Automatic damping estimation via bootstrap technique and Bayesian analysis for mechanical system condition monitoring

Abstract

Monitoring mechanical systems that are exposed to dynamic loads during operation requires a technical indicator that provides reliable information on degradation. In this paper, the damping ratio is used as an indicator and can be obtained from monitoring data such as acceleration. Its change from the initial value highly correlates with the system change that can lead to failure. The damping ratio can be relatively easily estimated from the free response data. Such events occur frequently for systems that are subjected to environmental loads such as wind gusts on structures, or sudden stops and changes in the operational cycle.The problem addressed by this research is the fully autonomous detection of these free-response events and the subsequent estimation of the damping ratio, including uncertainty. Therefore, a novel monitoring approach is proposed, utilising the Bootstrap technique and Bayesian analysis. Bootstrap provides automatic free response detection without monitoring the excitation force. Once the event is detected as a valid free response, Bayesian analysis in the form of a gamma-exponential conjugate prior is applied to estimate the damping ratio. As damping estimation is in the form of distribution, uncertainty is also quantified, which is a required feature when monitoring the degradation process and remaining useful life prediction.The monitoring approach is demonstrated and verified numerically and experimentally on a single degree of freedom air-bearing testbed as well as on multiple degrees of freedom beam system. As shown, the combination of the Bootstrap technique and Bayesian analysis provided satisfactory results, demonstrating that the degradation process can be reliably monitored by the proposed approach.