Artificial neural network methods

The brain is capable of high performance in natural information processing tasks, such as perception, language understanding, motor control, etc., given the suitability of the neuronal system, consisting of billions of neurons that are interconnected with a fan-in and fan-out, to elaborate simultaneously a large number of pieces of information and constraints (Rumelhart et al., 1986). The Artificial Neural Networks (ANNs) algorithm has been inspired exactly by the neuronal architecture and the operation of brain (Anderson & Davis, 1995; Adeli & Park, 1998; Haykin, 1999).

The basic model of an individual neuron was developed in 1943, by Warren McCulloch and Walter Pitts and it is still considered the heart of most neural networks (McCulloch & Pitts, 1943). Later, Rosenblatt (1962) extended their model providing to networks the capability of self-organization and learning. His models, characterized by only two-layered networks so unsuitable of learning certain types of functions, paved the way to modern multilayer networks, such as the Back Propagation Neural Networks (BP NNs).

ANNs are a modern and powerful artificial intelligence technique which operates as blackbox, model-free and adaptive tool to capture and learn significant structures in data. They are suitable particularly for problems too complex to be modeled and solved by classical mathematics and traditional procedures. Their computing abilities have been proven in many fields, such as prediction, estimation, pattern recognition and optimization (Zhang et al., 1998; Bishop, 1995; Cochocki & Unbehauen, 1993; Adeli, 2001). The development of the error Back Propagation (BP) training algorithm (Rumelhart et al., 1986; Hecht-Nielsen, 1989), which is based on a gradient-descent optimization technique, launches the use of the neural networks. The BP NN is usually constructed by three layers, an input layer, a hidden layer and an output layer and due to its strong non-linear mapping ability and simplicity it is the most commonly used NNs algorithm (Werbos, 1990; Hegazy et al., 1994; Paola & Schowengerdt, 1995).

The basic strategy for developing a NN-based approach to damage identification of a structural system is to train a BP NN algorithm to recognize the structural damage conditions from the measured response of the structure (Wu et al. 1992). The first step is to provide a data set to train an appropriate NN. Ideally, this data set should contain the response of the undamaged structure as well as the responses of the structure in various damaged states. This data can be generated through measurements of structural response, model test results, numerical simulations or a combination of them. Therefore, once a network architecture is defined and a training algorithm is selected, the NN is trained with the training data set. The trained network is then tested to verify its performance and its generalization capability. In this step, different data with respect to those used to train the network have to be used for testing. Note that how well a trained network is able to work is strongly dependent on the adequacy of the selected network architecture and the richness of the training data set. Often, changes in the network architecture and/or additions to training data set are needed. Such changes are followed by the repetition of the whole training and testing process. This quasi iterative fine tuning is repeated until satisfactory performance of the NN is obtained. Finally, the experimentally measured real structural damage data are inserted into the trained NN and the output of the NN will be able to provide the effective location and severity of the structural damage.

Numerous research papers on structural damage detection using NN techniques are available in the literature; in the following the most important works are reviewed. Pandey and Barai (1995) apply the multilayer perceptron in the damage detection of truss steel bridge structures. The training patterns are generated for multiple damaged zones in the structure and the performance of the NNs with one and two hidden layers are examined. The network architecture with two hidden layers appears to be better than that with a single layer. Furthermore, the authors underline the fact that measured input at only a few locations in the structure is needed in the identification process using ANNs. In the work of Yun and Bahng (2000) a BP NN-based substructural identification for estimating the stiffness parameters of a complex structural system, in the case of noisy and incomplete measurement of the modal data, is presented. The substructural technique and the concept of the submatrix scaling factor are employed to reduce the relevant number of unknown stiffness parameters to be estimated. The natural frequencies and mode shapes are used as input patterns to the NN, and the Latin hypercube sampling and the component mode synthesis methods are used to efficiently generate such training data. Two numerical examples on truss and frame structures demonstrate the satisfactory performance of the method. Chen et al. (2003) study by a NN-based approach the problem of damage identification in engineering structures when excitation signals are unavailable or inaccessible. BP NNs are trained by output only response data and

transmissibility functions, which demonstrate to be effective features in training NN for structural damage identification.

Some authors realize online damage detection and health monitoring combining wavelet-based damage feature extraction and ANN-based identification. Yam et al. (2003) apply a combined technique to identify effectively crack damage in PVC sandwich plates, both through numerical and experimental analysis. Piezoelectric smart structure technology is used for the generation of excitation and structural response measurement. In the work of Paya et al. (1997), single and multiple faults in rotating machinery are successfully detected and classified using multilayer ANNs on the sets of preprocessed data by wavelet transforms.