Bayesian Two-Phase Gamma Process Model for Damage Detection and Prognosis

This paper presents a data-driven approach to damage detection and prognosis in the context of structural health monitoring. One of the main issues in dealing with structural damage and degradation is its hidden stochastic nature, which could be gradual or accompanied by sudden changes resulting from shock events. Although gradual degradation could be related to age and operating conditions, shocks could arise from loss of stiffness/connectivity or from impact, resulting in a subsequent change in degradation path. In this paper, a unified degradation modeling approach is presented based on a gamma process, where both gradual degradation and change points caused by shock events are identified in a unified formulation. Because the exact degradation path depends upon both operating and loading conditions, the model parameters are estimated directly from the sensory data using Bayesian inference. In the first step, a degradation indicator is calculated based on time-series modeling, which is then used together with a multivariate Hotelling’s $p$ control chart for damage detection. In the next step, the degradation indicator forms an input to a gamma process degradation model (single- or two-phase gamma process), which enables damage prognosis using time-series model parameters as surrogates. The advantage of this approach is the ability to detect change points and changes to the degradation path using a purely data-driven approach without the need for experimental failure data. The model parameters and prognosis estimates can be updated with the availability of monitoring data, which makes it a powerful tool for damage detection and prognosis in long-term condition-monitoring settings. A numerical example is presented to illustrate the overall process using simulated vibration data and highlight the potential advantages of using this methodology.