Regularized Cubic B-spline Collocation Method with Modified L-curve Criterion for Impact Force Identification

The time history of the impact force, especially for the peak force, is vital to monitor the performance of mechanical products over the life-time. 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.