. When applied to large structures, these methods are very time consuming and costly. Vibration-based damage detection techniques are global methods and are based on the principle that the damage alters both the physical properties, such as mass, stiffness and damping, as well as the dynamic properties of a structure. Therefore, by utilizing the dynamic characteristics from the structural vibration, damage can be identified. In general, there are three types of measured dynamic quantities. They are time histories, frequency response functions (FRFs) and modal parameters. Traditionally, modal parameters such as natural frequencies, mode shapes and damping ratios are the most used dynamic features in damage detection. The use of resonant frequencies as the damage indicator was especially popular in the early years of vibration-based damage detection as they are easy to obtain [1,2]. Unfortunately, in many cases the resonant frequencies turned out to be insensitive to the structural damage, and especially to the lower levels of damage [3,4]. For field application, another handicap is that the natural frequencies are heavily affected by environmental changes such as temperature or humidity fluctuations [5]. Next, mode shapes can also be used as dynamic indicators for the structural damage. The mode shapes obtained before and after damage are either directly used [6] or indirectly used as measures such as mode shape curvatures [7] or modal strain energy differences [8,9] to detect the damage. Compared with frequency-based techniques, mode shaperelated techniques are less environmentally sensitive and provide better estimation for both the damage location and severity. However, these methods are often very sensitive to incompleteness of the measured modal data and require measurements from a large number of sensor arrays to ensure reliability of results. In addition, these methods are based on a complicated processing procedure known as experimental modal analysis to extract modal shapes. Experimental modal analysis is susceptible to human errors and often becomes less reliable when measured data are noise contaminated. On the other hand, using measured FRF data may have several advantages and is a more desirable dynamic quantity for vibration-based damage detection. FRF is a non-dimensional complex quantity that specifies how vibration is transmitted between the points on the structure as a function of frequency. FRF data are directly measured data and one of the easiest to obtain in real-time as it requires only a small number of sensors and very little human involvement [10]. Compared with modal parameters, FRFs require much less data processing, which reduce the susceptibility in contaminating or losing crucial information. Most vibration-based damage identification techniques can be considered as some form of the pattern recognition problem as they look for the discrimination between two or more signal categories, e.g. before and after a structure is damaged or differences in the damage levels or locations. Artificial neural networks (ANNs) are artificial intelligence, which are capable of learning, i.e. pattern recognition and classification. Using a combination of FRFs and ANNs in the structural damage identification has shown promising results [11,12]. However, there is an obstacle in application of ANN using FRF due to the large size of the FRF data. Utilizing fullsize FRFs in neural networks will result in a large number of input nodes, which will cause problems in training convergence and computational efficiency. If only partial sets of FRF data are used, an improper selection of data points from frequency windows will result in the loss of important information and errors will be introduced to the detection scheme [13]. Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

Principal component analysis (PCA) is a statistical technique for achieving dimensional data reduction and feature extraction. By projecting data onto the most important principal components (PCs), its size can greatly be reduced without significantly affecting the data. In structural dynamics, PCA has been extensively applied to measure vibration signals for dimensionality studies, reduced-order modelling, modal analysis, parameter identification of non-linear systems, and removal of the influence of environmental effects. Its application for vibration-based damage detection was first proposed by Worden et al. [14] and has been since reported in several papers [13,15–17]. This paper presents a novel damage detection method that utilizes damage fingerprints in FRF data to identify defects in beam structures. The proposed method uses ANNs to map changes in the residual FRFs, which are the differences in FRF data from the intact and the damaged structures, to identify the damage location and severity. To obtain suitable patterns for ANN inputs, the residual FRF data from measurement are compressed by adopting PCA techniques. The method is tested and validated on numerical and experimental data of pin–pin supported steel beam structures.

2. THEORETICAL BACKGROUND 2.1. ANNs and network ensembles ANNs imitate biological networks and consist of weighted interconnected processing elements, called neurons, which are grouped in sets of input, hidden and output layer. The main characteristics of a neural network is its ability to learn, i.e. to map a set of input variables pi (i 5 1, 2,y, d) to a set of output variables ak (k 5 1, 2,y, r). This is done by adjusting variables (weights) and constants (biases) of the neuron connections according to assigned transfer functions. Provided enough neurons exist, neural networks are able to represent any non-linear mathematical function with arbitrary accuracy [18]. Once the networks are trained, they are powerful pattern recognizers and classifiers that do not require any prior knowledge of the system being examined. They also have a fault tolerance and can distinguish between random errors and the desired systematic outputs, which make them a robust means for representing model-unknown systems encountered in the real world [19]. These properties make them attractive in the field of structural damage detection. The most commonly used networks in this field are multi-layer neural networks, coupled with the back-propagation algorithm. A schematic model of a four-layer neural network is shown in the circled illustration of Figure 1. The outputs of a multi-layer feed-forward network are given as ! m d X X ak ðpÞ ¼ wkj f wji pi 1bj0 1bk0 ð1Þ j¼1

i¼1

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 layers. The bias can be regarded as a special case of a weight from an extra input of 1, representing the firing threshold of the biological network. The transfer function f can be different for the hidden and output units. In this study, a hyperbolic tangent transfer function is implemented. In supervised learning, the training algorithm is provided with a set of examples (the training set) ðp1 ; t1 Þ; ðp2 ; t2 Þ . . . ðpq ; tq Þ, where pq is an input to the network and tq is the Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

