Sequential optimal experiment design for neural networks using multiple linearization

Abstract

Design of an optimal input signal in system identification using a multi-layer perceptron network is treated. Neural networks of the same structure differing only in parameter values are able to approximate various nonlinear mappings. To ensure high quality of network parameter estimates, it is crucial to find a suitable input signal. It is shown that utilizing the conditional probability density function of parameters for design of the input signal provides better results than currently used procedures based on parameter point estimates only. The conditional probability density function of parameters is unknown and hence it is estimated using the Gaussian sum approach approximating arbitrary probability density function by a sum of normal distributions. This approach is less computationally demanding than the Markov Chain Monte Carlo method and achieves better results in comparison with the commonly used local prediction error methods. The properties of the proposed input signal designs are illustrated in numerical examples.