A new hybrid conjugate gradient method for dynamic force reconstruction

Abstract

A new hybrid conjugate gradient method is proposed in this article based on the gradient operator and applied to the structural dynamic load identification problem. It has proved that the present method with the strong Wolfe line search possesses sufficient descent property. In addition, the present method is globally convergent when the parameter in the strong Wolfe line search conditions is restricted in some suitable intervals. Three example problems from engineering are solved by the newly developed conjugate gradient method to demonstrate the robustness and effectiveness of conjugate gradient method in solving multi-source dynamic load identification problems. Compared with the traditional Landweber iteration regularization method (Landweber), the proposed conjugate gradient method can more stably and effectively overcome the influences of noise, largely reduce the number of iterations, and provide accurate results in identifying multi-source dynamic force in practical engineering structure.

A novel strategy for force identification of nonlinear structures

“…Therefore, the number of extended forces containing nonlinear describing functions and excitation force needs to be no more than the number of response measurement points. Additionally, NSI algorithm was originally used to identify nonlinear parameter μ i on the basis of equation (10). Therefore, as shown in equations ( 2) and (4), μ i is contained in the coefficient matrix B c , and nonlinear describing function g nl ðtÞ is contained in extended force f ex ðtÞ.…”

“…where H L ðωÞ is the linear FRF corresponding to the underlying linear structure. This means that, in addition to forming a transfer matrix T, NSI algorithm can be introduced to calculate the linear FRF H L ðωÞ and nonlinear parameter μ by equation (10).…”

“…Gunawan 9 introduced the trust region strategy to enforce the regularization and extended the Levenberg–Marquardt iterative algorithm to solve an unknown impact force. 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.…”

A New Conjugate Gradient Method and Application to Dynamic Load Identification Problems

“…The corresponding equally spaced intervals can be obtained using the discretization of the time period, and then we give Eq. (13) in matrix form as: [28][29][30]…”

A Study on Impact Force Detection Method Based on Piezoelectric Sensing

“…Tian et al [ 15 ] utilized piezoelectric ceramic sensors to detect the dynamic response of pipes under impact loads. In addition to these, researchers have also developed other kinds of effective methods, i.e., analytical solutions [ 16 , 17 ], finite element methods [ 18 , 19 ], conjugate gradient methods [ 20 , 21 ], basis function expansion methods [ 22 , 23 ], regularization methods [ 24 , 25 , 26 ], experimental detection methods [ 4 , 5 , 27 , 28 ], and artificial neural networks [ 29 ] have all been developed for impact recognition tasks.…”