基于近似贝叶斯计算的包装件模型选择和参数估计

PDF(978 KB)

振动与冲击 ›› 2023, Vol. 42 ›› Issue (23) : 253-259.

论文

朱大鹏 1,曹兴潇 2

作者信息 +

Packaging model selection and parametric estimation based on approximate Bayesian calculation

ZHU Dapeng1,CAO Xingxiao2

Author information +

文章历史 +

摘要

准确构建包装件模型是进行运输包装安全评价的基础，构建包装件模型包括模型类型选择和模型参数估计。考虑到包装件模型的不确定性和误差，需在贝叶斯推断框架下构建包装件的参数不确定模型，由于在计算似然函数中存在着一系列困难，利用传统贝叶斯推断估计模型参数存在着计算效率低，计算误差大的缺点。本文结合序贯蒙特卡洛和重要性采样，采用近似贝叶斯计算替代传统的贝叶斯推断，该方法可以避免似然函数的计算，随着阈值的减小，该方法可在多种备选模型中优选出最佳模型，同时模型参数收敛至参数真值附近。对包装件进行随机振动实验，对实验数据进行分析，结果表明，Bouc-Wen模型(n=2)是最佳包装件模型，该模型可准确预测包装件的振动响应。

Abstract

Accurately modeling for package is the base of transport packaging safety assessment, the modeling of package includes two aspects: model selection and model parameters estimation. Taking the uncertainties and errors of package model into account, it is reasonable to formulate a uncertainty model for the package in the Bayesian inference framework. In Bayesian inference, the likelihood function is usually either intractable or unavailable, the model selection and parameters estimation can not be realized in efficient and accurate manner. In this paper, to circumvent the evaluation of likelihood function and alleviate the computation burden, an approximate Bayesian computation algorithm is proposed, with which one can realize the model selection and model parameters identification simultaneously. The algorithm is formulated based on the sequential Monte-Carlo and importance sampling. With the threshold decreases in approximate Bayesian computation, the optimal model which can best match the dynamical behavior of real structure in the competing models can be obtained. Simultaneously, the model parameters are convergent to adjacent areas of true parameters values. The random vibration experiment is carried out, the experiment data is analyzed using the algorithm, it is indicated that Bouc-Wen model(n=2) is the optimal model for package dynamic. The model response simulation with the identified parameters is accurate comparing with experiment data.

导出引用

朱大鹏 1,曹兴潇 2. 基于近似贝叶斯计算的包装件模型选择和参数估计[J]. 振动与冲击, 2023, 42(23): 253-259

ZHU Dapeng1,CAO Xingxiao2. Packaging model selection and parametric estimation based on approximate Bayesian calculation[J]. Journal of Vibration and Shock, 2023, 42(23): 253-259

