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Interval assessments of identified parameters for uncertain structures

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Abstract

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.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 51905257); the Natural Science Foundation of Hunan Province (Grant No: 2020JJ6075); the Outstanding Youth Foundation of Hunan Education Department (Grant No: 18B301); the Natural Science Foundation of Hebei Province (Grant No. A2019202171), the Changsha Municipal Natural Science Foundation (Grant No: kq2014050) and the Open Fund of State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body (Grant No. 31915004).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hunan University of Technology, Zhuzhou, 412007, People’s Republic of China

    Jiachang Tang & Chenji Mi

  2. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    Lixiong Cao

  3. College of Mechanical Engineering, University of South China, Hengyang, 421001, People’s Republic of China

    Chunming Fu

  4. State Key Laboratory of Reliability and Intelligence of Electrical Equipment, School of Mechanical Engineering, Hebei University of Technology, 300401, Tianjin, People’s Republic of China

    Qiming Liu

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Tang, J., Cao, L., Mi, C. et al. Interval assessments of identified parameters for uncertain structures. Engineering with Computers 38 (Suppl 4), 2905–2917 (2022). https://doi.org/10.1007/s00366-021-01432-5

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