Identification of nonlinear restoring force and dynamic loadings provides critical information for post-event damage diagnosis of structures. Due to high complexity and individuality of structural nonlinearities, it is difficult to provide an exact parametric mathematical model in advance to describe the nonlinear behavior of a structural member or a substructure under strong dynamic loadings in practice. Moreover, external dynamic loading applied to an engineering structure is usually unknown and only acceleration responses at limited degrees of freedom of the structure are available for identification. In this study, a nonparametric nonlinear restoring force and excitation identification approach combining the Legendre polynomial model and extended Kalman filter with unknown input is proposed using limited acceleration measurements fused with limited displacement measurements. Then, the performance of the proposed approach is first illustrated via numerical simulation with multi-degree-of-freedom frame structures equipped with magnetorheological dampers mimicking nonlinearity under direct dynamic excitation or base excitation using noise-polluted measurements. Finally, a dynamic experimental study on a four-story steel frame model equipped with a magnetorheological damper is carried out and dynamic response measurement is employed to validate the effectiveness of the proposed method by comparing the identified dynamic responses, nonlinear restoring force, and excitation force with the test measurements. The convergence and the effect of initial estimation errors of structural parameters on the final identification results are investigated. The effect of data fusion on improving the identification accuracy is also investigated.

非线性恢复力和动态载荷的识别为结构的事后损坏诊断提供了关键信息。由于结构非线性的高度复杂性和独特性，在实践中很难预先提供精确的参数数学模型来描述结构构件或子结构在强动态载荷下的非线性行为。此外，通常不知道施加到工程结构上的外部动态载荷，并且只有结构的有限自由度下的加速度响应才可用于识别。在这项研究中，提出了一种使用有限加速度测量和有限位移测量相结合的，结合了勒让德多项式模型和扩展卡尔曼滤波器的未知输入的非参数非线性恢复力和激励识别方法。然后，首先通过数值模拟说明了所提出方法的性能，该数值模拟配备了具有磁流变阻尼器的多自由度框架结构，该磁流变阻尼器模仿了直接动态激励或基础激励下使用噪声污染测量的非线性。最后，对装有磁流变阻尼器的四层钢框架模型进行了动态实验研究，并通过比较识别出的动态响应，非线性恢复力，通过动态响应测量来验证该方法的有效性。和激振力随测试测量。研究了结构参数的初始估计误差的收敛性和对最终识别结果的影响。还研究了数据融合对提高识别精度的影响。