Computationally Efficient Methods for Estimating Unknown Input Forces on Structural Systems

We consider the problem of estimating unknown input forces on structural systems using only noisy acceleration measurement data. This is an important task for condition monitoring, for example, to predict fatigue damage in a structure's body or to reduce transmission of vibrations in marine vessels. In this paper, we propose a new idea to estimate an input force with a sinusoidal form by formulating a force identification problem without a direct feed-through system. Consequently, the minimum variance unbiased (MVU) filter can be implemented coupled with a fast Fourier transform algorithm to estimate unknown input forces accurately in real-time. Moreover, when the input force is completely unknown, the ensemble sampling method combined with an augmented Kalman filter can be formulated to significantly reduce computation time. Experimental results confirm the effectiveness of our proposed methods and show that the formulations investigated outperform other state-of-the-art methods in term of computational cost whilst not compromising estimation performance.

[1]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[2]  Wim Desmet,et al.  Stable force identification in structural dynamics using Kalman filtering and dummy-measurements , 2015 .

[3]  Luca Caracoglia,et al.  On‐line monitoring of wind‐induced stresses and fatigue damage in instrumented structures , 2013 .

[4]  A. Smyth,et al.  Multi-rate Kalman filtering for the data fusion of displacement and acceleration response measurement in dynamic system monitoring , 2007 .

[5]  Geert Lombaert,et al.  An augmented Kalman filter for force identification in structural dynamics , 2012 .

[6]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[7]  Frederick E. Daum,et al.  New Theory and Numerical Results for Gromov's Method for Stochastic Particle Flow Filters , 2018, 2018 21st International Conference on Information Fusion (FUSION).

[8]  Zhang Yigong,et al.  Nonlinear structural identification using extended kalman filter , 1994 .

[9]  C. P. Fritzen,et al.  Updating of finite element models by means of measured information , 1991 .

[10]  Chih-Kao Ma,et al.  An inverse method for the estimation of input forces acting on non-linear structural systems , 2004 .

[11]  Nicole Kessissoglou,et al.  Optimisation of a resonance changer to minimise the vibration transmission in marine vessels , 2007 .

[12]  Dionisio Bernal,et al.  Kalman filter damage detection in the presence of changing process and measurement noise , 2013 .

[13]  Bart De Moor,et al.  Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough , 2007, Autom..

[14]  Florian Nadel,et al.  Stochastic Processes And Filtering Theory , 2016 .

[15]  G. Evensen.  Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[16]  D.S. Bernstein,et al.  Unbiased Minimum-variance Filtering for Input Reconstruction , 2007, 2007 American Control Conference.

[17]  Stefano Mariani,et al.  Unscented Kalman filtering for nonlinear structural dynamics , 2007 .

[18]  Guido De Roeck,et al.  Reference-based combined deterministic–stochastic subspace identification for experimental and operational modal analysis , 2006 .

[19]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[20]  D. Bernstein,et al.  What is the ensemble Kalman filter and how well does it work? , 2006, 2006 American Control Conference.

[21]  N. Gordon.  A hybrid bootstrap filter for target tracking in clutter , 1995, IEEE Transactions on Aerospace and Electronic Systems.

[22]  Costas Papadimitriou,et al.  Experimental validation of the Kalman-type filters for online and real-time state and input estimation , 2017 .

[23]  C. Papadimitriou,et al.  A dual Kalman filter approach for state estimation via output-only acceleration measurements , 2015 .

[24]  Eleni Chatzi,et al.  The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non‐collocated heterogeneous sensing , 2009 .

[25]  J. Beck,et al.  Bayesian State and Parameter Estimation of Uncertain Dynamical Systems , 2006 .

[26]  Eric M. Hernandez,et al.  A natural observer for optimal state estimation in second order linear structural systems , 2011 .

[27]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[28]  A. Corigliano,et al.  Parameter identification in explicit structural dynamics: performance of the extended Kalman filter , 2004 .

[29]  Daniel Toal,et al.  Remote acoustic analysis for tool condition monitoring , 2019 .

[30]  Wim Desmet,et al.  Online state and input force estimation for multibody models employing extended Kalman filtering , 2014 .

[31]  James P. Reilly,et al.  An EM Algorithm for Nonlinear State Estimation With Model Uncertainties , 2008, IEEE Transactions on Signal Processing.

[32]  M. Salman Leong,et al.  A Review of Acoustic Emission Technique for Machinery Condition Monitoring: Defects Detection & Diagnostic , 2012 .

[33]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[34]  James L. Beck,et al.  Real-time Reliability Estimation for Serviceability Limit States in Structures with Uncertain Dynamic Excitation and Incomplete Output Data , 2007 .

[35]  Li Zhou,et al.  An adaptive extended Kalman filter for structural damage identification , 2006 .

[36]  Kalil Erazo,et al.  A model-based observer for state and stress estimation in structural and mechanical systems: Experimental validation , 2014 .

[37]  G. Evensen.  Data Assimilation: The Ensemble Kalman Filter , 2006 .

[38]  J. Bather,et al.  Tracking and data fusion , 2001 .

[39]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[40]  David Frederic Crouse,et al.  Particle Flow Filters: Biases and Bias Avoidance , 2019, 2019 22th International Conference on Information Fusion (FUSION).

[41]  Ting Wang,et al.  A Novel Coupled State/Input/Parameter Identification Method for Linear Structural Systems , 2018 .

[42]  Nicholas A J Lieven,et al.  Extended Kalman filtering for the detection of damage in linear mechanical structures , 2009 .

[43]  Bart De Moor,et al.  Unbiased minimum-variance input and state estimation for linear discrete-time systems , 2007, Autom..

[44]  Feng Gao,et al.  A Kalman-filter based time-domain analysis for structural damage diagnosis with noisy signals , 2006 .