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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.

A copula-based approach for model bias characterization was previously proposed [18] aiming at improving prediction accuracy compared to other model characterization approaches such as regression and Gaussian Process. This paper proposes an adaptive copula-based approach for model bias identification to enhance the available methodology. The main idea is to use cluster analysis to preprocess data, then apply the copula-based approach using information from each cluster. The final prediction accumulates predictions obtained from each cluster. Two case studies will be used to demonstrate the superiority of the adaptive copula-based approach over its predecessor.

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.

Design optimization methods are commonly used for weight reduction subjecting to multiple constraints in automotive industry. One of the major challenges remained is to deal with a large number of design variables for large-scale design optimization problems effectively. In this paper, a new approach based on fuzzy rough set is proposed to address this issue. The concept of rough set theory is to deal with redundant information and seek for a reduced design variable set. The proposed method first exploits fuzzy rough set to screen out the insignificant or redundant design variables with regard to the output functions, then uses the reduced design variable set for design optimization. A vehicle body structure is used to demonstrate the effectiveness of the proposed method and compare with a traditional weighted sensitivity based main effect approach.

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.

In the automobile industry, the reliability and predictive capabilities of computer models for a dynamic system need to be assessed quantitatively. Quantitative validation allows engineers to assess and improve model reliability and quality objectively and ultimately lead to potential reduction in the number of prototypes built and tests. A good metric, which is essential in model validation, requires considering uncertainties in both testing and computer modeling. In addition, it needs to be able to compare multiple responses simultaneously, as multiple quantities are often encountered at different spatial and temporal points of a dynamic system. In this paper, a state-of-the-art validation technology is developed for multivariate complex dynamic systems by exploiting a probabilistic principal component analysis method and Bayesian statistics approach.

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.

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.

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.

With the increasing demands of developing vehicles for global markets, different regulations and public domain tests need to be considered simultaneously for side impact. Various side impact countermeasures, such as side airbags, door trim, energy absorbing foams etc., are employed to meet multiple side impact performance requirements. However, it is quite a challenging task to design a balanced side impact restraint system that can meet all side impact requirements for multiple crash modes. This paper presents an integrated multi-objective optimal design and robustness assessment framework for vehicle side impact restraint system design.

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.

Particle swarm optimization (PSO) is a relatively new stochastic optimization algorithm and has gained much attention in recent years because of its fast convergence speed and strong optimization ability. However, PSO suffers from premature convergence problem for quick losing of diversity. That is to say, if no particle discovers a new superiority position than its previous best location, PSO algorithm will fall into stagnation and output local optimum result. In order to improve the diversity of basic PSO, design of experiment technique is used to initialize the particle swarm in consideration of its space-filling property which guarantees covering the design space comprehensively. And the optimization procedure of PSO is divided into two stages, optimization stage and improving stage. In the optimization stage, the basic PSO initialized by Optimal Latin hypercube technique is conducted.

In structural design optimization, it is challenging to determine the optimal dimensions and material for each component simultaneously. Material selection of each part is always formulated as a categorical design variable in structural optimization problems. However, it is difficult to solve such mixed-variable problems using the metamodelbased strategy, because the prediction accuracy of metamodels deteriorates significantly when categorical variables exist. This paper investigates two different strategies of mixed-variable metamodeling: the “feature separating” strategy and the “all-in-one” strategy. A supervised learning-enhanced cokriging method is proposed, which fuses multi-fidelity information to predict new designs’ responses. The proposed method is compared with several existing mixed-variable metamodeling methods to understand their pros and cons. These methods include Neural Network (NN) regression, Classification and Regression Tree (CART) and Gaussian Process (GP).