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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.

An accurate and efficient Monte Carlo simulation (MCS) method is developed in this paper for limit state-based reliability analysis, especially at system levels, by using a response surface approximation of the failure indicator function. The Moving Least Squares (MLS) method is used to construct the response surface of the indicator function, along with an Optimum Symmetric Latin Hypercube (OSLH) as the sampling technique. Similar to MCS, the proposed method can easily handle implicit, highly nonlinear limit-state functions, with variables of any statistical distributions and correlations. However, the efficiency of MCS can be greatly improved. The method appears to be particularly efficient for multiple limit state and multiple design point problem. A mathematical example and a practical example are used to highlight the superior accuracy and efficiency of the proposed method over traditional reliability methods.

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.

This paper develops a reliability-based methodology for the evaluation of stiffness degradation of spot-welded joints under high mileage. A global-local finite element analysis is used, with the loads on the detailed three-dimensional joint model coming from finite element analysis of the entire car model with proving ground loads. Probabilistic fatigue crack propagation analysis is developed for multi-axial variable amplitude loading history on the joint. Multiple spot welds contribute to the stiffness of the joint. Hence the problem is addressed through system reliability techniques. The effect of spot-weld separation on joint stiffness, and on global vehicle stiffness, is incorporated. This results in the computation of the statistics of vehicle stiffness degradation with mileage.

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.