رديابي مستقيم و هندسي اعضا قطري ماتريس نرمي تعميم يافته با كمك روند بهينه يابي براي شناسايي آسيب در سازه ها

Direct and geometrical tracing of the diagonal members of the generalized flexibility matrix via optimization-based approach for structural damage identification

در اين نوشتار، دو روش جديد جهت تشخيص آسيب در سازه ها با كمك اطلاعات مودال ارايه شده است. اساس روش ها بر پايه‌ي تعريف مسيله به صورت يك مسيله‌ي بهينه يابي استوار است. ماتريس نرمي تعميم يافته، به عنوان عامل اصلي ايجاد ارتباط بين اطلاعات مودال و آسيب رخداده در سازه ها معرفي شده است. سپس دو تابع هدف پيشنهاد شده است، كه به ترتيب بر پايه‌ي تطابق نقطه ‌يي عناصر قطري ماتريس نرمي تعميم يافته و سنجش ميزان انطباق هندسي بردار متشكل از اين عناصر استوار هستند. در ادامه، مسيله‌ي بهينه يابي با كمك الگوريتم بهينه يابي رقابت استعماري حل شده است. كارآيي توابع پيشنهادي با مطالعه ي الگوهاي آسيبي مختلف روي 3 مثال عددي از سازه هاي مهندسي بررسي و چالش هايي نظير تاثيرات نوفه ها مطالعه شده است. همچنين مطالعاتي پيرامون دقت توابع هدف پيشنهادي و ميزان هم گرايي الگوريتم بهينه يابي در اجراهاي مختلف صورت پذيرفته و مقايسه يي بين روش هاي پيشنهادي و يكي از روش هاي موجود انجام شده است. نتايج به‌دست‌آمده بيان گر دقت بالا و كارآيي بهتر تابع هدف دوم هستند.

This paper presents two effective methods for damage identification in engineering structures by defining damage prognosis problem as an optimization problem. Both of the presented methods are based on the diagonal members of the Generalized Flexibility Matrix (GFMt). In the first method, the objective function is formulated by means of a direct fitting data strategy via inspecting the diagonal members of the GFMt. However, the second cost function is defined by searching the correlation of the diagonal members of the GFMt through Modal Assurance Criterion (MAC). In the proposed methods, we employ the Imperialist Competitive Optimization Algorithm (ICOA) to solve optimization problem. This algorithm is inspired by a socio-political event and applied to a number of scientific problems for finding the optimal solution. The applicability of the presented methods is investigated by studying three numerical examples of engineering structures, namely a three-story steel frame, a plane truss with fifteen elements, and a simply supported beam. Different damage patterns are considered and several challenges, such as the impacts of random noise on the measured modal data and the number of available modal data for creating GFMt, are studied. All of the obtained results emphasize the robustness and good performance of the presented methods in damage localization and quantification in the engineering structures. As a result, the comparison between the presented cost functions concluded that the second objective function can be more effective than the first one in terms of an accurate estimation of damage in the real applications. In addition, some studies are conducted for evaluating the robustness of the ICOA in solving optimization problem by running it five times for a special damage scenario. Under the same conditions, the problem is solved by using Genetic Algorithm (GA) for drawing a conclusion about the performance of the optimization procedures in reaching the global minimum point. Although the ICOA reaches to the general optimum point, the GA is arrested by local minimum points in a number of runs. So, it can be concluded that the ICOA is more effective than the GA in searching a complex domain for finding the optimal solution.