Damage Identification of Bridge Based on Chebyshev Polynomial Fitting and Fuzzy Logic without Considering Baseline Model Parameters

Shock and Vibration, Jan 2015

The paper presents an effective approach for damage identification of bridge based on Chebyshev polynomial fitting and fuzzy logic systems without considering baseline model data. The modal curvature of damaged bridge can be obtained through central difference approximation based on displacement modal shape. Depending on the modal curvature of damaged structure, Chebyshev polynomial fitting is applied to acquire the curvature of undamaged one without considering baseline parameters. Therefore, modal curvature difference can be derived and used for damage localizing. Subsequently, the normalized modal curvature difference is treated as input variable of fuzzy logic systems for damage condition assessment. Numerical simulation on a simply supported bridge was carried out to demonstrate the feasibility of the proposed method.

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Damage Identification of Bridge Based on Chebyshev Polynomial Fitting and Fuzzy Logic without Considering Baseline Model Parameters

Damage Identification of Bridge Based on Chebyshev Polynomial Fitting and Fuzzy Logic without Considering Baseline Model Parameters Yu-Bo Jiao, Han-Bing Liu, Yong-Chun Cheng, and Ya-Feng Gong Department of Transportation, Jilin University, No. 5988, Renmin Street, Changchun, Jilin 130025, China Received 15 August 2012; Accepted 16 February 2013 Academic Editor: Reza Jazar Copyright © 2015 Yu-Bo Jiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The paper presents an effective approach for damage identification of bridge based on Chebyshev polynomial fitting and fuzzy logic systems without considering baseline model data. The modal curvature of damaged bridge can be obtained through central difference approximation based on displacement modal shape. Depending on the modal curvature of damaged structure, Chebyshev polynomial fitting is applied to acquire the curvature of undamaged one without considering baseline parameters. Therefore, modal curvature difference can be derived and used for damage localizing. Subsequently, the normalized modal curvature difference is treated as input variable of fuzzy logic systems for damage condition assessment. Numerical simulation on a simply supported bridge was carried out to demonstrate the feasibility of the proposed method. 1. Introduction Bridge structures have endured progressive deterioration due to vehicle load and aging of material under the effect of external environment. In addition, the frequent occurrence of natural disasters could also cause damage and further accelerate the deterioration of bridge condition. Therefore, the damage assessment of bridge has attracted great interest of many researchers [1, 2]. Vibration-based damage identification method has been widely applied in the past few decades [3, 4]. Theoretical background of this method is that modal parameters (frequency, mode shape, etc.) are functions of physical properties (stiffness, mass, etc.) of bridge. Therefore, the changes of modal characteristics can be treated as the damage indicators. The commonly used modal parameters for damage identification include natural frequency, mode shape, and their derivatives, such as mode shape curvature, modal strain energy, and modal flexibility [5–9]. Among these modal characteristics, natural frequency has no relation with measuring positions and can be measured most conveniently and accurately. However, the frequency-based method possesses several apparent drawbacks. For instance, it is inferior sensitive to minor damage, and it is easily affected by environment [10]. Additionally, the simply supported reinforced concrete bridges are spatial symmetric structures. Natural frequency cannot distinguish damage at symmetric locations in these symmetric structures. Comparing with natural frequency, mode shape and its derivatives contain the spatial information with respect to location of damage, and they are found to be better indicators for damage identification. The modal curvature is recognized as a more advanced damage indicator which is calculated from the displacement mode shape and firstly proposed by Pandey et al. [7]. It is found that the absolute changes in the curvature mode shapes between undamaged and damaged structures can effectively locate the damage region for cantilever and simply supported beam model. The changes in the curvature mode shape increase with increasing size of damage. However, this method requires the baseline data from intact structures. This baseline model data can be obtained by finite element simulation. In actual simulation, the accuracy of finite element model is affected by temperature because the elastic modulus of concrete is temperature dependent [11]. However, the modulus of elasticity versus temperature curve for concrete is unclear and complicated [12, 13]. If their relationship is not reasonable to consider, it will lead to incorrect result for damage identification. To avoid this difficulty, several researchers have conducted effective work for damage detection without baseline model data. Ratcliffe [14] proposed a modified Laplacian operator-based method for 1D beam, which determines the damage location through a cubic curve fitting for the modal data obtained only from the damaged structure. Wu and Law [15] proposed a damage localization method based on uniform load surface (ULS) curvature for 2D plates, which can identify the damage using only the modal characteristics of damaged state if a gapped-smoothing technique is applied. Yoon et al. [16] extended the 1D gapped-smoothing method to the 2D gapped smoothing method for the damage identification of plate. And the baseline data of undamaged structure are not needed. Zhong and Oyadiji [17] presented a novel approach for crack detection based on difference between two (...truncated)


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Yu-Bo Jiao, Han-Bing Liu, Yong-Chun Cheng, Ya-Feng Gong. Damage Identification of Bridge Based on Chebyshev Polynomial Fitting and Fuzzy Logic without Considering Baseline Model Parameters, Shock and Vibration, 2015, 2015, DOI: 10.1155/2015/187956