Research Papers

Unit Impulse Response Estimation for Structural Damage Detection Under Planar Multiple Excitations

[+] Author and Article Information
Siu-seong Law

e-mail: cesslaw@polyu.edu.hk

Jian-fu Lin

Research Assistant
Department of Civil and
Environmental Engineering,
Hong Kong Polytechnic University,
Hunghom, Kowloon,
Hong Kong, China

1Corresponding author.

Manuscript received August 24, 2012; final manuscript received August 29, 2013; accepted manuscript posted September 3, 2013; published online October 16, 2013. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 81(2), 021015 (Oct 16, 2013) (15 pages) Paper No: JAM-12-1414; doi: 10.1115/1.4025320 History: Received August 24, 2012; Revised August 29, 2013; Accepted September 03, 2013

An unit impulse response (UIR) function is an inherent system function that depends only on the structure and the locations of excitation. When the structure is under general excitation, the effect can be obtained via Duhamel integral between the UIR function and the excitation. The possibility of the UIR function as a damage detection index under general excitation is studied here. However, the UIRs from multiple excitations will contribute to the identification equation together. Therefore, the estimation of UIRs will most probably become underdetermined with a limited number of measurements leading to an incorrect or nonfeasible solution of the inverse problem. This report addresses this problem by developing a transformation between the UIRs to facilitate the conversion of a multiple excitations problem into an equivalent single excitation problem. However, the method is limited to planar problems and the reference response is confined to those with larger vibration amplitude. The extraction of the UIR via Tikhonov regularization from the measured acceleration is then described. Numerical studies with a 31-bar plane truss structure are used to illustrate the performances of the proposed approach with different damage scenarios with or without noise effect and model errors. The stability of the UIR estimation with different periods of measured data is also studied. Moreover, this paper studies the effect of using a reduced number of sensors and an increased sampling rate. Results show that the regularization-based approach with the new transformation matrix is accurate and effective for the inverse solution and it is robust to measurement noise in the damage detection process.

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Fig. 1

Thirty-one planar truss structure

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Fig. 2

Two sets of seismic excitation data

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Fig. 3

Comparison of estimated UIR at nodes 5 and 12 with 5% noise

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Fig. 4

Stability check in different time periods

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Fig. 5

Identified results without and with noise using different time periods

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Fig. 6

Comparison of averaged identified results under difference noise levels

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Fig. 7

Averaged identified results under a different level of noise and model error

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Fig. 8

Averaged identified results using five sensors with 5% noise

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Fig. 9

A space steel cantilever mast structure

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Fig. 10

Unit impulse acceleration response excited in two perpendicularly horizontal directions



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