Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method

Liu, Jie; Sun, Xingsheng; Han, Xu; Jiang, Chao; Yu, Dejie

doi:10.1016/j.ymssp.2014.10.008

Cited by 151 publications

(58 citation statements)

References 46 publications

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“…The model of inverse problems encountered in science and engineering can be uniformly expressed by a Fredholm integral equation of the first kind [31][32][33]:…”

Section: Description Of Inverse Problem Modelmentioning

confidence: 99%

A Novel Fractional Tikhonov Regularization Coupled with an Improved Super-Memory Gradient Method and Application to Dynamic Force Identification Problems

Wang

Ren

Liu

2018

Mathematical Problems in Engineering

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This paper presents a novel inverse technique to provide a stable optimal solution for the ill-posed dynamic force identification problems. Due to ill-posedness of the inverse problems, conventional numerical approach for solutions results in arbitrarily large errors in solution. However, in the field of engineering mathematics, there are famous mathematical algorithms to tackle the illposed problem, which are known as regularization techniques. In the current study, a novel fractional Tikhonov regularization (NFTR) method is proposed to perform an effective inverse identification, then the smoothing functional of the ill-posed problem processed by the proposed method is regarded as an optimization problem, and finally a stable optimal solution is obtained by using an improved super-memory gradient (ISMG) method. The result of the present method is compared with that of the standard TR method and FTR method; new findings can be obtained; that is, the present method can improve accuracy and stability of the inverse identification problem, robustness is stronger, and the rate of convergence is faster. The applicability and efficiency of the present method in this paper are demonstrated through a mathematical example and an engineering example.

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“…The model of inverse problems encountered in science and engineering can be uniformly expressed by a Fredholm integral equation of the first kind [31][32][33]:…”

Section: Description Of Inverse Problem Modelmentioning

confidence: 99%

A Novel Fractional Tikhonov Regularization Coupled with an Improved Super-Memory Gradient Method and Application to Dynamic Force Identification Problems

Wang

Ren

Liu

2018

Mathematical Problems in Engineering

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“…For deterministic MDOF structures, the kinetic equation can be expressed by the following form [23]:…”

Section: Model Of Identified Forcementioning

confidence: 99%

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

Ren

Wang

Liu

2017

Mathematical Problems in Engineering

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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.

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“…Dynamic force reconstruction methods based on structural dynamic response have attracted great interest in the field of structural health monitoring (SHM), as it is often difficult or impractical to measure a dynamic force directly. Dynamic force reconstruction methods can generally be categorized into two groups: frequency-domain [1][2][3][4] and time-domain [5][6][7][8] methods. The frequency-and time-domain methods estimate dynamic forces by establishing the relationship between dynamic forces and structural responses based on frequency response functions [9,10] and impulse response functions [11,12], respectively.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

Yang

Zhu

2018

Shock and Vibration

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The shape function-based method is one of the very promising time-domain methods for dynamic force reconstruction, because it can significantly reduce the number of unknowns and shorten the reconstruction time. However, it is challenging to determine the optimum time unit length that can balance the tradeoff between reconstruction accuracy and efficiency in advance. To address this challenge, this paper develops an adaptive dynamic force reconstruction method based on multiscale wavelet shape functions and time-domain deconvolution. A concentrated dynamic force is discretized into units in time domain and the local force in each unit is approximated by wavelet scale functions at an initial scale. Subsequently, the whole response matrix is formulated by assembling the responses induced by the wavelet shape function forces of all time units which are calculated by the structural finite element model (FEM). Then, the wavelet shape function-based force-response equation is established for force reconstruction. Finally, the scale of the force-response equation is lifted by refining the wavelet shape function with high-scale wavelets and dynamic responses with more point data to improve the reconstruction accuracy gradually. Numerical examples of different structural types are analyzed to verify the feasibility and effectiveness of the proposed method.

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Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method

Cited by 151 publications

References 46 publications

A Novel Fractional Tikhonov Regularization Coupled with an Improved Super-Memory Gradient Method and Application to Dynamic Force Identification Problems

A Novel Fractional Tikhonov Regularization Coupled with an Improved Super-Memory Gradient Method and Application to Dynamic Force Identification Problems

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

Adaptive Reconstruction of a Dynamic Force Using Multiscale Wavelet Shape Functions

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