Statistical Regularization for Identification of Structural Parameters and External Loadings Using State Space Models

A novel numerical approach is presented, in the time domain, to simultaneously identify structural parameters and unmeasured input loadings using incomplete output measurement only. The identification problem is formulated as an optimization process, wherein the objective function is defined as the discrepancy between the measured and the predicted data, and is solved by a damped Gauss-Newton method. Because the proposed algorithm is a time domain technique, forward analyses are required to obtain predicted system responses so as to compute the discrepancy. Therefore, we propose an input force estimation scheme in the identification process to complete the task of input-output forward analyses, for the case of output-only measurement. The relationship between the unknown input loadings and the output measurement is established through a state space model, which basically formulates an ill-posed least squares problem. A statistical Bayesian inference-based regularization technique is presented to solve such a least squares problem. Finally, the proposed approach is illustrated by both numerical and experimental examples using output-only measurements of either acceleration or strain time histories. The results clearly show the robustness and the applicability of the proposed algorithm to simultaneously identify structural parameters and unmeasured input loadings with a high accuracy.

[1]  Bin Xu,et al.  Data-based Identification of nonlinear restoring force under spatially incomplete excitations with power series polynomial model , 2012 .

[2]  K. Yuen,et al.  A novel probabilistic method for robust parametric identification and outlier detection , 2012 .

[3]  L. M. See,et al.  Estimation of structural parameters in time domain: A substructure approach , 1991 .

[4]  Raimondo Betti,et al.  Simultaneous identification of structural parameters and dynamic input with incomplete output‐only measurements , 2014 .

[5]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[6]  Bin Xu,et al.  Parametric Identification for a Truss Structure Using Axial Strain , 2007, Comput. Aided Civ. Infrastructure Eng..

[7]  S. S. Law,et al.  Force Identification Based on Sensitivity in Time Domain , 2006 .

[8]  H. Adeli,et al.  Dynamic Fuzzy Wavelet Neural Network Model for Structural System Identification , 2006 .

[9]  Chan Ghee Koh,et al.  Output‐only structural identification in time domain: Numerical and experimental studies , 2008 .

[10]  Hojjat Adeli,et al.  Pseudospectra, MUSIC, and dynamic wavelet neural network for damage detection of highrise buildings , 2007 .

[11]  James L. Beck,et al.  Structural damage detection and assessment by adaptive Markov chain Monte Carlo simulation , 2004 .

[12]  X. Y. Li,et al.  Adaptive Tikhonov regularization for damage detection based on nonlinear model updating , 2010 .

[13]  Piotr Omenzetter,et al.  Particle Swarm Optimization with Sequential Niche Technique for Dynamic Finite Element Model Updating , 2015, Comput. Aided Civ. Infrastructure Eng..

[14]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[15]  Bangti Jin,et al.  A Bayesian inference approach to the ill‐posed Cauchy problem of steady‐state heat conduction , 2008 .

[16]  Siu-Seong Law,et al.  Explicit form of an implicit method for inverse force identification , 2014 .

[17]  B. Fischer.  Lessons Learned. , 2016, Schizophrenia bulletin.

[18]  Matthew J. Whelan,et al.  Wireless Monitoring of a Multispan Bridge Superstructure for Diagnostic Load Testing and System Identification , 2011, Comput. Aided Civ. Infrastructure Eng..

[19]  Sriram Narasimhan,et al.  Hybrid Time‐Frequency Blind Source Separation Towards Ambient System Identification of Structures , 2012, Comput. Aided Civ. Infrastructure Eng..

[20]  C. R. Farrar,et al.  Lessons learned from applications of vibration-based damage identification methods to a large bridge structure , 1997 .

[21]  Hojjat Adeli,et al.  A probabilistic neural network for earthquake magnitude prediction , 2009, Neural Networks.

[22]  Yongchao Yang,et al.  Blind modal identification of output‐only structures in time‐domain based on complexity pursuit , 2013 .

[23]  Qingshan Yang,et al.  Sensor placement methods for an improved force identification in state space , 2013 .

[24]  Maria Q. Feng,et al.  Variation of modal parameters of a highway bridge extracted from six earthquake records , 2013 .

