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CLC number: TU451

On-line Access: 2017-07-04

Received: 2016-06-14

Revision Accepted: 2016-10-26

Crosschecked: 2017-06-26

Cited: 0

Clicked: 1815

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Jian Zhang

http://orcid.org/0000-0003-2457-9558

Chao Jia

http://orcid.org/0000-0002-2448-894X

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Journal of Zhejiang University SCIENCE A 2017 Vol.18 No.7 P.567-578

http://doi.org/10.1631/jzus.A1600440


Powell inversion mechanical model of foundation parameters with generalized Bayesian theory


Author(s):  Jian Zhang, Chu-wei Zhou, Chao Jia, Jing Lin

Affiliation(s):  Department of Mechanics and Structural Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; more

Corresponding email(s):   zjmech@163.com

Key Words:  Powell inversion, Mechanical model, Foundation parameter, Bayesian objective function, Stochastic property


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Jian Zhang, Chu-wei Zhou, Chao Jia, Jing Lin. Powell inversion mechanical model of foundation parameters with generalized Bayesian theory[J]. Journal of Zhejiang University Science A, 2017, 18(7): 567-578.

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DOI - 10.1631/jzus.A1600440


Abstract: 
The inversion mechanical model of foundation parameters based on Powell optimizing theory was studied with generalized Bayesian theory. First, the generalized bayesian objective function for foundation parameters was deduced with maximum likelihood theory. Then, the expectation expression and the covariance expression of the foundation parameters were obtained. After selecting the Winkler foundation as representative, the governing differential equations of the typical foundation were derived. With the orthogonal series transform method, the Fourier closed form solution of a moderately-thick plate on the Winkler foundation was achieved. After the optimal step length was determined with the quadratic parabolic interpolation method, the powell inversion mechanical model of foundation parameters was resolved, and the corresponding inversion procedure was completed. Through particular example analysis, the highlight is that the powell inversion mechanical model of foundation parameters with generalized Bayesian theory is correct and the derived powell inversion model has universal significance, which can be applied in other kinds of foundation parameters. Besides, the powell inversion iterative processes of foundation parameters have excellent numerical stability and convergence. The Powell optimizing theory is unconcerned with the partial derivatives of systematic responses to foundation parameters, which undoubtedly has a satisfying iterative efficiency compared with the available Kalman filtering or conjugate gradient inversion of the foundation parameters. The generalized bayesian objective function can synchronously take the stochastic property of systematic parameters and systematic responses into account.

基于广义Bayes理论地基参数的Powell反演力学模型

目的:通过Powell优化反演方法建立Winkler地基参数的反演力学模型,获得地基参数的稳定数值解。
创新点:根据Bayes理论,推导广义Bayes目标函数;利用Fourier变换,推求Winkler地基上简支板的Fourier闭式解,建立地基参数的反演力学模型。
方法:1. 根据Bayes理论,推导广义Bayes目标函数(公式(4))及地基参数的广义Bayes均值和方差表达式(公式(9)和(11));2. 引入Mindlin理论,推导Winkler地基上板的控制微分方程,推求Winkler地基上简支板的Fourier闭式解;3. 提出步长的一维自动寻优方案,结合Powell优化方法建立Winkler地基参数的广义Bayes反演力学模型。
结论:1. 地基参数的反演迭代过程稳定收敛于参数真值;2. 与Kalman滤波方法和共轭梯度法不同,Powell优化方法的迭代过程不涉及目标函数的偏导数计算;3. 广义Bayes目标函数能同时考虑不同测量点和不同测量次数的位移实测资料,计算效率更高。

关键词:Powell反演;力学模型;地基参数;Bayes目标函数;随机性

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Belabed, Z., Houari, M.S.A., Tounsi, A., et al., 2014. An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates. Composites Part B: Engineering, 60:274-283.

[2]Bennoun, M., Houari, M.S.A., Tounsi, A., 2016. A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates. Mechanics of Advanced Materials and Structures, 23(4):423-431.

[3]Bouderba, B., Houari, M.S.A., Tounsi, A., 2013. Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations. Steel and Composite Structures, 14(1):85-104.

[4]Bourada, M., Kaci, A., Houari, M.S.A., et al., 2015. A new simple shear and normal deformations theory for functionally graded beams. Steel and Composite Structures, 18(2):409-423.

[5]Bousahla, A.A., Houari, M.S.A., Tounsi, A., et al., 2014. A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates. International Journal of Computational Methods, 11(06):1350082.

