A segmental hidden semi-Markov model (HSMM)-based diagnostics and prognostics framework and methodology.pdf

ARTICLE IN PRESS
Mechanical Systems
and
Signal Processing
Mechanical Systems and Signal Processing 21 (2007) 2248–2266
ate/jnlabr/ymssp
A segmental hidden semi-Markov model (HSMM)-based
diagnostics and prognostics framework and methodology
Ming Donga,Ã, David Heb
aDepartment of Industrial Engineering and Management, School of Mechanical Engineering (Room 618),
Shanghai Jiao Tong University, 800 Dongchuan Road, Min-Hang District, Shanghai 200240, PR China
bDepartment of Mechanical and Industrial Engineering, The University of Illinois at Chicago, Chicago, IL 60607, USA
Received 30 April 2006; received in revised form 21 August 2006; accepted 4 October 2006
Available online 30 November 2006
Abstract
Diagnostics and prognostics are two important aspects in a condition-based maintenance (CBM) program. However,
these two tasks are often separately performed. For example, data might be collected and analysed separately for diagnosis
and prognosis. This practice increases the cost and reduces the efficiency of CBM and may affect the accuracy of the
diagnostic and prognostic results.
In this paper, a statistical modelling methodology for performing both diagnosis and prognosis in a unified framework is
presented. The methodology is developed based on segmental hidden semi-Markov models (HSMMs). An HSMM is a
hidden Markov model (HMM) with temporal structures. Unlike HMM, an HSMM does not follow the unrealistic
Markov chain assumption and therefore provides more powerful modelling and analysis capability for real problems. In
addition, an HSMM allows modelling the time duration of the hidden states and therefore is capable of prognosis. To
facilitate putation in the proposed HSMM-based diagnostics and prognostics, new forward–backward variables
are defined and a modified forward–backward algorithm is developed. The existing state duration estimation methods are
inefficient because they require a huge storage putational load. Therefore, a ne