参考文献

[1] 朱大鹏. 非线性包装件加速度响应首次穿越问题分析[J]. 振动与冲击, 2018, 37(24): 166-171.
ZHU Dapeng. Acceleration response first passage failure probability analysis for a nonlinear package[J]. Journal of vibration and shock, 2018, 37(24): 166-171.
[2] WANG Zhiwei, JIANG Jiuhong. Evaluation of product dropping damage based on key component[J]. Packaging Technology and Science, 2010, 23(4): 227-238.
[3] 朱大鹏, 周世生, 张志昆. 蜂窝纸板动态特性建模与参数识别[J]. 振动与冲击, 2010, 29(4):213-217.
ZHU Dapeng, ZHOU Shisheng, ZHANG Zhikun. Dynamic properties modeling and parameter identification for a honeycomb fibreboard[J]. Journal of vibration and shock, 2010, 29(4):213-217.
[4] 朱大鹏. 蜂窝纸板静态弹性与黏弹性特性建模与参数识别[J]. 包装工程, 2015, 36(21):1-6.
ZHU Dapeng. Modelling for Static Elasticity and Viscoelasticity of Honeycomb Paperboard and Parameters Identification[J]. Package Engineering, 2015, 36(21):1-6.
[5] 葛正浩, 王凯, 金龙. 基于有限元法的结构发泡材料参数识别方法研究[J]. 包装工程, 2015, 36(23):78-82.
GE Zhenghao, WANG Kai, JIN Long. Parameter identification method of structure foam material based on finite element method[J]. Package Engineering, 2015,36(23):78-82.
[6] 卢富德, 任梦成, 高德,等. 超弹塑性泡沫连续冲击动力学行为分析的新方法[J]. 振动与冲击, 2022, 41(15):196-200.
LU Fude, REN Mengcheng, GAO De, et al. A new method for analyzing dynamic behavior of hyper-elastoplastic foam under continuous impact[J]. Journal of vibration and shock, 2022, 41(15):196-200.
[7] 李光, 王佳颖, 李津乐. 立式瓦楞复合纸板的平面压缩本构模型[J]. 应用力学学报, 2021, 38(3):886-892.
LI Guang, WANG Jiaying, LI Jinle. Plane compression constitutive model of vertical corrugated composite paperboard[J]. Chinese Journal of Applied Mechanics,2021, 38(3):886-892.
[8] 卢富德, 滑广军, 王丽姝,等. 梯形聚乙烯泡沫结构动态压缩响应有限元分析[J]. 振动与冲击, 2019, 38(14):234-238.
LU Fude, HUA Guangjun, WANG Lishu, et al. Finite element analysis of dynamic compression response of trapezoidal polyethylene foam structure[J]. Journal of vibration and shock, 2019, 38(14):234-238.
[9] 李光, 阮丽, 高德,等. 非线性运输包装系统动力学建模研究进展[J]. 包装工程, 2015, 36(19):1-6.
LI Guang, RUAN Li, GAO De, et al. Research progress of dynamic modeling of nonlinear transport packaging system[J]. Package Engineering, 2015, 36(19):1-6.
[10] 张衬英, 杨小俊, 葛东坡. 振动特性参数对单自由度系统振动响应的影响[J]. 包装工程, 2020, 41(19):75-81.
ZHANG Chenying, YANG Xiaojun, GE Dongpo. Influence of vibration characteristic parameters on vibration response of single degree of freedom system[J]. Package Engineering, 2020, 41(19):75-81.
[11] 郑明亮. 非线性包装系统自由振动特性的对称性解法[J]. 包装工程, 2018, 39(9):7-11.
ZHENG Mingliang. A symmetric solution for the free vibration characteristics of a nonlinear packaging system[J]. Package Engineering, 2018, 39(9):7-11.
[12] 许富华, 武剑锋, 陈思佳,等. 考虑摩擦效应的包装件跌落冲击响应研究[J]. 包装工程, 2015, 36(19):33-37.
XU Fuhua, WU Jianfeng, CHEN Sijia et al. Dropping impact response research of package considering frictional effects[J]. Package Engineering, 2015, 36(19):33-37.
[13] Fuentes R, Dervilis N, Worden K, et al. Efficient parameter identification and model selection in nonlinear dynamical systems via sparse Bayesian learning[J]. Journal of Physics: Conference Series. IOP Publishing, 2019, 1264(1): 012050.
[14] Fuentes R, Nayek R, Gardner P, et al. Equation discovery for nonlinear dynamical systems: a Bayesian viewpoint[J]. Mechanical Systems and Signal Processing, 2021, 154: 107528.
[15] De S, Brewick P T, Johnson E A, et al. A hybrid probabilistic framework for model validation with application to structural dynamics modeling[J]. Mechanical Systems and Signal Processing, 2019, 121: 961-980.
[16] Safari S, Monsalve J M L. Direct optimisation based model selection and parameter estimation using time-domain data for identifying localised nonlinearities[J]. Journal of Sound and Vibration, 2021, 501: 116056.
[17] Civera M, Calamai G, Fragonara L Z. System identification via fast relaxed vector fitting for the structural health monitoring of masonry bridges[J]. Structures. 2021, 30: 277-293.
[18] Civera M, Calamai G, Zanotti Fragonara L. Experimental modal analysis of structural systems by using the fast relaxed vector fitting method[J]. Structural Control and Health Monitoring, 2021, 28(4): e2695.
[19] Ramancha M K, Conte J P, Parno M D. Accounting for model form uncertainty in Bayesian calibration of linear dynamic systems[J]. Mechanical Systems and Signal Processing, 2022, 171: 108871.
[20] Beck J L, Katafygiotis L S. Updating models and their uncertainties. I: Bayesian statistical framework[J]. Journal of Engineering Mechanics-Proceedings of the ASCE, 1998, 124(4): 455-462.
[21] Beck J L, Au S K. Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation[J]. Journal of engineering mechanics, 2002, 128(4): 380-391.
[22] Worden K, Hensman J J. Parameter estimation and model selection for a class of hysteretic systems using Bayesian inference[J]. Mechanical Systems and Signal Processing, 2012, 32: 153-169.
[23] Ritto T G, Nunes L C S. Bayesian model selection of hyperelastic models for simple and pure shear at large deformations[J]. Computers & Structures, 2015, 156: 101-109.
[24] Jin Y F, Yin Z Y, Zhou W H, et al. Identifying parameters of advanced soil models using an enhanced transitional Markov chain Monte Carlo method[J]. Acta Geotechnica, 2019, 14(6): 1925-1947.
[25] Green P L, Worden K. Bayesian and Markov chain Monte Carlo methods for identifying nonlinear systems in the presence of uncertainty[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015, 373(2051): 20140405.
[26] Marjoram P, Molitor J, Plagnol V, et al. Markov chain Monte Carlo without likelihoods[J]. Proceedings of the National Academy of Sciences, 2003, 100(26): 15324-15328.
[27] Sisson S A, Fan Y, Tanaka M M. Sequential monte carlo without likelihoods[J]. Proceedings of the National Academy of Sciences, 2007, 104(6): 1760-1765.
[28] Del Moral P, Doucet A, Jasra A. Sequential monte carlo samplers[J]. Journal of the Royal Statistical Society: Series B, 2006, 68(3): 411-436.
[29] Pritchard J K, Seielstad M T, Perez-Lezaun A, et al. Population growth of human Y chromosomes: a study of Y chromosome microsatellites[J]. Molecular biology and evolution, 1999, 16(12): 1791-1798.
[30] Wen Y K. Method for random vibration of hysteretic systems[J]. Journal of the engineering mechanics division, 1976, 102(2): 249-263.
[31] Kyprianou A, Worden K, Panet M. Identification of hysteretic systems using the differential evolution algorithm[J]. Journal of Sound and vibration, 2001, 248(2): 289-314.
[32] Filippi S, Barnes C P, Cornebise J, et al. On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo[J]. Statistical applications in genetics and molecular biology, 2013, 12(1): 87-107.