عنوان مقاله [English]
In this research, a new modified matrix subtraction method is proposed using square time-frequency representations to detect bridge pier damage and its location. The new proposed method is confirmed, using the seismic response of the 448 meter long Ghotour Bridge model, and compared with correlation and
least square distance methods. Time frequency plans of damaged and non-damaged bridge matrix elements are calculated using reduced interference distribution. The difference matrix is calculated by subtraction of corresponding matrix elements. The possibility of an existing damage index is calculated by summation of all elements of difference matrices and then normalizing them with a maximum value. Linear time history analyses and earthquake acceleration records of San Fernando, Loma Prieta and Northridge earthquakes are used for seismic response analysis.
In previous response analyses of the Ghotour Bridge, as stated in reference , the third pier from the left is considered more vulnerable to seismic damage. Therefore, for the purpose of this study, a reduction of thirty percent in the stiffness of that pier is considered, to simulate the seismic damage in the damaged analytical model. It is shown that the proposed method could satisfactorily identify the damage location. For the seismic response of the top of the bridge piers, the maximum error in locating the damage is 6 percent, while, for the seismic response of the middle of the bridge piers, it is 14 percent.
The time-frequency representations used include: the short time Fourier transform spectrum, wavelet transform spectrum, Wigner-Ville Distribution, Choi-Williams distribution, smoothed pseudo Wigner-Ville distribution and
reduced interference distribution, which are finally identified as optimal performance time-frequency epresentation for bridge seismic response signal processing. Reduced interference distribution and Wigner-Ville distribution are both in the Cohen class, but reduced interference distribution methods are more appropriate for processing seismic bridge transient nonstationary response signals. Time-frequency planes have been calculated and dynamic specifications of the system have been estimated.
The proposed algorithm is a seismic output-only method. Therefore, it has the advantage of not needing to define the bridge analytical model and measuring seismic input loading, and, also, not needing to use harmonic forced vibration analysis after earthquake occurrence for bridge seismic damage detection, as is general in some other methods.