A novel shape function approach of dynamic load identification for the structures with interval uncertainty

Liu, Jie; Sun, Xingsheng; Meng, Xianghua; Li, Kun; Guang, Zeng; Wang, Xianyi

doi:10.1007/s10999-015-9304-3

Cited by 39 publications

(16 citation statements)

References 26 publications

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“…We can see that { } is monotone bounded according to (24) and Assumption A, so we can obtain the following conclusion based on (24) and (33) and Lemma 3:…”

Section: Assumption a (I)mentioning

confidence: 79%

“…The initial velocity and initial displacement of the system are assumed to be x 0 and x 0 , respectively. So in (2) can be expressed as follows: It is well known that 1 ( ) can be obtained by the homogeneous equation of (1), which can be described as follows [24]:…”

Section: Model Of Identified Forcementioning

confidence: 99%

“…Suppose that Assumption A holds, the step length is calculated by (24) and the search direction ℎ is calculated by (26), and there is a constant 2 > 0, then…”

Section: Assumption a (I)mentioning

confidence: 99%

“…Set 2 = min{(1 − 1 ), (1 − )/ }, because the step length is calculated by (24), then ≤ 1. When = 1, according to Theorem 2, we can obtain the following:…”

Section: Assumption a (I)mentioning

confidence: 99%

“…Owing to the fact that the step length and the search direction ℎ new are generated by (24) and (26), respectively, then…”

Section: Theorem 4 Suppose That the Step Length And The Search Direcmentioning

confidence: 99%

See 4 more Smart Citations

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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“…We can see that { } is monotone bounded according to (24) and Assumption A, so we can obtain the following conclusion based on (24) and (33) and Lemma 3:…”

Section: Assumption a (I)mentioning

confidence: 79%

Section: Model Of Identified Forcementioning

confidence: 99%

“…Suppose that Assumption A holds, the step length is calculated by (24) and the search direction ℎ is calculated by (26), and there is a constant 2 > 0, then…”

Section: Assumption a (I)mentioning

confidence: 99%

“…Set 2 = min{(1 − 1 ), (1 − )/ }, because the step length is calculated by (24), then ≤ 1. When = 1, according to Theorem 2, we can obtain the following:…”

Section: Assumption a (I)mentioning

confidence: 99%

“…Owing to the fact that the step length and the search direction ℎ new are generated by (24) and (26), respectively, then…”

Section: Theorem 4 Suppose That the Step Length And The Search Direcmentioning

confidence: 99%

See 3 more Smart Citations

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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show abstract

Identification of dynamic load for prosthetic structures

Zhang

Han

Zhang

et al. 2017

Numer Methods Biomed Eng

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Dynamic load exists in numerous biomechanical systems, and its identification signifies a critical issue for characterizing dynamic behaviors and studying biomechanical consequence of the systems. This study aims to identify dynamic load in the dental prosthetic structures, namely, 3-unit implant-supported fixed partial denture (I-FPD) and teeth-supported fixed partial denture. The 3-dimensional finite element models were constructed through specific patient's computerized tomography images. A forward algorithm and regularization technique were developed for identifying dynamic load. To verify the effectiveness of the identification method proposed, the I-FPD and teeth-supported fixed partial denture structures were investigated to determine the dynamic loads. For validating the results of inverse identification, an experimental force-measuring system was developed by using a 3-dimensional piezoelectric transducer to measure the dynamic load in the I-FPD structure in vivo. The computationally identified loads were presented with different noise levels to determine their influence on the identification accuracy. The errors between the measured load and identified counterpart were calculated for evaluating the practical applicability of the proposed procedure in biomechanical engineering. This study is expected to serve as a demonstrative role in identifying dynamic loading in biomedical systems, where a direct in vivo measurement may be rather demanding in some areas of interest clinically.

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Multisource uncertain dynamic load identification fitted by Legendre polynomial based on precise integration and the Savitzky–Golay filters

Wang

et al. 2022

Numerical Meth Engineering

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In this article, a precise integral method (PIM) for the load identification of continuous structures based on the polynomial nonlinear hypothesis is presented.Essentially, load identification can be regarded as solving a dynamic equation in an inverse process. PIM is famous for its high precision in positive engineering problems. It has been already used in load reconstruction, but most cases are with discrete structures. In each time step, the dynamic responses of the measured points are used to identify the load without establishing a recursive chain, so PIM is not sensitive to the initial value and has no accumulated error. Legendrepolynomials (LPIM) is a computational scheme. The dynamic load is assumed to be a polynomial fitting nonlinear function in each integral time step with LPIM. Just with the first modal, LPIM can reliably identify the concentrated load. In addition, as uncertainty is getting more and more attention in engineer, it is also needed to be considered in load identification. In linear systems, interval vertex is a reliable method to obtain the load bounds in the virtue of multisource uncertainties. The results of identified load are too lumpy because of the polynomial fitting. To improve the precision, Savitsky-Golay (S-G) filters which fit the curves by polynomials in a frame length is introduced to smooth down the load in high fidelity. Eight numerical examples are investigated to demonstrated the efficiency and precision of the developed method.

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A novel shape function approach of dynamic load identification for the structures with interval uncertainty

Cited by 39 publications

References 26 publications

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

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

Identification of dynamic load for prosthetic structures

Multisource uncertain dynamic load identification fitted by Legendre polynomial based on precise integration and the Savitzky–Golay filters

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