Reliability-Based Multidisciplinary Design Optimization Using Probabilistic Gradient-Based Transformation Method

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Po Ting Lin ◽  
Hae Chang Gea
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Transformation Method ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Multidisciplinary Design ◽  
Sensitivity Analyses ◽  
Chance Constrained Programming ◽  
Complex Design ◽  
Gradient Based

Recently, solving the complex design optimization problems with design uncertainties has become an important but very challenging task in the communities of reliability-based design optimization (RBDO) and multidisciplinary design optimization (MDO). The MDO algorithms decompose the complex design problem into the hierarchical or nonhierarchical optimization structure and distribute the workloads to each discipline (or subproblem) in the decomposed structure. The coordination of the local responses is crucial for the success of finding the optimal design point. The problem complexity increases dramatically when the existence of the design uncertainties is not negligible. The RBDO algorithms perform the reliability analyses to evaluate the probabilities that the random variables violate the constraints. However, the required reliability analyses build up the degree of complexity. In this paper, the gradient-based transformation method (GTM) is utilized to reduce the complexity of the MDO problems by transforming the design space to multiple single-variate monotonic coordinates along the directions of the constraint gradients. The subsystem responses are found using the monotonicity principles (MP) and then coordinated for the new design points based on two general principles. To consider the design uncertainties, the probabilistic gradient-based transformation method (PGTM) is proposed to adapt the first-order probabilistic constraints from three different RBDO algorithms, including the chance constrained programming (CCP), reliability index approach (RIA), and performance measure approach (PMA), to the framework of the GTM. PGTM is efficient because only the sensitivity analyses and the reliability analyses require function evaluations (FE). The optimization processes of monotonicity analyses and the coordination procedures are free of function evaluations. Several mathematical and engineering examples show the PGTM is capable of finding the optimal solutions with desirable reliability levels.

Multidisciplinary Design Optimization of a Naval Surface Combatant

2003 ◽  
Vol 47 (01) ◽  
pp. 1-12 ◽  
Author(s):  
Daniele Peri ◽  
Emilio F. Campana
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Optimization Methods ◽  
Ship Design ◽  
Multidisciplinary Design ◽  
Construction Costs ◽  
Gradient Based ◽  
Numerical Tools ◽  
Surface Combatant ◽  
Hydrodynamic Optimization

Whereas shape optimal design has received considerable attention in many industrial contexts, the application of automatic optimization procedures to hydrodynamic ship design has not yet reached the same maturity. Nevertheless, numerical tools, combining together modern computational fluid dynamics and optimization methods, can aid in the ship design, enhancing the operational performances and reducing development and construction costs. This paper represents an attempt of applying a multidisciplinary design optimization (MDO) procedure to the enhancement of the performances of an existing ship. At the present stage the work involves modeling, development, and implementation of algorithms only for the hydrodynamic optimization. For a naval surface combatant, the David Taylor Model Basin (DTMB) model ship 5415, a three-objective functions optimization for a two-discipline design problem is devised and solved in the framework of the MDO approach. A simple decision maker is used to order the Pareto optimal solutions, and a gradient-based refinement is performed on the selected design.

A Collaborative Approach for Multidisciplinary Systems Reliability Design and Optimization

2013 ◽  
Vol 694-697 ◽  
pp. 911-914 ◽  
Author(s):  
Jun Zhang ◽  
Bing Zhang
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Optimization Procedure ◽  
Performance Measure ◽  
Multidisciplinary Design ◽  
Sequential Optimization ◽  
Optimization Strategy ◽  
Reliability Design ◽  
Design And Optimization ◽  
Subspace Optimization

In order to improve the efficiency and robustness of reliability-based multidisciplinary design optimization (RBMDO), a new collaborative strategy (named C-RBMDO) which integrates performance measure approach (PMA) and concurrent subspace optimization strategy (CSSO) is proposed. Both the mathematical model and optimization procedure are put forward. The traditional triple-level nested flowchart of RBMDO is decoupled with the sequential optimization and reliability assessment (SORA). The deterministic multidisciplinary design optimization and the multidisciplinary reliability analysis are executed by CSSO and PMA respectively. Finally, the proposed method is verified through the design example of gear transmission.

