Applied Mathematics and Mechanics >
An improved interval model updating method via adaptive Kriging models
Received date: 2023-10-26
Online published: 2024-02-24
Supported by
the National Natural Science Foundation of China(12272211);the National Natural Science Foundation of China(12072181);the National Natural Science Foundation of China(12121002);Project supported by the National Natural Science Foundation of China (Nos. 12272211, 12072181, and 12121002)
Copyright
Interval model updating (IMU) methods have been widely used in uncertain model updating due to their low requirements for sample data. However, the surrogate model in IMU methods mostly adopts the one-time construction method. This makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU methods. Therefore, an improved IMU method via the adaptive Kriging models is proposed. This method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey numbers. These optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization (PSO) method to quantify the uncertain parameters, and the IMU is accomplished. During the construction of these adaptive Kriging models, the sample space is gridded according to sensitivity information. Local sampling is then performed in key subspaces based on the maximum mean square error (MMSE) criterion. The interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy requirements. The effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical shell. The results show that the updated results of the interval model are in good agreement with the experimental results.
Sha WEI, Yifeng CHEN, Hu DING, Liqun CHEN . An improved interval model updating method via adaptive Kriging models[J]. Applied Mathematics and Mechanics, 2024 , 45(3) : 497 -514 . DOI: 10.1007/s10483-024-3093-7
| 1 | HEMEZ, F. M., and DOEBLING, S. W. Review and assessment of model updating for non-linear, transient dynamics. Mechanical Systems and Signal Processing, 15 (1), 45- 74 (2001) |
| 2 | REZAIEE-PAJAND, M., ENTEZAMI, A., and SARMADI, H. A sensitivity-based finite element model updating based on unconstrained optimization problem and regularized solution methods. Structural Control and Health Monitoring, 27 (5), e2481 (2020) |
| 3 | WAN, H. P., and REN, W. X. Parameter selection in finite-element-model updating by global sensitivity analysis using Gaussian process metamodel. Journal of Structural Engineering, 141 (6), 04014164 (2015) |
| 4 | GRIP, N., SABOUROVA, N., and TU, Y. Sensitivity-based model updating for structural damage identification using total variation regularization. Mechanical Systems and Signal Processing, 84, 365- 383 (2017) |
| 5 | HE, Y., YANG, J. P., and YU, J. Surrogate-assisted finite element model updating for detecting scour depths in a continuous bridge. Journal of Scientific Computing, 69, 101996 (2023) |
| 6 | WANG, X. M., ZHANG, J. D., SUN, Y., WU, Z. F., TCHUENTE, N. F. C., and YANG, F. Stiffness identification of deteriorated PC bridges by a FEMU method based on the LM-assisted PSO-Kriging model. Structures, 43, 374- 387 (2022) |
| 7 | ZHU, Q. Y., HAN, Q. K., LIU, J. G., and YU, C. S. High-accuracy finite element model updating a framed structure based on response surface method and partition modification. Aerospace, 10 (1), 79 (2023) |
| 8 | FRISWELL, M. I., and MOTTERSHEAD, J. E. Finite Element Model Updating in Structural Dynamics, Springer Netherlands, Dordrecht (1995) |
| 9 | EREIZ, S., DUVNJAK, I.., and FERNANDO JIMÉNEZ-ALONSO, J. Review of finite element model updating methods for structural applications. Structures, 41, 684- 723 (2022) |
| 10 | SEHGAL, S., and KUMAR, H. Structural dynamic model updating techniques: a state of the art review. Archives of Computational Methods in Engineering, 23 (3), 515- 533 (2016) |
| 11 | SIMOEN, E., DE ROECK, G., and LOMBAERT, G. Dealing with uncertainty in model updating for damage assessment: a review. Mechanical Systems and Signal Processing, 56-57, 123- 149 (2015) |
| 12 | CELIK, O. C., and ELLINGWOOD, B. R. Seismic fragilities for non-ductile reinforced concrete frames-role of aleatoric and epistemic uncertainties. Structural Safety, 32 (1), 1- 12 (2010) |