[25]  Li Zhou,et al.  Impact load identification of composite structure using genetic algorithms , 2009 .

[26]  Bin Xu,et al.  Data‐Based Model‐Free Hysteretic Restoring Force and Mass Identification for Dynamic Systems , 2015, Comput. Aided Civ. Infrastructure Eng..

[27]  K. Yuen,et al.  Modal decomposition using multi-channel response measurements , 2014 .

[28]  Bin Xu,et al.  Structural parameters and dynamic loading identification from incomplete measurements: Approach and validation , 2012 .

[29]  K. Yuen.  Bayesian Methods for Structural Dynamics and Civil Engineering , 2010 .

[30]  Hojjat Adeli,et al.  Dynamic Wavelet Neural Network for Nonlinear Identification of Highrise Buildings , 2005 .

[31]  Xinqun Zhu,et al.  Time-varying wind load identification from structural responses , 2005 .

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

[33]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[34]  J. Chen,et al.  Simultaneous identification of structural parameters and input time history from output-only measurements , 2004 .

[35]  Erin Santini-Bell,et al.  A Two‐Step Model Updating Algorithm for Parameter Identification of Linear Elastic Damped Structures , 2013, Comput. Aided Civ. Infrastructure Eng..

[36]  Guido De Roeck,et al.  REFERENCE-BASED STOCHASTIC SUBSPACE IDENTIFICATION FOR OUTPUT-ONLY MODAL ANALYSIS , 1999 .

[37]  Filippo Ubertini,et al.  Wind Analysis of a Suspension Bridge: Identification and Finite-Element Model Simulation , 2011 .

[38]  S. S. Law,et al.  Identification of system parameters and input force from output only , 2007 .

[39]  G. Golub,et al.  Generalized cross-validation for large scale problems , 1997 .

[40]  Enrique F. Castillo,et al.  Application of Observability Techniques to Structural System Identification , 2013, Comput. Aided Civ. Infrastructure Eng..

[41]  Sankaran Mahadevan,et al.  Bayesian wavelet packet denoising for structural system identification , 2007 .

[42]  Hojjat Adeli,et al.  Signal Processing Techniques for Vibration-Based Health Monitoring of Smart Structures , 2016 .

[43]  Raimondo Betti,et al.  Identification of structural models using a modified Artificial Bee Colony algorithm , 2013 .

[44]  Maria Q. Feng,et al.  Simultaneous identification of bridge structural parameters and vehicle loads , 2015 .

[45]  Jann N. Yang,et al.  Sequential non-linear least-square estimation for damage identification of structures with unknown inputs and unknown outputs , 2007 .

[46]  Lambros S. Katafygiotis,et al.  Model updating using noisy response measurements without knowledge of the input spectrum , 2005 .

[47]  Hojjat Adeli,et al.  Self-constructing wavelet neural network algorithm for nonlinear control of large structures , 2015, Eng. Appl. Artif. Intell..

[48]  Raimondo Betti,et al.  Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm , 2013 .

[49]  Maria Q. Feng,et al.  Modeling of Traffic Excitation for System Identification of Bridge Structures , 2006, Comput. Aided Civ. Infrastructure Eng..

[50]  Vincenzo Gattulli,et al.  Output‐Only Identification and Model Updating by Dynamic Testing in Unfavorable Conditions of a Seismically Damaged Building , 2014, Comput. Aided Civ. Infrastructure Eng..

[51]  Raimondo Betti,et al.  A Hybrid Optimization Algorithm with Bayesian Inference for Probabilistic Model Updating , 2015, Comput. Aided Civ. Infrastructure Eng..

[52]  Ka-Veng Yuen,et al.  Peak Ground Acceleration Estimation by Linear and Nonlinear Models with Reduced Order Monte Carlo Simulation , 2010, Comput. Aided Civ. Infrastructure Eng..

[53]  C. Fuggini,et al.  Combining Genetic Algorithms with a Meso‐Scale Approach for System Identification of a Smart Polymeric Textile , 2013, Comput. Aided Civ. Infrastructure Eng..

[54]  H. Adeli,et al.  Synchrosqueezed wavelet transform-fractality model for locating, detecting, and quantifying damage in smart highrise building structures , 2015 .