شناسايي مشخصه و تشخيص آسيب در پايه هاي بتني پل ها با استفاده از توابع زمان- بسامد مربعي و روش جديد تفاضل ماتريسي اصلاح‌شده

SYSTEM IDENTIFICATION AND DAMAGE DETECTION OF BRIDGE CONCRETE PIERS, USING TIME-FREQUENCY REPRESENTATION AND A NEW MODIFIED MATRIX SUBTRACTION METHOD

در اين تحقيق روش اصلاح‌شده‌ي تفاضل ماتريسي با استفاده از توابع زمان- بسامد مربعي براي شناسايي آسيب در پايه‌ي پل‌ها و محل آن پيشنهاد شده است. براي تاييد روش پيشنهادي از مدل پل قطور به ‌طول 448 متر و براي پردازش سيگنال‌هاي پاسخ لرزه‌يي پل‌ها از توابع زمان- بسامد شامل طيف تبديل فوريه‌ي زمان كوتاه، طيف تبديل موجك، توزيع‌هاي ويگنر- ويل، چوي- ويليامز، شبه ويگنر- ويل هموارشده، و تداخلي كاهش‌يافته استفاده شده است و تابع زمان-بسامد تداخلي كاهش‌يافته به‌منزله‌ي تابع مطلوب براي پردازش سيگنال‌هاي پاسخ لرزه ‌يي پل‌ها شناسايي شده است. پلان‌هاي زمان- بسامد محاسبه و مشخصه هاي ديناميكي سيستم استخراج شده است. روش پيشنهادي براساس پردازش سيگنال‌هاي لرزه‌يي خروجي پايه‌ريزي شده است، و لذا از مزيت‌هاي اين روش بي‌نيازي به تعريف مدل تحليلي و اندازه‌گيري نيروي ورودي و همچنين بي‌نيازي به تحريك اجباري هارمونيك پل پس از وقوع زلزله براي تشخيص آسيب لرزه ‌يي است.

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 [23], 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 representation 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.