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Vehicle restraint system design is a difficult optimization problem to solve because (1) the nature of the problem is highly nonlinear, non-convex, noisy, and discontinuous; (2) there are large numbers of discrete and continuous design variables; (3) a design has to meet safety performance requirements for multiple crash modes simultaneously, hence there are a large number of design constraints. Based on the above knowledge of the problem, it is understandable why design of experiment (DOE) does not produce a high-percentage of feasible solutions, and it is difficult for response surface methods (RSM) to capture the true landscape of the problem. Furthermore, in order to keep the restraint system more robust, the complexity of restraint system content needs to be minimized in addition to minimizing the relative risk score to achieve New Car Assessment Program (NCAP) 5-star rating.

In vehicle design, response surface model (RSM) is commonly used as a surrogate of the high fidelity Finite Element (FE) model to reduce the computational time and improve the efficiency of design process. However, RSM introduces additional sources of uncertainty, such as model bias, which largely affect the reliability and robustness of the prediction results. The bias of RSM need to be addressed before the model is ready for extrapolation and design optimization. This paper further investigates the Bayesian inference based model extrapolation method which is previously proposed by the authors, and provides a systematic and integrated stochastic bias corrected model extrapolation and robustness design process under uncertainty. A real world vehicle design example is used to demonstrate the validity of the proposed method.

One of the major challenges in multiobjective, multidisciplinary design optimization (MDO) is the long computational time required in evaluating the new designs' performances. To shorten the cycle time of product design, a data mining-based strategy is developed to improve the efficiency of heuristic optimization algorithms. Based on the historical information of the optimization process, clustering and classification techniques are employed to identify and eliminate the low quality and repetitive designs before operating the time-consuming design evaluations. The proposed method improves design performances within the same computation budget. Two case studies, one mathematical benchmark problem and one vehicle side impact design problem, are conducted as demonstration.

Due to magnesium alloy's poor weldability, other joining techniques such as laser assisted self-piercing rivet (LSPR) are used for joining magnesium alloys. This research investigates the fatigue performance of LSPR for magnesium alloys including AZ31 and AM60. Tensile-shear and coach peel specimens for AZ31 and AM60 were fabricated and tested for understanding joint fatigue performance. A structural stress - life (S-N) method was used to develop the fatigue parameters from load-life test results. In order to validate this approach, test results from multijoint specimens were compared with the predicted fatigue results of these specimens using the structural stress method. The fatigue results predicted using the structural stress method correlate well with the test results.

Morphological features of voids were characterized for T300/924 12-ply and 16-ply composite laminates at different porosity levels through the implementation of a digital microscopy (DM) image analysis technique. The composite laminates were fabricated through compression molding. Compression pressures of 0.1MPa, 0.3MPa, and 0.5MPa were selected to obtain composite plaques at different porosity levels. Tension-tension fatigue tests at load ratio R=0.1 for composite laminates at different void levels were conducted, and the dynamic stiffness degradation during the tests was monitored. Fatigue mechanisms were then discussed based on scanning electron microscope (SEM) images of the fatigue fracture surfaces. The test results showed that the presence of voids in the matrix has detrimental effects on the fatigue resistance of the material, depending on the applied load level.

Process integration and optimization is the key enabler of the Integrated Computational Materials Engineering (ICME) of carbon fiber composites. In this work, automated workflows are developed for two types of composites: Sheet Molding Compounds (SMC) short fiber composites, and multi-layer unidirectional (UD) composites. For SMC, the proposed workflow integrates material processing simulation, microstructure representation volume element (RVE) models, material property prediction and structure preformation simulation to enable multiscale, multidisciplinary analysis and design. Processing parameters, microstructure parameters and vehicle subframe geometry parameters are defined as the design variables; the stiffness and weight of the structure are defined as the responses. For multi-layer UD structure, this work focuses on the discussion of different design representation methods and their impacts on the optimization performance.

Woven fabric carbon fiber/epoxy composites made through compression molding are one of the promising choices of material for the vehicle light-weighting strategy. Previous studies have shown that the processing conditions can have substantial influence on the performance of this type of the material. Therefore the optimization of the compression molding process is of great importance to the manufacturing practice. An efficient way to achieve the optimized design of this process would be through conducting finite element (FE) simulations of compression molding for woven fabric carbon fiber/epoxy composites. However, performing such simulation remains a challenging task for FE as multiple types of physics are involved during the compression molding process, including the epoxy resin curing and the complex mechanical behavior of woven fabric structure.

Design optimization techniques are widely used to drive designs toward a global or a near global optimal solution. However, the achieved optimal solution often appears to be the only choice that an engineer/designer can select as the final design. This is caused by either problem topology or by the nature of optimization algorithms to converge quickly in local/global optimal or both. Problem topology can be unimodal or multimodal with many local and/or global optimal solutions. For multimodal problems, most global algorithms tend to exploit the global optimal solution quickly but at the same time leaving the engineer with only one choice of design. The paper explores the application of genetic algorithms (GA), simulated annealing (SA), and mixed integer problem sequential quadratic programming (MIPSQP) to find multiple local and global solutions using single objective optimization formulation.

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.