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

corresponding correct output, also referred to as target. As the input samples are applied to the network, the outputs are compared with the targets utilizing the generalized delta-learning algorithm. Based on q training samples, the learning algorithm is designed to minimize recursively the error function Eq ¼

r 1X ðtqk  aqk Þ 2 k¼1

ð2Þ

with tqk and aqk being the target output and actual output vectors of the kth output variable, respectively. Thereby, the weights and biases are iteratively adjusted and the network outputs are moved closer to the targets. This process is called learning or training. 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 [20]. Neural network ensembles, developed by Hansen & Salamon [21], are learning paradigms where a collection of neural networks is trained simultaneously for the same task [22]. First, each network in the ensemble is trained individually and then the outputs of each of the networks ae ðe ¼ 1; 2; . . . ; nÞ 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 [23]. Generally, the individual 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 Figure 1. Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

2.2. PCA PCA, also known as Karhunen–Loe`ve transform or proper orthogonal decomposition, was developed by Pearson in 1901 [24] and is one of the most powerful statistical multivariate data analysis techniques for achieving dimensionality reduction. It is a statistical technique that linearly transforms an original set of k variables into a smaller set of n (npk) uncorrelated variables, the so-called PCs. Eigenvalue decomposition of the covariance matrix forms the basis of PCA. The direction of the resulting eigenvectors represents the direction of the PCs, which are weighted according to the value of the corresponding eigenvalues. Each PC is a linear combination of the original variables. All the PCs are orthogonal to each other and form an orthogonal basis for the space of the data. The full set of PCs is equal to the original set of the variables. By removing PCs of low power, a dimensional reduction is achieved without significantly affecting the original data [25]. Besides the benefit of data reduction, PCA is also a powerful tool for disregarding unwanted measurement noise. As noise has a random feature, which is not correlated with a global characteristic of the data set, it is represented by less significant PCs. Therefore, by disregarding PCs of low power, measurement noise is filtered. Following is a description of the derivation of PCA. Given is the data set [Xij] with ði ¼ 1; 2; . . . ; mÞ and ðj ¼ 1; 2; . . . ; kÞ, where m is the total number of observations (i.e. FRFs data here) and k the dimension (variables) of the observations (i.e. spectral lines). First, the mean x j and the standard deviation sj of the jth column is obtained from m 1 X x j ¼ xij ð3Þ m i¼1 and

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pm  j Þ2 i¼1 ðxij  x sj ¼ m

ð4Þ

Then, the data set [X] is transformed into the standard normal space yielding the variation ~ A normalized element x~ ij is given by matrix ½X. x~ ij ¼

xij  x j sj

ð5Þ

~ T ½X ~ ½X m1

ð6Þ

The covariance matrix [C] is expressed as ½C ¼ Finally, the PCs are obtained from ½CfPi g ¼ li fPi g

ð7Þ

which is the eigenvalue decomposition of the covariance matrix [C], with li being the ith eigenvalue and fPi g the corresponding eigenvector. The first PC, which is the largest eigenvalue and its associated eigenvector, represents the direction and amount of the maximum variability in the original data set. The second PC, which is orthogonal to the first PC, represents the second most significant contribution from the data set, and so on. The most significant PCs represent the features that are most dominant in the data set. By discarding components that Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

contribute least to the overall variance, the dimension of the original data set can significantly be reduced [11].

