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

2021 ◽  
Vol 26 (2) ◽  
pp. 121-130
Author(s):  
Lin J. Wang ◽  
Xiang Gao ◽  
You X. Xie ◽  
Jun J. Fu ◽  
Yi X. Du
Keyword(s):  
Conjugate Gradient ◽  
Mathematical Theory ◽  
Load Identification ◽  
Identification Problems ◽  
Force Reconstruction ◽  
Practical Engineering ◽  
Regularization Operator ◽  
Sufficient Descent ◽  
Composite Laminated Cylindrical Shell ◽  
Laminated Cylindrical Shell

In this paper, a modified conjugate gradient (MCG) algorithm is proposed for solving the force reconstruction problems in practical engineering. This new method is derived from a stable regularization operator and is also strictly proved using the mathematical theory. Moreover, we also prove the sufficient descent and global convergence characteristic of the newly developed algorithm. Finally, the proposed algorithm is applied to force reconstruction for the airfoil structure and composite laminated cylindrical shell. Numerical simulations show that the proposed method is highly efficient and has robust convergence performances. Additionally, the accuracy of the proposed algorithm in identifying the expected loads is satisfactory and acceptable in practical engineering.

scholarly journals On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Min Sun ◽  
Jing Liu
Keyword(s):  
Strong Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Line Searches ◽  
Unconstrained Optimization Problems ◽  
Sufficient Descent ◽  
Large Scale Unconstrained Optimization

Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP) conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense thatlim infk→∞∥∇f(xk)∥=0when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense thatlimk→∞∥∇f(xk)∥=0under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.

scholarly journals A New Modified Three-Term Hestenes–Stiefel Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Bakhtawar Baluch ◽  
Zabidin Salleh ◽  
Ahmad Alhawarat
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Gradient Methods ◽  
Conjugate Gradient Methods ◽  
Sufficient Descent Property ◽  
Descent Property ◽  
Sufficient Descent

This paper describes a modified three-term Hestenes–Stiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees global convergence using the inexact Wolfe–Powell line search. The numerical efficiency of the modified three-term HS method is checked using 75 standard test functions. It is known that three-term conjugate gradient methods are numerically more efficient than two-term conjugate gradient methods. Importantly, this paper quantifies how much better the three-term performance is compared with two-term methods. Thus, in the numerical results, we compare our new modification with an efficient two-term conjugate gradient method. We also compare our modification with a state-of-the-art three-term HS method. Finally, we conclude that our proposed modification is globally convergent and numerically efficient.

scholarly journals A new regularization method for dynamic load identification

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042093128 ◽  
Author(s):  
Linjun Wang ◽  
Yang Huang ◽  
Youxiang Xie ◽  
Yixian Du
Keyword(s):  
Dynamic Load ◽  
Regularization Method ◽  
Inverse Analysis ◽  
Vibration Isolation ◽  
Frame Structure ◽  
Tikhonov Regularization Method ◽  
Strength Analysis ◽  
Regularization Methods ◽  
Load Identification ◽  
Practical Engineering

Dynamic forces are very important boundary conditions in practical engineering applications, such as structural strength analysis, health monitoring and fault diagnosis, and vibration isolation. Moreover, there are many applications in which we have found it very difficult to directly obtain the expected dynamic load which acts on a structure. Some traditional indirect inverse analysis techniques are developed for load identification by measured responses. These inverse problems about load identification mentioned above are complex and inherently ill-posed, while regularization methods can deal with this kind of problem. However, most of regularization methods are only limited to solve the pure mathematical numerical examples without application to practical engineering problems, and they should be improved to exclude jamming of noises in engineering. In order to solve these problems, a new regularization method is presented in this article to investigate the minimum of this minimization problem, and applied to reconstructing multi-source dynamic loads on the frame structure of hydrogenerator by its steady-state responses. Numerical simulations of the inverse analysis show that the proposed method is more effective and accurate than the famous Tikhonov regularization method. The proposed regularization method in this article is powerful in solving the dyanmic load identification problems.

scholarly journals A New Hybrid PRPFR Conjugate Gradient Method for Solving Nonlinear Monotone Equations and Image Restoration Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yingjie Zhou ◽  
Yulun Wu ◽  
Xiangrong Li
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Convex Combination ◽  
Trust Region ◽  
Step Length ◽  
Monotone Equations ◽  
Global Convergence Property ◽  
Sufficient Descent

A new hybrid PRPFR conjugate gradient method is presented in this paper, which is designed such that it owns sufficient descent property and trust region property. This method can be considered as a convex combination of the PRP method and the FR method while using the hyperplane projection technique. Under accelerated step length, the global convergence property is gained with some appropriate assumptions. Comparing with other methods, the numerical experiments show that the PRPFR method is more competitive for solving nonlinear equations and image restoration problems.

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