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

Jie Liu,Bingbing Hu,Jingsong Xie,Bing Li

doi:10.1109/access.2020.2973919

Jie Liu, Bingbing Hu + Show 2 more

Open Access

https://doi.org/10.1109/access.2020.2973919

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Abstract

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.

Highlights

Impact events are one of the main factors that aggravate the vibration of mechanical systems, and the time history of impact force is the vital index for structural health monitoring, reliability analysis and optimal design [1]–[4]
NUMERICAL SIMULATION VERIFICATION a five degree-of-freedoms (DOFs) chain type structure is established in MATLAB so as to verify the effectiveness of regularized cubic B-spline collocation (RCBSC) method for impact force identification, and the advantage of modified L-curve criterion on determining optimal RCBSC regularization parameter ms is discussed by comparing with modified GCV criterion
This paper presents a regularized cubic B-spline collocation method combined with the modified L-curve criterion (RCBSC-ML) to conduct impact force identification

Summary

INTRODUCTION

Impact events are one of the main factors that aggravate the vibration of mechanical systems, and the time history of impact force (especially for the peak force) is the vital index for structural health monitoring, reliability analysis and optimal design [1]–[4]. When the basis function collocation method is applied to solve the force identification problem, the identification accuracy depends on the approximation degree of the basis function to the force identification model and the improvement degree of the ill-posedness of inverse matrix. A novel method combined regularized cubic B-spline collocation (RCBSC) method and a modified L-curve criterion (RCBSC-ML) is proposed to solve ill-posed inverse problem to obtain the unknown impact force.

FORCE IDENTIFICATION EQUATION

NUMERICAL SIMULATION VERIFICATION

SIMULATION RESULTS AND DISCUSSIONS

CONCLUSION