Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm

Cara Cañas, Francisco Javier and Carpio Huertas, Jaime and Juan Ruiz, Jesús and Alarcón Álvarez, Enrique (2010). Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm. In: "10th. International Conference on Computational Structures Technology", 14/09/2010-17/09/2010, Valencia, España. ISBN 978-1-905088-38-6.

Description

Title: Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm
Author/s:
  • Cara Cañas, Francisco Javier
  • Carpio Huertas, Jaime
  • Juan Ruiz, Jesús
  • Alarcón Álvarez, Enrique
Item Type: Presentation at Congress or Conference (Article)
Event Title: 10th. International Conference on Computational Structures Technology
Event Dates: 14/09/2010-17/09/2010
Event Location: Valencia, España
Title of Book: Proceedings of the Tenth International Conference on Computational Structures Technology
Date: 2010
ISBN: 978-1-905088-38-6
Subjects:
Freetext Keywords: System identification in structures ; State space models ; Kalman filter ; Stochastic subspace methods ; Modal analysis ; Benchmark problems.
Faculty: E.T.S.I. Industriales (UPM)
Department: Ingeniería de Organización, Administración de Empresas y Estadística
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method. There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI)method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail. The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters.

More information

Item ID: 16659
DC Identifier: http://oa.upm.es/16659/
OAI Identifier: oai:oa.upm.es:16659
Official URL: http://www.ctresources.info/ccp/paper.html?id=5773
Deposited by: Biblioteca ETSI Industriales
Deposited on: 31 Jul 2013 08:27
Last Modified: 21 Apr 2016 17:01
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