| 13 | HARIRI-ARDEBILI, M. A., SEYED-KOLBADI, S. M., and NOORI, A. Response surface method for material uncertainty quantification of infrastructures. Shock and Vibration, 2018, 1784203 (2018) |
| 14 | JIANG, C., ZHENG, J., and HAN, X. Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: a review. Structural and Multidisciplinary Optimization, 57 (6), 2485- 2502 (2018) |
| 15 | JENSEN, H. A., MILLAS, E., KUSANOVIC, D., and PAPADIMITRIOU, C. Model-reduction techniques for Bayesian finite element model updating using dynamic response data. Computer Methods in Applied Mechanics and Engineering, 279, 301- 324 (2014) |
| 16 | WU, Z., HUANG, B., CHEN, H., and ZHANG, H. A new homotopy approach for stochastic static model updating with large uncertain measurement errors. Applied Mathematical Modelling, 98, 758- 782 (2021) |
| 17 | NI, P. H., LI, J., HAO, H., HAN, Q., and DU, X. L. Probabilistic model updating via variational Bayesian inference and adaptive Gaussian process modeling. Computer Methods in Applied Mechanics and Engineering, 383, 113915 (2021) |
| 18 | LIU, Y., and DUAN, Z. Fuzzy finite element model updating of bridges by considering the uncertainty of the measured modal parameters. Science China Technological Sciences, 55 (11), 3109- 3117 (2012) |
| 19 | KHODAPARAST, H. H., GOVERS, Y., DAYYANI, I., ADHIKARI, S., LINK, M., FRISWELL, M. I., MOTTERSHEAD, J. E., and SIENZ, J. Fuzzy finite element model updating of the DLR AIRMOD test structure. Applied Mathematical Modelling, 52, 512- 526 (2017) |
| 20 | LIAO, B., ZHAO, R., YU, K., and LIU, C. A novel interval model updating framework based on correlation propagation and matrix-similarity method. Mechanical Systems and Signal Processing, 162, 108039 (2022) |
| 21 | ZHAO, Y., YANG, J., FAES, M. G.R., BI, S., and WANG, Y. The sub-interval similarity: a general uncertainty quantification metric for both stochastic and interval model updating. Mechanical Systems and Signal Processing, 178, 109319 (2022) |
| 22 | SU, J. B., SHAO, G. J., and CHU, W. J. Sensitivity analysis of soil parameters based on interval. Applied Mathematics and Mechanics (English Edition), 29 (12), 1651- 1662 (2008) |
| 23 | FEDELE, F., MUHANNA, R. L., XIAO, N., and MULLEN, R. L. Interval-based approach for uncertainty propagation in inverse problems. Journal of Engineering Mechanics, 141 (1), 06014013 (2015) |
| 24 | CHEN, N., YU, D., and XIA, B. Hybrid uncertain analysis for the prediction of exterior acoustic field with interval and random parameters. Computers & Structures, 141, 9- 18 (2014) |
| 25 | QIU, Z., and WANG, P. Parameter vertex method and its parallel solution for evaluating the dynamic response bounds of structures with interval parameters. Science China Physics, Mechanics & Astronomy, 61 (6), 064612 (2018) |
| 26 | FENG, H., RAKHEJA, S., and SHANGGUAN, W. B. Analysis and optimization for generated axial force of a drive-shaft system with interval uncertainty. Structural and Multidisciplinary Optimization, 63 (1), 197- 210 (2021) |
| 27 | MO, J., YAN, W. J., YUEN, K. V., and BEER, M. Efficient inner-outer decoupling scheme for non-probabilistic model updating with high dimensional model representation and Chebyshev approximation. Mechanical Systems and Signal Processing, 188, 110040 (2023) |
| 28 | SHI, Q., WANG, X., WANG, R., CHEN, X., and MA, Y. An interval updating model for composite structures optimization. Composite Structures, 209, 177- 191 (2019) |
| 29 | LI, S. L., LI. H., and OU, J. P. Model updating for uncertain structures with interval parameters. Proceedings of the Asia-Pacific Workshop on Structural Health Monitoring, Yokohama (2006) |
| 30 | DENG, Z. M., GUO, Z. P., and ZHANG, X. J. Interval model updating using perturbation method and radial basis function neural networks. Mechanical Systems and Signal Processing, 84, 699- 716 (2017) |
| 31 | ZHENG, B., YU, K., LIU, S., and ZHAO, R. Interval model updating using universal grey mathematics and Gaussian process regression model. Mechanical Systems and Signal Processing, 141, 106455 (2020) |
