Hidden Markov model parameters estimation with independent multiple observations and inequality constraints
- Author(s): Lisha Xia 1 ; Huajing Fang 1 ; Xiaoyong Liu 1
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View affiliations
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Affiliations:
1:
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
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Affiliations:
1:
School of Automation, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
- Source:
Volume 8, Issue 9,
December 2014,
p.
938 – 949
DOI: 10.1049/iet-spr.2013.0505 , Print ISSN 1751-9675, Online ISSN 1751-9683
In this study, the authors focus on hidden Markov model (HMM) parameters estimation with independent multiple observations and non-linear inequality constraints. The parameters estimation process is divided into four steps: initialisation, parameters pre-estimation, parameters re-estimation and termination. The pre-estimation results are used to approximate non-linear inequality constraints to linear inequality constraints. In parameters re-estimation step, the active-set optimisation is combined with the expectation maximisation (EM) algorithm in M-step and the active set-based EM algorithm is proposed to re-estimate HMM parameters when inequality constraints are not satisfied in pre-estimation. An auxiliary function is devised for reconstructing the optimisation objective function and the convergence of the proposed algorithm is also demonstrated. Simulation results indicate that the proposed algorithm provides better performance by modifying the random error of observation data appropriately and it is powerful for industry process fault diagnosis.
Inspec keywords: parameter estimation; approximation theory; fault diagnosis; hidden Markov models; expectation-maximisation algorithm; nonlinear estimation; optimisation
Other keywords: approximate nonlinear inequality constraint; HMM parameter estimation; initialisation step; random error modification; optimisation objective function reconstruction; termination step; hidden Markov model parameter estimation; parameters reestimation step; independent multiple observation; expectation maximisation algorithm; active set-based EM algorithm; industry process fault diagnosis; active-set optimisation; parameters pre-estimation step; M-step algorithm; linear inequality constraint
Subjects: Interpolation and function approximation (numerical analysis); Optimisation; Markov processes; Optimisation techniques; Numerical analysis; Optimisation techniques; Numerical approximation and analysis; Probability theory, stochastic processes, and statistics; Interpolation and function approximation (numerical analysis); Markov processes; Statistics
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