Application of stochastic subspace identification for stay cables with an alternative stabilization diagram and hierarchical sifting process

Summary The modal parameters of numerous modes for a stay cable are usually required in engineering practice. The application of conventional stochastic subspace identification techniques without delicate cautions, however, has been found to be unsuccessful in this case. Aiming to attack such a difficulty, this study establishes a new methodology based on the covariance type of stochastic subspace identification for extensively identifying the modal parameters of a stay cable. Several details of choosing the parameters in performing stochastic subspace identification are first discussed. An important discovery is that the lower limit for setting the time lag parameter can be decided by the ratio of the fundamental period of cable to the sampling time increment for a valid identification with the conventional stabilization diagram. Inspired by the aforementioned criterion, an alternative stabilization diagram is further proposed to more conveniently distinguish stable modal parameters of cable. A hierarchical sifting process including three stages is then developed to systematically and automatically extract reliable modal parameters from the alternative stabilization diagram. Demonstrated by analyzing the ambient vibration measurements for three stay cables of Chi-Lu Bridge, the feasibility of this new approach is verified with successfully obtaining the modal frequencies, damping ratios, and mode shape ratios for almost all the cable modes in the examined frequency range. Another interesting finding is that the modal frequencies and damping ratios of bridge deck can also be effectively identified from the ambient vibration signals of cable. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  F. Javier Cara,et al.  An approach to operational modal analysis using the expectation maximization algorithm , 2012 .

[2]  Maurice Goursat,et al.  STOCHASTIC SUBSPACE-BASED STRUCTURAL IDENTIFICATION AND DAMAGE DETECTION AND LOCALISATION—APPLICATION TO THE Z24 BRIDGE BENCHMARK , 2003 .

[3]  Stefanie Reese,et al.  Experimental investigation of damage evolution by data-driven stochastic subspace identification and iterative finite element model updating , 2007 .

[4]  Jean-Claude Golinval,et al.  Null subspace-based damage detection of structures using vibration measurements , 2006 .

[5]  Wen-Hwa Wu,et al.  Determination of stay cable force based on effective vibration length accurately estimated from multiple measurements , 2013 .

[6]  Rune Brincker,et al.  Modal identification of output-only systems using frequency domain decomposition , 2001 .

[7]  E. Parloo,et al.  Maximum likelihood identification of non-stationary operational data , 2003 .

[8]  James M. W. Brownjohn,et al.  Fuzzy Clustering of Stability Diagrams for Vibration-Based Structural Health Monitoring , 2008, Comput. Aided Civ. Infrastructure Eng..

[9]  Pelin Gundes Bakir.  Automation of the stabilization diagrams for subspace based system identification , 2011, Expert Syst. Appl..

[10]  B. Dickinson,et al.  Canonical matrix fraction and state-space descriptions for deterministic and stochastic linear systems , 1974 .

[11]  Rik Pintelon,et al.  Uncertainty bounds on modal parameters obtained from stochastic subspace identification , 2008 .

[12]  Guido De Roeck,et al.  Modal contribution and state space order selection in operational modal analysis , 2013 .

[13]  Michel Verhaegen,et al.  Identification of the deterministic part of MIMO state space models given in innovations form from input-output data , 1994, Autom..

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

[15]  Hilmi Luş,et al.  Ambient Vibration Analysis with Subspace Methods and Automated Mode Selection: Case Studies , 2008 .

[16]  Bart Peeters,et al.  System identification and damage detection in civil engineering , 2000 .

[17]  Jer-Nan Juang,et al.  An eigensystem realization algorithm for modal parameter identification and model reduction. [control systems design for large space structures] , 1985 .

[18]  Jan C. Willems,et al.  From time series to linear system - Part II. Exact modelling , 1986, Autom..

[19]  G. De Roeck,et al.  Vibration based Structural Health Monitoring using output-only measurements under changing environment , 2008 .

[20]  Jan C. Willems,et al.  From time series to linear system - Part I. Finite dimensional linear time invariant systems , 1986, Autom..

[21]  Filipe Magalhães,et al.  Damping Estimation Using Free Decays and Ambient Vibration Tests , 2010 .

[22]  P. Van Overschee,et al.  Subspace algorithms for the stochastic identification problem , 1991 .

[23]  Guido De Roeck,et al.  Fully automated (operational) modal analysis , 2012 .

[24]  M. Scionti,et al.  Stabilisation diagrams: Pole identification using fuzzy clustering techniques , 2005, Adv. Eng. Softw..

[25]  Filipe Magalhães,et al.  LabVIEW toolkits for output-only modal identification and long-term dynamic structural monitoring , 2010 .

[26]  Bart De Moor,et al.  Subspace algorithms for the stochastic identification problem, , 1993, Autom..

[27]  A. Swindlehurst,et al.  Subspace-based signal analysis using singular value decomposition , 1993, Proc. IEEE.

[28]  H. Akaike.  Markovian Representation of Stochastic Processes by Canonical Variables , 1975 .

[29]  Chin-Hsiung Loh,et al.  Input force identification: Application to soil–pile interaction , 2009 .

[30]  Matthew J. Whelan,et al.  In-Service Diagnostics of a Highway Bridge from a Progressive Damage Case Study , 2010 .

[31]  Bhaskar D. Rao,et al.  Model based processing of signals: a state space approach , 1992, Proc. IEEE.

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

[33]  Bart De Moor,et al.  N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems , 1994, Autom..

[34]  Chin-Hsiung Loh,et al.  SSA-based stochastic subspace identification of structures from output-only vibration measurements , 2012 .

[35]  Carmelo Gentile,et al.  Automated modal identification in operational conditions and its application to bridges , 2013 .

[36]  Jan C. Willems,et al.  From time series to linear system - Part III: Approximate modelling , 1987, Autom..

[37]  Wen-Hwa Wu,et al.  A Multiple Random Decrement Method for Modal Parameter Identification of Stay Cables Based on Ambient Vibration Signals , 2012 .