3. METHODOLOGY This paper presents a vibration-based method that locates and quantifies damage in numerical and experimental beam structures from residual FRFs. ANNs are utilized to map pattern changes from residual FRF data to damage characteristics. To obtain suitable input data for network training, the residual FRFs are compressed to a few PCs adopting PCA techniques. To simulate field-testing conditions, white Gaussian noise is added to the numerical data and issues with limited number of sensor arrays are incorporated. A hierarchy of neural network ensembles is utilized to respect the different characteristics obtained by individual measurements from various sensor locations. The method is tested on two types of damage indicators; direct residual FRFs, and compressed and normalized residual FRF data. Firstly, time history data are obtained from the numerical and the experimental beams by finite element (FE) analysis or experimental testing, respectively. That is, impact hammer testing is conducted for the laboratory beams, and FE transient analysis with subsequent noise contamination is performed for the numerical structures. Secondly, FRFs are calculated from the time history data and residual FRFs are obtained by computing FRF differences between the undamaged and the damaged beams. Thirdly, by adopting PCA techniques, the residual FRFs are compressed and the most important PCs identified. Fourthly, sets of individual sensor neural networks are trained and tested with PCA-compressed residual FRFs separated by measurement location. Finally, a neural network ensemble fuses the outcomes of the individual networks and an overall damage prediction is obtained. A flow-chart of the damage identification procedure of the numerical beams is presented in Figure 2. To investigate the robustness of the developed method to noise, a noise sensitivity study examining four different noise pollution levels is conducted for the numerical data.

4. DAMAGE IDENTIFICATION PROCEDURE 4.1. System modelling and identification 4.1.1. Numerical model. A numerical model of a steel beam is created using the general-purpose FE analysis software ANSYS [26]. The beam structure is 2400 mm long and has a cross-section of 12 mm by 32 mm. The support conditions are set as pin–pin and the modulus of elasticity is set to 200 000 N/mm2. The element type used is SOLID45, which is a three-dimensional structural solid defined by eight nodes having translations in the nodal x, y and z directions. The cross-section of the beam is modelled with 4 elements across the height and 4 elements along the width. In longitudinal direction, the model is divided into 200 elements. This division was established after sensitivity studies undertaken by Choi et al. [27]. A schematic model of the numerical beam is shown in Figure 3. Sixteen damage cases are considered. Damage is introduced at four different locations with four alternative severities. The damage locations are situated at 4/8th, 5/8th, 6/8th and 7/8th of the span length and are denoted as ‘4’, ‘5’, ‘6’ and ‘7’ in Figure 3. The introduced damage is a notch-type damage, with 1 mm in length and 1, 4, 8 and 12 mm, respectively, in height. The four Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

Figure 2. Flow chart of damage identification procedure of the numerical steel beam.

Figure 3. Finite element (FE) modelling of a pin–pin supported steel beam.

damage severities are termed as extra light (‘XL’), light (‘L’), medium (‘M’) and severe (‘S’). Damage is modelled by rectangular openings from the soffit of the beam along the span length. The mesh density is refined in the vicinity of the defects and the corresponding Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

Figure 4. Finite element (FM) modelling of damage with a width of 1 mm and varying heights of (a) 1 mm, (b) 4 mm, (c) 8 mm and (d) 12 mm.

damage elements are eliminated. The FE modelling of the four different damage severities is displayed in Figure 4. Transient analysis is performed with ANSYS to obtain the response time history data of the beam models under impulse loading. An impact force of 800 N is applied at a reference point (here at location ‘5’) and the response time histories of the beam are obtained at seven equally spaced points, which correspond to sensor locations in experimental testing. To further simulate real testing conditions, white Gaussian noise of four intensities (1, 2, 5 and 10% noise-to-signalratio) is added to both, the input impact force signal and the response time histories, obtained from FE analysis. For each level of noise, three sets of noise-contaminated data are generated to simulate three repeated tests. The noise-contaminated time history data are then transformed into the frequency spectra using Fast Fourier Transform (FFT). The FRFs are estimated by dividing cross-spectra between the input and output with auto-spectra of input. In order to get the first seven vibrational modes, a frequency range of 0–1000 Hz is captured. Each FRF comprises of 1638 spectral lines with a frequency resolution of 0.61 Hz per data point. To determine pattern changes caused by damage, residual FRFs, which are the FRF differences between the intact and the damaged beams, are calculated. For each noise level a total of 144 residual FRFs are generated by comparing each noise-polluted undamaged case with each of the noise-polluted damaged cases (4 damage locations  4 damage severities  3 noise-polluted undamaged data sets  3 noise-polluted damaged data sets). 4.1.2. Experimental model. To validate the proposed damage identification method, experimental tests were performed. Four pin–pin supported steel beam specimens were tested in the Structures Laboratory of the University of Technology Sydney (UTS). The dimensions of the beams were 12 mm by 32 mm by 2400 mm, which comply with the measurements of the numerical models. A picture of the experimental set-up is shown in Figure 5. Each of the steel beams was inflicted with a single damage of the four severities (‘XL’, ‘L’, ‘M’ and ‘S’) at one of the four locations ‘4’, ‘5’, ‘6’ or ‘7’. The damage was introduced by 1 mm wide saw cuts of the heights, 1, 4, 8 and 12 mm. A picture of a medium size damage is depicted in Figure 6 for illustrative purposes. Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

Figure 5. Experimental test set-up.

