Structural response reconstruction under non-Gaussian measurement noise

PDF(4976 KB)

Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (11) : 206-216.

QI Yibo, PENG Zhenrui

Author information +

History +

Abstract

The accuracy of response reconstruction using the Kalman Filter (KF) algorithm is degraded under non-Gaussian noise. To tackle this issue, a non-Gaussian Kalman filter algorithm for structural response reconstruction is proposed. Firstly, the L1 Kalman Filter (L1KF) algorithm is introduced to structural response reconstruction, followed by a revised definition of the loss function within the L1KF. Secondly, the coefficient matrix derived according to the loss function penalizes the noise covariance matrix of the state equation and the observation equation, making the KF algorithm applicable to non-Gaussian noise. Finally, the acceleration, velocity, and displacement responses of the structure are computed from a limited number of acceleration measurements. Both numerical simulations and an overhanging beam test show that the proposed method has good noise robustness using only a limited number of accelerometers, effectively reducing the reconstruction error. The large bias in response reconstruction using KF algorithm under multiple non-Gaussian noises is improved.

Key words

response reconstruction / non-Gaussian noise / Kalman filtering

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

QI Yibo, PENG Zhenrui. Structural response reconstruction under non-Gaussian measurement noise[J]. Journal of Vibration and Shock, 2024, 43(11): 206-216

References

[1] ZHANG C W, MOUSAVI A A, GHOLIPOUR G, et al. Vibration feature extraction using signal processing techniques for structural health monitoring: A review[J]. Mechanical Systems and Signal Processing, 2022, 177: 109175. [2] FAN G, HE Z, LI J. Structural dynamic response reconstruction using self-attention enhanced generative adversarial networks[J]. Engineering Structures, 2023, 276: 115334. [3] CAU J, BU F, WANG J, et al. Reconstruction of full-field dynamic responses for large-scale structures using optimal sensor placement[J]. Journal of Sound and Vibration, 2023, 554: 117693. [4] KAMMER D C. Estimation of structural response using remote sensor locations[J]. Journal of guidance, control, and dynamics, 1997, 20(3): 501-508. [5] LAW S S, LI J, DING Y. Structural response reconstruction with transmissibility concept in frequency domain[J]. Mechanical Systems and Signal Processing, 2011, 25(3): 952-968. [6] LI J, HAO H. Substructure damage identification based on wavelet-domain response reconstruction[J]. Structural Health Monitoring, 2014, 13(4): 389-405. [7] YANG J S, FU Z Y, ZOU Y F, et al. A response reconstruction method based on empirical mode decomposition and modal synthesis method[J]. Mechanical Systems & Signal Processing, 2023, 184: 109716. [8] 邹云峰, 付正亿, 何旭辉, 等. 基于经验模态分解和模型缩聚的动力响应重构方法研究[J]. 工程力学, 2022, 39(2): 67-75. ZOU Yunfeng, FU Zhengyi, He Xuhui, et al. Dynamic response reconstruction method based on empirical mode decomposition and model condensation[J]. Engineering Mechanics, 2022, 39(2): 67-75. [9] ZHU Z, ZHU S, WANG Y W, et al. Structural dynamic response reconstruction with multi-type sensors, unknown input, and rank deficient feedthrough matrix[J]. Mechanical Systems and Signal Processing, 2023, 187: 109935. [10] HUANG J, LI X, ZHANG F, et al. Identification of joint structural state and earthquake input based on a generalized Kalman filter with unknown input[J]. Mechanical Systems and Signal Processing, 2021, 151: 107362. [11] TATSIS K E, AGATHOS K, CHATZI E N, et al. A hierarchical output-only Bayesian approach for online vibration-based crack detection using parametric reduced-order models[J]. Mechanical Systems and Signal Processing, 2022, 167: 108558. [12] 张笑华, 周海洋, 吴志彪. 子结构传感器位置优化和响应重构[J]. 振动与冲击, 2020, 39(6): 257-262+270. ZHANG Xiaohua, ZHOU Haiyang, WU Zhibiao. Sensor location selection and response reconstruction of a substructure[J]. Journal of Vibration and Shock, 2020, 39(6): 257-262+270. [13] HE J, ZHANG X, XU B. KF-based multiscale response reconstruction under unknown inputs with data fusion of multitype observations[J]. Journal of Aerospace Engineering, 2019, 32(4): 04019038. [14] AZAM S E, CHATZI E, PAPADIMITRIOU C. A dual Kalman filter approach for state estimation via output-only acceleration measurements[J]. Mechanical systems and signal processing, 2015, 60: 866-886. [15] ZHANG X H, ZHU Z, YUAN G K, et al. Adaptive Mode Selection Integrating Kalman Filter for Dynamic Response Reconstruction[J]. Journal of Sound and Vibration, 2021, 515: 116497. [16] 张笑华, 吴志彪, 吴圣斌, 等. 基于移动窗卡尔曼滤波算法的结构响应重构[J]. 振动与冲击, 2021, 40(21):90-96+105. ZHANG Xiaohua, WU Zhibiao, WU Shengbin. Structural response reconstruction based on moving window Kalman filtering algorithm[J]. Journal of Vibration and Shock, 2021, 40(21): 90-96+105. [17] NAYEK R, CHAKRABORTY S, NARASIMHAN S. A Gaussian process latent force model for joint input-state estimation in linear structural systems[J]. Mechanical Systems and Signal Processing, 2019, 128: 497-530. [18] ROONIZI A K. Kalman Filtering in Non-Gaussian Model Errors: A New Perspective [Tips & Tricks] [J]. IEEE Signal Processing Magazine, 2022, 39(3): 105-114. [19] YUEN K V, LIU Y S, YAN W J. Estimation of time-varying noise parameters for unscented Kalman filter[J]. Mechanical Systems and Signal Processing, 2022, 180: 109439. [20] GANDHI M A, MILI L. Robust kalman filter based on a generalized maximum-likelihood-type estimator[J]. IEEE Transactions on Signal Processing, 2009, 58(5): 2509-2520. [21] ZHU H, ZHANG G, LI Y F, et al. A novel robust Kalman filter with unknown non-stationary heavy-tailed noise[J]. Automatica, 2021, 127: 109511. [22] KHODARAHMI M, MAIHAMI V. A review on Kalman filter models[J]. Archives of Computational Methods in Engineering, 2023, 30(1): 727-747. [23] KONG X, YANG W, LI B. Application of stabilized numerical integration method in acceleration sensor data processing[J]. IEEE Sensors Journal, 2021, 21(6): 8194-8203.