Unknown initial conditions can affect the identified accuracy of dynamic forces. Direct measurement of initial conditions is relatively difficult. This study proposes a sparse regularization–based method for identifying forces considering influences of unknown initial conditions. The initial conditions are embedded in a classical governing equation of force identification. The key idea is to introduce a concept of concomitant mapping matrix for reasonably expressing the initial conditions. First, a dictionary is introduced for expanding the dynamic forces. Then, the concomitant mapping matrix is formulated by using free vibrating responses, which correspond to structural responses happening after the structure is subjected to each atom of the force dictionary. A sparse regularization strategy is applied for solving the ill-conditioned equation. After that, the problem of force identification is converted into an optimization problem, and it can be solved by using a one-step strategy. Numerical simulations are carried out for verifying the feasibility and effectiveness of the proposed method. Illustrated results clearly show the applicability and robustness of the proposed method for dealing with force reconstruction and moving force identification.

未知的初始条件会影响所确定的动态力的准确性。直接测量初始条件相对困难。这项研究提出了一种基于稀疏正则化的方法，该方法用于在考虑未知初始条件影响的情况下识别力。初始条件被嵌入到力识别的经典控制方程中。关键思想是引入用于合理表达初始条件的伴随映射矩阵的概念。首先，引入字典以扩展动态力。然后，通过使用自由振动响应来制定伴随的映射矩阵，自由振动响应对应于结构经受力字典的每个原子之后发生的结构响应。稀疏正则化策略用于求解病态方程。之后，将力识别问题转换为优化问题，并且可以通过使用一步策略来解决。通过数值模拟验证了所提方法的可行性和有效性。图示结果清楚地表明了所提出的方法用于处理力重建和运动力识别的适用性和鲁棒性。