Probability Based Prediction of Degrading Dynamic Systems

Abstract

This paper presents a methodology to provide the cumulative failure distribution (CDF) for degrading, uncertain, and dynamic systems. The uniqueness and novelty of the methodology is that long service time over which degradation occurs has been augmented with much shorter cycle time over which there is uncertainty in the system dynamics due to uncertain design variables. The significance of the proposed methodology is that it sets the foundation for setting realistic lifecycle management policies for dynamic systems. The methodology first replaces the implicit mechanistic model with a simple explicit metamodel with the help of design of experiments and singular value decomposition, then transforms the dynamic, time variant, probabilistic problem into a sequence of time invariant steadystate probability problems using cycletime performance measures and discrete service time, and finally, builds the CDF as the summation of the incremental servicetime failure probabilities over the planned life time. For multiple failure modes and multiple discrete service times, set theory establishes a sequence of true incremental failure regions. A practical implementation of the theory requires only two contiguous servicetimes. Probabilities may be evaluated by any convenient method, such as Monte Carlo and the firstorder reliability method. Error analysis provides ways to control errors with regards to probability calculations and metamodel fitting. A case study of a common servocontrol mechanism shows that the new methodology is sufficiently fast for design purposes and sufficiently accurate for engineering applications.