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Computer Aided Engineering (CAE) has become a vital tool for product development in automotive industry. Various computer models for occupant restraint systems are developed. The models simulate the vehicle interior, restraint system, and occupants in different crash scenarios. In order to improve the efficiency during the product development process, the model quality and its predictive capabilities must be ensured. In this research, an objective model validation metric is developed to evaluate the model validity and its predictive capabilities when multiple occupant injury responses are simultaneously compared with test curves. This validation metric is based on the probabilistic principal component analysis method and Bayesian statistics approach for multivariate model assessment. It first quantifies the uncertainties in both test and simulation results, extracts key features, and then evaluates the model quality.

Response surface methodologies (RSMs) have been proposed as surrogate models in vehicle design processes to gain insight and improve turnaround time for optimization and robust design. However, when studying the vehicle occupants during crash events, nonlinearities in responses, coupled with the relatively high dimensionality of vehicle design, can yield misleading results with little or no warning from the response surface algorithms. To ensure the accuracy and reliability of RSMs, fast and dependable error estimation procedures are essential for enlightening how well a response surface predicts highly nonlinear phenomena, given a limited number of model simulations. Such error estimation methods are also useful for providing guidance on how many simulation runs are needed for reliable RSM construction. In this paper, a fast cross validation error estimate procedure is first presented, applied to the multivariable adaptive regression spline (MARS) response surface method.

Response surface methods have been widely used in robust design for reducing turn-around time and improving quality. That is, from a given set of CAE data (design-of-experiments results), many different robust optimization studies can be performed with different constraints and objectives without large, recurring, computation costs. However, due to the highly nonlinear and non-convex nature of occupant injury responses, it is difficult to generate high quality response surface models from them. In this paper, we apply a cross validation technique to estimate the accuracy of response surface models, particularly in the context of robustness assessment. We then decompose selected occupant injury responses into more fundamental signals before fitting surfaces to improve the predictivity of the response surface models. Real-world case studies on an occupant restraint system robust design problem are used to demonstrate the methodology.

This paper focuses on the methodology development and application of reliability-based design optimization to a vehicle exhaust system under noise, vibration and harshness constraints with uncertainties. Reliability-based design optimization provides a systematic way for considering uncertainties in product development process. As traditional reliability analysis itself is a design optimization problem that requires many function evaluations, it often requires tremendous computational resources and efficient optimization methodologies. Multiple functional response constraints and large number of design variables add further complexity to the problem. This paper investigates an integrated approach by taking advantages of variable screening, design of experiments, response surface model, and reliability-based design optimization for problems with functional responses. A typical vehicle exhaust system is used as an example to demonstrate the methodology.

Reliability-based design optimization (RBDO) has been widely used to obtain a reliable design via an existing CAE model considering the variations of input variables. However, most RBDO approaches do not consider the CAE model bias and uncertainty, which may largely affect the reliability assessment of the final design and result in risky design decisions. In this paper, the Gaussian Process Modeling (GPM) approach is applied to statistically correct the model discrepancy which is represented as a bias function, and to quantify model uncertainty based on collected data from either real tests or high-fidelity CAE simulations. After the corrected model is validated by extra sets of test data, it is integrated into the RBDO formulation to obtain a reliable solution that meets the overall reliability targets while considering both model and parameter uncertainties.