Gaussian Sum Approach with Optimal Experiment Design for Neural Network

P. Hering and M. Šimandl (Czech Republic)


System identification, optimal experiment design, nonlin ear parameters estimation, probability density function, multi-layer perceptron network.


System identification is a discipline for construction of mathematical models of stochastic systems based on mea sured experimental data. Significant role in the system identification plays a selection of input signal which influ ences quality of obtained model. Design of optimal input signal for system modeled by multi-layer perceptron net work is treated. Because the true system is unknown, the design can be constructed only from the actually obtained model. However, neural networks with the same structure differing only in parameters values are able to approximate various nonlinear mappings therefore it is crucial maxi mally to use available informations to select suitable input data. Hence a global estimation method allowing to deter mine conditional probability density functions of network parameters will be used. The Gaussian sum approach based on approximation of arbitrary probability density function by a sum of normal distributions seems to be suitable to use. This approach is a less computationally demanding alterna tive to the sequential Monte Carlo methods and gives bet ter results than the commonly used prediction error meth ods. The properties of the proposed experimental design are demonstrated in a numerical example.

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