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Viewing 1 to 27 of 27
2011-04-12
Technical Paper
2011-01-0245
Zhenfei Zhan, Yan Fu, Ren-Jye Yang
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.
2014-04-01
Journal Article
2014-01-0731
Zhenfei Zhan, Yan Fu, Ren-Jye Yang
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.
2014-04-01
Journal Article
2014-01-0735
Zhimin Xi, Pan Hao, Yan Fu, Ren-Jye Yang
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.
2014-04-01
Journal Article
2014-01-0564
Monica Majcher, Hongyi Xu, Yan Fu, Ching-Hung Chuang, Ren-Jye Yang
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.
2015-04-14
Journal Article
2015-01-0443
Zhenfei Zhan, Junqi Yang, Yan Fu, Ren-Jye Yang, Saeed Barbat, Ling Zheng
Abstract 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.
2015-04-14
Journal Article
2015-01-0452
Junqi Yang, Zhenfei Zhan, Chong Chen, Yajing Shu, Ling Zheng, Ren-Jye Yang, Yan Fu, Saeed Barbat
Abstract 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.
2015-04-14
Journal Article
2015-01-0453
Zhimin Xi, Hao Pan, Yan Fu, Ren-Jye Yang
Abstract 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.
2010-04-12
Technical Paper
2010-01-0419
Yan Fu, Zhenfei Zhan, Ren-Jye Yang
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.
2010-04-12
Technical Paper
2010-01-0647
Ren-Jye Yang, Ching-Hung Chuang, Yan Fu
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.
2014-04-01
Technical Paper
2014-01-0400
Hongyi Xu, Monica T. Majcher, Ching-Hung Chuang, Yan Fu, Ren-Jye Yang
Abstract 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.
2013-04-08
Journal Article
2013-01-1384
Zhen Jiang, Wei Chen, Yan Fu, Ren-Jye Yang
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.
2013-04-08
Journal Article
2013-01-1386
Zhenfei Zhan, Yan Fu, Ren-Jye Yang
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.
2013-04-08
Journal Article
2013-01-1387
Zhimin Xi, Yan Fu, Ren-Jye Yang
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.
2011-04-12
Technical Paper
2011-01-0107
Yan Fu, Guosong Li, Ren-Jye Yang, Baohua xiao, Krishnakanth Aekbote
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.
2012-04-16
Journal Article
2012-01-0578
Zhendan Xue, Sumeet Parashar, Guosong Li, Yan Fu
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.
2012-04-16
Journal Article
2012-01-0223
Zhenfei Zhan, Yan Fu, Ren-Jye Yang, Zhimin Xi, Lei Shi
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.
2012-04-16
Technical Paper
2012-01-0228
Zhimin Xi, Yan Fu, Ren-Jye Yang
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.
2006-04-03
Technical Paper
2006-01-0760
Brian Kachnowski, Yan Fu
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.
2004-03-08
Technical Paper
2004-01-1624
Yan Fu, Eung Lee, Stephen Kang
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.
2005-04-11
Technical Paper
2005-01-1306
Brian Kachnowski, Yan Fu
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.
2005-04-11
Technical Paper
2005-01-0814
Yan Fu, Edward Abramoski
Computational analysis of occupant safety has become an efficient tool to reduce the development time for a new product. Multi-body computer models (e.g. Madymo models) that simulate vehicle interior, restraint system and occupants in various crash modes have been widely used in the occupant safety area. To ensure public safety, many injury numbers, such as head injury criteria, chest acceleration, chest deflection, femur loads, neck load, and neck moment, are monitored. Deterministic optimization methods have been employed to meet various safety requirements. However, with the further emphasis on product quality and consistency of product performance, variations in modeling, simulation, and manufacturing, need to be considered.
2009-04-20
Technical Paper
2009-01-1402
Yan Fu, Xiaomo Jiang, Ren-Jye Yang
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.
2004-03-08
Technical Paper
2004-01-1128
Yan Fu, C. H. Chuang, G. Li, R. J. Yang
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.
2005-04-11
Technical Paper
2005-01-1227
Isheng Yeh, Yan Fu, Brian Kachnowski, Thiag Subbian
In an attempt to make vehicle restraint systems more effective in protecting occupants, many advanced safety technologies have been introduced. These advanced technologies are mostly adaptive technologies. The ability of a restraint system to adapt itself to crash parameters like crash speed and type, occupant size, and belt-usage status, offers possible enhancements in occupant protection. Designing a restraint system boils down to the determination of the design variables of either the restraint technologies or vehicle interiors. A restraint system of adaptive technologies involves much more design variables than a restraint system containing only load-limited belts and dual stage inflators, possibly posing a challenge to safety engineers. In this paper, a genetic algorithm (GA) tailored for restraint system optimization will be presented.
2017-03-28
Journal Article
2017-01-0243
Zhenghui Sha, Veronica Saeger, Mingxian Wang, Yan Fu, Wei Chen
Abstract 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.
2017-03-28
Journal Article
2017-01-0246
Sentao Miao, Xiuli Chao, Michael Tamor, Yan Fu, Margaret Strumolo
Abstract Over half of the greenhouse gas (GHG) emissions in the United States come from the transportation and electricity generation sectors. To analyze the potential impact of cross-sector cooperation in reducing these emissions, we formulate a bi-level optimization model where the transportation sector can purchase renewable energy certificates (REC) from the electricity generation sector. These RECs are used to offset emissions from transportation in lieu of deploying high-cost fuel efficient technologies. The electricity generation sector creates RECs by producing additional energy from renewable sources. This additional renewable capacity is financed by the transportation sector and it does not impose additional cost on the electricity generation sector. Our results show that such a REC purchasing regime significantly reduces the cost to society of reducing GHG emissions. Additionally, our results indicate that a REC purchasing policy can create electricity beyond actual demand.
2003-03-03
Technical Paper
2003-01-0881
Yan Fu
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.
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