Model Validation For Vehicle Safety Oriented Multivariate Dynamic Systems Under Uncertainty: Theories And Applications

Computer modeling and simulations are playing an increasingly important role in complex engineering system applications such as reducing vehicle prototype tests and shortening product development time. Increasing computer models are developed to simulate vehicle crashworthiness, dynamic, and fuel efficiency. Before applying these models for product development, model validation needs to be conducted to assess the validity of the models. Model validation is to assess the validity and predictive capabilities of computer models by comparing computer output with test data. Developing quantitative validation methods for complex dynamic systems has attracted considerable researchers' interest in recent years. However, how to effectively validate the computer models of multivariate dynamic systems under uncertainty has become the bottleneck in the application of modeling and simulations in various industries.In order to provide general model validation methodology and tool for multivariate dynamic systems under uncertainty, and develop ISO standards on validation metrics to evaluate computer aided engineering model quality compared to physical test for safety applications, the author has spent three years in the Research and Innovation center of Ford Motor Company (Dearborn, MI, USA) to conduct related research. This dissertation investigates and develops methods for the key issues in model validation including: (1) univariate dynamic response comparison and analysis, (2) multivariate dynamic responses analysis, and (3) uncertainty analysis and quantification. A systematic model validation method for complex multivariate dynamic system is proposed. Further more, an objective rating prototype system is developed. This study is supported and funded by Ford Motor Company University Research Programs (URP), International Organization for Standardization (ISO) working group (TC22 ISO WG4), National Natural Science Foundation of China, and so on.The main contributions of the dissertation can be summarized as follows:(1) A comprehensive analysis tool for dynamic response comparison named Enhanced Error Assessment of Response time histories (EEARTH) is proposed. It provides one intuitive rating based on the physical-based thresholds and subject matter experts (SMEs)' knowledge, and three independent error measures that associated with physically meaningful characteristics (phase, magnitude, and slope). The effectiveness and advantages of the proposed metric over existing methods are demonstrated. An automatic model calibration method, based on EEARTH error measures and multi-objective optimization algorithm, is proposed to automatically update CAE model parameters.(2) An integrated validation method and process are developed for dynamic system with multivariate functional response time histories. The principal component analysis approach is used to address multivariate correlation and dimensionality reduction, the dynamic time warping and correlation coefficient calculation are used to for error assessment, the subject matter experts'opinions are incorporated to provide the overall rating of the dynamic system. This method solves multivariate dynamic response comparison issue.(3) The uncertainty analysis methods are investigated and developed to quantify various errors from repeated physical tests, multiple computer models and multivariate dimension reduction. An interval Bayesian hypothesis testing based validation process is proposed to quantify the confidence of computer simulations, thus providing rational, objective decision-making support for model assessment. A comparison study is performed to demonstrate the advantages of the proposed method.(4) A Bayesian based model validation method together with statistical data analysis and probabilistic principal component analysis (PPCA) is proposed for multivariate dynamic system under uncertainty. The statistical data analysis is used calculate the variability from repeated tests and CAE data, the PPCA is employed to handle multivariate correlation and to reduce the dimension of the functional responses. The Bayesian interval hypothesis testing is used to quantitatively assess the quality of the dynamic system. The differences between the mean values of test and CAE data are extracted for dimension reduction through PPCA, and the variability is propagated through the data transformation. Bayesian interval hypothesis testing is then performed on the reduced difference data to assess the model validity. In addition, physics-based threshold is defined and transformed to the PPCA space for Bayesian interval hypothesis testing. A real-world dynamic system with one set of test data and two CAE models is used to demonstrate this new approach.(5) An objective rating prototype system, based on the proposed theoretical methodologies and the evaluation requirement of ISO committee, is developed. A frontal impact case study for New Car Assessment Program (NCAP) is used to demonstrate the validity of this rating tool.