L. S. Kuravsky, S. N. Baranov, G. A. Yuryev
Under consideration are technologies for synthesis and identification of hidden Markov models which are based on a novel technique and applied for fatigue damage diagnostics. The approach can be used for both continuous- and discrete-time systems. An initial rough model results from statistical multivariate analysis of observed data or their analysis by means of Kohonen self-organizing feature maps. Then it suffers proper corrections. Histograms of observed frequencies of being in different system states after the given exploitation periods are employed to train the constructed models. Free model parameters are identified by the method of chi-square minimum. The synthesis may be carried out in case of some uncertainties: absence of complete information on system states and their connections is assumed. Undefined observed cases are partially identified by the method of classification propagation with the aid of either self-organizing feature maps or cluster analysis. Connections between different system states are determined according to contiguity of their clusters or areas of winning units on the topological maps and statistical goodness-of-fit tests. In case of models represented by discrete-time structures (Markov chains) conversion to continuous-time trained structures (Markov networks) is performed to obtain more reliable results with the following return to discrete time and identification of transition probabilities. The methods presented are available for specialists responsible for maintenance of technical products. Obtained Markov models are useful for diagnostics, forecasting structure service lives and establishing the justified routine maintenance. An example of synthesis and identification of Markov models representing fatigue damages of an aircraft air-intake panel is given for illustration.