基于随机建模与Bayes推断的结构热传导数字孪生建模方法研究

李建宇; 付介祥; 郝鑫野; 李广利

doi:10.21656/1000-0887.460055

基于随机建模与Bayes推断的结构热传导数字孪生建模方法研究

doi: 10.21656/1000-0887.460055

1. 天津科技大学机械工程学院，天津 300457;
2. 大连理工大学工业装备结构分析优化与CAE 软件全国重点实验室，辽宁大连 116024;
3. 中国科学院力学研究所高温气动国家重点实验室，北京 100190

基金项目:

国家自然科学基金（12002347）

详细信息

作者简介:
李建宇（1978—），男，教授，博士(通讯作者. Email: lijianyu@tust.edu.cn).

通讯作者:
李建宇（1978—），男，教授，博士(通讯作者. Email: lijianyu@tust.edu.cn).

中图分类号: TK124|TP391.9
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- 文章访问数: 13
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出版历程
- 收稿日期: 2025-03-24
- 修回日期: 2025-05-22
- 网络出版日期: 2025-09-10

A Digital Twin Modeling Approach for Structural Heat Conduction Analysis Based on Stochastic Modeling and Bayesian Inference

1. State Key Laboratory of Target Vulnerability Assessment, Luoyang, Henan 471023, P.R.China;
2. Engineering Protection Research Department, Defense Engineering Institute, AMS, PLA, Luoyang, Henan 471023, P.R.China;
3. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, P.R.China;

Funds:

The National Science Foundation of China(12002347)

摘要

摘要: 极端热环境条件下结构传热温度场的准确预测是评估装备热力耦合性能的关键基础.数字孪生（digital twin）技术通过对观测数据与仿真模型的深度融合，可实现温度场的高精度动态重构.然而，考虑观测噪声、模型参数不确定性、边界条件扰动等多源不确定性因素的结构传热温度场预测数字孪生模型目前还不多见.该文基于Bayes推断框架，提出了一种结合随机传热分析的数据与模型融合方法，旨在构建考虑不确定性量化的热传导数字孪生模型.首先，在热传导方程中引入随机扰动热源项，以模拟未被原模型量化表征的不确定性因素；其次，采用随机有限元方法求解随机扰动热传导模型，获得包含物理信息的温度场先验分布；最后，基于Bayes法则，将含噪声的观测数据与模型预测先验分布进行融合，并针对Gauss分布情形推导出温度场后验分布的解析表达式.通过一维和二维热传导算例验证，所提方法不仅能够实现对温度场的高精度预测，还可有效量化预测结果的不确定性.
- 热传导分析 /
- 数字孪生 /
- 随机有限元 /
- Bayes推断 /
- 不确定性量化
Abstract: The accurate prediction of structural heat transfer temperature fields under extreme thermal environments is a critical foundation for evaluating the thermo-mechanical performance of equipment. The digital twin technology enables high-precision dynamic reconstruction of temperature fields through the deep integration of observed data and simulation models. However, digital twin models for predicting structural heat transfer temperature fields with multi-source uncertainties, such as observation noise, model parameter uncertainty, and boundary condition disturbances, are still relatively scarce. Aimed to construct a heat conduction digital twin model with uncertainty quantification, a data-model fusion method combined with stochastic heat conduction analysis was proposed based on the Bayesian inference framework. First, a Gaussian random perturbation heat source term was introduced into the heat conduction equation to simulate uncertainty factors not quantified by the original model. Second, the stochastic heat conduction model was solved with the stochastic finite element method to obtain a prior distribution of the temperature field incorporating physical information. Finally, based on Bayes’ theorem, the noisy observation data was fused with the model-predicted prior distribution, and an analytical expression for the posterior distribution of the temperature field was derived for the Gaussian case. The results of 1D and 2D heat conduction examples demonstrate that, the proposed method not only achieves high-precision prediction of the temperature field but also effectively quantifies the uncertainty of the prediction results.
- heat conduction analysis /
- digital twin /
- stochastic finite element /
- Bayesian inference /
- uncertainty quantification

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