时域内动态载荷识别的径向基形函数法

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In order to reduce the ill--condition arising from the inverse problem of load reconstruc- tion,and restructure the time history of dynamic load stably,a new method which named radial basis shape function method was presented. Through discretizing the dynamic load into small elements in the time domain,the shape function was constructed in each time element by RBF interpolation. In this way,the forward model of load reconstruction was established. Then based on this method,the time history of dynamic load was reconstructed. This method can reduce the scale of the nucleus matrix and whereby obtain a well--conditioned inverse problem,realize the dynamic load identification effectively and stably under bigger time step and the measurement noise in the load reconstruction.为了减小载荷识别过程中的不适定性，稳定地实现动态载荷的时域重构，提出了基于径向基形函数的时域动态载荷识别方法。在离散化系统动力响应卷积关系式的基础上，将载荷在时间域内划分单元，采用径向基函数构造载荷形函数，并在整个时间域内进行组装，得到整体形函数响应矩阵，建立载荷识别的正向模型；在此基础上，利用正则化方法实现动态载荷识别。算例表明，该方法能够有效减小核矩阵的规模，改善核矩阵的病态性，在采样时间步长较大且响应存在测量噪声的情况下，可保证动态载荷反演的稳定性和精确性。