A Unified Optimization Design Model Under Uncertainty

2009 ◽  
Author(s):  
Zhonglai Wang ◽  
Hong-Zhong Huang ◽  
Huanwei Xu ◽  
Xiaoling Zhang
Keyword(s):  
Objective Function ◽  
Robust Design ◽  
Optimization Design ◽  
Optimization Problem ◽  
Sequential Optimization ◽  
Multi Objective Optimization ◽  
Probabilistic Characteristic ◽  
Unified Framework ◽  
Reliability Based Design ◽  
Practical Engineering

It is necessary to combine reliability-based design and robust design in the practical engineering. In this paper, a unified framework for integrated reliability-based design and robust design is proposed. In the proposed framework, traditional multi-objective optimization problem is converted to a single objective optimization problem to integrate reliability-based design and robust design without weight factors. The conversion from probabilistic objective function to deterministic objective function is achieved by inverse reliability strategy under the consideration of the probabilistic characteristic of the objective function. After that, an improved sequential optimization and reliability assessment (SORA) method is proposed to deal with the unified framework. Overall, two examples are implemented to illustrate the benefits of the proposed methods.

A Unified Framework for Integrated Optimization Under Uncertainty

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Zhonglai Wang ◽  
Hong-Zhong Huang ◽  
Yu Liu
Keyword(s):  
Objective Function ◽  
Robust Design ◽  
Taylor Series Expansion ◽  
Assessment Method ◽  
Optimization Under Uncertainty ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Design Stage ◽  
Unified Framework ◽  
Reliability Based Design

Reliability and robustness are two main attributes of design under uncertainty. Hence, it is necessary to combine reliability-based design and robust design at the design stage. In this paper, a unified framework for integrating reliability-based design and robust design is proposed. In the proposed framework, the probabilistic objective function is converted to a deterministic objective function by the Taylor series expansion or inverse reliability strategy with accounting for the probabilistic characteristic of the objective function. Therefore, with this unified framework, there is no need to deal with a multiobjective optimization problem to integrate reliability-based design and robust design any more. The probabilistic constraints are converted to deterministic constraints with inverse reliability strategy at the same time. In order to solve the unified framework, an improved sequential optimization and reliability assessment method is proposed. Three examples are given to illustrate the benefits of the proposed methods.

Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

2002 ◽  
Author(s):  
Xiaoping Du ◽  
Wei Chen
Keyword(s):  
Robust Design ◽  
Optimization Design ◽  
Reliability Assessment ◽  
Assessment Method ◽  
Side Impact ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Probabilistic Design ◽  
Probabilistic Optimization ◽  
Reliability Based Design

Probabilistic optimization design offers tools for making reliable decisions with the consideration of uncertainty associated with design variables/parameters and simulation models. In a probabilistic design, such as reliability-based design and robust design, the design feasibility is formulated probabilistically such that the probability of the constraint satisfaction (reliability) exceeds the desired limit. The reliability assessment for probabilistic constraints often involves an iterative procedure; therefore, two loops are involved in a probabilistic optimization. Due to the double-loop procedure, the computational demand is extremely high. To improve the efficiency of a probabilistic design, a novel method – sequential optimization and reliability assessment (SORA) is developed in this paper. The SORA method employs a single-loop strategy where a serial of cycles of optimization and reliability assessment is employed. In each cycle optimization and reliability assessment are decoupled from each other; no reliability assessment is required within optimization and the reliability assessment is only conducted after the optimization. The key concept of 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. Hence 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.

