Statistical evaluation of Hidden Markov Models topologies, based on industrial synthetic model

Prediction of physical particular phenomenon is based on knowledges of the phenomenon. Theses knowledges help us to conceptualize this phenomenon throw different models. Hidden Markov Models (HMM) can be used for modeling complex processes. We use this kind of models 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 three Hidden Markov Models topologies of Vrignat et al. (2010), based on upstream industrial synthetic Hidden Markov Model. Our synthetic model gives us simulation such as real industrial Computerized Maintenance Management System. Evaluation is made by two statistical tests. Therefore, we evaluate two learning algorithms: Baum-Welch Baum et al. (1970) and segmental K-means Viterbi (1967). We also evaluate two different distributions for stochastic generation of synthetic HMM labels. After a brief introduction on Hidden Markov Model, we present some statistical tests used in current literature for model selection. Afterwards, we support our study by an example of simulated industrial process by using synthetic HMM. This paper examines stochastic parameters of the various tested models on this process, for finally come up with the most relevant model and the best learning algorithm for our predictive maintenance system.