Figure 6. Experimental medium size damage (8 mm cut).

To determine time response data of the beams, impulse hammer testing was performed. Thereby, the beams were excited by a modally tuned impact hammer. Seven piezoelectric accelerometers, which were mounted at locations ‘1’ to ‘7’ on the top surface of the beams, were used to measure the beam response. The signals of the hammer and the accelerometers were first amplified by signal conditioners and then recorded by a data acquisition system. To minimize spectral leakage, force and exponential windows were applied to the excitation and response time signals, respectively. The sampling rate was set to 10 000 Hz for a frequency range of 5000 Hz and 8192 data points, thus giving a frequency resolution of 0.61 Hz per data point. The average of three recordings was used to obtain one set of data. The main data acquisition system consisted of a Hewlett Packard state-of-the-art VXI system equipped with LMS CADA-X. The acquired time history data were then transformed into the frequency domain and the FRFs were computed. The set up of the experimental modal testing and the identification of the FRFs are shown in Figure 7. Residual FRFs were calculated from the FRF data obtained from tests of beam specimens before and after damage. For each damage case, five sets of signals were acquired. Thereby, a total of 400 FRFs were generated (4 damage locations  4 damage severities  5 undamaged data sets  5 damaged data sets).

4.2. Feature pre-processing In order to obtain suitable input pattern for neural network training, different FRF-based damage indicators are investigated. The objective here was to determine an indicator that is highly sensitive to damage. An ideal damage indicator should contain compressed information on the damage features and should be easily acquired without major human processing efforts. The selected damage fingerprint is then transferred into the PC space to further reduce its size and to filter uncertainties such as noise interferences. To determine the optimal number of PCs, the sensitivity of the PCs to damage and noise is investigated. Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

Figure 7. Schematic diagram of experimental modal testing and FRF determination.

4.2.1. Damage indicator selection. To determine a suitable FRF-based damage indicator, first, FRF data from various damage cases are investigated with respect to their susceptibility to damage. In Figure 8(a) the effects of medium damage at location ‘5’ on the FRF of the numerical beam, polluted with 1% white Gaussian noise, is depicted. It is observed that damage causes a change of the FRF amplitude and a shift of the frequency peaks. To enhance these changes, the residual FRFs are determined. This second damage quantity is displayed for the same damage case in Figure 8(b). The residual FRF values closest to the frequency peaks are most affected by the damage, or in other words, the frequency ranges in-between the resonant frequencies are much less or even not affected by the defects. Also, at some frequencies the FRF change appears to be more sensitive to damage than others. This is particularly visible for the fourth resonant frequency of 205 Hz, which shows the biggest amplitude change. Therefore, to further condense the damage fingerprint, a third damage quantity termed as the compressed normalized residual FRF (CNR-FRF) is established. Here, only the residual FRF values around the frequency peaks are considered. That is a frequency bandwidth of 10 Hz for the first two natural frequencies and a band of 25 Hz for the third to the seventh frequency. In addition, the residual FRFs of each selected frequency range are normalized by their maximum value. Figure 8(c) displays CNR-FRFs of various severities (extra-light, light, medium and severe damage at location ‘5’) and Figure 8(d) illustrates CNR-FRFs of damages at different locations (location ‘4’, location ‘5’, location ‘6’ and location ‘7’ of a medium type damage). In the graphs, changes of the CNR-FRFs to the different damage scenarios are clearly visible and distinguishable. The different damage severities of Figure 8(c) show an explicit amplitude change (the larger the damage extend the bigger the amplitude change). Also, the various damage locations of Figure 8(d) show specific alterations. Here, however, the changes follow a more complicated relationship. For example, for the fifth frequency a medium size damage at location ‘7’ causes the largest amplitude change followed by a damage at location ‘4’, then location ‘6’ and the smallest shift is seen for damage at location ‘5’. For the frequency band around the seventh mode, however, medium damage of location ‘4’ experiences the greatest change in amplitude, then damages at location ‘5’, then location ‘6’ and then location ‘7’ follows. A very complex pattern of residual FRF changes of varying amplitudes, shifting peaks and altering shapes in regards to different damage locations and damage severities is observed. These unique patterns are the basis of the presented damage identification method. For further investigation, only the damage fingerprints of the residual FRFs and the CNR-FRFs are considered. 4.2.2. PC selection. To produce the damage indices that are suitable for neural network training, the size of the selected damage quantities, residual FRFs and CNR-FRFs, must be greatly reduced. A full-size residual FRF, which covers a frequency range of 0–700 Hz (capturing the first seven flexural modes), contains 1146 spectral lines. This corresponds to 1146 Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

Figure 8. Effects of different damage cases on (a) directly measured FRFs, (b) residual FRFs and (c) and (d) CNR-FRFs.