The Effect of Different Optimization Methods on Robustness for Robust Optimization Design

2014 ◽  
Vol 721 ◽  
pp. 464-467
Author(s):  
Tao Fu ◽  
Qin Zhong Gong ◽  
Da Zhen Wang
Keyword(s):  
Robust Optimization ◽  
Objective Function ◽  
Robust Design ◽  
Optimization Design ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Parameters ◽  
Hybrid Particle Swarm Optimization ◽  
Design Variables ◽  
Robust Optimization Design

In view of robustness of objective function and constraints in robust design, the method of maximum variation analysis is adopted to improve the robust design. In this method, firstly, we analyses the effect of uncertain factors in design variables and design parameters on the objective function and constraints, then calculate maximum variations of objective function and constraints. A two-level optimum mathematical model is constructed by adding the maximum variations to the original constraints. Different solving methods are used to solve the model to study the influence to robustness. As a demonstration, we apply our robust optimization method to an engineering example, the design of a machine tool spindle. The results show that, compared with other methods, this method of HPSO(hybrid particle swarm optimization) algorithm is superior on solving efficiency and solving results, and the constraint robustness and the objective robustness completely satisfy the requirement, revealing that excellent solving method can improve robustness.

Multi-Objective Optimization Design of Screw Conveyor Using Genetic Algorithm

2013 ◽  
Vol 732-733 ◽  
pp. 402-406
Author(s):  
Duan Yi Wang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Optimization Design ◽  
Optimization Problem ◽  
Machine Design ◽  
Screw Conveyor ◽  
Optimized Design ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
The Mathematical Model

The weight minimum and drive efficiency maxima1 of screw conveyor were considered as double optimizing objects in this paper. The mathematical model of the screw conveyor has been established based on the theory of the machine design, and the genetic algorithm was adopted to solving the multi-objective optimization problem. The results show that the mass of spiral shaft reduces 13.6 percent, and the drive efficiency increases 6.4 percent because of the optimal design based on genetic algorithm. The genetic algorithm application on the screw conveyor optimized design can provided the basis for designing the screw conveyor.

Multi-Objective Optimization Design of Tanker Ships via a Genetic Algorithm

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Marcelo Ramos Martins ◽  
Diego F. Sarzosa Burgos
Keyword(s):  
Genetic Algorithm ◽  
Optimization Design ◽  
Optimization Problem ◽  
Pareto Frontier ◽  
Ship Design ◽  
Design Parameters ◽  
Multi Objective Optimization ◽  
Total Cost ◽  
Multi Objective ◽  
The Cost

The cost of a new ship design heavily depends on the principal dimensions of the ship; however, dimensions minimization often conflicts with the minimum oil outflow (in the event of an accidental spill). This study demonstrates one rational methodology for selecting the optimal dimensions and coefficients of form of tankers via the use of a genetic algorithm. Therein, a multi-objective optimization problem was formulated by using two objective attributes in the evaluation of each design, specifically, total cost and mean oil outflow. In addition, a procedure that can be used to balance the designs in terms of weight and useful space is proposed. A genetic algorithm was implemented to search for optimal design parameters and to identify the nondominated Pareto frontier. At the end of this study, three real ships are used as case studies.

A Closeness Degree Method for Multi-Objective Optimization of Belt Transmission

1992 ◽  
Author(s):  
Lin Qun ◽  
Wu Meijuan
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Design ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Objective Function Values ◽  
Belt Transmission ◽  
Fuzzy Subsets ◽  
The Ideal

Abstract A mathematical model for multi objective optimization design of belt transmission is proposed in this paper. The normal fuzzy distribution is used to convert the ideal and non-inferior solutions into fuzzy subsets over the space of objective function values. The optimal solution which is closest to the ideal one could then be found on the basis of closeness degree method.

