A Bayesian Model for Monitoring and Generating Alarms for Deteriorating Systems Working Under Varying Operating Conditions

Most mechanical systems work under varying operating conditions and stress levels that can potentially influence how the degradation and damage processes evolve over time. To analyze the progression of damage in such systems over time, this chapter develops a new stochastic model based on a well-known damage model using Bayesian hierarchical structure that takes into account uncertainty and interpretability in a mathematically convenient and structured manner. First, a hierarchical model is defined that can track the damage level of a deteriorating system over time based on the number of cycles spent at each stress level. A parameter estimation model is then defined that can employ past data to train the structure of the model. A method for predicting remaining useful life and the uncertainty associated with it is developed that can dynamically be updated based on the history of the operating conditions. An optimal decision policy is introduced that can determine the optimal time to issue an alarm given an ideal warning time defined by the maintenance decision makers. Finally, the application of the model and its accuracy are demonstrated through simulation experiments and a real-world case study for wind turbine health monitoring.