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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.

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.

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.

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.

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.

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.

This paper presents an enhanced Bayesian based model validation method together with probabilistic principal component analysis (PPCA). The PPCA is employed to address multivariate correlation and to reduce the dimensionality of the multivariate functional responses. The Bayesian hypothesis testing is used to quantitatively assess the quality of a multivariate dynamic system. Unlike the previous approach, the differences between test and CAE results are used for dimension reduction though PPCA and then to assess the model validity. In addition, physics-based thresholds are defined and transformed to the PPCA space for Bayesian hypothesis testing. This new approach resolves some critical drawbacks of the previous method and provides desirable properties of a validation method, e.g., symmetry. A dynamic system with multiple functional responses is used to demonstrate this new approach.

Computer Aided Engineering (CAE) has become a vital tool for product development in automotive industry. 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. However, one of the key difficulties for model validation of dynamic systems is that most of the responses are functional responses, such as time history curves. This calls for the development of an objective metric which can evaluate the differences of both the time history and the key features, such as phase shift, magnitude, and slope between test and CAE curves. One of the promising metrics is Error Assessment of Response Time Histories (EARTH), which was recently developed. Three independent error measures that associated with physically meaningful characteristics (phase, magnitude, and slope) were proposed.

Noise-vibration-harshness (NVH) design optimization problems have become major concerns in the vehicle product development process. The Body-in-White (BIW) plays an important role in determining the dynamic characteristics of vehicle system during the concept design phase. Finite Element (FE) models are commonly used for vehicle design. However, even though the speed of computers has been increased a lot, the simulation of FE models is still too time-consuming due to the increase in model complexity. For complex systems, like vehicle body structures, the numerous design variables and constraints make the FE simulations based optimization design inefficient. This calls for the development of a systematic and efficient approach that can effectively perform optimization to further improve the NVH performance, while satisfying the stringent design constraints.

To obtain higher efficiency in analysis process, simplification methods for computer-aided engineering (CAE) models are required in engineering. Current model simplification methods can meet certain precision and efficiency requirement, but these methods mainly concentrate on model features while ignoring model mesh which is also critical to efficiency of the analysis process and preciseness of the results. To address such issues, an integrated mesh simplification and evaluation process is proposed in this paper. The mesh is simplified to fewer features (e.g. faces, edges, and vertices) through edge collapsing based on quadric error metric. Then curvatures and normal vectors which are the objects to be evaluated are extracted from the original and simplified models for comparison. To obtain accurate results, the geometric information of mesh nodes and elements are both considered in this evaluation process. The proposed method is implemented on a vehicle crash test.

Several surrogate models such as response surface model and radial basis function and Kriging models are developed to speed the optimization design of vehicle body and improve the vehicle crashworthiness. The error analysis is used to investigate the accuracy of different surrogate models. Furthermore, the Kriging model is used to fit the model of B-pillar acceleration and foot well intrusion. The response surface model is used to fit the model of the entire vehicle mass. These models are further used to calculate the acceleration response in B-pillar, foot well intrusion and vehicle mass instead of the finite element model in the optimization design of vehicle crashworthiness. A multi-objective optimization problem is formulated in order to improve vehicle safety performance and keep its light weight. The particle swarm method is used to solve the proposed multi-objective optimization problem.

Collaborative optimization is an important design tool in complex vehicle system engineering. However, there are many problems yet to be resolved when applying the conventional collaborative optimization method in vehicle body weight reduction, such as convergence difficulties and low optimization efficiency. To solve these problems, a maximum incompatibility constrained collaborative optimization method is proposed in the paper. First, the 1-norm equality constraints expression of the system level is used to replace the traditional 2-norm inequality constraints. Then, a maximum incompatibility is selected from modified inequality constraints to improve optimization efficiency. Finally, an overall compatibility constraint is introduced to decrease the influence caused by the initial point. A mathematical example is used to verify the effectiveness and stability of the proposed method.

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.

In order to improve the comprehensive protection for children with variable shapes and sizes, this paper conducted studies on the impact injury for obese children based on a 10-YO finite element model. Some specific geometrics on the body surface were firstly acquired by the combination of pediatric anthropometric database and generator of body (GEBOD). A Radial Basis Function (RBF) based mesh morphing technique was then used to modify the original standard size FE model using the obtained geometrics. The morphed FE model was validated based on the experimental data of frontal sled test and chest-abdomen impact test. The effects of obesity on injury performances were analyzed through simplified high-speed and low-speed crash simulations.

Surrogate model based design optimization has been widely adopted in automotive industry. Hybrid surrogate model with multiple component surrogates is considered to be a better choice when simulating highly non-linear responses in vehicle crashworthiness analysis. Currently, the number of component surrogates has to be decided before-hand when constructing of a hybrid surrogate model. This paper conducts a comparative study on the performances of three popular hybrid modeling methods including heuristic computation strategy, and two kinds of optimal weighted surrogates. The effects of samples size on the number of individual surrogates that should be included into the final hybrid surrogate models for crashworthiness responses are investigated. Different hybrid modeling techniques and multiple validation criteria are evaluated. Some observations and conclusions on the selection of component surrogates in hybrid surrogate modeling are given in the end.

Finite element (FE) models are commonly used for automotive crashworthiness design. However, even with increasing speed of computers, the FE-based simulation is still too time-consuming when simulating the complex dynamic process such as vehicle crashworthiness. To improve the computational efficiency, the response surface model, as the surrogate of FE model, has been widely used for crashworthiness optimization design. Before introducing the surrogate model into the design optimization, the surrogate should satisfy the accuracy requirements. However, the bias of surrogate model is introduced inevitably. Meanwhile, it is also very difficult to decide how many samples are needed when building the high fidelity surrogate model for the system with strong nonlinearity. In order to solve the aforementioned problems, the application of a kind of surrogate optimization method called Efficient Global Optimization (EGO) is proposed to conduct the crashworthiness design optimization.