A general substructure-based framework for input-state estimation using limited output measurements

Abstract This paper presents a general framework for estimating the state and unknown inputs at the level of a system subdomain using a limited number of output measurements, enabling thus the component-based vibration monitoring or control and providing a novel approach to model updating and hybrid testing applications. Under the premise that the system subdomain dynamics are driven by the unknown (i) externally applied inputs and (ii) interface forces, with the latter representing the unmodeled system components, the problem of output-only response prediction at the substructure level can be tailored to a Bayesian input-state estimation context. As such, the solution is recursively obtained by fusing a Reduced Order Model (ROM) of the structural subdomain of interest with the available response measurements via a Bayesian filter. The proposed framework is without loss of generality established on the basis of fixed- and free-interface domain decomposition methods and verified by means of three simulated Wind Turbine (WT) structure applications of increasing complexity. The performance is assessed in terms of the achieved accuracy on the estimated unknown quantities.

[1]  Ke Huang,et al.  Identifiability‐Enhanced Bayesian Frequency‐Domain Substructure Identification , 2018, Comput. Aided Civ. Infrastructure Eng..

[2]  Vasilis K. Dertimanis,et al.  A substructure approach for fatigue assessment on wind turbine support structures using output-only measurements , 2017 .

[3]  R. Guyan.  Reduction of stiffness and mass matrices , 1965 .

[4]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[5]  Benjamin Peherstorfer,et al.  Dynamic data-driven reduced-order models , 2015 .

[6]  M. Géradin,et al.  Mechanical Vibrations: Theory and Application to Structural Dynamics , 1994 .

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

[8]  Costas Papadimitriou,et al.  An enhanced substructure coupling technique for dynamic re-analyses: Application to simulation-based problems , 2016 .

[9]  Costas Papadimitriou,et al.  Input-state-parameter estimation of structural systems from limited output information , 2019, Mechanical Systems and Signal Processing.

[10]  Jason Jonkman,et al.  Development of performance specifications for hybrid modeling of floating wind turbines in wave basin tests , 2018 .

[11]  Kana Horikiri,et al.  Aerodynamics of wind turbines , 2011 .

[12]  G. Roeck,et al.  Design of sensor networks for instantaneous inversion of modally reduced order models in structural dynamics , 2015 .

[13]  Erich Hau,et al.  Wind Turbines: Fundamentals, Technologies, Application, Economics , 1999 .

[14]  Andrew J. Kurdila,et al.  『Fundamentals of Structural Dynamics』(私の一冊) , 2019, Journal of the Society of Mechanical Engineers.

[15]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[16]  M Feyzollahzadeh,et al.  Wind load response of offshore wind turbine towers with fixed monopile platform , 2016 .

[17]  J. C. Marín,et al.  Study of fatigue damage in wind turbine blades , 2009 .

[18]  M. K. Au-Yang.  Fundamentals of Structural Dynamics , 2001 .

[19]  D. Rixen.  A dual Craig-Bampton method for dynamic substructuring , 2004 .

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

[21]  Costas Papadimitriou,et al.  Computational Framework for Online Estimation of Fatigue Damage using Vibration Measurements from a Limited Number of Sensors , 2017 .

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

[23]  Sriram Narasimhan,et al.  A Gaussian process latent force model for joint input-state estimation in linear structural systems , 2019, Mechanical Systems and Signal Processing.

[24]  Dionisio Bernal,et al.  Sequential deconvolution input reconstruction , 2015 .

[25]  Randall L. Mayes,et al.  Advancements in hybrid dynamic models combining experimental and finite element substructures , 2012 .

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

[27]  Costas Papadimitriou,et al.  Component mode synthesis techniques for finite element model updating , 2013 .

[28]  M. Kang,et al.  Fatigue failure of a composite wind turbine blade at its root end , 2015 .

[29]  Dimitris I. Chortis,et al.  Structural Analysis of Composite Wind Turbine Blades , 2013 .

[30]  R. Macneal.  A hybrid method of component mode synthesis , 1971 .

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

[32]  U. T. Tygesen,et al.  A Bayesian Filtering Approach to Operational Modal Analysis with Recovery of Forcing Signals , 2018 .

[33]  Eliz-Mari Lourens,et al.  Full-field response monitoring in structural systems driven by a set of identified equivalent forces , 2019, Mechanical Systems and Signal Processing.

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

[35]  P. Moylan.  Stable inversion of linear systems , 1977 .

[36]  W. Desmet,et al.  An online coupled state/input/parameter estimation approach for structural dynamics , 2015 .

[37]  Costas Papadimitriou,et al.  Model-reduction techniques for Bayesian finite element model updating using dynamic response data , 2014 .

[38]  Morten Hartvig Hansen,et al.  Aeroelastic instability problems for wind turbines , 2007 .

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

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

[41]  B. Irons.  Structural eigenvalue problems - elimination of unwanted variables , 1965 .

[42]  Mahendra P. Singh,et al.  An adaptive unscented Kalman filter for tracking sudden stiffness changes , 2014 .

[43]  Jann N. Yang,et al.  An adaptive extended Kalman filter for structural damage identifications II: unknown inputs , 2007 .

[44]  Daniel C. Kammer,et al.  Comparison of the Craig-Bampton and residual flexibility methods of substructure representation , 1987 .

[45]  Costas Papadimitriou,et al.  Fatigue predictions in entire body of metallic structures from a limited number of vibration sensors using Kalman filtering , 2011 .

[46]  Andrew W. Smyth,et al.  Nonlinear System Identification: Particle-Based Methods , 2014 .

[47]  T. Patrik Nordberg,et al.  A time delay method to solve non-collocated input estimation problems , 2004 .

[48]  C. Pierre,et al.  Characteristic Constraint Modes for Component Mode Synthesis , 2001 .

[49]  Olivier A. Bauchau,et al.  On the nonlinear extension-twist coupling of beams , 2018, European Journal of Mechanics - A/Solids.

[50]  Daniel C. Kammer,et al.  Selection of Component Modes for Craig-Bampton Substructure Representations , 1996 .

[51]  Paolo Tiso,et al.  State estimation of geometrically non-linear systems using reduced-order models , 2018 .

[52]  S. Rubin.  Improved Component-Mode Representation for Structural Dynamic Analysis , 1975 .

[53]  Dionisio Bernal,et al.  Non-recursive sequential input deconvolution , 2017 .

[54]  Paolo Tiso,et al.  A modal derivatives enhanced Rubin substructuring method for geometrically nonlinear multibody systems , 2018, Multibody System Dynamics.