Identification of shear buildings using an instrumental variable method and linear integral filters

Abstract This paper develops a method for estimating the parameters of a seismically excited building. Acceleration measurements of the ground and of the building floors, containing offsets and noise, are used for identification purposes. The proposed scheme estimates the complete model of the building if all the floors are equipped with accelerometers. Moreover, it also estimates a reduced model of the structure if only some floors are instrumented. The methodology is based on the combined use of the Instrumental Variable method and Linear Integral Filters. The Instrumental Variable method employs as instrument an auxiliary model of the structure, and it is able to directly identify the continuous-time structure model using discrete-time data without resorting on model transformations from continuous-time to discrete-time, and vice-versa. Using Linear Integral Filters allows obtaining a linear in the parameters expression that depends only on acceleration measurements suitable for parameter identification purposes. These filters eliminate measurement offsets and attenuate high-frequency measurement noise. The above features together with the use of the Instrumental variable method reduce the likelihood of biased parameter estimates. Experiments on a testbed employing a reduced-scale five-story structure allow comparing the results obtained using the Instrumental Variable method and those produced by the standard Least Squares method.

[1]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[2]  George A. Bekey,et al.  Non‐parametric identification of a class of nonlinear multidegree dynamic systems , 1982 .

[3]  S. Lyshevski.  Nano- and Micro-Electromechanical Systems: Fundamentals of Nano- and Microengineering, Second Edition , 2005 .

[4]  Richard W. Longman,et al.  Identification of linear structural systems using earthquake‐induced vibration data , 1999 .

[5]  N. Huang,et al.  System identification of linear structures based on Hilbert–Huang spectral analysis. Part 1: normal modes , 2003 .

[6]  C. Manohar,et al.  New forms of extended Kalman filter via transversal linearization and applications to structural system identification , 2007 .

[7]  M. Hoshiya,et al.  Structural Identification by Extended Kalman Filter , 1984 .

[8]  Reza Tarinejad,et al.  Modal identification of structures by a novel approach based on FDD-wavelet method , 2014 .

[9]  P. Young.  An instrumental variable method for real-time identification of a noisy process , 1970 .

[10]  J. Marsden,et al.  Elementary classical analysis , 1974 .

[11]  Shih Chieh Lo,et al.  Application of the on‐line recursive least‐squares method to perform structural damage assessment , 2011 .

[12]  L. Alvarez-Icaza,et al.  A real-time estimation scheme for buildings with intelligent dissipation devices☆ , 2007 .

[13]  Erik A. Johnson,et al.  Substructure identification for shear structures I: Substructure identification method , 2013 .

[14]  Rosario Ceravolo,et al.  Comparison of restoring force models for the identification of structures with hysteresis and degradation , 2013 .

[15]  Genda Chen,et al.  Analytical mode decomposition with Hilbert transform for modal parameter identification of buildings under ambient vibration , 2014 .

[16]  R. Andrew Swartz,et al.  Output-only cyclo-stationary linear-parameter time-varying stochastic subspace identification method for rotating machinery and spinning structures , 2015 .

[17]  Henri P. Gavin,et al.  Drift-free integrators , 1998 .

[18]  M. Phan,et al.  Identification of observer/Kalman filter Markov parameters: Theory and experiments , 1993 .

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

[20]  W. C. Su,et al.  Identification of modal parameters of a time invariant linear system by continuous wavelet transformation , 2007 .

[21]  Fereidoun Amini,et al.  Underdetermined blind modal identification of structures by earthquake and ambient vibration measurements via sparse component analysis , 2016 .

[22]  Sriram Narasimhan,et al.  Extended Kalman filter for modal identification of structures equipped with a pendulum tuned mass damper , 2014 .

[23]  N. Sinha,et al.  Identification of Continuous-Time Systems: Methodology and Computer Implementation , 1991 .

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

[25]  J. Kayal.  Microearthquake Seismology and Seismotectonics of South Asia , 2008 .

[26]  Alexandre Janot,et al.  An instrumental variable approach for rigid industrial robots identification , 2014 .

[27]  S. Sagara,et al.  Recursive identification of transfer function matrix in continuous systems via linear integral filter , 1989 .

[28]  Rolf Isermann,et al.  Identification of Dynamic Systems , 2011 .

[29]  G. Favier,et al.  Numerical integration approach to on-line identification of continuous-time systems , 1990 .

[30]  Swarup Mahato,et al.  Adaptive HHT (AHHT) based modal parameter estimation from limited measurements of an RC‐framed building under multi‐component earthquake excitations , 2015 .

[31]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[32]  Erik A. Johnson,et al.  Controlled substructure identification for shear structures , 2014 .

[33]  Wook Hyun Kwon,et al.  A receding horizon Kalman FIR filter for discrete time-invariant systems , 1999, IEEE Trans. Autom. Control..

[34]  I. Takewaki,et al.  Stiffness-damping simultaneous identification using limited earthquake records , 2000 .

[35]  Jann N. Yang,et al.  Sequential non-linear least-square estimation for damage identification of structures , 2006 .

[36]  Dongyu Zhang,et al.  Substructure identification for shear structures: cross-power spectral density method , 2012 .

[37]  Erdal Şafak.  Identification of Linear Structures Using Discrete‐Time Filters , 1991 .

[38]  Richard W. Longman,et al.  Output‐only observer/Kalman filter identification (O3KID) , 2015 .

[39]  Firdaus E. Udwadia,et al.  Uniqueness of Damping and Stiffness Distributions in the Identification of Soil and Structural Systems , 1978 .