ABSTRACT
Chapter 13 presents a multi-paradigm dynamic time-delay fuzzy wavelet neural network
(WNN) model for nonparametric identification of structures using the nonlinear
autoregressive moving average with exogenous inputs (NARMAX) approach. The model adroitly integrates four different computing concepts: dynamic neural networks,
wavelets, fuzzy logic, and chaos theory with the goal of improving the accuracy and adaptability of nonparametric system identification. The model balances the global and
local influences of the training data and effectively incorporates the imprecision existing
in the sensor data. The focus of this chapter is on application of the dynamic time-delay fuzzy WNN
model to three-dimensional high-rising building structures taking into account their
geometric nonlinearity. It should be noted that the training of a dynamic neural network is substantially more complicated and time-consuming than the training of conventional
neural networks because in the former both input and output are not single-valued but in
the form of time-series. An effective training algorithm is essential for identification
accuracy and real-time implementation of the dynamic fuzzy WNN model for health
monitoring or control of large-scale structures. In this chapter, a hybrid adaptive learning algorithm, called Levenberg-Marquardt-Least-Squares (LM-LS) algorithm, is presented for training and adjusting the parameters of the dynamic fuzzy WNN model. The LM algorithm, an approximate combination of the Gauss-Newton and steepest descent
algorithms, is employed to train the parameters of the nonlinear wavelet functions. The approximation avoids the second-order differentiation required in the Gauss-Newton
algorithm and overcomes the numerical instabilities encountered in the steepest descent algorithm. The LS algorithm is employed to determine the parameters of the linear part of the dynamic fuzzy WNN approximator. Next, a backtracking inexact linear search algorithm is developed to automatically update the iteration step length with the goal of
accelerating the learning convergence rate of the model and achieving high
computational efficiency.
