Researches On Fault Diagnosis Of Complex Mechanical Systems Based On Hidden Markov Model And EM Algorithm

Since the20th century, with the development and progress of industrial production, Mechanical system reliability and security issues have become increasingly prominent. And grasping the state of the machinery and equipment during operation, its whole or part is normal or abnormal. If the machine fails, how to identify the fault type. These is critical for the monitoring and control system of production. The hidden Markov model (HMM) is a pattern recognition method based on the statistical theory. It has been widely used in the field of speech recognition. Based on the similarity of the vibration signals and voice signals, hidden Markov model (HMM) can also be applied in the field of mechanical fault diagnosis. In this paper a systematic introduction to the basic theory of hidden Markov model is given, An example about rotating machinery fault diagnosis is shown to illustrate the application of hidden Markov models in fault diagnosis. The basic theory of HMM includes the basic elements of HMM,the basic assumptions of the HMM, as well as the three basic questions of HMM and their solutions. Derive the forward-backward to solve the estimation problem of HMM,and the Viterbi algorithm to solve the decoding problem of HMM. The theory of EM (Expectation Maximization) algorithm is introduced. Based the EM algorithm, this paper presents a formal treatment of HMM multiple observation training without imposing the dependence or independence assumptions of multiple observations. In this treatment, the multiple observation probability is expressed as a combination of individual observation probabilities without losing generality. And with the introduction of the relevant theorems, The parameters’revaluation formula of the HMM with multiple observations is deduced. The paper introduces time-reversible hidden Markov chains and the conditions of being reversible. High-order hidden Markov models consider the relevance of between the two probabilities which are the state transition probability and the output probability of the observed signals, and the system historical states. Thus, it has a stronger ability to identify the observed signals. This paper describes the definition of a higher-order hidden Markov model, and proposes a simple method that transforms any high order HMM into an equivalent first order one, and thus makes the first order HMM theories applicable to models of any order. Finally, this paper describes the application technology of HMM in the mechanical fault diagnosis. And its realization on the computer in the MATLAB environment.