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Non-probabilistic uncertain inverse problem method considering correlations for structural parameter identification

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2021年第3期64卷 1327-1342页

作者： Ouyang, Heng Liu, Jie Han, Xu Ni, Bingyu Liu, Guirong Lin, Yixin Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Peoples R China Hebei Univ Technol Sch Mech Engn State Key Lab Reliabil & Intelligence Elect Equip Tianjin 300401 Peoples R China Univ Cincinnati Dept Aerosp Engn & Engn Mech Cincinnati OH 45221 USA

This paper presents an effective sequence interval and correlation inverse strategy for the uncertain inverse problem, aiming to identify the uncertainties and non-probabilistic correlations of the structural parameters simultaneously. First, an ellipsoidal convex model is adopted to quantify the uncertainty boundary of the measured responses with limited samples. Then, the uncertain inverse problem based on the ellipsoidal convex model is decoupled into an interval inverse problem and a correlation inverse problem. For the interval inverse problem, a subinterval decomposition analysis method constrained by the ellipsoidal convex model is developed to evaluate the intervals of the structural responses with a low computational cost. For the correlation inverse problem, the correlation propagation equations are derived to calculate the non-probabilistic correlation coefficient matrix of the structural responses. After that, by using optimization algorithms to circularly reduce the errors of the intervals and the correlation coefficients between the measured responses and calculated structural responses, the intervals and the non-probabilistic correlation coefficient matrix of the structural parameters are identified effectively, and an ellipsoidal convex model of the structural parameters can be established eventually. Two numerical examples and one experimental example are investigated to verify the effectiveness and accuracy of the proposed sequence interval and correlation inverse strategy.

关键词： uncertain inverse problem uncertainty quantification Correlation identification Non-probabilistic convex model Subinterval decomposition analysis

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Optimal sensor placement for uncertain inverse problem of structural parameter estimation

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2021年 160卷

作者： Liu, Jie Ouyang, Heng Han, Xu Liu, Guirong Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Hebei Univ Technol Sch Mech Engn State Key Lab Reliabil & Intelligence Elect Equip Tianjin 300401 Peoples R China Univ Cincinnati Dept Aerosp Engn & Engn Mech Cincinnati OH 45221 USA

This paper presents an optimal sensor placement approach for the uncertain inverse prob-lem of structural parameter estimation, aiming to mitigate the ill-posedness problem that often exists in inverse procedures. The key idea is to select the sensor positions with the most sensitive measured responses to the structural parameters and the least correlated measured responses at the selected positions. Our optimization strategy is to convert the traditional minimum variance criterion of structural parameters to be identified into a new maximum independent mean-variance criterion of structural responses, so that the complex optimal sensor placement problem is transformed into a forward uncertainty propagation problem. Then, two orthogonal matching pursuit (OMP) methods based on Monte Carlo simulation (MCS) and dimension reduction integration (DRI) method are pre-sented in this work, in which the MCS and the much more efficient DRI method are employed to solve the forward uncertainty propagation problem, and the OMP methods in sample form and moment form are developed to determine the optimal sensor place -ment for the identification procedure by considering the uncertainties in the measured responses. A Markov Chain Monte Carlo algorithm is adopted to identify the distributions of structural parameters eventually. Numerical and experimental examples are presented to verify the practicability and effectiveness of the proposed methods. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Optimal sensor placement uncertain inverse problem Structural parameter estimation Orthogonal matching pursuit procedure Dimension reduction integration method Maximum independent mean-variance criterion

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An effective nonlinear interval sequential quadratic programming method for uncertain inverse problems

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STRUCTURES 2023年 51卷 615-627页

作者： Tang, Jiachang Lei, Yong Zhang, Taolin Yao, Qishui Fu, Chunming Zhan, Lina Mi, Chengji Hunan Univ Technol Dept Mech Engn Zhuzhou 412007 Peoples R China Univ South China Coll Mech Engn Hengyang 421001 Peoples R China

An effective nonlinear interval sequential quadratic programming method is proposed to provide an efficient tool for uncertain inverse problems. Assisted by the ideology of sequential quadratic programming and dimension -reduction analysis theory, the interval inverse problem is transformed into several interval arithmetic and deterministic optimizations, which could enhance computational efficiency without losing much accuracy. The novelty of the proposed method lies in two main aspects. First, an alternate updating strategy is proposed to identify the radii and midpoints of the interval inputs in each cycle, which could reduce the number of iterative steps. Second, the standard quadratic models are constructed based on the dimension-reduction analysis results, rather than the second-order Taylor expansion. Therefore, the interval arithmetic can be applied to efficiently calculate the interval response, which avoids the inner optimization. Moreover, a novel iterative mechanism is developed to accelerate the convergence rate of the proposed method. Finally, two numerical examples and an engineering application are adopted to verify its feasibility, accuracy and efficiency.

