An artificial neural network approach to structural damage detection using frequency response functions

Structural damage detection in a twenty-bay planar truss was accomplished using an artificial neural network. Instead of using natural frequencies and mode shapes, the frequency response functions (FRF's) experimentally obtained from accelerometers at two locations on the truss were directly used to distinguish among damage cases and to train the network. Unlike conventional approaches based on system identification techniques, the neural network approach does not require an analytical model of the structure. The direct use of the FRF's eliminates the need for modal parameter identification. Out of the 60 damage cases considered in this study, the neural network was able to identify uniquely 21 damage cases and narrowed 38 others down to two possible damaged struts. Introduction To maintain the performance and safe operation of aerospace vehicles, structural integrity must be monitored periodically. Numerous studies (e.g., Smith and Hendricks, 1988; Lim, 1991; Zimmerman and Kaouk, 1992; Lim and Kashangaki, 1994) have been conducted to detect structural damage using measured mode data and system identification techniques. A survey on the subject is available [Kashangaki, 19911. Recently, attention was given to the application of the artificial neural network to structural damage detection (Tsou and Shen, 1993; Yen and Kwak, 1993). The natural frequencies and mode shapes were used to train the network and to conduct damage detection. Unlike the conventional approaches based on system identification techniques, the neural network approach does not require a refined model of the undamaged structure. The fact that damage detection can be performed using the measured mode data alone without an analytical model relieves the burden of conducting analytical model refinement to match measured mode data, which is typically costly and time consuming. This paper investigates an effective use of the artificial neural network to conduct structural damage detection. In a typical modal test, the modal parameters are identified using the frequency response functions (FRF's). Instead of using mode shapes and frequencies, the neural network can be trained directly using the "Graduate Student, Department of Aerospace Engineering, Member, AIAA. **Assistant Professor, Department of Aerospace Engineering, Member, AIAA. Copyright O 1994 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. W ' s . Some of the advantages using the FRF's directly include: (1) the modal parameter identification process is not required and thus the error and cost associated with it are eliminated, (2) nonlinear behavior exhibited in FRF's can be incorporated in the damage detection process, and (3) the number of transducers quired to perform damage detection can be significantly reduced as will be shown in the twentybay truss structure example. Test Apparatus and Procedure The focus of this study is damage detection in a twenty-bay two-dimensional truss as shown in Fig. 1. The 7.07 m long truss fixed at one end and free at the other lies flat on a table. The truss consists of hollow aluminum tubes and steel node balls. Underneath each batten, a steel bar is bolted to the node balls. Each steel bar rests on two steel ball bearings that allow the truss to move in the horizontal plane. For detailed information on the truss, refer to Rallauer and Larnberson (1989). At the end of the truss, a shaker is attached to provide force excitation. Accelerometers are located at the numbered positions as shown in Fig. 1. Since the minimum number of accelerometers needed was unknown, eleven accelerometers were installed to provide scfficient modal test data. The minimum number of accelerometers and their locations are determined by inspecting the FRFs and evaluating the damage detection performance of the trained neural network. Consequently, only the FRF's from accelerometers 5 and 11 are selected to train the neural network and to conduct damaged detection. Accelerometer 11 is chosen because the FRF's at this point displayed the greatest diversity. The other accelerometer is used to provide uniqueness to the few damage cases that exhibit similar FRF's at accelerometer 1 1. A different strut is removed for each of the 60 damage cases investigated to simulate complete damage in that strut. In each bay, only the diagonals and longerons are removed. It is difficult to remove the battens because of the steel bars connecting the node balls underneath each batten. Thus, they are eliminated from damage consideration in this study. The FRF's are then found using a Fourier analyzer. The Fourier analyzer controls the random force input to the shaker and records the FRF's over a range of 0 to 50 Hz, which were obtained using 20 averagings. The FRF's obtained for all damaged and undamaged cases contain at least four bending modes below 50 Hz. Figures 2 and 3 show the FRF's measured at accelerometers 5 and 11, respectively. The figures show the changes in FRF's due to damage in upper longerons, diagonals, and lower longerons. These changes were used to train the neural network and to detect damage. Each figure has 21 FRF's corresponding to the undamaged case and the damage cases in bay 1 through 20. Thus, the FRF corresponding to damage case number 10 for the upper longeron case in Fig. 2 indicates the FRF measured at accelerometer 5 with upper longeron removed in bay 9. Figure 4 shows in detail the FRF of a typical damage case plotted with the FRF of the undamaged case at accelerometer 1 1. The sample rate employed to measure the FRF's was 2.56 times the bandwidth (50 Hz) and 512 samples were taken for each test. Since only da& up to 50 Hz is desired, each FRF consists of 200 frames (201 data points). Of these 201 points, the first four are not included in the neural network training due to the large 'spike' in the data at these points in nearly every FRF of every damage case. The resulting FRF's then have a range of 1.25 to 50 Hz (197 data points). Finally, the FRF data is converted to a Matlab file to conduct neural network training. Artificial Neural Network The Matlab Neural Network Toolbox (Demuth and Beale, 1992) was used to construct and train the neural network. As shown in Fig. 5, the type of network used in this study was a three-layer neural network using log-sigmoid neurons. The backpropagation method @urnelhart et al., 1986) was used to train the network. A neural network is composed of one or more layers and each layer contains a series of processing units (neurons) that act in parallel within the layer. Input data arranged in a vector (or a matrix of vectors) is transferred through the layers. Each data value within an input vector is multiplied by the weight associated with each neuron in a layer and the results are summed at each neuron input creating a new vector with a size equal to the number of neurons in that layer. Then, the transfer function at each neuron converts its input, which is a sum of weighted input and bias, into a neuron layer output. For hidden layers, the neuron layer output vector is used as input to the next layer. For the output layer, the output vector represents the final output of the entire neural network. The transfer function used in this study is a logsigmoid neuron which converts any real number to a value between 0 and 1. In the target output for the network, a '1' signifies no damage in a strut while a '0' indicates complete damage (missing). Initially, the weights and biases for all of the neurons are randomly chosen. After one pass (epoch) through the network, the output vectors are compared to the target output vectors. The neural network computes the delta error vectors (derivatives of error) which are backpropagated through the network until delta vectors are found for each layer. The learning rate is then used to change the weights and biases in the direction of steepest decent with respect to the delta vectors. For example, the change in a weight, delW, and the change in a bias, delB, in a layer, are found as