input nodes in the neural network. Even the already compressed CNR-FRFs still comprise 481 spectral lines. Such large numbers of input points cause severe problems in training convergence in addition to computational inefficiency. Therefore, PCA is desirable in such applications to reduce the size and to filter noise. To compress the FRF data, two matrices are formed, i.e. one for residual FRFs and one for CNR-FRFs and are subsequently projected onto its PCs utilizing the ‘princomp’ function in MATLAB. The rows of the matrices comprise of the samples of the damage quantities. These are either the 400 samples of the laboratory beams or the 576 of the numerical beam data, which contain the 144 samples with noise intensities of 1, 2, 5 and 10%. The columns of the matrices are the 1146 or 481 spectral lines of the residual FRFs or the Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

CNR-FRFs, respectively. After projection, each sample is represented by 1146 or 481 PCs, respectively. A plot of the individual and the cumulative contribution of the first 50 PCs of the residual FRFs of the numerical beam data is shown in Figure 9. It is found that the first 50 PCs account for 99.13% contribution of the original data. The individual contribution percentage of each of the first five PCs is 54.0, 27.0, 7.8, 3.7 and 1.7%. To determine the optimal number of PCs that contain sufficient data for the damage identification and are independent of noise, a study on the sensitivity of the PCs to damage and noise is undertaken. In Figure 10, the first 10 PCs of the residual FRFs of different damage scenarios of numerical data polluted with 1% noise are presented. Figure 10(a) displays damage at location ‘5’ of severities ‘XL’, ’L’, ‘M’ and ‘S’ and Figure 10(b) shows medium size damage at locations ‘4’, ‘5’, ‘6’ and ‘7’. For each damage scenario, three different data sets, each polluted with different numbers of 1% white Gaussian noise, are displayed. From the figures, it can be seen that the first four PCs show clear distinguishable patterns for the various damage cases. The PC values from the fifth component onwards are very small, indicating their insignificant

Figure 9. Individual and cumulative contribution of the first 50 PCs of the residual FRFs of the numerical beam data.

Figure 10. The first 10 PCs of residual FRFs of numerical beam data polluted with 1% white Gaussian noise of different damage cases. Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

contribution for the damage cases investigated. Further, the three data sets of each damage scenario group together, and thus they are represented by the same PCs. To investigate the influence of noise, the PCs of one damage scenario (medium damage at location ‘5’) is plotted for the noise levels of 1, 2, 5 and 10% in Figure 11. In each graph, 15 different data sets are shown. They are contaminated with the same intensity of noise but being randomly generated individually. From the four graphs, it is observed that up to a noise level of 5% the first 10 PCs of different data sets bunch together. For a noise intensity of 10%, however, the PC values of rank five or higher are significantly different. This suggests that the component values from the fifth PC onward are more affected by noise presence. Thus, it seems reasonable to choose the first four PCs as inputs for the neural networks. For the PCs derived from CNR-FRFs of numerical beams, similar patterns are observed. However, instead of the first five components, the first seven components showed the signs of clearly distinguishable noise-independent patterns and are therefore chosen as inputs for ANN. Similar patterns are found with the laboratory beam data when investigating the projected FRF-based damage indicators. The effect of noise, however, is less obvious for the experimental data. For the laboratory beam data, the first ten PCs of the residual FRFs and the CNR-FRFs, respectively, are used as final inputs for the neural networks.

Figure 11. First 10 PCs obtained from residual FRFs of numerical data contaminated with (a) 1%, (b) 2%, (c) 5% and (d) 10% noise of medium size damage at location ‘5’. Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

4.3. ANN model To identify the damage locations and severities, ensembles of supervised feed-forward multilayer neural networks are designed. The derived and selected PCs of the residual FRFs and CNR-FRFs are utilized as input patterns to the networks to estimate the locations and severities of damage. First, seven individual networks are created, each trained with FRF-based data from one of the measurements of the locations ‘1’ to ‘7’. Then, the outcomes of the individual neural networks are fused by a neural network ensemble and an overall damage prediction is obtained. As a comparison to demonstrate advantage of the network ensemble, another individual neural network is created and is trained with data from summarized FRFs that are obtained by adding up the FRFs from all individual FRF measurements. The outcomes of this network will then be compared against the outcomes of the neural network ensemble. All individual neural networks consist of an input layer of 4, 7 and 10 nodes, respectively, representing the number of the selected PCs; five hidden layers of 10, 8, 6, 4 and 2 nodes and one single node output layer estimating the location or the severity of the damage. The network ensemble is designed with seven input nodes, which are the outputs of the seven individual networks; five hidden layers also consisting of 10, 8, 6, 4 and 2 nodes and one output node predicting the damage location or severity. The transfer functions used are hyperbolic tangent sigmoid functions. Training is performed utilizing 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 is trained with the training samples, its performance is supervised utilizing 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 generalization ability of the network is lost and overfitting occurs. For the numerical beam data, the 144 samples of PCs for each noise intensity level are divided into three sets, i.e. 82 for training and 31 each for validation and testing. The training, validation and testing sets of all noise levels are then grouped together and fed to the network. The data of the laboratory beam are divided into sets of 240 for training and 80 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.

