基于Wasserstein距离测度的非精确概率模型修正方法

doi:10.3901/JME.2022.24.300

机械工程学报 ›› 2022, Vol. 58 ›› Issue (24): 300-311.doi: 10.3901/JME.2022.24.300

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基于Wasserstein距离测度的非精确概率模型修正方法

杨乐昌^1,2, 韩东旭³, 王丕东¹

1. 北京科技大学机械工程学院北京 100083;
2. 香港城市大学先进设计与系统工程系香港 999077;
3. 中国科学院空间应用工程与技术中心北京 100096

收稿日期:2022-03-22 修回日期:2022-09-05 出版日期:2022-12-20 发布日期:2023-04-03
通讯作者: 杨乐昌(通信作者),男,1987年出生,博士,副教授,硕士研究生导师。主要研究方向为机械可靠性建模与分析、不确定性量化方法等。E-mail:yanglechang@ustb.edu.cn
作者简介:杨乐昌(通信作者),男,1987年出生,博士,副教授,硕士研究生导师。主要研究方向为机械可靠性建模与分析、不确定性量化方法等。E-mail:yanglechang@ustb.edu.cn;韩东旭,女,1999年出生,博士研究生。主要研究方向为非精确概率可靠性,不确定性量化。E-mail:h18611579799@163.com;王丕东,男,1987年出生,博士,讲师。主要研究方向为系统工程与可靠性等。E-mail:pidongwang@ustb.edu.cn
基金资助:
国家重点研发计划（2021YFB3401500）、国家自然科学基金（52005032，72271025）、航空科学基金（2018ZC74001）资助项目。

Imprecise Probabilistic Model Updating Using A Wasserstein Distance-based Uncertainty Quantification Metric

YANG Lechang^1,2, HAN Dongxu³, WANG Pidong¹

1. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083;
2. Department of Advanced Design and Systems Engineering, City University of Hong Kong, Hong Kong 999077;
3. Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, Beijing 100096

Received:2022-03-22 Revised:2022-09-05 Online:2022-12-20 Published:2023-04-03

摘要/Abstract

摘要： 复杂物理系统的数学代理模型往往包含多类不确定性因素。在实际工程问题如机械系统可靠性优化设计中，可结合系统响应的部分实测数据，校准模型关键参数取值，修正模型结构，提高代理模型的保真性。但对于具有混合不确定性的非精确概率模型，传统基于欧式距离的模型修正方法并不适用。针对这一问题，提出一种基于Wasserstein距离测度的模型修正方法，该方法基于Wasserstein距离测度构建核函数，利用p维参数空间中Wasserstein距离的几何性质以量化不同概率分布之间的差异，相较于现有模型修正方法，可校准模型的高阶超参数，显著降低模型结构及参数不确定性。针对工程实际需求，进一步采用近似贝叶斯推理与切片分割技术以降低计算成本。通过受迫振动钢板本构参数校核问题与NASA Langley多学科不确定性量化问题验证了本方法在静力学与动力学等实际工程问题中的有效性。

关键词: Wasserstein距离, 贝叶斯方法, 非精确概率, 不确定性量化, 近似推理

Abstract: Uncertainty factors are usually contained in the mathematical proxy model of complex physical system. In practical engineering problems such as mechanical system reliability optimization design, the key parameters of the model can be calibrated and the model structure can be modified to improve the fidelity of the proxy model. However, for imprecise probabilistic models with mixed uncertainties, the traditional model updating method based on the Euclidean distance is not applicable. To solve this problem, a new model updating method based on the Wasserstein distance measure is proposed, which builds the kernel function based on the Wasserstein distance measure, and uses the geometric properties of Wasserstein distance in P-dimensional parameter space to quantify the differences between different probability distributions. Compared with the existing model updating methods, high-order hyper-parameters of the model can be calibrated to significantly reduce the uncertainty of model structure and parameters. In order to reduce the calculation cost, the approximate Bayesian inference and sliced segmentation technology is further adopted to meet the engineering requirements. The validity of this method for practical engineering problems, such as statics and dynamics, is verified by the constitutive parameter checking problem of forced vibration steel plate and the multidisciplinary uncertainty quantification problem of NASA Langley.

Key words: Wasserstein distance, Bayesian methods, imprecise probability, model updating, approximate reasoning

中图分类号:

TH122

杨乐昌, 韩东旭, 王丕东. 基于Wasserstein距离测度的非精确概率模型修正方法[J]. 机械工程学报, 2022, 58(24): 300-311.

YANG Lechang, HAN Dongxu, WANG Pidong. Imprecise Probabilistic Model Updating Using A Wasserstein Distance-based Uncertainty Quantification Metric[J]. Journal of Mechanical Engineering, 2022, 58(24): 300-311.

