scholarly journals A Novel Method of Dynamic Force Identification and Its Application

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Nengjian Wang ◽  
Qinhui Liu ◽  
Chunping Ren ◽  
Chunsheng Liu
Keyword(s):  
Conjugate Gradient ◽  
Optimization Problems ◽  
Stability And Convergence ◽  
Future Research ◽  
Dynamic Force ◽  
Force Identification ◽  
Unconstrained Optimization Problems ◽  
Practical Engineering ◽  
Gradient Parameter ◽  
Spectral Conjugate Gradient

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.

scholarly journals A Mixed Spectral CD-DY Conjugate Gradient Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Liu Jinkui ◽  
Du Xianglin ◽  
Wang Kairong
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Descent Method ◽  
Unconstrained Optimization Problems ◽  
Global Convergence Property ◽  
Wolfe Line Search ◽  
Spectral Conjugate Gradient

A mixed spectral CD-DY conjugate descent method for solving unconstrained optimization problems is proposed, which combines the advantages of the spectral conjugate gradient method, the CD method, and the DY method. Under the Wolfe line search, the proposed method can generate a descent direction in each iteration, and the global convergence property can be also guaranteed. Numerical results show that the new method is efficient and stationary compared to the CD (Fletcher 1987) method, the DY (Dai and Yuan 1999) method, and the SFR (Du and Chen 2008) method; so it can be widely used in scientific computation.

scholarly journals Identification of Random Dynamic Force Using an Improved Maximum Entropy Regularization Combined with a Novel Conjugate Gradient

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
ChunPing Ren ◽  
NengJian Wang ◽  
ChunSheng Liu
Keyword(s):  
Maximum Entropy ◽  
Conjugate Gradient ◽  
Regularization Parameter ◽  
Engineering Application ◽  
Optimal Solution ◽  
Identification Problem ◽  
Dynamic Force ◽  
Force Identification ◽  
Mathematical Algorithm ◽  
Practical Engineering

We propose a novel mathematical algorithm to offer a solution for the inverse random dynamic force identification in practical engineering. Dealing with the random dynamic force identification problem using the proposed algorithm, an improved maximum entropy (IME) regularization technique is transformed into an unconstrained optimization problem, and a novel conjugate gradient (NCG) method was applied to solve the objective function, which was abbreviated as IME-NCG algorithm. The result of IME-NCG algorithm is compared with that of ME, ME-CG, ME-NCG, and IME-CG algorithm; it is found that IME-NCG algorithm is available for identifying the random dynamic force due to smaller root mean-square-error (RMSE), lower restoration time, and fewer iterative steps. Example of engineering application shows that L-curve method is introduced which is better than Generalized Cross Validation (GCV) method and is applied to select regularization parameter; thus the proposed algorithm can be helpful to alleviate the ill-conditioned problem in identification of dynamic force and to acquire an optimal solution of inverse problem in practical engineering.

New hyrid conjugate gradient method as a convex combination of HZ and CD methods

2021 ◽  
pp. 2150187
Author(s):  
Amira Hamdi ◽  
Badreddine Sellami ◽  
Mohammed Belloufi
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient ◽  
Line Search ◽  
Optimization Problems ◽  
Convex Combination ◽  
Gradient Algorithm ◽  
Unconstrained Optimization Problems ◽  
Gradient Parameter ◽  
Sufficient Descent ◽  
Wolfe Line Search

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems, the conjugate gradient parameter [Formula: see text] is computed as a convex combination of [Formula: see text] and [Formula: see text]. Under the wolfe line search, we prove the sufficient descent and the global convergence. Numerical results are reported to show the effectiveness of our procedure.

scholarly journals A Spectral Dai-Yuan-Type Conjugate Gradient Method for Unconstrained Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Guanghui Zhou ◽  
Qin Ni
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Sufficient Descent Condition ◽  
Unconstrained Optimization Problems ◽  
Spectral Conjugate Gradient ◽  
Nonlinear Unconstrained Optimization

A new spectral conjugate gradient method (SDYCG) is presented for solving unconstrained optimization problems in this paper. Our method provides a new expression of spectral parameter. This formula ensures that the sufficient descent condition holds. The search direction in the SDYCG can be viewed as a combination of the spectral gradient and the Dai-Yuan conjugate gradient. The global convergence of the SDYCG is also obtained. Numerical results show that the SDYCG may be capable of solving large-scale nonlinear unconstrained optimization problems.

scholarly journals Global Convergence of a Modified Spectral Conjugate Gradient Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Huabin Jiang ◽  
Songhai Deng ◽  
Xiaodong Zheng ◽  
Zhong Wan
Keyword(s):  
Global Convergence ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Line Search ◽  
Optimization Problems ◽  
Step Length ◽  
Mild Conditions ◽  
Unconstrained Optimization Problems ◽  
Spectral Conjugate Gradient

A modified spectral PRP conjugate gradient method is presented for solving unconstrained optimization problems. The constructed search direction is proved to be a sufficiently descent direction of the objective function. With an Armijo-type line search to determinate the step length, a new spectral PRP conjugate algorithm is developed. Under some mild conditions, the theory of global convergence is established. Numerical results demonstrate that this algorithm is promising, particularly, compared with the existing similar ones.

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