Performance Measure Approach Based Multidisciplinary Design Optimization of Gear Transmission

2013 ◽  
Vol 694-697 ◽  
pp. 868-871
Author(s):  
Jun Zhang ◽  
Bing Zhang
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Performance Measure ◽  
Collaborative Optimization ◽  
Gear Transmission ◽  
System Level ◽  
Multidisciplinary Design ◽  
Engineering Systems ◽  
Performance Measure Approach ◽  
Design Cost

In order to reduce the influence of uncertainties on complicated engineering systems performance, a new method is proposed based on the performance measure approach and collaborative optimization (PMA-CO) to implement the reliability-based multidisciplinary design optimization of gear transmission. Both the mathematical model and procedures of PMA-CO are presented. With the adoption of slack factors in the system-level of collaborative optimization, both CO and PMA-CO are applied to the optimization of gear transmission. The proposed PMA-CO improves the reliability of the gear transmission and gained a tradeoff solution between design cost and reliability. Therefore, the PMA-CO is effective and practical in engineering design.

A PMA-Based Collaborative Strategy for Reliability Design and Optimization of Multidisciplinary Systems

2011 ◽  
Vol 418-420 ◽  
pp. 411-414 ◽  
Author(s):  
Rong Gang Yu ◽  
Jun Zhang ◽  
Bing Zhang
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Main Idea ◽  
Performance Measure ◽  
Collaborative Optimization ◽  
Multidisciplinary Design ◽  
Sequential Optimization ◽  
Reliability Design ◽  
Design And Optimization ◽  
Index Approach

To tackle the computing efficiency and robustness problems caused by the reliability index approach (RIA) in reliability-based multidisciplinary design optimization (RBMDO), a new performance measure approach-based method for RBMDO is proposed. Meanwhile, the traditional triple-level nested flowchart of RBMDO is decoupled through the main idea of sequential optimization and reliability assessment (SORA). Both deterministic multidisciplinary design optimization and the multidisciplinary reliability analysis are executed by collaborative optimization (CO). Finally, the proposed method is verified through the design example of gear transmission.

Sensitivity Analyses of FORM-Based and DRM-Based Performance Measure Approach for Reliability-Based Design Optimization

2008 ◽  
Author(s):  
Ikjin Lee ◽  
Kyung K. Choi ◽  
Liu Du ◽  
David Gorsich
Keyword(s):  
Design Optimization ◽  
Performance Measure ◽  
Second Order ◽  
Probabilistic Constraints ◽  
Sensitivity Analyses ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Measure Approach ◽  
Reliability Based Design ◽  
Reliability Method

In a gradient-based design optimization, it is necessary to know sensitivities of the constraint with respect to the design variables. In a reliability-based design optimization (RBDO), the constraint is evaluated at the most probable point (MPP) and called the probabilistic constraint, thus it requires the sensitivities of the probabilistic constraints at MPP. This paper presents the rigorous analytic derivation of the sensitivities of the probabilistic constraint at MPP for both First Order Reliability Method (FORM)-based Performance Measure Approach (PMA) and Dimension Reduction Method (DRM)-based PMA. Numerical examples are used to demonstrate that the analytic sensitivities agree very well with the sensitivities obtained from the finite difference method (FDM). However, since the sensitivity calculation at the true DRM-based MPP requires the second-order derivatives and additional MPP search, the sensitivity derivation at the approximated DRM-based MPP, which does not require the second-order derivatives and additional MPP search to find the DRM-based MPP, is proposed in this paper. A convergence study illustrates that the sensitivity at the approximated DRM-based MPP converges to the sensitivity at the true DRM-based MPP as the design approaches the optimum design. Hence, the sensitivity at the approximated DRM-based MPP is proposed to be used for the DRM-based RBDO to enhance the efficiency of the optimization.

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