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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.

Available methodologies for model bias identification are mainly regression-based approaches, such as Gaussian process, Bayesian inference-based models and so on. Accuracy and efficiency of these methodologies may degrade for characterizing the model bias when more system inputs are considered in the prediction model due to the curse of dimensionality for regression-based approaches. This paper proposes a copula-based approach for model bias identification without suffering the curse of dimensionality. The main idea is to build general statistical relationships between the model bias and the model prediction including all system inputs using copulas so that possible model bias distributions can be effectively identified at any new design configurations of the system. Two engineering case studies whose dimensionalities range from medium to high will be employed to demonstrate the effectiveness of the copula-based approach.

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.

Vehicle weight reduction has become one of the viable solutions to ever-growing energy and environmental crisis. 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 affects 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. For the purpose of constructing and correcting the bias in RSMs, scheduling Design of Experiments (DOEs) must be conducted properly. This paper develops a method to arrange DOEs in order to build RSMs with high quality, considering the influence of input uncertainty.

Computer programs and models are playing an increasing role in simulating vehicle crashworthiness, dynamic, and fuel efficiency. To maximize the effectiveness of these models, the validity and predictive capabilities of these models need to be assessed quantitatively. For a successful implementation of Computer Aided Engineering (CAE) models as an integrated part of the current vehicle development process, it is necessary to develop objective validation metric that has the desirable metric properties to quantify the discrepancy between multiple tests and simulation results. However, most of the outputs of dynamic systems are multiple functional responses, such as time history series. This calls for the development of an objective metric that can evaluate the differences of the multiple time histories as well as the key features under uncertainty.

To date, model validation metric is prominently designed for non-dynamic model responses. Though metrics for dynamic responses are also available, they are specifically designed for the vehicle impact application and uncertainties are not considered in the metric. This paper proposes the validation metric for general dynamic system responses under uncertainty. The metric makes use of the popular U-pooling approach and extends it for dynamic responses. Furthermore, shape deviation metric was proposed to be included in the validation metric with the capability of considering multiple dynamic test data. One vehicle impact model is presented to demonstrate the proposed validation metric.

Simulation based design optimization has become the common practice in automotive product development. Increasing computer models are developed to simulate various dynamic systems. Before applying these models for product development, model validation needs to be conducted to assess their validity. In model validation, for the purpose of obtaining results successfully, it is vital to select or develop appropriate metrics for specific applications. For dynamic systems, one of the key obstacles of model validation is that most of the responses are functional, such as time history curves. This calls for the development of a metric that can evaluate the differences in terms of phase shift, magnitude and shape, which requires information from both time and frequency domain. And by representing time histories in frequency domain, more intuitive information can be obtained, such as magnitude-frequency and phase-frequency characteristics.

As the world's largest auto producer and consumer, China is both the most promising and complex market given the country's rapid economic growth, huge population, and many regional and segment preference differences. This research is aimed at developing data-driven demand models for customer preference analysis and prediction under a competitive market environment. Regional analysis is first used to understand the impact of geographical factors on customer preference. After a comprehensive data exploration, a customer-level mixed logit model is built to shed light on fast-growing vehicle segments in the Chinese auto market. By combining the data of vehicle purchase, consideration, and past choice, cross-shopping behaviors and brand influence are explicitly modeled in addition to the impact of customer demographics, usage behaviors, and attributes of vehicles.

For achieving viable mass customization of products, product configuration is often performed that requires deep understanding on the impact of product features and feature combinations on customers’ purchasing behaviors. Existing literature has been traditionally focused on analyzing the impact of common customer demographics and engineering attributes with discrete choice modeling approaches. This paper aims to expand discrete choice modeling through the incorporation of optional product features, such as customers’ positive or negative comments and their satisfaction ratings of their purchased products, beyond those commonly used attributes. The paper utilizes vehicle as an example to highlight the range of optional features currently underutilized in existing models. First, data analysis techniques are used to identify areas of particular consumer interest in regards to vehicle selection.

Vehicle hood design is a typical multi-disciplinary task. The hood has to meet the demands of different attributes like safety, dynamics, statics, and NVH (Noise, Vibration, Harshness). Multi-disciplinary optimization (MDO) of vehicle hood at early design phase is an efficient way to support right design decision and avoid late-phase design changes. However, due to lacking in CAD models, it is difficult to realize MDO at early design phase. In this research, a new method of design and optimization is proposed to improve the design efficiency. Firstly, an implicit parametric hood model is built to flexibly change shape and size of hood structure, and generate FE models automatically. Secondly, four types of stiffness analysis, one type of modal analysis, together with pedestrian head impact analysis were established to describe multi-disciplinary concern of vehicle hood design.

