虚拟样机环境下不确定性多元动态系统模型验证

针对虚拟样机开发环境中不确定多元输出响应动态系统的模型验证问题,提出了基于误差统计分析、统计主元分析(Probabilistic principal component analysis,PPCA)、基于领域专家知识的阈值定义与转化和贝叶斯区间假设检验的不确定性动态系统模型验证方法和流程。概率误差分析方法用于处理物理试验和仿真结果的重复误差,PPCA用于处理多元相关数据和降维,基于领域专家知识的阈值定义与转化用于确定降维数据空间中的阈值区间,贝叶斯区间假设检验通过贝叶斯可信度提供模型验证结果。该方法解决了不确定性多元动态系统验证中的重复误差量化、多元相关数据处理、领域专家知识融合及提供具有明确物理意义和直观的验证结果等关键问题。对某汽车正向碰撞中乘员保护系统的实例研究表明,该方法能有效实现虚拟样机环境下的不确定性动态系统模型验证,并进一步推动数字化仿真模型的改进。

Bayesian Based Model Validation Method for Uncertain Multivariate Dynamic Systems under Virtual Prototype Environment

In the virtual prototype environment,validation of computational models with multiple and correlated functional responses under uncertainty requires the consideration of multivariate data correlation,uncertainty quantification and propagation,and objective robust metrics.It presents a Bayesian based model validation method,together with statistic error analysis,probabilistic principal component analysis(PPCA),and subjective matter experts’ based threshold definition and transformation,to address these critical issues.The statistic error analysis is used to quantify the errors from the repeated test data and computational simulation results.The PPCA is employed to handle multivariate correlation and to reduce the dimension of the multivariate functional responses.The subjective matter experts’ based threshold definition and transformation is used to decide the threshold interval in the reduced data space.The Bayesian interval hypothesis testing is used to quantitatively assess the quality of a multivariate dynamic system.The differences between the average test data and computer simulation results are extracted for dimension reduction,and then Bayesian interval hypothesis testing is performed on the reduced difference data to assess the model validity.In addition,physics-based threshold is defined and transformed to the reduced space for Bayesian interval hypothesis testing.This new approach resolves some critical drawbacks of the previous methods and adds some desirable properties of a model validation metric for uncertain dynamic systems,such as symmetry.A real-world dynamic system with multiple,repeated functional responses is used to demonstrate this new approach,and shows its potential in promoting the continual improvement of virtual prototype testing.