A Gaussian-process assisted model-form error estimation in multiple-degrees-of-freedom systems

被引:0
作者
Kashyap, Sahil [1 ]
Rogers, Timothy J. [2 ]
Nayek, Rajdip [1 ]
机构
[1] Indian Inst Technol Delhi, Dept Appl Mech, Delhi 110016, India
[2] Univ Sheffield, Dept Mech Engn, Mappin St, Sheffield S1 3JD, England
关键词
Model discrepancy; Model form errors; Gaussian process; Correlated noise model; Kalman filter; Bayesian state estimation; STATE ESTIMATION; KALMAN FILTER; IDENTIFICATION; CALIBRATION; INPUT;
D O I
10.1016/j.ymssp.2024.111474
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
In many applications involving modelling of complex structural dynamical systems, the mathematical models employed are often simplified abstractions of a real -world phenomenon. This presents a challenge in accurately depicting and simulating physical reality. In this study, we focus on locally nonlinear shear -storey -type MDOF systems, which are simplistically assumed as linear dynamic models. The disparity between the presumed linear model and the true nonlinear data -generating phenomenon introduces what we term as model -form error (MFE). The essence of MFEs lies in the mismatch between the governing equations of motion of the assumed mathematical model and the true data -generating model. To tackle these MFEs, we treat the MFEs as externally applied latent forces (LFs) and employ stationary Gaussian processes to model them. Through a Bayesian state estimation process, encompassing both the Kalman filter and smoother, we derive estimates of not only the structural state variables but also the MFEs themselves. The two main novelties of our study lie in (a) the extension of the GPLFMbased MFE identification to MDOF systems, and (b) the exploration of the GPLFM's ability to detect and localise the MFEs within the assumed mathematical model without the need for prior knowledge regarding the nature and/or the locations of these MFEs. Furthermore, the study delves into various scenarios of inference dealing with incomplete measurements and highlights identifiability issues encountered in different incomplete measurement scenarios.
引用
收藏
页数:20
相关论文
共 33 条
[1]  
Alvarez M., 2009, AISTATS, V5, P9
[2]  
[Anonymous], 2011, P 27 C UNCERTAINTY A
[3]   Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability [J].
Arendt, Paul D. ;
Apley, Daniel W. ;
Chen, Wei .
JOURNAL OF MECHANICAL DESIGN, 2012, 134 (10)
[4]   A dual Kalman filter approach for state estimation via output-only acceleration measurements [J].
Azam, Saeed Eftekhar ;
Chatzi, Eleni ;
Papadimitriou, Costas .
MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2015, 60-61 :866-886
[5]   Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference [J].
Bisaillon, Philippe ;
Sandhu, Rimple ;
Pettit, Chris ;
Khalil, Mohammad ;
Poirel, Dominique ;
Manohar, C. S. ;
Sarkar, Abhijit .
JOURNAL OF SOUND AND VIBRATION, 2022, 522
[6]   Learning about physical parameters: the importance of model discrepancy [J].
Brynjarsdottir, Jenny ;
O'Hagan, Anthony .
INVERSE PROBLEMS, 2014, 30 (11)
[7]   Uncertainty Quantification of Locally Nonlinear Dynamical Systems Using Neural Networks [J].
De, Subhayan .
JOURNAL OF COMPUTING IN CIVIL ENGINEERING, 2021, 35 (04)
[8]   Physics-integrated hybrid framework for model form error identification in nonlinear dynamical systems [J].
Garg, Shailesh ;
Chakraborty, Souvik ;
Hazra, Budhaditya .
MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2022, 173
[9]   Unbiased minimum-variance input and state estimation for linear discrete-time systems [J].
Gillijns, Steven ;
De Moor, Bart .
AUTOMATICA, 2007, 43 (01) :111-116
[10]  
Hartikainen Jouni, 2010, Proceedings of the 2010 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), P379, DOI 10.1109/MLSP.2010.5589113