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Wavelet neural network (WNN) has been widely used in the field of civil engineering. However, WNN can only effectively handle problems of small dimensions as the computational cost for constructing wavelets of large dimensions is prohibitive. To expand the application of WNN to higher dimensions, this article develops a new wavelet support vector machine (SVM)-based neural network metamodel for reliability analysis. The method first develops an autocorrelation wavelet kernel SVM and then uses a set of wavelet SVMs with different resolution as the activation function of WNN. The output of network is obtained through aggregating outputs of different wavelet SVMs. The method takes advantage of the excellent capacities of SVM to handle high-dimensional problems and of the attractive properties of wavelet to represent complex functions. Four examples are given to demonstrate the application and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A new multiwavelet neural network-based response surface method is proposed for efficient structural reliability assessment. Although multiwavelet network can be used for approximating nonlinear functions, its application has been limited to small dimension problems due to computational cost. The new method expands the application of multiwavelet network to moderate dimension by introducing a series of intermediate nodes, and the number of these intermediate nodes is determined by the multiwavelet theory. Thus, a multidimensional function learning problem is transformed into a one-dimensional function learning problem. Four examples involving one stochastic finite element-based reliability problem illustrate the effectiveness of the proposed method, which indicate that the new method is more efficient up to 10 random variables than the classical multilayer perceptron-based response surface method. [ABSTRACT FROM AUTHOR]

Artificial neural networks (ANNs) method is widely used in reliability analysis. However, the performance of ANNs cannot be guaranteed due to the fitting problems because there is no efficient constructive method for choosing the structure and the learning parameters of the network. To mitigate these difficulties, this article presents a new adaptive wavelet frame neural network method for reliability analysis of structures. The new method uses the single-scaling multidimensional wavelet frame as the activation function in the network to deal with the multidimensional problems in reliability analysis. Because the wavelet frame is highly redundant, the time-frequency localization and matching pursuit algorithm are respectively utilized to eliminate the superfluous wavelets, thus the obtained wavelet frame neural network can be implemented efficiently. Five examples are given to demonstrate the application and effectiveness of the proposed method. Comparisons of the new method and the classical radial basis function network method are made. [ABSTRACT FROM AUTHOR]

The surrogate model method is widely used in structural reliability analysis to approximate complex limit state functions. Accurate results can only be obtained when the surrogate model for the limit state function is approximated sufficiently close to the failure region. This study develops a novel local approximation method for efficient structural reliability assessment. The adaptive Markov chain simulation is utilized to generate samples in the failure region (the 'region of most interest'). The support vector regression technique is then used to obtain an explicit approximation of the original complex limit state function around the region of most interest. Four examples are given to demonstrate the application and efficiencies of the proposed method. [ABSTRACT FROM AUTHOR]