A new regularization method and application to dynamic load identification problems

Force identification is a classical inverse problem in which the measured data and the mathematical models of mechanical structures are used to determine the applied force. However, the identified force may seriously diverge from the true solution due to the unknown noise contaminating the measured data and the inverse of the ill-posed transfer matrix characterizing the mechanical structure. In this paper, a novel method based on the discrete cosine transform (DCT) in the time domain is proposed for force identification, which overcomes the deficiency of the ill-posedness of the transfer matrix. The unknown force is expanded by a set of cosine basis functions and then the original governing equation is reformulated to find the coefficient of each cosine basis function. Furthermore, a modified generalized cross-validation (GCV) criterion for determining the regularization parameter is developed for the truncated singular value decomposition (TSVD), Chebyshev polynomial and DCT solutions. Numerical simulation reveals that compared with the L-curve criterion, the modified GCV criterion is quite robust in the presence of noise.Finally, a clamped-free shell structure that is excited by an impact hammer is selected as an example to validate the performance of the proposed method. Experimental results demonstrate that compared with the TSVD-based and Chebyshev-based methods, the DCT-based method combined with the modified GCV criterion can reconstruct the force time history and identify the peak of impact force with high accuracy. Additionally, the identification of force location using the DCT-based method is also discussed.

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“…(20)(21)(22), it can be noted that DCT is a unitary transform. Moreover, DCT is easily written in a matrix-vector form.…”

Section: The Dct-based Methodsmentioning

confidence: 99%

A Novel Method for Force Identification Based on the Discrete Cosine Transform

Qiao

Chen

Luo

et al. 2015

Journal of Vibration and Acoustics

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“…In some cases, small varieties in the right-hand side of (15) may lead to dramatic varieties in the solution [25][26][27][28]. In other words, they are very susceptible to error, in the inverse problem, this may directly lead to greater deviations of the identified results [29][30][31], and thus it is not realistic to solve (15) using traditional mathematical methods [32][33][34].…”

Section: Mathematical Problems In Engineeringmentioning

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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“…Furthermore, the inverse problem has been developed as a hot subject which has been widely applied in the fields of many practical engineering problems, such as dynamic isolation, health monitoring, and fault diagnosis [1,2]. e primary concern of mathematical workers and engineering technicians in the inverse problem derives from the development of the theory of solving the problems of universal existence and ill-posed problems in practical engineering applications in recent years [3,4]. However, in many practical engineering problems today, for instance, the knowledge of dynamic loads in machinery dynamic systems is always required.…”

Section: Introductionmentioning

confidence: 99%

“…Identification of dynamic loads on coalrock structure has been a major concern in fatigue failure analysis of rotary machinery; once accurate dynamic load sources are obtained, it is possible to apply some advanced algorithms to analyze the characteristics of the dynamic load signals. In general, an input load signal can be directly measured by the force transducer, but sometimes it is difficult in calculating accurate results, and this would be mainly caused by the noise data of measured responses and the ill-conditioned characteristic of system; dynamic load sources identification is classified as a kind of complex inverse problems with inherent ill-posedness and will not be resolved directly and accurately through some traditional mathematical methods [3,5,6]. Aiming to overcome this difficulty of instability, we consider that it is essential to develop a stabilization technique for effective solutions.…”

Section: Introductionmentioning

confidence: 99%

A Novel Improved Maximum Entropy Regularization Technique and Application to Identification of Dynamic Loads on the Coal Rock

Liu

Ren

2019

Journal of Electrical and Computer Engineering

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A new signal processing algorithm was proposed to identify the dynamic load acting on the coal-rock structure. First, the identification model for dynamic load is established through the relationship between the uncertain load vector, and the assembly matrix of the responses was measured by the machinery dynamic system. Then, the entropy item of maximum entropy regularization (MER) is redesigned using the robust estimation method, and the elongated penalty function according to the ill-posedness characteristics of load identification, which was named as a novel improved maximum entropy regularization (IMER) technique, was proposed to process the dynamic load signals. Finally, the load identification problem is transformed into an unconstrained optimization problem and an improved Newton iteration algorithm was proposed to solve the objective function. The result of IMER technique is compared with MER technique, and it is found that IMER technique is available for analyzing the dynamic load signals due to higher signal-noise ratio, lower restoration time, and fewer iterative steps. Experiments were performed to investigate the effect on the performance of dynamic load signals identification by different regularization parameters and calculation parameters, pi, respectively. Experimental results show that the identified dynamic load signals are closed to the actual load signals using IMER technique combined with the proposed PSO-L regularization parameter selection method. Selecting optimal calculated parameters pi is helpful to overcome the ill-condition of dynamic load signals identification and to obtain the stable and approximate solutions of inverse problems in practical engineering. Meanwhile, the proposed IMER technique can also play a guiding role for the coal-rock interface identification.

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A new regularization method and application to dynamic load identification problems

Cited by 30 publications

References 24 publications

A Novel Method for Force Identification Based on the Discrete Cosine Transform

A Novel Method for Force Identification Based on the Discrete Cosine Transform

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

A Novel Improved Maximum Entropy Regularization Technique and Application to Identification of Dynamic Loads on the Coal Rock

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