Finite Element (FE) models are widely used in automotive for vehicle design. Even with increasing speed of computers, the simulation of high fidelity FE models is still too time-consuming to perform direct design optimization. As a result, response surface models (RSMs) are commonly used as surrogates of the FE models to reduce the turn-around time. However, RSM may introduce additional sources of uncertainty, such as model bias, and so on. The uncertainty and model bias will affect the trustworthiness of design decisions in design processes. This calls for the development of stochastic model interpolation and extrapolation methods that can address the discrepancy between the RSM and the FE results, and provide prediction intervals of model responses under uncertainty.

As an alternative lightweight material, chopped carbon fiber reinforced Sheet Molding Compound (SMC) composites, formed by compression molding, provide a new material for automotive applications. In the present study, the monotonic and fatigue behavior of chopped carbon fiber reinforced SMC is investigated. Tensile tests were conducted on coupons with three different gauge length, and size effect was observed on the fracture strength. Since the fiber bundle is randomly distributed in the SMC plaques, a digital image correlation (DIC) system was used to obtain the local modulus distribution along the gauge section for each coupon. It was found that there is a relationship between the local modulus distribution and the final fracture location under tensile loading. The fatigue behavior under tension-tension (R=0.1) and tension-compression (R=-1) has also been evaluated.

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.

Multidisciplinary design optimization (MDO) methods are commonly used for weight reduction in automotive industry. The design variables for MDO are often selected based on critical parts, which usually are close to optimal after many design iterations. As a result, the real weight reduction benefit may not be fully realized due to poor selection of design parameters. In addition, most applications require running design of experiments (DOE) to explore the full design space and to build response surfaces for optimization. This approach is often too costly if too many design variables are simultaneously considered. In this research, an alternative approach to address these issues is presented. It includes two optimization phases. The first phase uses critical parts for design iterations and the second phase use non-critical for weight reduction. A vehicle body structure is used to demonstrate the proposed strategy to show its effectiveness.

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.

Computer modeling has played important roles and gained great momentum in product development as numerical methods, computer software and hardware technologies advance rapidly. Computer models (e.g. MADYMO) that simulate vehicle interior, restraint system and occupants in various crash modes have been widely used to improve occupant safety. However, to build good occupant models, engineers often have to spend tremendous time on model correlation. The challenge of model correlation for occupant safety is that it requires matching numerous injury curves with tests, for examples: head G, chest G, chest deflection, shoulder belt load, femur loads, neck load and moment. Traditionally, this model correlation task is done by a trial and error method. This paper attempts to solve the problem systematically by using a genetic algorithm. It demonstrates that the genetic algorithm is a valuable optimization tool to obtain a high quality MADYMO model.

With the continuous improvement of powerful computers, vehicle structural designs have been addressed using computational methods, resulting in more efficient development of new vehicles. Most simulation-based optimization generates deterministic optimal designs without considering variability effects in modeling, simulation, and/or manufacturing. This paper presents a new hybrid stochastic optimization method for vehicle side impact design. Nonlinear response surface models are employed as the ’real’ models for the side impact related performance functions to conduct this study. The main goal is to maintain or enhance the vehicle side impact performance while minimizing the vehicle weight under various uncertainties. The new method alleviates the computational burden of excessive model evaluations by estimating the objective and constraint functions during the optimization process through a reweighting approach.

This paper presents a design process with data mining technique and advanced optimization strategy. The proposed design method provides insights in three aspects. First, data mining technique is employed for analysis to identify key factors of design variables. Second, relationship between multiple types of size and shape design variables and performance responses can be analyzed. Last but not least, design preference can be initialized based on data analysis to provide priori guidance for the starting design points of optimization algorithm. An exhaust system design problem which largely contributes to the improvement of vehicular Noise, Vibration and Harshness (NVH) performance is employed for the illustration of the process. Two types of design parameters, structural variable (gauge of component) and layout variable (hanger location), are considered in the studied case.

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.

Response Surface Model (RSM)-based optimization is widely used in engineering design. The major strength of RSM-based optimization is its short computational time. The expensive real simulation models are replaced with fast surrogate models. However, this method may have some difficulties to reach the full potential due to the errors between RSM and the real simulations. RSM's accuracy is limited by the insufficient number of Design of Experiments (DOE) points and the inherent randomness of DOE. With recent developments in advanced optimization algorithms and High Performance Computing (HPC) capability, Direct Multidisciplinary Design Optimization (DMDO) receives more attention as a promising future optimization strategy. Advanced optimization algorithm reduces the number of function evaluations, and HPC cut down the computational turnaround time of function evaluations through fully utilizing parallel computation.

The prediction of residual stresses due to manufacturing is of high importance in product development. For the accurate prediction of residual stresses in metallic components, an understanding of the quenching process that occurs in many heat treatments is required. In this paper, the experimental techniques developed to quantify the temperature fields during quenching and to quantify the residual stresses in the quenched part are presented. The temperature fields were quantified using thermocouples embedded in the components. The residual stresses were quantified using a newly developed strain gauging, sectioning and dynamic data acquisition technique. The techniques were verified using thermal histories and residual stresses for an engine cylinder head quenched at two different quenchant temperatures. The measurements obtained were incorporated into an analytical program (finite element) to study the residual stresses produced during the quenching process.