On noise covariance estimation for Kalman filter-based damage localization

In Structural Health Monitoring, Kalman filters can be used as prognosis models, and for damage detection and localization. For a proper functioning, it is necessary to tune these filters with noise covariance matrices for process and measurement noise, which are unknown in practice. Therefore, in the presented work, we apply an autocovariance least-squares method with semidefinite constraints solely based on model parameters. We facilitate this novel approach by formulating the considered innovations covariance function in infinite horizon, which follows inherently from the assumption of linear time-invariant systems. For damage analysis, we adapt a framework based on state-projection estimation errors that was recently established, and yet only applied using H-infinity fillers. These estimators represent an alternative to Kalman fillers, and are considered robust. Because of this property, the necessity of filter tuning is relaxed, and a naive design is often considered. Based on the damage analysis framework, we derive a new damage indicator that features a high sensitivity towards localized damage. We demonstrate the efficacy of the proposed schemes for noise covariance estimation and damage analysis in a series of simulations inspired by a preceding laboratory test. We finally offer experimental validation, based on vibration test data of a cantilever beam featuring damages at multiple positions, where high sensitivity towards small local stiffness changes is achieved. In our investigations, we compare the damage detection and localization performance of Kalman and H-infinity filters as well as differences in mode shape curvatures (MSC). In the simulation studies, the proposed Kalman filter-based approach outperforms the alternative strategy using H-infinity estimators. The experimental investigations demonstrate a significantly higher sensitivity of the filters towards localized damage compared to differences in MSCs. Considering the totality of investigations, the combined application of both estimators can lead to an increased robustness and sensitivity regarding damage detection and localization.

Automated summary

In this study, we introduced a method for noise covariance estimation and damage analysis in structural health monitoring using Kalman filters. By utilizing an autocovariance least-squares method based on model parameters, we simplified the tuning of the filters. Additionally, we proposed a new damage indicator that exhibits high sensitivity towards localized damage. Through simulation and experimental studies, we demonstrated the effectiveness of the proposed methods and found that the combined application of different filters can enhance the robustness and sensitivity of damage detection and localization.