A Novel Method of Dynamic Force Identification and Its Application

Nengjian Wang,Chunsheng Liu,Chunping Ren,Qinhui Liu

doi:10.1155/2019/1534560

Abstract

In this paper, an efficient mixed spectral conjugate gradient (EMSCG, for short) method is presented for solving unconstrained optimization problems. In this work, we construct a novel formula performed by using a conjugate gradient parameter which takes into account the advantages of Fletcher–Reeves (FR), Polak–Ribiere–Polyak (PRP), and a variant Polak-Ribiere-Polyak (VPRP), prove its stability and convergence, and apply it to the dynamic force identification of practical engineering structure. The analysis results show that the present method has higher efficiency, stronger robust convergence quality, and fewer iterations. In addition, the proposed method can provide more efficient and numerically stable approximation of the actual force, compared with the FR method, PRP method, and VPRP method. Therefore, we can make a clear conclusion that the proposed method in this paper can provide an effective optimization solution. Meanwhile, there is reason to believe that the proposed method can offer a reference for future research.

Highlights

It is of great significance to solve the engineering problem about the identification of the dynamic loads acting on the practical engineering structure with the improvement of engineering requirements and the progress of engineering technology [1,2,3]
Based on the above literature, an efficient mixed spectral conjugate gradient method with sufficient descent is proposed, which was abbreviated as the EMSCG method, and parameters θk and βk are expressed as βEkMSCG gk 2 −
The present method is applied to an engineering example of the identification problem of dynamic force generated between conical pick and coal-seam structure

Summary

Introduction

It is of great significance to solve the engineering problem about the identification of the dynamic loads acting on the practical engineering structure with the improvement of engineering requirements and the progress of engineering technology [1,2,3]. The spectral conjugate gradient (SCG) method does a lot of important works among various methods for solving unconstrained optimization problems [17]. The search direction of the spectral conjugate gradient method proposed by Birgin and Martinez does not satisfy the descent property, and it does not have global convergence. In order to obtain global convergence, Wang et al [19, 33] constructed the FR-type spectral conjugate gradient method; spectral parameters θk and βk are expressed as θk d Tkg− k1−y1k −21,. Based on the above literature, an efficient mixed spectral conjugate gradient method with sufficient descent is proposed, which was abbreviated as the EMSCG method, and parameters θk and βk are expressed as βEkMSCG gk 2 −. From the selection of spectral coefficient of Algorithm 1, we can select the different parameters c to optimize the numerical effect of Algorithm 1

Convergent Analysis of the Proposed Method

An Example of Engineering Application

Miωid t

F2 F3 M

Conclusions