Multi-objective optimization-inspired set theory-based regularization approach for force reconstruction with bounded uncertainties

In force reconstruction, multi-source incomplete information makes it difficult for traditional methods to model and solve the problem accurately, especially with noise or measurement errors. Inspired by multi-objective optimization, this paper proposes a novel set theory-based regularization approach (STR) to enhance adaptability to uncertainties and improve reconstruction accuracy and robustness. The nominal force inversion is constituted and then extended into the interval uncertainty framework, and an effective orthogonal sampling-based interval prediction method is proposed to analyze the coupled effect of force inversion and uncertainty propagation. Once the uncertainty level of the complex structure is known, this prediction method can accurately and quickly estimate the fluctuation bound of the identified force. Enlightened by the completely same logic between the regularization method used in force inversion and multi-objective optimization problem, namely, simultaneously satisfying the norm minimization of the solution and the residual parameter, this study develops a novel multi-objective optimization-inspired set theory-based regularization parameter selection method. This method incorporates the interval dominance relationship to select the most competitive regularization parameter under interval uncertainties. Therefore, an accurate reconstuction framework with bounded uncertainties is finally proposed and verified by two numerical examples.