Shared autonomous vehicles (SAVs) encompassing autonomous driving technology and car-sharing service are expected to become an essential part of transportation system in the near future. Although many studies related to SAV system design and optimization have been conducted, most of them are focused on shared autonomous battery electric vehicle (SABEV) systems, which employ battery electric vehicles (BEVs) as SAVs. As fuel cell electric vehicles (FCEVs) emerge as alternative fuel vehicles along with BEVs, the need for research on shared autonomous fuel cell electric vehicle (SAFCEV) systems employing FCEVs as SAVs is increasing. Therefore, this study newly presents a design framework of SAFCEV system by developing an SAFCEV design model based on a proton-exchange membrane fuel cell (PEMFC) model. The test bed for SAV system design is Seoul, and optimization is conducted for SABEV and SAFCEV systems to minimize the total cost while satisfying the customer wait time constraint, and the optimization results of both systems are compared. From the results, it is verified that the SAFCEV system is feasible and the total cost of the SAFCEV system is even lower compared to the SABEV system. In addition, several observations on various operating environments of SABEV and SAFCEV systems are obtained from parametric studies.

Reliability analysis that evaluates a probabilistic constraint is an important part of reliability-based design optimization (RBDO). Inverse reliability analysis evaluates the percentile value of the performance function that satisfies the reliability. To compute the percentile value, analytical methods, surrogate model based methods, and sampling-based methods are commonly used. In case the dimension or nonlinearity of the performance function is high, sampling-based methods such as Monte Carlo simulation, Latin hypercube sampling, and importance sampling can be directly used for reliability analysis since no analytical formulation or surrogate model is required in these methods. The sampling-based methods have high accuracy but require a large number of samples, which can be very time-consuming. Therefore, this paper proposes methods that can improve the accuracy of reliability analysis when the number of samples is not enough and the sampling-based methods are considered to be better candidates. This study starts with the idea of training the relationship between the realization of the performance function at a small sample size and the corresponding true percentile value of the performance function. Deep feedforward neural network (DFNN), which is one of the promising artificial neural network models that approximates high dimensional models using deep layered structures, is trained using the realization of various performance functions at a small sample size and the corresponding true percentile values as input and target training data, respectively. In this study, various polynomial functions and random variables are used to create training data sets consisting of various realizations and corresponding true percentile values. A method that approximates the realization of the performance function through kernel density estimation and trains the DFNN with the discrete points representing the shape of the kernel distribution to reduce the dimension of the training input data is also presented. Along with the proposed reliability analysis methods, a strategy that reuses samples of the previous design point to enhance the efficiency of the percentile value estimation is explained. The results show that the reliability analysis using the DFNN is more accurate than the method using only samples. In addition, compared to the method that trains the DFNN using the realization of the performance function, the method that trains the DFNN with the discrete points representing the shape of the kernel distribution improves the accuracy of reliability analysis and reduces the training time. The proposed sample reuse strategy is verified that the burden of function evaluation at the new design point can be reduced by reusing the samples of the previous design point when the design point changes while performing RBDO.

An accurate input statistical model has been assumed in most of reliability-based design optimization (RBDO) to concentrate on variability of random variables. However, only limited number of data are available to quantify the input statistical model in practical engineering applications. In other words, irreducible variability and reducible uncertainty due to lack of knowledge exist simultaneously in random design variables. Therefore, the uncertainty in reliability induced by insufficient data has to be accounted for RBDO to guarantee confidence of reliability. The uncertainty of input distributions is successfully propagated to a cumulative distribution function (CDF) of reliability under normality assumptions, but it requires a number of function evaluations in double-loop Monte Carlo simulation (MCS). To tackle this challenge, reliability measure approach (RMA) in confidence-based design optimization (CBDO) is proposed to handle the randomness of reliability following the idea of performance measure approach (PMA) in RBDO. Input distribution parameters are transformed to the standard normal space for most probable point (MPP) search with respect to reliability. Therefore, the reliability is approximated at MPP with respect to input distribution parameters. The proposed CBDO can treat confidence constraints employing the reliability value at the target confidence level that is approximated by MPP in P-space. In conclusion, the proposed method can significantly reduce the number of function evaluations by eliminating outer-loop MCS while maintaining acceptable accuracy.

