TY - JOUR

T1 - On noise covariance estimation for Kalman filter-based damage localization

AU - Wernitz, Stefan

AU - Chatzi, Eleni

AU - Hofmeister, Benedikt

AU - Wolniak, Marlene Theresa

AU - Rolfes, Raimund

N1 - Funding Information: This research has been funded by the Federal Ministry of Economic Affairs and Energy of the Federal Republic of Germany (project: German Research Facility for Wind Energy, FKZ 0325936E) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 434502799 – SFB 1463. The authors would like to acknowledge the support gratefully.

PY - 2022/5/1

Y1 - 2022/5/1

N2 - 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 ∞ filters. These estimators represent an alternative to Kalman filters, 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 ∞ 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 ∞ 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.

AB - 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 ∞ filters. These estimators represent an alternative to Kalman filters, 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 ∞ 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 ∞ 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.

KW - Damage localization

KW - Kalman filter

KW - Noise covariance estimation

KW - ℋ filter

UR - http://www.scopus.com/inward/record.url?scp=85123766211&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2022.108808

DO - 10.1016/j.ymssp.2022.108808

M3 - Article

VL - 170

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 108808

ER -