Uncertainty Propagation in Multi-Disciplinary Design Optimization of Undersea Vehicles

2008 ◽  
Vol 1 (1) ◽  
pp. 70-79 ◽  
Author(s):  
Jim He ◽  
Geng Zhang ◽  
Nickolas Vlahopoulos
2005 ◽  
Vol 128 (2) ◽  
pp. 503-508 ◽  
Author(s):  
Michael Kokkolaras ◽  
Zissimos P. Mourelatos ◽  
Panos Y. Papalambros

This paper presents a methodology for design optimization of hierarchically decomposed systems under uncertainty. We propose an extended, probabilistic version of the deterministic analytical target cascading (ATC) formulation by treating uncertain quantities as random variables and posing probabilistic design constraints. A bottom-to-top coordination strategy is used for the ATC process. Given that first-order approximations may introduce unacceptably large errors, we use a technique based on the advanced mean value method to estimate uncertainty propagation through the multilevel hierarchy of elements that comprise the decomposed system. A simple yet illustrative hierarchical bilevel engine design problem is used to demonstrate the proposed methodology. The results confirm the applicability of the proposed probabilistic ATC formulation and the accuracy of the uncertainty propagation technique.


Author(s):  
Tingting Xia ◽  
Mian Li ◽  
Jianhua Zhou

The real challenge for multi-disciplinary design optimization (MDO) problems to gain a robust solution is the propagation of uncertainty from one discipline to another. Most existing methods only consider a MDO problem in deterministic manner or find a solution which is robust for a single-disciplinary optimization problem. These rare methods for solving MDO problems under uncertainty are usually computational expensive. This research proposes a robust sequential MDO (RS-MDO) approach based on a sequential MDO (S-MDO) framework. Firstly, a robust solution is obtained by giving each discipline full autonomy to perform optimization. Tolerance range is specified for the coupling variable to model uncertainty propagation in the original coupled system. Then the obtained robust extreme points of global variable and coupling variable are dispatched into subsystems to perform optimization sequentially. Additional constraints are added to keep consistency and guarantee a robust solution. To find a solution with such strict constraints, genetic algorithm (GA) is used as a solver in each optimization stage. Since all iterations in the sequential optimization stage can be processed in parallel, this robust MDO approach can be more time-saving. Numerical examples are provided to demonstrate the availability and effectiveness of proposed approach.


Author(s):  
Kyung K. Choi ◽  
Byeng D. Youn ◽  
Jun Tang

Mechanical fatigue subject to external and inertia transient loads in the service life of mechanical systems often leads a structural failure due to accumulated damage. Structural durability analysis that predicts the fatigue life of mechanical components subject to dynamic stresses and strains is a compute intensive multidisciplinary simulation process, since it requires an integration of several computer-aided engineering tools and large amount of data communication and computation. Uncertainties in geometric dimensions due to manufacturing tolerances cause the indeterministic nature of fatigue life of the mechanical component. Due to the fact that uncertainty propagation to structural fatigue under transient dynamic loading is not only numerically complicate but also extremely expensive, it is a challenging task to develop structural durability-based design optimization process and reliability analysis to ascertain whether the optimal design is reliable. The objective of this paper is development of an integrated CAD-based computer-aided engineering process to effectively carry out the design optimization for a structural durability, yielding a durable and cost-effectively manufacturable product. In addition, a reliability analysis is executed to assess the reliability for the deterministic optimal design.


2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Tangfan Xiahou ◽  
Yu Liu ◽  
Qin Zhang

Abstract Multi-state is a typical characteristic of engineered systems. Most existing studies of redundancy allocation problems (RAPs) for multi-state system (MSS) design assume that the state probabilities of redundant components are precisely known. However, due to lack of knowledge and/or ambiguous judgements from engineers/experts, the epistemic uncertainty associated with component states cannot be completely avoided and it is befitting to be represented as belief quantities. In this paper, a multi-objective RAP is developed for MSS design under the belief function theory. To address the epistemic uncertainty propagation from components to system reliability evaluation, an evidential network (EN) model is introduced to evaluate the reliability bounds of an MSS. The resulting multi-objective design optimization problem is resolved via a modified non-dominated sorting genetic algorithm II (NSGA-II), in which a set of new Pareto dominance criteria is put forth to compare any pair of feasible solutions under the belief function theory. A numerical case along with a SCADA system design is exemplified to demonstrate the efficiency of the EN model and the modified NSGA-II. As observed in our study, the EN model can properly handle the uncertainty propagation and achieve narrower reliability bounds than that of the existing methods. More importantly, the original nested design optimization formulation can be simplified into a one-stage optimization model by the proposed method.


Author(s):  
J Roshanian ◽  
AA Bataleblu ◽  
M Ebrahimi

Uncertainty-based design optimization has been widely acknowledged as an advanced methodology to address competing objectives of aerospace vehicle design, such as reliability and robustness. Despite the usefulness of uncertainty-based design optimization, the computational burden associated with uncertainty propagation and analysis process still remains a major challenge of this field of study. The metamodeling is known as the most promising methodology for significantly reducing the computational cost of the uncertainty propagation process. On the other hand, the nonlinearity of the uncertainty-based design optimization problem's design space with multiple local optima reduces the accuracy and efficiency of the metamodels prediction. In this article, a novel metamodel management strategy, which controls the evolution during the optimization process, is proposed to alleviate these difficulties. For this purpose, a combination of improved Latin hypercube sampling and artificial neural networks are involved. The proposed strategy assesses the created metamodel accuracy and decides when a metamodel needs to be replaced with the real model. The metamodeling and metamodel management strategy are conspired to propose an augmented strategy for robust design optimization problems. The proposed strategy is applied to the multiobjective robust design optimization of an expendable launch vehicle. Finally, based on non-dominated sorting genetic algorithm-II, a compromise between optimality and robustness is illustrated through the Pareto frontier. Results illustrate that the proposed strategy could improve the computational efficiency, accuracy, and globality of optimizer convergence in uncertainty-based design optimization problems.


Author(s):  
Mian Li ◽  
Shapour Azarm

Real-world engineering design optimization problems often involve systems that have coupled disciplines with uncontrollable variations in their parameters. No approach has yet been reported for the solution of these problems when there are multiple objectives in each discipline, mixed continuous-discrete variables, and when there is a need to account for uncertainty and also uncertainty propagation across disciplines. We present a Multiobjective collaborative Robust Optimization (McRO) approach for this class of problems that have interval uncertainty in their parameters. McRO obtains Multidisciplinary Design Optimization (MDO) solutions which are as best as possible in a multiobjective and multidisciplinary sense. For McRO solutions, the sensitivity of objective and/or constraint functions is kept within an acceptable range. McRO involves a technique for interdisciplinary uncertainty propagation. The approach can be used for robust optimization of MDO problems with multiple objectives, or constraints, or both together at system and subsystem levels. Results from an application of the approach to a numerical and an engineering example are presented. It is concluded that the McRO approach can solve fully coupled MDO problems with interval uncertainty and can obtain solutions that are comparable to an all-at-once robust optimization approach.


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