Structural Optimization Design Considering Reliability Constraints

2013 ◽  
Vol 477-478 ◽  
pp. 723-726
Author(s):  
Li Rong Sha ◽  
Yong Chun Shi
Keyword(s):  
Optimization Design ◽  
Optimization Problem ◽  
Structural Reliability ◽  
Structural Parameters ◽  
Dominant Role ◽  
Structural Performance ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Network Method ◽  
Reliability Based Optimization

In engineering applications the uncertainties of the structural parameters are inherent and the scatter from their nominal ideal values is in most cases unavoidable. These uncertainties play a dominant role in structural performance and the reliability-based design optimization is a useful method to assess the uncertainty influence. Compared to the basic deterministic-based optimization problem, the latter considers additional non-deterministic constraint functions and will provide the structure more safety. This paper proposed a Fourier orthogonal neural network method to the structural reliability analysis and reliability-based optimization considering uncertainties, the main aim is to minimize the weight of the structure under certain reliability constraints, and to obtain economic benefit meanwhile ensure the safety of the structure.

Robust Optimization Design on Vehicle Divided Steering Linkage

2011 ◽  
Vol 130-134 ◽  
pp. 270-273
Author(s):  
Hua Zhu ◽  
Yong Zhang
Keyword(s):  
Robust Design ◽  
Optimization Design ◽  
Optimization Problem ◽  
Design Method ◽  
Kinematic Pair ◽  
Objective Functions ◽  
Robust Model ◽  
Structural Error ◽  
Steering Mechanism ◽  
Robust Optimization Design

In view of the great fluctuation on objective functions which cause constraints dissatisfied, robust design is applied to the vehicle divided steering linkage optimization problem. A robust model is established by considering the kinematic pair clearance and structural error both in the objective functions and constrains. Optimum results show that,the design method can effectively guarantee the kinematics precision of steering mechanism and the transmission stability.

Particle Swarm Optimization for Ship Degaussing Coils Calibration

2012 ◽  
Vol 182-183 ◽  
pp. 1446-1451
Author(s):  
Ming Ming Yang ◽  
Da Ming Liu ◽  
Li Ting Lian
Keyword(s):  
Magnetic Field ◽  
Particle Swarm Optimization ◽  
Objective Function ◽  
Optimization Problem ◽  
Particle Swarm ◽  
Multi Objective Optimization ◽  
Swarm Optimization ◽  
Multi Objective ◽  
Scale Factors ◽  
Single Objective

In this paper, we deal with the problem of the ship degaussing coils optimal calibration by a linearly decreasing weight particle swarm optimization (LDW-PSO). Taking the ship’s magnetic field and its gradient reduction into account, the problem is treated as a multi-objective optimization problem. First a set of scale factors are calculated by LDW-PSO to scale the two kinds of objective function, then the multi-objective optimization problem is transformed to a single objective optimization problem via a set of proper weights, and the problem is solved by LDW-PSO finally. A typical ship degaussing system is applied to test the method’s validity, and the results are good.

Research on Multi-Objective Optimization Design of Thrust Vector Control Actuator

2012 ◽  
Vol 591-593 ◽  
pp. 15-20
Author(s):  
Jun Zhou ◽  
Jiao Long Zhang ◽  
Feng Qi Zhou
Keyword(s):  
Objective Function ◽  
Vector Control ◽  
Optimization Design ◽  
Nonlinear Problems ◽  
Multi Objective Optimization ◽  
Weighting Method ◽  
Thrust Vector Control ◽  
Multi Objective ◽  
Functional Relations ◽  
Thrust Vector

Aiming at the seriously nonlinear problems of the single nozzle thrust vector control servo system, this paper detailedly deduced the functional relations between the layout of actuators and system dynamic parameters, on the basis of which, a multi-objective optimization model was established with coupling degree, angular asymmetry, as well as length and variation degree of initial swinging arm taken into consideration. Linear weighting method was adopted to convert the multi-objective function into a uni-objective one and an improved genetic algorithm with good robustness was utilized to solve the optimization problem. Calculation results demonstrated that, with this optimization algorithm, sub-objective functions all reach the ideal effects when uni-objective function achieves optimum. The optimization method guarantees that coupling degree, angular asymmetry and swinging arm variation achieve minimum when the initial swinging arm length is at its maximum, which provides theoretical basis for the actuator layout of thrust vector control.

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