关键词： uncertain inverse problem Interval model Sequential quadratic programming Dimension -reduction analysis

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Probability assessments of identified parameters for stochastic structures using point estimation method

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2016年 156卷 51-58页

作者： Liu, Jie Hu, Yifeng Xu, Can Jiang, Chao Han, Xu Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China

In this paper, a kind of inverse problem for assessing the probabilities of identified parameters with uncertainties in structural parameters and limited experimental results is investigated. The point estimation method and maximum entropy principle are adopted to efficiently evaluate the effect of uncertain parameters on the identified parameters. First, the probability distribution function of each uncertain parameter can be approximately represented by several nodes. Thus, the uncertain inverse problem can be transformed into several deterministic inverse problems through multivariate Taylor expansion and point estimation method. Then, to obtain the moments of identified parameters, the deterministic inverse process for each selected node with concentrated probability are conducted by the genetic algorithm. Finally, the probability distribution functions of the identified parameters can be assessed by the obtained moments based on the maximum entropy principle. The proposed method effectively avoids the low efficiency of uncertain inverse problem, which commonly involves a double loop procedure with uncertainty propagation and inverse calculation. Numerical examples and the engineering application demonstrate the feasibility and effectiveness of the proposed method. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： uncertain inverse problem Point estimation Maximum entropy uncertainty propagation Stochastic structure

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Interval assessments of identified parameters for uncertain structures

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ENGINEERING WITH COMPUTERS 2022年第SUPPL 4期38卷 2905-2917页

作者： Tang, Jiachang Cao, Lixiong Mi, Chenji Fu, Chunming Liu, Qiming Hunan Univ Technol Dept Mech Engn Zhuzhou 412007 Peoples R China Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Peoples R China Univ South China Coll Mech Engn Hengyang 421001 Peoples R China Hebei Univ Technol Sch Mech Engn State Key Lab Reliabil & Intelligence Elect Equip Tianjin 300401 Peoples R China

This paper investigates a kind of inverse problem for assessing the uncertainties of identified parameters with uncertainties in structural parameters and limited experimental data. The uncertainty is described by the interval model in which only the bounds of uncertain parameters are required. Directly solving this kind of inverse problem involves a double-loop problem where the outer-loop is interval analysis and the inner-loop is deterministic optimization, which requires a large number of calculations. To efficiently evaluate the effect of interval parameters on the identified parameters, a novel method based on the dimension-reduction method and adaptive collocation strategy is proposed. First, the interval inverse problem is transformed into an inverse-propagation problem, and the dimension-reduction interval method is adopted to transform the interval inverse-propagation problem into several one-dimensional interval inverse-propagation problems. Then, an adaptive collocation strategy is proposed to efficiently estimate the lower and upper bounds of identified parameters. Therefore, the double-loop problem can be transformed into several deterministic inverse problems, and the efficiency of solving the uncertain inverse problem is dramatically improved. Two numerical examples and an engineering application are applied to demonstrate the feasibility and efficiency of the proposed method.

关键词： uncertain inverse problem Interval model Dimension-reduction method Adaptive strategy

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Impact load identification of composite laminated cylindrical shell with stochastic characteristic

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ARCHIVE OF APPLIED MECHANICS 2022年第4期92卷 1397-1411页

作者： Wang, Linjun Liu, Yang Xie, Youxiang Chen, Baojia China Three Gorges Univ Coll Mech & Power Engn Hubei Key Lab Hydroelect Machinery Design & Maint Yichang 443002 Hubei Peoples R China Queensland Univ Technol Sch Chem Phys & Mech Engn Brisbane Qld 4001 Australia China Three Gorges Univ Coll Sci Technol Yichang 443002 Hubei Peoples R China

Based on augmented Tikhonov regularization (ATR) method and matrix perturbation method, a new computational inverse method is proposed to reconstruct impact loads acting on composite laminated cylindrical shell with random characteristics. Firstly, the stability and effectiveness of augmented Tikhonov regularization method are investigated in solving deterministic inverse problem about impact load identification of composite laminated cylindrical shell structure. Secondly, exploiting the matrix perturbation method, the impact load identification of composite laminated cylindrical shell structure with uncertain factors is transformed into a range of traditional impact load identification with deterministic structure. Lastly, using the knowledge of statistical theory, the statistical features of identified impact force are also analyzed. Numerical simulations validate that the proposed algorithm in this paper successfully solves the impact load identification of composite laminated cylindrical shell with and without random characteristics.

关键词： uncertain inverse problem Impact load identification Interval analysis method Matrix perturbation method Stochastic mechanics

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