In this study, a method based on the substructure method, element relative modal strain energy, and improved whale optimization algorithm (LWOA) is implemented to identify structural damage. In this method, firstly, the global structure is decomposed into several substructures based on the substructure method, which greatly reduces the size of the model to be analyzed and improves the efficiency of analysis. Secondly, LWOA algorithm is used to calculate the severity of structural damage, Levy-flight is introduced to improve the performance of the whale optimization algorithm and solve the convergence problem of the optimization algorithm. The performance of the improved WOA algorithm is verified by four benchmarks. Then, the objective function is constructed by using the element relative mode strain energy index, which is mainly based on the change of the ratio of the element modal strain energy before and after structural damage to the modal strain energy of the global structure as the damage index. Finally, three examples, a numerical plane frame, an experimental simply supported beam, and an ASCE Benchmark frame, are used to identify the assumed damage under different conditions using the proposed method. It is found that the element relative modal strain energy near the damage location changes greatly after structural damage occurs, while that of the element relatively far away from the damaged element area is less affected. The results show that the method can accurately identify the exact location and severity of damage in different structures, which can effectively improve the efficiency of damage identification.

在这项研究中，基于子结构方法，单元相对模态应变能和改进的鲸鱼优化算法（LWOA）的方法被用来识别结构损伤。在这种方法中，首先，基于子结构方法将全局结构分解为几个子结构，从而大大减小了待分析模型的尺寸，提高了分析效率。其次，采用LWOA算法计算结构破坏的严重程度，引入征航来提高鲸鱼优化算法的性能，解决了优化算法的收敛性问题。改进的WOA算法的性能通过四个基准进行了验证。然后，使用单元相对模式应变能指数构造目标函数，这主要是基于结构破坏前后的单元模态应变能与整体结构的模态应变能之比的变化作为破坏指标。最后，使用所提出的方法，使用三个示例，一个数值平面框架，一个实验性简单支撑梁和一个ASCE基准框架，来识别在不同条件下的假定损伤。发现在结构损伤发生后，损伤位置附近的单元相对模态应变能发生很大变化，而相对远离损伤单元区域的单元的相对模态应变能受到的影响较小。结果表明，该方法可以准确识别出不同结构中损伤的确切位置和严重程度，可以有效提高损伤识别的效率。