Self-piercing rivets (SPR) are efficient and economical joining methods used in the manufacturing of lightweight automotive bodies. The finite element method (FEM) is a potentially effective way to assess the joining process of SPRs. However, uncertain parameters could lead to significant mismatches between the FEM predictions and physical tests. Thus, a sensitivity study on critical model parameters is important to guide the high-fidelity modeling of the SPR insertion process. In this paper, an axisymmetric FEM model is constructed to simulate the insertion process of the SPR using LS-DYNA/explicit. Then, several surrogate models are evaluated and trained using machine learning methods to represent the relations between selected inputs (e.g., material properties, interfacial frictions, and clamping force) and outputs (cross-section dimensions).

As pedestrian protection tests and evaluations have been officially incorporated into new C-NCAP, more stringent requirements have been placed on pedestrian protection performance. In this study, in order to reduce the injury of the vehicle front end structure to the pedestrian's lower extremity during the collision, the advanced pedestrian legform impactor (aPLI) model was used in conjunction with the finite element vehicle model for collision simulation based on the new C-NCAP legform test evaluation regulation. This paper selected the key components which have significant influences on the pedestrian's leg protection performance based on the CAE vehicle model, including front bumper, front-cover plate, upper impact pillar, impact beam and lower support plate, to form a simplified model and conducted parametric modeling based on it.

The transportation sector is facing three revolutions: shared mobility, electrification, and autonomous driving. To inform decision making and guide smart transportation system development at the city-level, it is critical to model and evaluate how travelers will behave in these systems. Two key components in such models are (1) individual travel demands with high spatial and temporal resolutions, and (2) travelers’ sociodemographic information and trip purposes. These components impact one’s acceptance of autonomous vehicles, adoption of electric vehicles, and participation in shared mobility. Existing methods of travel demand generation either lack travelers’ demographics and trip purposes, or only generate trips at a zonal level. Higher resolution demand and sociodemographic data can enable analysis of trips’ shareability for car sharing and ride pooling and evaluation of electric vehicles’ charging needs.

Accident statistics have shown that older and obese occupants are less adaptable to existing vehicle occupant restraint systems than ordinary middle-aged male occupants, and tend to have higher injury risk in vehicle crashes. However, the current research on injury mechanism of aging and obese occupants in vehicle frontal impacts is scarce. This paper focuses on the optimization design method of occupant restraint system parameters for specific body type characteristics. Three parameters, namely the force limit value of the force limiter in the seat belt, pretensioner preload of the seat belt and the proportionality coefficient of mass flow rate of the inflator were used for optimization. The objective was to minimize the injury risk probability subjected to constraints of occupant injury indicator values for various body regions as specified in US-NCAP frontal impact tests requirements.

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.

Model validation is a process to assess the validity and predictive capabilities of a computer model by comparing simulation results with test data for its intended use of the model. One of the key difficulties for model validation is to evaluate the quality of a computer model at different test configurations in design space, and interpolate or extrapolate the evaluation results to untested new design configurations. In this paper, an integrated model interpolation and extrapolation framework based on Bayesian inference and Response Surface Models (RSM) is proposed to validate the designs both within and outside of the original design space. Bayesian inference is first applied to quantify the distributions' hyper-parameters of the bias between test and CAE data in the validation domain. Then, the hyper-parameters are extrapolated from the design configurations to untested new design. They are then followed by the prediction interval of responses at the new design points.

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.

Model validation is a process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model. In reliability based design, the intended use of the model is to identify an optimal design with the minimum cost function while satisfying all reliability constraints. It is pivotal that computational models should be validated before conducting the reliability based design. This paper presents an ensemble approach for model bias prediction in order to correct predictions of computational models. The basic idea is to first characterize the model bias of computational models, then correct the model prediction by adding the characterized model bias. The ensemble approach is composed of two prediction mechanisms: 1) response surface of model bias, and 2) Copula modeling of a series of relationships between design variables and the model bias, between model prediction and the model bias.

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.

Head restraint has become an important element in seat design due to the severity of neck injuries in rear-end collisions. The objective of this paper is to present an analytical and efficient approach to assist engineers in analyzing the design parameters of the seat and head restraint system. The CAE simulation models with Bio-RID dummy were assembled to correlate to 10 mph rear impact sled tests. The correlated models were then adopted in Design of Experiment (DOE) studies to explore all the significant design parameters influencing occupant neck injuries. Based on the results from the DOE studies, we are able to improve the seat and head restraint designs for reducing the risk of neck injuries in rear-end impacts.