5. RESULTS AND DISCUSSION 5.1. Numerical beam outcomes 5.1.1. Neural network outcomes of numerical beam data. First, individual neural networks are trained with PCs of residual FRFs and CNR-FRFs, respectively, to identify locations and severities of damage. It is observed that the outcomes of both network types, trained with either PCA-compressed residual FRFs or PCA-compressed CNR-FRFs, are very similar to each other. Even though the actual CNR-FRFs show clearer damage patterns and contain less excessive data than the residual FRFs, the network prediction accuracy is about the same. The decisive features of the different damage characterizations are projected for both damage quantities onto the first most significant PCs, which are then used as network inputs to identify the damage. Consequently, this leads to similar outcome precisions for both network types. These findings highlight the potential of the combined use of PCA and neural network techniques in damage detection. A condensation and normalization of the residual FRFs has Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

therefore no benefit in the presented damage identification algorithm and in the following, only outcomes of networks trained with PCs of residual FRFs are presented. Summaries of the quantification and localization results of the individual networks are shown in Table I and II. In the tables, the damage cases are sorted by their severities (SXL, SL, SM and SS) and their noise pollution levels (1, 2, 5 and 10%). From Table I it can be seen that the severities of all damage cases sampled with noise levels of 1, 2 and 5% are accurately identified by all individual sensor networks. For data of 10% noise intensity, only damages of severe and medium extent are quantified correctly. Here, some extra-light and light damage cases are wrongly estimated by a number of individual sensor networks (details are discussed below). Table II summarizes the localization outcomes of the networks. Extra-light damage cases of all noise pollution levels are falsely located by almost all individual sensor networks. The locations of light defects contaminated with noise of 1 and 2% intensity are correctly identified by all networks. Light damage cases of noise pollution levels of 5 and 10% cause false damage localizations for some individual sensor networks. All damage cases of medium and severe severity are allocated accurately by all networks. To evaluate the outcomes of the individual networks more closely; the results of all seven individual sensor networks and the sensor summation network trained with PCA-compressed residual FRFs to quantify damage are displayed in Figure 12(a–h). The depicted graphs show only damage cases with 10% noise pollution. In these and subsequent figures, the horizontal axis displays the damage cases that are sorted by their locations (L4, L5, L6 and L7) and their severities (SXL, SL, SM and SS). The vertical axis represents the normalized error of either the localization or the quantification outcomes. The

Table I. Summary of individual network outcomes for damage quantification. Noise intensity

Damage severity

SXL SL SM SS

1%

2%

5%

10%

o o o o

o o o o

o o o o

x x o o

(o) All damage cases are correctly identified by all individual sensor networks. (x) At least one individual sensor network wrongly identifies some damage cases.

Table II. Summary of individual network outcomes for damage localisation. Noise intensity

Damage severity

SXL SL SM SS

1%

2%

5%

10%

x o o o

x o o o

x x o o

x x o o

(o) All damage cases are correctly identified by all individual sensor networks. (x) At least one individual sensor network wrongly identifies some damage cases. Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

Figure 12. Damage severity outcomes of 10% noise polluted data of individual neural networks trained with data from measurements at (a) location ‘1’, (b) location ‘2’, (c) location ‘3’, (d) location ‘4’, (e) location ‘5’, (f) location ‘6’, (g) location ‘7’ and (h) summarized FRFs of all measurement locations.

