Modeling Multi-State Equipment Degradation with Non-Homogeneous Continuous-Time Hidden Semi-Markov Process

Introduction

In the domain of reliability and maintenance, significant attention has been paid in recent years to equipment with discrete multi-state health conditions. Multi-state models, particularly for mechanical equipment under stress or load conditions that deteriorates or degrades over time, can properly model the transitions among the intermediate health states, ranging from perfect functioning to complete failure. These intermediate health states can either be directly observable (completely observable states) or partially observable (partially observable states). Currently, due to the complexity of the degradation process and other technical problems, most mechanical equipment is only partially observable through condition monitoring (CM) techniques (Moghaddass & Zuo, 2011b), such as vibration analysis and signal processing. Therefore, modeling multi-state equipment with partially observable states involves two types of processes; namely, the degradation process and the observation process. The degradation process deals with the behavior of transitions between health states, while the observation process deals with the stochastic relationship between the degradation states and condition monitoring information. Details for different types of degradation and observation processes can be found in (Moghaddass & Zuo, 2011b).

The primary step before using a condition-based diagnostic and prognostic method for multi-state equipment with unobservable states is to determine the type of stochastic models to be used for degradation and observation process modeling. The subsequent step is to estimate the characteristic parameters of these models from real-time condition monitoring data. These parameters are needed to characterize the degradation and observation processes. Dealing with the observation process is more straightforward than evaluating the degradation process. With regard to the observation process, the relationship between the condition monitoring information and the actual health state is investigated. A common approach to study the observation process for a piece of mechanical equipment is to artificially create damage that corresponds to the particular discrete health states, and then extract condition monitoring data for each health condition. Machine learning techniques and statistical data-driven methods have been developed to explore this relationship in the literature (Worden & Manson, 2007; Zhang et al., 2011). However, there is less work involved in the degradation process modeling especially for multi-state equipment (Wu et al., 2010; Petrovic et al., 2011).

In this chapter, we focus on degradation process modeling for multi-state equipment with unobservable states. From both the theoretical and practical points of view, we first consider the characteristics of the continuous-time stochastic models that are available for multi-state equipment modeling in the literature, and then present generalized results for multi-state degradation modeling using the non-homogenous continuous-time hidden semi-Markov process (NHCTHSMP). We will show that NHCTHSMP is capable of overcoming some of the limitations of reported methods, while covering much of the previously research, since it makes more general assumptions for the equipment being studied. Finally, we present an estimation method to find the unknown parameters of an NHCTHSMP that is applicable to the modeling of multi-state equipment with unobservable states. In this chapter, we aim to present a general method that can model the stochastic characteristics of the degradation and observation processes of a piece of multi-state equipment.