参考文献

[1] 王龙华.数学模型校准问题研究[D].长沙:国防科学技术大学, 2012.WANG Longhua.Research on the calibration of mathematical model[D].Changsha:National University of Defense Technology, 2012.
[2] 朱战霞, 张红文, 罗秋月.自由漂浮空间机器人神经网络自适应控制律设计[J].西北工业大学学报, 2017, 35(1):59-65.ZHU Zhanxia, ZHANG Hongwen, LUO Qiuyue.Design of neural network adaptive control law for free-floating space robot[J].Journal of Northwestern Polytechnical University, 2017, 35(1):59-65.
[3] 喻天翔, 赵庆岩, 尚柏林, 等.考虑间隙不确定性的花键概率疲劳寿命预测方法[J/OL].机械工程学报, 1-12[2022-04-05].http://kns.cnki.net/kcms/detail/11.2187.TH.20210514.1138.002.html YU Tianxiang, ZHAO Qingyan, SHANG Bolin, et al.Probabilistic fatigue life prediction method of spline considering clearance uncertainty[J].Journal of Mechanical Engineering, 1-12[2022-04-05].http://kns.cnki.net/kcms/detail/11.2187.TH.20210514.1138.002.html
[4] 张小强.随机与认知不确定性下机械系统可靠性分析与优化设计方法研究[D].成都:电子科技大学, 2018.ZHANG Xiaoqiang.Research on reliability analysis and optimization design method of mechanical system under stochastic and cognitive uncertainty[D].Chengdu:University of Electronic Science and Technology of China, 2018.
[5] 李彦锋, 黄洪钟, 黄意贤.太阳翼驱动机构的故障模式影响分析与时变可靠性研究[J].机械工程学报, 2020, 56(5):108-115.LI Yanfeng, HUANG Hongzhong, HUANG Yixian.Analysis of failure mode influence and time-varying reliability of solar wing driving mechanism[J].Journal of Mechanical Engineering, 2020, 56(5):108-115.
[6] KHODAPARAST H H, MOTTERSHEAD J E, BADCOCK K J.Interval model updating with irreducible uncertainty using the Kriging predictor[J].Mechanical Systems and Signal Processing, 2011, 25(4):1204-1226.
[7] ABU HUSAIN N, KHODAPARAST H H, OUYANG H.Parameter selection and stochastic model updating using perturbation methods with parameter weighting matrix assignment[J].Mechanical Systems and Signal Processing, 2012, 32:135-152.
[8] 彭卫文, 黄洪钟, 李彦锋, 等.基于数据融合的加工中心功能铣头贝叶斯可靠性评估[J].机械工程学报, 2014, 50(6):185-191.PENG Weiwen, HUANG Hongzhong, LI Yanfeng, et al.Bayesian reliability evaluation of machining center functional milling head based on data fusion[J].Journal of Mechanical Engineering, 2014, 50(6):185-191.
[9] BI S, PRABHU S, COGAN S, et al.Uncertainty quantification Metrics with varying statistical information in model calibration and validation[J].AIAA Journal, 2017, 55(10):3570-3583.
[10] YANG L C, BI S F, FAES M G R, et al.Bayesian inversion for imprecise probabilistic models using a novel entropy-based uncertainty quantification metric[J].Mech.Syst.Signal Proc., 2022, 162:21.
[11] BI S, BROGGI M, BEER M.The role of the Bhattacharyya distance in stochastic model updating[J].Mechanical Systems and Signal Processing, 2019, 117:437-452.
[12] 张建军, 乔松珊.正态总体下参数的优化极大似然估计方法[J].统计与决策, 2012(2):16-18.ZHANG Jianjun, QIAO Songshan.Optimized maximum likelihood estimation method for parameters in normal population[J].Statistics and Decision, 2012(2):16-18.
[13] MOTTERSHEAD J E, FRISWELL M I.Model updating in structural dynamics:A survey[J].Journal of Sound and Vibration, 1993, 167(2):347-375.
[14] ROY C J, OBERKAMPF W L.A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing[J].Computer Methods in Applied Mechanics and Engineering, 2011, 200(25-28):2131-2144.
[15] RENS V D S, SARAH D, RUTH K, et al.Bayesian statistics and modelling[J].Nature Reviews Methods Primers, 2021, 1(1):3.https://doi.org/10.1038/s43586-020-00003-0
[16] CRANMER K, BREHMER J, LOUPPE G.The frontier of simulation-based inference[J].Proceedings of the National Academy of Sciences of the United States of America, 2020, 117(48):30055-30062.
[17] BARAGATTI M, PUDLO P.An overview on approximate Bayesian computation[J].ESAIM:Proceedings, 2014, 44:291-299.
[18] CHING J, CHEN Y C.Transitional Markov Chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging[J].Journal of Engineering Mechanics, 2007, 133:816-832.
[19] RUBNER Y, TOMASI C, GUIBAS L J.The Earth mover's distance as a metric for image retrieval[J].International Journal of Computer Vision, 2000, 40(2):99-121.
[20] PANARETOS V M, ZEMEL Y.Statistical aspects of wasserstein distances[J].Annual Review of Statistics and Its Application, 2019, 6:405-431.
[21] NADJAHI K, DE BORTOLI V, DURMUS A, et al.Approximate Bayesian computation with the sliced-wasserstein distance[C]//ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 1, 2020, Barcelona.SPAIN:IEEE, 2020:5470-5474.
[22] FANG S E, ZHANG Q H, REN W X.An interval model updating strategy using interval response surface models[J].Mechanical Systems and Signal Processing, 2015, 60-61:909-927.
[23] CRESPO L G, KENNY S P, GIESY D P.The NASA langley multidisciplinary uncertainty quantification challenge[C]//AIAA Non-Deterministic Approaches conference, January 13-17, 2014, Maryland.National Harbor:AIAA, 2014:13-47.
[24] SAFTA C, SARGSYAN K, NAJM H N, et al.Probabilistic methods for sensitivity analysis and calibration in the NASA challenge problem[J].Journal of Aerospace Information Systems, 2015, 12(1):219-234.
[25] SRIVASTAVA A, SUBRAMANIYAN A K, WANG L.Hybrid Bayesian solution to NASA langley research center multidisciplinary uncertainty quantification challenge[J].Journal of Aerospace Information Systems, 2015, 12(1):114-139.

基于Wasserstein距离测度的非精确概率模型修正方法

Imprecise Probabilistic Model Updating Using A Wasserstein Distance-based Uncertainty Quantification Metric

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