Statistical Model Validation for Reliable Design of Engineering Products

Model Validation;Copula;Clustering Analysis;U-pooling;PCA;RBDO;Automotive Systems Engineering;CECS Automotive Systems Engineering

Pan, HaoMi, Chris ;

University of Michigan

关键词: Model Validation;    Copula;    Clustering Analysis;    U-pooling;    PCA;    RBDO;    Automotive Systems Engineering;    CECS Automotive Systems Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/134042/Hao%20Pan%20Final%20Dissertation.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Computer models have been used to simulate engineering product and system performances in applications such as vehicle crashworthiness, structural safety, thermal responses, etc. If these predictions were accurate in the product and system design space, these models can help reduce product development cycle, cut down the cost of physical tests, and identify the optimal design. However, models are built on assumptions and simplifications. Therefore, model prediction could be problematic without referring to the corresponding test data. More importantly, design errors could be created because of the model error. Model validation is to determine the degree to which the model is an accurate representation of the real world from the perspective of the intended uses of the model and is a critical process to ensure the improved design efficiency and accuracy while minimizing the overall design cost. The objective of this dissertation is to study a systematic and practical model validation framework for the design of engineering products. To achieve this goal, five research thrusts are developed. First of all, a copula-based model bias characterization approach is developed to capture the relationship between model inputs, outputs, and the model bias. The contribution is to overcome the limitations of regression-based model bias modeling approaches including: i) the curse of dimensionality; ii) assumption of regression forms; and iii) low accuracy to the model outputs with unexplained portion of model bias defined by model parameters. Secondly, an adaptive copula-based model bias characterization approach is developed to further enhance the accuracy of the copula-based approach with the aid of clustering analysis. Thirdly, a novel validation metric for dynamic responses under uncertainty is developed so that model accuracy with dynamic responses can be quantitatively assessed considering limited test data. Fourthly, a stochastic model bias calibration and approximation approach is proposed with the aid of the developed dynamic validation metric for reliability analysis. Finally, reliability-based design optimization is integrated with the proposed model uncertainty characterization approach for reliable design of various engineering products. Various numerical examples and practical engineering problems are employed to demonstrate the proposed model validation framework for designing reliable engineering products.