Determination of probability density from statistical moments by neural network approach

It is known that response probability densities, although important in failure analysis, are seldom achievable for stochastically excited systems except for linear systems under additive excitations of Gaussian processes. Most often, statistical moments are obtainable analytically or experimentally. It is proposed in this thesis to determine the probability density from the known statistical moments using artificial neural networks. A multi-layered feed-forward type of neural networks with error back-propagation training algorithm is proposed for the purpose and the parametric method is adopted for identifying the probability density function. Three examples are given to illustrate the applicability of the approach. All three examples show that the neural network approach gives quite accurate results in comparison with either the exact or simulation ones.