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This paper proposes a novel probabilistic approach for multidisciplinary design optimization (MDO) under uncertainty, especially for systems with feedback coupled analyses with multiple coupling variables. The proposed approach consists of four components: multidisciplinary analysis, Bayesian network, copula-based sampling, and design optimization. The Bayesian network represents the joint distribution of multiple variables through marginal distributions and conditional probabilities, and updates the distributions based on new data. In this methodology, the Bayesian network is pursued in two directions: (1) probabilistic surrogate modeling to estimate the output uncertainty given values of the design variables, and (2) probabilistic multidisciplinary analysis (MDA) to infer the distributions of the coupling and output variables that satisfy interdisciplinary compatibility conditions.

This paper proposes a methodology to estimate errors in computational models and to include them in reliability-based design optimization (RBDO). Various sources of uncertainties, errors and approximations in model form selection and numerical solution are considered. The solution approximation error is quantified based on the model itself while the model form error is quantified based on the comparison of model prediction with physical observations using an interpolated resampling approach. The error in reliability analysis is also quantified and included in the RBDO formulation. The proposed methods are illustrated through numerical examples.

A general methodology for fatigue reliability analysis and inspection of railroad wheels is proposed in this paper. Both fatigue crack initiation and crack propagation life are included in the proposed methodology using previously developed multiaxial fatigue models by the authors. The life prediction is validated with field data. A methodology for calculating the optimized inspection schedule of railroad wheels is then developed using the reliability methodology. The optimized inspection scheduling methodology combines clustering analysis, to identify critical samples, reliability analysis, to calculate the expected life of the critical samples, and reliability-based optimization into an overall methodology which optimizes the inspection schedule. The proposed methodology minimizes the number of wheels inspected while at the same time maintaining or exceeding the desired reliability of the population.

This paper develops a multiobjective optimization methodology for automotive door quality design under uncertainty, in which the tradeoffs between two competing objectives need to be considered. Two important quality issues, door closing effort and wind noise, are of concern and the corresponding probabilities of unsatisfactory performance are considered in the optimization. Model-based reliability analysis methods are used to compute these probabilities. Both component and system-level reliability analyses need to be performed in RBDO. While a first order reliability method (FORM) is found adequate for the reliability estimation with respect to door closing effort, an adaptive Monte Carlo simulation method is found suitable for reliability analysis of the wind noise problem with multiple limit states. An efficient decoupled RBDO approach is used to solve the multiobjective optimization and the Pareto frontier is generated for decision-making.

Research in design optimization methods has increasingly become concerned with mathematical treatment of uncertainties in system demands and capacity, boundary conditions, component interactions, and available resources. Recent efforts in this context seek to integrate advances in two directions: computational reliability analysis methods and deterministic design optimization. Much current work is focused on developing computationally efficient strategies for such integration, using de-coupled or single loop formulations instead of earlier nested formulations. The extension of reliability-based optimization to include robustness requirements leads to multi-objective optimization under uncertainty. Another important application concerns multidisciplinary problems, where the various reliability constraints are evaluated in different disciplinary analysis codes and there is feedback coupling between the codes.

In this paper, an efficient method for the reliability analysis of systems with nonlinear limit states is described. It combines optimization-based and simulation-based approaches and is particularly applicable for problems with highly nonlinear and implicit limit state functions, which are difficult to solve by conventional reliability methods. The proposed method consists of two major parts. In the first part, an optimization-based method is used to search for the most probable point (MPP) on the limit state. This is achieved by using adaptive response surface approximations. In the second part, a multi-modal adaptive importance sampling method is proposed using the MPP information from the first part as the starting point. The proposed method is applied to the reliability estimation of a vehicle body-door subsystem with respect to one of the important quality issues -- the door closing effort.