Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

• Published in: Chinese journal of mechanical engineering 2024-07, Vol.37 (1), p.63-19, Article 63
• Main Authors: Wang, Yanan, Chen, Lin, Liu, Junjiang, Qiao, Baijie, He, Weifeng, Chen, Xuefeng
• Format: Article
• Language: English
• Subjects: Aircraft performance; Alternating direction method of multipliers; Composite structures; Electrical Machines and Networks; Electronics and Microelectronics; Engineering; Engineering Thermodynamics; Heat and Mass Transfer; Identification methods; Impact force identification; Impact loads; Instrumentation; Intelligent Manufacturing Technology; Localization; Machines; Manufacturing; Mechanical Engineering; Non-convex sparse regularization; Original Article; Parameter identification; Parameter sensitivity; Power Electronics; Processes; Proximal operators; Reconstruction; Regularization; Regularization methods; Theoretical and Applied Mechanics
• ISSN: 2192-8258; 1000-9345; 2192-8258
• DOI: 10.1186/s10033-024-01044-2

In practice, simultaneous impact localization and time history reconstruction can hardly be achieved, due to the ill-posed and under-determined problems induced by the constrained and harsh measuring conditions. Although ℓ 1 regularization can be used to obtain sparse solutions, it tends to underestimate solution amplitudes as a biased estimator. To address this issue, a novel impact force identification method with ℓ p regularization is proposed in this paper, using the alternating direction method of multipliers (ADMM). By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators, ADMM can address the challenge effectively. To mitigate the sensitivity to regularization parameters, an adaptive regularization parameter is derived based on the K -sparsity strategy. Then, an ADMM-based sparse regularization method is developed, which is capable of handling ℓ p regularization with arbitrary p values using adaptively-updated parameters. The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure. Additionally, an investigation into the optimal p value for achieving high-accuracy solutions via ℓ p regularization is conducted. It turns out that ℓ 0.6 regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic ℓ 1 regularization method. The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.