The confidence of reliability indicates that reliability has randomness induced by any epistemic uncertainties, and these uncertainties can be reduced and manipulated by additional knowledge. In this paper, the uncertainty of input statistical models is mainly treated in the context of confidence-based design optimization (CBDO). Thus, the objective of this paper is to determine the optimal number of data for reliability-based design optimization (RBDO) under input model uncertainty. The uncertainty of input statistical models due to insufficient data is frequent in practical applications since collecting and testing samples of random variables requires engineering efforts. There are two ways to increase the confidence of reliability to be satisfied, which are shifting design vector and supplementing input data. The purpose of this research is to find balanced optimum accounting for a trade-off between two operations since both operations lead to the growth of overall cost. Therefore, it is necessary to optimally distribute the resources to two costs which are denoted as the operating cost of design vector and the development cost of acquiring new data. In this study, two types of costs are integrated as a bi-objective function, satisfying the probabilistic constraint for the confidence of reliability. The number of data is regarded as design variable to be optimized, and stochastic sensitivity analysis of reliability with respect to the number of data is developed. The proposed bi-objective CBDO can determine the optimal number of input data based on the current dataset. Then, the designers decide the additional number of tests for collecting input data according to the optimum of bi-objective CBDO to minimize the overall cost.

The conventional most probable point (MPP)-based dimension reduction method (DRM) and following researches show high accuracy in reliability analysis and thus have been successfully applied to reliability-based design optimization (RBDO). However, improvement in accuracy usually leads to reduction in efficiency. The MPP-based DRM is certainly better from the perspective of accuracy than first-order reliability methods (FORM). However, it requires additional function evaluations which could require heavy computational cost such as finite element analysis (FEA) to improve accuracy of probability of failure estimation. Therefore, in this paper, we propose MPP-based approximated DRM (ADRM) that performs one more approximation at MPP to maintain accuracy of DRM with efficiency of FORM. In the proposed method, performance functions will be approximated in original X-space with simplified bivariate DRM and linear regression using available function information such as gradients obtained during the previous MPP searches. Therefore, evaluation of quadrature points can be replaced by the proposed approximation. In this manner, we eliminate function evaluations at quadrature points for reliability analysis, so that the proposed method requires function evaluations for MPP search only, which is identical with FORM. In RBDO where sequential reliability analyses in different design points are necessary, ADRM becomes more powerful due to accumulated function information, which will lead to more accurate approximation. To further improve efficiency of the proposed method, several techniques, such as local window and adaptive initial point, are proposed as well. Numerical study verifies that the proposed method is as accurate as DRM and as efficient as FORM by utilizing available function information obtained during MPP searches.

Recent advances in deep learning enable machines to learn existing designs by themselves and to create new designs. Generative adversarial networks (GANs) are widely used to generate new images and data by unsupervised learning. Certain limitations exist in applying GANs directly to product designs. It requires a large amount of data, produces uneven output quality, and does not guarantee engineering performance. To solve these problems, this paper proposes a design automation process by combining GANs and topology optimization. The suggested process has been applied to the wheel design of automobiles and has shown that an aesthetically superior and technically meaningful design can be automatically generated without human interventions.

When designing a product, both engineering uncertainty and market heterogeneity should be considered to reduce the risk of failure in the market. Reliability-based design optimization (RBDO) approach allows decision makers to achieve target confidence in product performance under engineering uncertainty. Design for market systems (DMS) approach helps decision makers to find profit-maximized product design under market heterogeneity. This paper integrates RBDO and DMS approaches for an Electric vehicle (EV) design. Consumers’ preferences on warranted battery lifetime are heterogeneous while battery life itself is affected by various uncertainties such as battery characteristics and driving patterns. We optimized and compared four scenarios depending on whether engineering systems are deterministic or probabilistic, and whether a market is homogeneous or heterogeneous. The results provide some insight on how the optimal EV design should be altered depending on engineering uncertainty and market heterogeneity.