[6]Chen, B.H., Zhao, H.B., Ru, Z.L., et al., 2015. Probabilistic back analysis for geotechnical engineering based on Bayesian and support vector machine. Journal of Central South University, 22(12):4778-4786.

[7]Ching, J., Phoon, K.K., Wu, S.H., 2016. Impact of statistical uncertainty on geotechnical reliability estimation. Journal of Engineering Mechanics, 142(6):04016027.

[8]Fathi, A., Poursartip, B., Stokoe II, K.H., et al., 2016. Three-dimensional P- and S-wave velocity profiling of geotechnical sites using full-waveform inversion driven by field data. Soil Dynamics and Earthquake Engineering, 87(8):63-81.

[9]Hamdia, K.M., Zhuang, X.Y., He, P.F., et al., 2016. Fracture toughness of polymeric particle nanocomposites: evaluation of models performance using Bayesian method. Composites Science and Technology, 126:122-129.

[10]Hamidi, A., Houari, M.S.A., Mahmoud, S.R., et al., 2015. A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates. Steel and Composite Structures, 18(1):235-253.

[11]Hebali, H., Tounsi, A., Houari, M.S.A., et al., 2014. New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Journal of Engineering Mechanics, 140(2):374-383.

[12]Jia, Y.F., Chi, S.C., 2015. Back-analysis of soil parameters of the Malutang II concrete face rockfill dam using parallel mutation particle swarm optimization. Computers and Geotechnics, 65:87-96.

[13]Kim, J., Kim, J., Kim, M., et al., 2015. Prediction of ground load by performing back analysis using composite support model in concrete lining design. KSCE Journal of Civil Engineering, 19(6):1697-1706.

[14]Li, T.C., Lyu, L.X., Zhang, S.L., et al., 2015. Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 16(8):644-655.

[15]Meziane, M.A.A., Abdelaziz, H.H., Tounsi, A., 2014. An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions. Journal of Sandwich Structures and Materials, 16(3):293-318.

[16]Nanthakumar, S.S., Lahmer, T., Rabczuk, T., 2013. Detection of flaws in piezoelectric structures using XFEM. International Journal for Numerical Methods in Engineering, 96(6):373-389.

[17]Nanthakumar, S.S., Lahmer, T., Zhuang, X., et al., 2016. Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Problems in Science and Engineering, 24(1):153-176.

[18]Ong, D.E.L., Choo, C.S., 2016. Back-analysis and finite element modeling of jacking forces in weathered rocks. Tunnelling and Underground Space Technology, 51:1-10.

[19]Sarp Arsava, K., Nam, Y.Y., Kim, Y., 2016. Nonlinear system identification of smart reinforced concrete structures under impact loads. Journal of Vibration and Control, 22(16):3576-3600.

[20]Xie, Y.F., 2011. Least square inversed analysis of soil parameter for foundation with two-order gradient theoretic method. Advanced Materials Research, 243-249:2294-2299.

[21]Xin, Y., Zhang, J., Han, X.D., et al., 2014. Research on ultimate load of highway prestressed concrete U-shaped continuous rigid frame bridge based on nonlinear finite method. Applied Mechanics and Materials, 501-504: 1398-1402.

[22]Yahia, S.A., Atmane, H.A., Houari, M.S.A., et al., 2015. Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories. Structural Engineering and Mechanics, 53(6):1143-1165.

[23]Zhang, J., Ye, J.S., Tang, X.S., 2008. Kalman filtering identification of Winkler foundation’s parameter based on Mindlin theory. Rock and Soil Mechanics, 29(2):425-430 (in Chinese).

[24]Zhang, J., Zhou, C.W., Lin, J., 2012. Dynamic Bayesian identification of mechanical parameters of multi-cell curve box girder based on conjugate gradient theory. Science China Technological Sciences, 55(4):1057-1065.

[25]Zhao, X.M., 2007. Dynamic Bayesian identification of Winkler subgrade parameter based on Mindlin theory. Engineering Mechanics, 24(10):57-63 (in Chinese).

[26]Zidi, M., Tounsi, A., Houari, M.S.A., et al., 2014. Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory. Aerospace Science and Technology, 34:24-34.

[27]Zong, Z.H., Zhou, R., Huang, X.Y., et al., 2014. Seismic response study on a multi-span cable-stayed bridge scale model under multi-support excitations. Part I: shaking table tests. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 15(5):351-363.

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