normalized error is defined as Enorm ðdÞ ¼

ðTd  Od Þ Lmax

ð8Þ

Enorm ðdÞ ¼

ðTd  Od Þ Smax

ð9Þ

and

Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

respectively, where d and subscript d indicates the damage scenarios, Td the target value of d, Od the network output value of d, Lmax the total length of the beam (here 2.4 m) and Smax the maximum severity of a damage (here 100% loss of the second moment of area, I). A marked band around the 0% error axis symbolises the area in which the network estimations must fall in order to correctly categorise the damage. For the localization of damage, the band ranges from 6.25 to 16.25% normalized error, representing the mid points in-between two damage locations. The band of the damage quantifications ranges from 12 to 112% normalized error. In the figures all damage cases of the training, the validation and the testing sets are displayed. From Figure 12(a–h) it is observed that, as expected, the outcome accuracy among the individual networks differ a lot in regards to the different severities and locations of the damage cases. It can be seen that the network trained with data from measurements at location ‘5’ correctly identifies all damage cases. For the networks of measurement locations ‘1’, ‘2’, ‘3’ and ‘7’ only extra-light damage cases are misidentified. The estimations from networks trained with PCs from locations ‘4’ and ‘6’, however, give false predictions of some extra-light and light damage cases. The network trained with summation FRFs predicts light, medium and severe damage cases accurately but fails in the extra light case. In fact, it is shown that a simple summation of the different FRFs does not necessarily result in better damage identification as the individual networks of measurement locations ‘1’, ‘5’ and ‘7’ give better outcomes than the network trained with summation FRF data. From the results above, it can be observed that it is problematic for damage identification when relying only on the outcomes of the individual networks as their outcomes differ significantly to each other based on different damage scenarios. In addition, training a network with the summation of FRFs improves but does not give the best results. To achieve reliable damage identification, a conclusive, intelligent fusion of the individual network outcomes is necessary. This can be achieved by a neural network ensemble, which combines the outcomes of the individual networks. The outcomes of these neural network ensembles are shown in Figure 13 and Figure 14, which display the damage severity and the damage location predictions, respectively. Figure 13 shows that the neural network ensemble is capable of precisely identifying the severities of all damage cases for all levels of noise pollution. Figure 14 displays accurate damage localization outcomes by the network ensemble for all damage cases at all noise pollution levels except extra light case. As expected, the accuracy of damage localization decreases as the noise level increases. These final damage identification outcomes clearly show the efficiency of the network ensemble. The outcomes of the ensembles give results that are more accurate than any of the outcomes of the individual neural networks. 5.1.2. Noise sensitivity study. In order to investigate the effects of noise, a noise sensitivity study is conducted. For each of the four noise intensity levels (1, 2, 5 and 10%,), five different sets of noise-contaminated data are generated, each polluted with randomly generated noise at the same noise-to-signal ratio. Thereby, a total of 720 data samples (144 for each set) are produced. The residual FRFs are again determined and compressed using PCA. The most significant PCs are used as input patterns for the multiple-noise-set neural networks. One of the five data sets is used for network training (set1), one for validation (set2), and the remaining three for network testing (set3, set4 and set5). The design of the multiple-noise-set networks complies with the features of the single-noise-set networks. That is for the individual networks, four input nodes, which are the four selected PCs, five hidden layers and one single node output layer. The Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

Figure 13. Neural network ensemble outcomes of data polluted with (a) 1%, (b) 2%, (c) 5% and (d) 10% noise to quantify damage.

Figure 14. Neural network ensemble outcomes of data polluted with (a) 1%, (b) 2%, (c) 5% and (d) 10% noise to locate damage.

network ensemble is also designed with seven input nodes, representing the outputs of the seven individual networks, five hidden layers and one output node. To evaluate the findings, the absolute means and standard deviations of averages of normalized outcome errors from all 144 Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

Figure 15. Absolute mean (a) and (b), and standard deviation (c) and (d), of normalized error of network outcomes trained, validated and tested with data from location ‘1’ of all noise intensity levels to quantify damage. (a) and (c) depict the results of each individual set (set1: training, set2: validation, and set3, set4 and set5: testing), (b) and (d) show the average values of all five sets.

damage cases of each data set are determined and compared against each other. Figures 15 and 16 show the graphs of absolute mean and standard deviation values of the damage severity and the damage location outcomes, respectively. The graphs (a) and (b) of the figures depict the absolute mean values and the graphs of (c) and (d) display the standard deviations of the normalized outcome errors. Graphs (a) and (c) show the outcomes of each individual data set whereas graphs (b) and (d) display averaged values of the five sets of each noise pollution level. These neural network outcomes confirm the results of the single-noise-set networks. For damage quantification, damage cases of extra-light and light severity cannot all be identified correctly if the noise level is 10% or larger. This is clearly shown in Figure 15 where extra-light and light damages are wrongly identified by all three testing sets of 10% noise polluted data. The damage localization results show that damage cases of extra-light severity are false for data of all noise intensity levels. From Figure 16, it is seen that besides the testing sets also the training and validation sets give wrong location estimations for all noise pollution levels. This indicates that the effects of extra-light damage do not have a clear pattern in the PCs with respect to their locations. However, a trend of the accuracy of the damage location outcomes in regards to the level of noise is observed—the smaller the noise intensity the more precisely the Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

Figure 16. Absolute mean (a) and (b), and standard deviation (c) and (d), of normalized error of network outcomes trained, validated and tested with data from location ‘5’ of all noise intensity levels to locate damage. (a) and (c) depict the results of each individual set (set1: training, set2: validation, and set3, set4 and set5: testing), (b) and (d) show the average values of all five sets.

