Evaluation of relevance of stochastic parameters on Hidden Markov Models

Prediction of physical particular phenomenon is based on knowledge of the phenomenon. This knowledge helps us to conceptualize this phenomenon around different models. Hidden Markov Models (HMM) can be used for modeling complex processes. This kind of models is used as tool for fault diagnosis systems. Nowadays, industrial robots living in stochastic environment need faults detection to prevent any breakdown. In this paper, we wish to evaluate relevance of Hidden Markov Models parameters, without a priori knowledges. After a brief introduction of Hidden Markov Model, we present the most used selection criteria of models in current literature and some methods to evaluate relevance of stochastic events resulting from Hidden Markov Models. We support our study by an example of simulated industrial process by using synthetic model of Vrignat’s study (Vrignat 2010). Therefore, we evaluate output parameters of the various tested models on this process, for finally come up with the most relevant model. literature are the AIC: Akaike Information Criterion (Akaike 1973), the BIC: Bayesian Information Criterion (Schwarz 1978). In this work, the emphasis is on measuring relevance of Hidden Markov Models (HMM) parameters, based on several criteria used in current literature. Then, we try to evaluate best HMM topology. The structure is as follows: in section 2, we outline hidden Markov model and define its parameters. We present criteria used to evaluate relevance of HMM parameters (Shannon’s entropy (Shannon 1948), likelihood, AIC and BIC), in section 3. Finally, we use our synthetic model to compare several HMM topologies, from among a candidate set, with previous criterion and try to give the best one, in section 4. 2 HIDDEN MARKOV MODEL Hidden Markov Model (Rabiner 1989), (Fox et al. 2006) is an automaton with hidden states which consists of unobservable variable. This one represents the system status to be modeled. Only output variable is observable. Then we get observations sequence from output of the automaton; from now, we rename observations sequence as symbols, representing these observations (see an example of model figure 1). This is precisely relevance of