基于Wilson-θ显式算法的动载荷快速定位及重建方法

Dynamic load fast localization and reconstruction based on the Wilson-θexplicit algorithm

通过将Wilson-θ数值算法转变为一种等效的显式表达式,由此建立了一种基于Wilson-θ显式算法的动载荷识别方法。在选取合适的参数θ值以后,该算法是无条件稳定的,并且避免了以往隐式识别算法中由于递推计算产生误差累积导致识别结果严重发散的问题。通过引入响应系数矩阵,该显式算法可以灵活地选取响应类型用于载荷识别计算。同时结合分离变量方法,将载荷位置信息从建立的模型矩阵中提取出来,由此减少矩阵求逆的次数,提高载荷定位计算的效率。结合简支梁的仿真算例与试验测试对该载荷识别方法进行验证。研究结果表明,基于Wilson-θ显式算法的动载荷快速定位及重建方法能够有效地识别得到载荷位置及相应的时间历程。相对于传统载荷识别方法,该方法计算结果的准确性更好,且运算效率更高。

By transforming the Wilson-θnumerical algorithm into an equivalent explicit expression,a dynamic load identification method based on the Wilson-θexplicit algorithm was established.It is shown that the algorithm is unconditionally stable when the appropriate parameterθis selected,and it can avoid the problem that the identified results may diverge seriously due to the error accumulation caused by recursive calculation in previous implicit identification algorithms.By introducing the response coefficient matrix,the explicit algorithm can flexibly select response types for load identification calculation.At the same time,combined with the variable separation method,the load location information can be extracted from the established model matrix,so as to reduce the times of matrix inversion and improve the efficiency of load localization.The load identification method was verified by simulation examples and experimental tests of a simply supported beam.The results show that the dynamic load fast localization and reconstruction method based on the Wilson-θexplicit algorithm can effectively identify the load position and the corresponding time history.Compared with the traditional load identification method,the method has higher accuracy and faster operation efficiency.