damage identification outcomes. The results of this study show that the developed damage identification scheme is robust with respect to noise. In other words, the influence of noise to the damage prediction outcomes is steady and predictable in regards to the intensity of noise contamination. 5.2. Experimental beam outcomes To validate the developed damage identification method, it is applied to the laboratory beam data. Residual FRFs are determined from the measured experimental FRFs and transferred to the PC space. The first 10 PCs are used as inputs to individual neural networks and estimations of the damage locations and severities are obtained. The outcomes of the individual sensor networks are again fed to neural network ensembles and an overall prediction of the damage of the experimental beam is produced. The results of the individual networks that are trained to estimate the damage severities are displayed in Figure 17. From the graphs it is observed that there are a few extra-light damage cases that are falsely identified by the networks of location ‘2’, ‘4’ and ‘6’. The measurement locations of the erroneous networks (location ‘2’, ‘4’ and ‘6’) are related to node points of the mode shapes of two of the seven relevant resonant frequencies; Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

Figure 17. Damage severity outcomes of individual neural networks trained with data from experimental testing from measurements at (a) location ‘1’, (b) location ‘2’, (c) location ‘3’, (d) location ‘4’, (e) location ‘5’, (f) location ‘6’, (g) location ‘7’ and (h) summarized FRFs of all measurement locations.

more precisely, mode 2 has a node point at location ‘4’ and mode 4 has node points at locations ‘2’, ‘4’ and ‘6’. This means that the FRF measurements at these locations do not show any resonant peaks for these modes, i.e. they are insensitive to damage. It is also noticed that the network trained with FRF summation can correctly identify damage severities. It is suspected that the inaccurate damage estimations of the individual sensor networks are due to the Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

J. LI ET AL.

Figure 18. Neural network ensemble outcomes trained with experimental data to (a) quantify and (b) locate damage.

measurement errors or noise interferences during the data acquisition. The outcomes of the individual sensor networks that are trained to estimate the damage locations are precise for all but one damage case. Here, it is also suspected that an error during the experimental testing is responsible for the false damage identification. The outcomes of the neural network ensembles, which give a final prediction of damage severities and locations, are displayed in Figure 18. It is seen that eventually both the damage location and severity of all experimental damage cases are accurately estimated by the network ensembles.

6. CONCLUSIONS This paper presents a thorough investigation of a vibration-based damage identification method, which utilizes dimensionally reduced residual FRF data in combination with neural networks, to identify locations and severities of damage in numerical and experimental beam structures. PCA techniques are adopted to extract damage features and to compress the large size of measured FRF data and only the most significant PCs are used as input pattern to neural networks. White Gaussian noise of up to 10% noise-to-signal-ratio is added to numerical data to simulate field-testing conditions, and a noise sensitivity study is conducted to investigate the noise robustness of the developed method. The damage prediction outcomes of the network ensembles show that the presented method is robust, reliable and precise in identifying defects in numerical and experimental beam structures. The results also show the effectiveness of the neural network ensemble approach, which gives outcomes that are more accurate than any of the outcomes of the individual neural networks. The proposed method has the capability to cope with incomplete FRF data obtained from a limited number of sensors. Compared with modal based approaches, the proposed method requires much less post-processing on the recorded data; especially there is no need for manual processing, which makes the developed method more suitable for on-line health monitoring. Due to the dependency of the presented method on the availability of excitation input measurements, its applicability is limited to structures of relatively small mass size such as shortor medium-span bridges. To extent the range of applications and to encompass the structural health monitoring, studies on an output-only FRF/ANN method will be undertaken in near future. Copyright r 2009 John Wiley & Sons, Ltd.

Struct. Control Health Monit. (2009) DOI: 10.1002/stc

DAMAGE IDENTIFICATION IN CIVIL ENGINEERING STRUCTURES

Effects of environmental changes such as temperature and humidity fluctuations have not been investigated in this paper but the filtering capabilities of PCA and ANN to environmental uncertainties will be investigated in the next phase of the research. Further, the next phase of the research will involve the application of the presented FRF/ ANN method to a more complicated structure (e.g. a two-storey framed structure) as well as implementation of the method in field applications.

ACKNOWLEDGEMENTS

The authors wish to thank the Centre for Built Infrastructure Research (CBIR), Faculty of Engineering and Information Technology, University of Technology Sydney (UTS) for supporting this project. Within the Faculty of Engineering, the authors wish to express their gratitude to the staff of UTS Structures Laboratory for their assistance in conducting the experimental works. Alyuda Research Inc. is gratefully acknowledged for providing a free copy of their Alyuda NeuroIntelligence software.

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Struct. Control Health Monit. (2009) DOI: 10.1002/stc