Regularized Cubic B-Spline Collocation Method With Modified L-Curve Criterion for Impact Force Identification

Abstract

The time history of the impact force, especially for the peak force, is vital to monitor the performance of mechanical products over the lifetime. However, considering the limitation of sensing technology and inaccessibility of installing, it is always difficult or even impossible to measure the force directly in engineering practice. Therefore, a regularized cubic B-spline collocation (RCBSC) method combined with the modified L-curve criterion (RCBSC-ML) is presented to identify the impact force by easily measurable dynamic response. Because the profile of cubic B-spline is close to that of impact force, a linear combination of cubic B-spline functions is used to approximate the unknown impact force. Then the force identification equation is reformed, wherein the unknown variable changes from impact force vector to weight coefficient vector. Furthermore, the modified L-curve criterion is developed to select the optimal number of collocation points which is the regularization parameter of RCBSC method. Rich simulation studies on a five degree-of-freedoms structure and experimental studies on a simplified artillery test-bed are performed to validate the performance of RCBSC-ML method. The results illustrate that RCBSC-ML method can be used to accurately identify the unknown impact force, and compared with modified generalized cross validation criterion, the presented modified L-curve criterion is more suitable to determine the optimal regularization parameter of RCBSC method. Furthermore, compared with classical Tikhonov regularization method, RCBSC-ML method is more efficient and accurate in impact force identification. INDEX TERMS Cubic B-spline, impact force identification, ill-posed inverse problem, modified L-curve criterion.

A novel strategy for force identification of nonlinear structures

“…Nonlinear parameters are not included in matrix boldBc, and the extended force vector contains only the excitation force. 11,12 Instead of NSI method, the LSI method 38 is applied to estimate new coefficient matrices to obtain a new transfer matrix. Then, the solving method is also TTLS combined with GCV criterion.…”

“…Wang et al 10 proposed a novel hybrid conjugate gradient algorithm to iteratively solve multisource force identification problems, and the identification results showed that the stability, robustness, and computational efficiency of the proposed iterative algorithm were superior to those of the traditional Landweber iteration regularization method. Since the profile of the impact force is similar to that of a cubic B-spline, Liu et al 11 presented a modified regularized cubic B-spline collocation method to identify the impact force. Because of the sparsity of the impact signal, Liu et al 12 introduced a fast iterative shrinkage-thresholding algorithm to solve a sparse regularization model developed from the dynamic response and impact force reconstruction equation, so as to synthetically estimate the above two physical quantities.…”

Time series analysis and sparse sensor network-based impact monitoring for aircraft complex structures

“…Impact energy is another characteristic parameter for characterizing impact damage of composite structures, the estimation of the impact energy is important for the evaluation of the health status of composite structures. At present, the estimation methods for impact energy can be classified into two main categories, namely (1) inverse the time history of the impact load by constructing a response model, and then estimate the impact energy magnitude 26–31 ; (2) directly study the relationship between the magnitude of impact energy and signal characteristics, and then estimate the impact energy based on the signal characteristics. 32,33 In comparison, the second category of methods has the advantage of simplicity and efficiency by avoiding the need for extensive and complex modeling work.…”

Embedded FBG Sensor Based Impact Identification of CFRP Using Ensemble Learning

“…The use of regularization methods, which mainly include direct regularization and indirect regularization, is the most effective way to improve these issues. The most used direct regularization methods are the Tikhonov regularization methods [ 21 , 22 , 23 , 24 , 25 , 26 , 27 ] and the singular value decomposition (SVD) methods [ 28 , 29 , 30 ]. By comparing the generalized SVD method, the Tikhonov regularization method, and the truncated SVD method, Jacquelin [ 31 ] found that these methods have better robustness, and the convergence speeds are faster, but how to calculate the regularization parameters is still a difficult problem.…”