Conventional reliability-based design optimization (RBDO) uses the means of input random variables as its design variables; and the standard deviations (STDEVs) of the random variables are fixed constants. However, the fixed STDEVs may not correctly represent certain RBDO problems well, especially when a specified tolerance of the input random variable is presented as a percentage of the mean value. For this kind of design problem, the coefficients of variations (COVs) of the input random variables should be fixed, which means STDEVs are not fixed. In this paper, a method to calculate the design sensitivity of probability of failure for RBDO with fixed COV is developed. For sampling-based RBDO, which uses Monte Carlo simulation for reliability analysis, the design sensitivity of the probability of failure is derived using a first-order score function. The score function contains the effect of the change in the STDEV in addition to the change in the mean. As copulas are used for the design sensitivity, correlated input random variables also can be used for RBDO with fixed COV. Moreover, the design sensitivity can be calculated efficiently during the evaluation of the probability of failure. Using a mathematical example, the accuracy and efficiency of the developed method are verified. The RBDO result for mathematical and physical problems indicates that the developed method provides accurate design sensitivity in the optimization process.

According to order of approximation, there are two types of analytical reliability analysis methods; first-order reliability method and second-order reliability method. Even though FORM gives acceptable accuracy and good efficiency for mildly nonlinear performance functions, SORM is required in order to accurately estimate the probability of failure of highly nonlinear functions due to its large curvature. Despite its necessity, SORM is not commonly used because the calculation of the Hessian is required. To resolve the heavy computational cost in SORM due to the Hessian calculation, a quasi-Newton approach to approximate the Hessian is introduced in this study instead of calculating the Hessian directly. The proposed SORM with the approximated Hessian requires computations only used in FORM leading to very efficient and accurate reliability analysis. The proposed SORM also utilizes the generalized chi-squared distribution in order to achieve better accuracy. Furthermore, an SORM-based inverse reliability method is proposed in this study as well. A reliability index corresponding to the target probability of failure is updated using the proposed SORM. Two approaches in terms of finding more accurate most probable point using the updated reliability index are proposed and compared with existing methods through numerical study. The numerical study results show that the proposed SORM achieves efficiency of FORM and accuracy of SORM.

This study presents a reliability analysis of vehicle sideslip and rollover in highway horizontal curves, mainly focusing on exit ramps and interchanges. To accurately describe failure modes of a ground vehicle, analytic models for sideslip and rollover are derived considering nonlinear characteristics of vehicle behavior using the commercial software, TruckSim ® , with high fidelity. Then, the probability of accident is evaluated using the First-Order Reliability Method (FORM). Furthermore, sensitivity functions of each failure mode are analytically derived to apply FORM. Numerical studies are conducted using a single-unit truck model. The results show that a truck is more likely to rollover than to slip at dry load. To propose practical application of the study, the reliability analysis for the minimum radius recommended by American Association of State Highway and Transportation Officials (AASHTO) at various speeds and bank angles is conducted. The reliability analysis of current design method shows that the method cannot provide the sufficient margin of safety against both of rollover and sideslip when there are deviations from assumed conditions, especially at low speed of vehicles.

This paper proposes a methodology for sampling-based design optimization in the presence of interval variables. Assuming that an accurate surrogate model is available, the proposed method first searches the worst combination of interval variables for constraints when only interval variables are present or for probabilistic constraints when both interval and random variables are present. Due to the fact that the worst combination of interval variables for probability of failure does not always coincide with that for a performance function, the proposed method directly uses the probability of failure to obtain the worst combination of interval variables when both interval and random variables are present. To calculate sensitivities of constraints and probabilistic constraints with respect to interval variables by the sampling-based method, the behavior of interval variables at the worst case is defined by utilizing the Dirac delta function. Then, Monte Carlo simulation is applied to calculate constraints and probabilistic constraints with the worst combination of interval variables, and their sensitivities. The important merit of the proposed method is that it does not require gradients of performance functions and transformation from X-space to U-space for reliability analysis after the worst combination of interval variables is obtained, thus there is no approximation or restriction in calculating the sensitivities of constraints or probabilistic constraints. Numerical results indicate that the proposed method can search the worst case probability of failure with both efficiency and accuracy and that it can perform design optimization with mixture of random and interval variables by utilizing the worst case probability of failure search.

