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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.

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.

Computer Aided Engineering (CAE) models have proven themselves to be efficient surrogates of real-world systems in automotive industries and academia. To successfully integrate the CAE models into analysis process, model validation is necessarily required to assess the models’ predictive capabilities regarding their intended usage. In the context of model validation, quantitative comparison which considers specific measurements in real-world systems and corresponding simulations serves as a principal step in the assessment process. For applications such as side impact analysis, surface deformation is frequently regarded as a critical factor to be measured for the validation of CAE models. However, recent approaches for such application are commonly based on graphical comparison, while researches on the quantitative metric for surface-surface comparison are rarely found.

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.

Analytical models (math or computer simulation models) are typically built on the basis of many assumptions and simplifications and hence model prediction could be inaccurate in intended applications. Model validation is thus critical to quantify and improve the degree of accuracy of these models. So far, little work considers model validation for various design configurations so that model prediction is accurate in the intended design space. Furthermore, there is a lack of effective approaches that can be used to quantify model accuracy considering different number of experimental data. To overcome these limitations, objective of this paper is to develop a model validation approach for various design configurations with a reference metric for model accuracy check considering different number of experimental data.

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.

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.

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.

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.

In automobile industry, computational models built to predict the performances of the prototype vehicles are on the rise. To assess the validity or predictive capability of the model for its intended usage, validation activities are conducted to compare computational model outputs with test measurements. Validation becomes difficult when dealing with dynamic systems which often involve multiple functional responses, and the complex characteristics need to be appropriately considered. Many promising data analysis tools and metrics were previously developed to handle data correlation and evaluate the errors in magnitude, phase shift, and shape. However, these methods show their limitations when dealing with nonlinear multivariate dynamic systems. In this paper, kernel function based projection is employed to transform the nonlinear data into linear space, followed by the regular principal component analysis (PCA) based data processing.

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.

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.

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 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.

Computer modeling and simulation have significantly facilitated the efficiency of product design and development in modern engineering, especially in the automotive industry. For the design and optimization of car models, optimization algorithms usually work better if the initial searching points are within or close to a feasible domain. Therefore, finding a feasible design domain in advance is beneficial. A data mining technique, Iterative Dichotomizer 3 (ID3), is exploited in this paper to identify sets of reduced feasible design domains from the original design space. Within the reduced feasible domains, optimal designs can be efficiently obtained while releasing computational burden in iterations. A mathematical example is used to illustrate the proposed method. Then an industrial application about automotive structural optimization is employed to demonstrate the proposed methodology. The results show the proposed method’s potential in practical engineering.

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.

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.

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.

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.