Xiaoping Du (dux@mst.edu, 573-341-7249)

1. “The First Order Saddlepoint Approximation for Reliability Analysis,�? X. Du and A. Sudjianto, to appear in AIAA Journal, 2004.

Abstract: In the approximation methods of reliability analysis, non-normal random variables are transformed into equivalent standard normal random variables. This transformation tends to increase the nonlinearity of a limit-state function and hence results in less accurate reliability estimation. The First Order Saddlepoint Approximation for reliability analysis is proposed to improve the accuracy of reliability analysis. By approximating a limit-state function at the Most Likelihood Point in the original random space and employing the accurate saddlepoint approximation, the proposed method reduces the chance of increasing linearity of the limit-state function and generates more accurate reliability estimation than the First Order Reliability Method without increasing the computational effort. The effectiveness of the proposed method is demonstrated by three examples in comparison with the First and Second Order Reliability Methods.

2. “An Integrated Framework for Optimization under Uncertainty Using Inverse Reliability Strategy,�? X. Du, A. Sudjianto, and W. Chen, to appear in ASME Journal of Mechanical Design, 2004.

Abstract: In this work, we propose an integrated framework for optimization under uncertainty that can bring both the design objective robustness and the probabilistic design constraints into account. The fundamental development of this work is the employment of an inverse reliability strategy that uses percentile performance for assessing both the objective robustness and probabilistic constraints. The percentile formulation for objective robustness provides us an accurate evaluation of the variation of an objective performance and a probabilistic measurement of the robustness. We can obtain more reasonable compound noise combinations for a robust design objective compared to using the traditional approach proposed by Taguchi. For the probabilistic constraints, compared to a traditional probabilistic model, the proposed formulation is more efficient to solve since it only needs to evaluate the constraint functions at the required reliability levels. The other major development of this work is a new search algorithm for the Most Probable Point of Inverse Reliability (MPPIR) that can be used to efficiently evaluate the performance robustness and percentile performance in the proposed formulation. Multiple techniques are employed in the MPPIR search, including using the steepest ascent direction and an arc search. The algorithm is applicable to general non-concave and non-convex performance functions of random variables following any continuous distributions. The effectiveness of the MPPIR search algorithm is verified using example problems. Overall, an engineering example on integrated robust and reliability design of a vehicle combustion engine piston is used to illustrate the benefits of our proposed method.

3. “Collaborative Reliability Analysis under the Framework of Multidisciplinary Systems Design,�? X. Du and W. Chen, to appear in Optimization and Engineering, 2004.

Abstract: Traditional Multidisciplinary Design Optimization (MDO) generates deterministic optimal designs, which are frequently pushed to the limits of design constraint boundaries, leaving little or no room to accommodate uncertainties in system input, modeling, and simulation. As a result, the design solution obtained may be highly sensitive to the variations of system input which will lead to performance loss and the solution is often risky (high likelihood of undesired events). Reliability-based design is one of the alternative techniques for design under uncertainty. The natural method to perform reliability analysis in multidisciplinary systems is the all-in-one approach where the existing reliability analysis techniques are applied directly to the system-level multidisciplinary analysis. However, the all-on-one reliability analysis method requires a double loop procedure and therefore is generally very time consuming. To improve the efficiency of reliability analysis under the MDO framework, a collaborative reliability analysis method is proposed in this paper. The procedure of the traditional Most Probable Point (MPP) based reliability analysis method is combined with the collaborative disciplinary analyses to automatically satisfy the interdisciplinary consistency when conducting reliability analysis. As a result, only a single loop procedure is required and all the computations are conducted concurrently at the individual discipline-level. Compared with the existing reliability analysis methods in MDO, the proposed method is efficient and therefore provides a cheaper tool to evaluate design feasibility in MDO under uncertainty. Two examples are used for the purpose of verification.

4. “Sequential Optimization and Reliability Assessment for Probabilistic Design,�? X. Du and W. Chen, to appear in ASME Journal of Mechanical Design, 2004.

Abstract: Probabilistic optimization design, such as reliability-based design and robust design, offers tools for making reliable decisions with the consideration of uncertainty associated with design variables/parameters and simulation models. Since a probabilistic optimization often involves a double-loop procedure for the overall optimization and iterations for probabilistic assessment, the computational demand is extremely high. In this paper, the sequential optimization and reliability assessment (SORA) is developed to improve the efficiency of a probabilistic design. The SORA method employs a single-loop strategy with a serial of cycles of optimization and reliability assessment. In each cycle, optimization and reliability assessment are decoupled from each other; the reliability assessment is only conducted after the optimization. The key to the proposed method is to shift the boundaries of violated deterministic constraints (with low reliability) to the feasible direction based on the reliability information obtained in the previous cycle. The design is quickly improved from cycle to cycle and the computational efficiency is improved significantly. Two engineering applications, the reliability-based design for vehicle crashworthiness of side impact and the integrated reliability and robust design of a speed reducer, are presented to demonstrate the effectiveness of the SORA method.

5. “Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design,�? X. Du and W. Chen, AIAA Journal, Vol. 4 No. 3, pp. 545 - 552, 2002.

Abstract: Robust design has been gaining wide attention, and its applications have been extended to making reliable decisions when designing complex engineering systems in a multidisciplinary design environment. Though the usefulness of robust design is widely acknowledged for multidisciplinary design systems, its implementation is rare. One of the reasons is due to the complexity and computational burden associated with the evaluation of performance variations caused by the randomness (uncertainty) of a system. In this paper, a multidisciplinary robust design procedure that utilizes efficient methods for uncertainty analysis is developed. Different from the existing uncertainty analysis techniques, our proposed techniques bring the features of MDO framework into consideration. The system uncertainty analysis (SUA) method and the concurrent subsystem uncertainty analysis (CSSUA) method are developed to estimate the mean and variance of system performance subject to uncertainties associated with both design parameters and design models. As shown both analytically and empirically, compared to the conventional Monte Carlo simulation approach, the proposed techniques used for uncertainty analysis will significantly reduce the amount of design evaluations at the system level, and therefore improve the efficiency of robust design in the domain of MDO. A mathematical example and an electronic packaging problem are used as examples to verify the effectiveness of these approaches