In this paper, a sampling-based RBDO method using a classification method is presented. The probabilistic sensitivity analysis is used to compute sensitivities of probabilistic constraints with respect to random variables. Since the probabilistic sensitivity analysis requires only the limit state function, and not the response surface or sensitivity of the response, an efficient classification method can be used for a sampling-based RBDO. The proposed virtual support vector machine (VSVM), which is a classification method, is a support vector machine (SVM) with virtual samples. By introducing virtual samples, VSVM overcomes the deficiency in existing SVM that uses only classification information as their input. In this paper, the universal Kriging method is used to obtain locations of virtual samples to improve the accuracy of the limit state function for highly nonlinear problems. A sequential sampling strategy effectively inserts new samples near the limit state function. In sampling-based RBDO, Monte Carlo simulation (MCS) is used for the reliability analysis and probabilistic sensitivity analysis. Since SVM is an explicit classification method, unlike implicit methods, computational cost for evaluating a large number of MCS samples can be significantly reduced. Several efficiency strategies, such as the hyper-spherical local window for generation of the limit state function and the Transformations/Gibbs sampling method to generate uniform samples in the hyper-sphere, are also applied. Examples show that the proposed sampling-based RBDO using VSVM yields better efficiency in terms of the number of required samples and the computational cost for evaluating MCS samples while maintaining accuracy similar to that of sampling-based RBDO using the implicit dynamic Kriging (D-Kriging) method.

In practical engineering problems, often only limited input data are available to generate the input distribution model. The insufficient input data induces uncertainty on the input distribution model, and this uncertainty will cause us to lose confidence in the optimum design obtained using the reliability-based design optimization (RBDO) method. Uncertainty on the input distribution model requires us to consider the reliability analysis output, which is defined as the probability of failure, to follow a probabilistic distribution. This paper proposes a new formulation for the confidence-based RBDO method and design sensitivity analysis of the confidence level. The probability of the reliability analysis output is obtained with consecutive conditional probabilities of input distribution parameters and input distribution types using a Bayesian approach. The approximate conditional probabilities of input distribution parameters and types are suggested under certain assumptions. The Monte Carlo simulation is applied to practically calculate the output distribution, and the copula is used to describe the correlated input distribution types. A confidence-based RBDO problem is formulated using the derived the distribution of output. In this new formulation, the probabilistic constraint is modified to include both the target reliability and the target confidence level. Finally, the sensitivity of the confidence level, which is a new probabilistic constraint, is derived to support an efficient optimization process. Using accurate surrogate models, the proposed method does not require generation of additional surrogate models during the RBDO iteration; it only requires several evaluations of the same surrogate models. Hence, the efficiency of the method is obtained. For the numerical example, the confidence level is calculated and the accuracy of the derived sensitivity is verified when only limited data are available.

This paper proposes a novel second-order reliability method (SORM) using non-central or general chi-squared distribution to improve the accuracy of reliability analysis in existing SORM. Conventional SORM contains three types of errors: (1) error due to approximating a general nonlinear limit state function by a quadratic function at most probable point (MPP) in the standard normal U-space, (2) error due to approximating the quadratic function in U-space by a hyperbolic surface, and (3) error due to calculation of the probability of failure after making the previous two approximations. The proposed method contains the first type of error only which is essential to SORM and thus cannot be improved. However, the proposed method avoids the other two errors by describing the quadratic failure surface with the linear combination of non-central chi-square variables and using the linear combination for the probability of failure estimation. Two approaches for the proposed SORM are suggested in the paper. The first approach directly calculates the probability of failure using numerical integration of the joint probability density function (PDF) over the linear failure surface and the second approach uses the cumulative distribution function (CDF) of the linear failure surface for the calculation of the probability of failure. The proposed method is compared with first-order reliability method (FORM), conventional SORM, and Monte Carlo simulation (MCS) results in terms of accuracy. Since it contains fewer approximations, the proposed method shows more accurate reliability analysis results than existing SORM without sacrificing efficiency.