| 32 | DING, Y. J., WANG, Z. C., CHEN, G. D., REN, W. X., and XIN, Y. Markov chain Monte Carlo-based Bayesian method for nonlinear stochastic model updating. Journal of Sound and Vibration, 520, 116595 (2022) |
| 33 | REN, Y., LIU, Z., KANG, Z., and PANG, Y. Data-driven optimization study of the multi-relaxation-time lattice Boltzmann method for solid-liquid phase change. Applied Mathematics and Mechanics (English Edition), 44 (1), 159- 172 (2023) |
| 34 | ZHOU, L. R., WANG, L., CHEN, L., and OU, J. P. Structural finite element model updating by using response surfaces and radial basis functions. Advances in Structural Engineering, 19 (9), 1446- 1462 (2016) |
| 35 | KESHTEGAR, B., MERT, C., and KISI, O. Comparison of four heuristic regression techniques in solar radiation modeling: Kriging method vs RSM, MARS and M5 model tree. Renewable and Sustainable Energy Reviews, 81, 330- 341 (2018) |
| 36 | GIOVANIS, D. G., PAPAIOANNOU, I., STRAUB, D., and PAPADOPOULOS, V. Bayesian updating with subset simulation using artificial neural networks. Computer Methods in Applied Mechanics and Engineering, 319, 124- 145 (2017) |
| 37 | ZHAO, K., GAO, Z. H., and HUANG, J. T. Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method. Applied Mathematics and Mechanics (English Edition), 35 (2), 191- 202 (2014) |
| 38 | LIN, C. H. Composite recurrent Laguerre orthogonal polynomials neural network dynamic control for continuously variable transmission system using altered particle swarm optimization. Nonlinear Dynamics, 81 (3), 1219- 1245 (2015) |
| 39 | XU, Z. Y., DU, L., WANG, H. P., and DENG, Z. C. Particle swarm optimization-based algorithm of a symplectic method for robotic dynamics and control. Applied Mathematics and Mechanics (English Edition), 40 (1), 111- 126 (2019) |
| 40 | LI, Q. X., LIU, S. F., and FORREST, J. Y. L. Fundamental definitions and calculation rules of grey mathematics: a review work. Journal of Systems Engineering and Electronics, 26 (6), 1254- 1267 (2015) |
| 41 | QIAN, J. C., YI, J. X., CHENG, Y. S., LIU, J., and ZHOU, Q. A sequential constraints updating approach for Kriging surrogate model-assisted engineering optimization design problem. Engineering with Computers, 36 (3), 993- 1009 (2020) |
| 42 | GARUD, S. S., KARIMI, I. A., and KRAFT, M. Design of computer experiments: a review. Computers & Chemical Engineering, 106, 71- 95 (2017) |
| 43 | CHEN, C. H., LONG, J. Q., CHEN, W. Z., LIU, Z. F., and GUO, J. Y. Modeling and prediction of spindle dynamic precision using the Kriging-based response surface method with a novel sampling strategy. Nonlinear Dynamics, 111 (1), 559- 579 (2023) |
| 44 | SOBOL, I. On sensitivity estimation for nonlinear mathematical models. Matematicheskoe Modelirovanie, 1, 112- 118 (1990) |
| 45 | KUCHERENKO, S., DELPUECH, B., IOOSS, B., and TARANTOLA, S. Application of the control variate technique to estimation of total sensitivity indices. Reliability Engineering and System Safety, 134, 251- 259 (2015) |
| 46 | YOU, T., GONG, D., ZHOU, J., SUN, Y., and CHEN, J. Frequency response function-based model updating of flexible vehicle body using experiment modal parameter. Vehicle System Dynamics, 60 (11), 3930- 3954 (2022) |
| 47 | REN, M. L., HUANG, X. D., ZHU, X. X., and SHAO, L. J. Optimized PSO algorithm based on the simplicial algorithm of fixed point theory. Applied Intelligence, 50 (7), 2009- 2024 (2020) |
| 48 | MARES, C., MOTTERSHEAD, J. E., and FRISWELL, M. I. Stochastic model updating: part 1-theory and simulated example. Mechanical Systems and Signal Processing, 20 (7), 1674- 1695 (2006) |
| 49 | KHODAPARAST, H. H., MOTTERSHEAD, J. E., and BADCOCK, K. J. Interval model updating with irreducible uncertainty using the Kriging predictor. Mechanical Systems and Signal Processing, 25 (4), 1204- 1226 (2011) |
| 50 | KHODAPARAST, H. H., MOTTERSHEAD, J. E., and BADCOCK, K. J. Interval model updating: method and application. International Conference on Noise and Vibration Engineering (ISMA)/Conference of USD, Leuven, Belgium, 5277- 5289 (2010) |
/
| 〈 |
|
〉 |
Email Alert
RSS