Abstract As a typical inverse problem, impact force identification tends to be a challenge owing to its ill-posedness. Recently, the sparse characteristic of the impact force in time domain are taken into consideration to convert the ill-posed problem into a sparse recovery task. The classic way to obtain sparse approximate solutions of impact force is to use the L1-norm regularization. However, underestimating the exact solution inevitably happens when applying the L1-norm regularization to impact force identification. In this paper, a novel sparse regularization method with generalized minimax-concave (GMC) penalty is proposed to deal with the impact force identification problem. Even if the GMC penalty turns out to be a nonconvex regularizer to promote sparsity in the sparse estimation, it retains the convexity of the sparsity-regularized least squares cost function and the global optimal solution can be found by convex optimization. Additionally, an approach to adaptively set regularization parameters is presented. Finally, simulations and experiments are conducted to verify the performances of the proposed method, and the results are compared with those of the L1-norm regularization method. Results demonstrate that the nonconvex sparse regularization based on GMC can produce more accurate estimations for impact force identification.

中文翻译：

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通过具有广义极小极大-凹面惩罚的稀疏正则化进行冲击力识别

摘要 作为一个典型的逆问题，冲击力识别由于其不适定性而成为一个挑战。最近，考虑了时域冲击力的稀疏特性，将不适定问题转换为稀疏恢复任务。获得冲击力稀疏近似解的经典方法是使用 L1 范数正则化。然而，在将 L1 范数正则化应用于冲击力识别时，不可避免地会出现低估精确解的情况。在本文中，提出了一种具有广义极小极大凹（GMC）惩罚的新型稀疏正则化方法来处理冲击力识别问题。即使 GMC 惩罚被证明是一个非凸正则化器，以促进稀疏估计中的稀疏性，它保留了稀疏正则化最小二乘代价函数的凸性，并且可以通过凸优化找到全局最优解。此外，还提出了一种自适应设置正则化参数的方法。最后，通过仿真和实验验证了所提出方法的性能，并将结果与​​L1范数正则化方法的结果进行了比较。结果表明，基于 GMC 的非凸稀疏正则化可以为冲击力识别产生更准确的估计。并将结果与​​L1范数正则化方法的结果进行比较。结果表明，基于 GMC 的非凸稀疏正则化可以为冲击力识别产生更准确的估计。并将结果与​​L1范数正则化方法的结果进行比较。结果表明，基于 GMC 的非凸稀疏正则化可以为冲击力识别产生更准确的估计。