A Performance-Based Representation for Engineering Design

1999 ◽  
Vol 123 (4) ◽  
pp. 486-493 ◽  
Author(s):  
Liang Zhu ◽  
David Kazmer
Keyword(s):  
Linear System ◽  
Performance Space ◽  
Design Representation ◽  
Pareto Optimal Set ◽  
Performance Requirements ◽  
Decision Variables ◽  
System Characterization ◽  
Transformation Algorithms ◽  
Optimal Set ◽  
A Performance

A design representation is developed to model multi-attribute systems utilizing multi-dimensional clipping and transformation algorithms. Given a linear system characterization, three types of supporting information is generated for the decision maker: (1) a function matrix that describes the performance attributes dependent upon the decision variables; (2) a decision space that corresponds to the feasible decision set that meets performance requirements, and; (3) a performance space that represents the feasible performance region and the Pareto Optimal set. The analytical method developed for solving these feasible spaces is described for a linear system model. A case study is presented to demonstrate how to utilize the representation to locate a feasible solution and proceed to the desired trade-off of multiple attributes. Moreover, the potential incorporations of the representation with other influential design methodologies are discussed.

A Performance-Based Representation of Constraint Based Reasoning and Decision Based Design

2000 ◽  
Author(s):  
Liang Zhu ◽  
David Kazmer
Keyword(s):  
Parametric Design ◽  
Performance Space ◽  
Pareto Optimal Set ◽  
Performance Requirements ◽  
Beam Design ◽  
Decision Variables ◽  
Transformation Algorithms ◽  
Decision Based Design ◽  
Optimal Set ◽  
A Performance

Abstract A performance-based representation is developed utilizing multi-dimensional clipping and transformation algorithms. Given analytic performance functions, three types of supporting information is presented to the decision maker: 1) a function matrix that describes the performance attributes varying with the decision variables; 2) a decision space that illustrates the feasible decision set that meets performance requirements, and; 3) a performance space that provides the feasible performance region and the Pareto Optimal set. The performance-based representation is compatible with other influential design methodologies. A case study is presented for aircraft beam design utilizing constraint based reasoning and decision based design. The results demonstrate not only the benefit of the representation on interactive parametric design, but also an intriguing comparison between constraint based reasoning and decision based design approaches incorporated with the described representation. While a linearized parametric design problem is implemented, the approach shows a potential extension to non-linear systems.

Process Window Derivation With an Application to Optical Media Manufacturing

2000 ◽  
Vol 123 (2) ◽  
pp. 303-311 ◽  
Author(s):  
David Kazmer ◽  
Liang Zhu ◽  
David Hatch
Keyword(s):  
Quality Attributes ◽  
Process Models ◽  
Process Window ◽  
Feasible Region ◽  
Part Quality ◽  
Performance Space ◽  
Pareto Optimal Set ◽  
Optical Media ◽  
Quality Specifications ◽  
Optimal Set

This paper derives the process window from quantitative process models. Multi-dimensional clipping algorithms are developed that operate on half-spaces defined from the quality specifications. The resulting polytope is difficult to directly interpret. To support interactive tuning and optimization of manufacturing processes, three types of graphical matrices are presented to the decision maker: (1) the function matrix describes the relations between the process parameters and the manufactured part quality attributes; (2) the process space illustrates the feasible processing space constrained by the product quality specifications; (3) the performance space provides the feasible region of the part quality attributes and the Pareto Optimal set corresponding to the processing space. Optimization of optical media manufacturing is presented to demonstrate the use of the process window to locate a feasible solution and proceed to a desired trade-off of multiple quality attributes.

Analytical Derivation of the Pareto-Optimal Set with Application to Structural Design

2020 ◽  
pp. 43-66
Author(s):  
Federico Maria Ballo ◽  
Massimiliano Gobbi ◽  
Giampiero Mastinu ◽  
Giorgio Previati
Keyword(s):  
Structural Design ◽  
Pareto Optimal ◽  
Analytical Derivation ◽  
Pareto Optimal Set ◽  
Optimal Set

Multi-Objective Optimization Analysis of Motor Cooling System in Articulated Dump Truck

2011 ◽  
Vol 383-390 ◽  
pp. 4715-4720
Author(s):  
Yan Zhang ◽  
Yan Hua Shen ◽  
Wen Ming Zhang
Keyword(s):  
Field Distribution ◽  
Cooling System ◽  
Dump Truck ◽  
Water Cooling ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Temperature And Pressure ◽  
Water Cooling System ◽  
Optimal Set

In order to ensure the reliable and safe operation of the electric driving motor of the articulated dump truck, water cooling system is installed for each motor. For the best performance of the water cooling system, not only the heat transfer should be enhanced to maintain the motor in relatively low temperature, but also the pressure drop in the water cooling system should be reduced to save energy by reducing the power consumption of the pump. In this paper, the numerical simulation of the cooling progress is completed and the temperature and pressure field distribution are obtained. The multi-objective optimization model is established which involves the cooling system structure, temperature field distribution and pressure field distribution. To improve the computational efficiency, the surrogate model of the simulation about the cooling process is established based on the Response Surface Methodology (RSM). After the multi-objective optimization, the Pareto optimal set is obtained. The proper design point, which could make the average temperature and pressure drop of the cooling system relative desirable, is chosen from the Pareto optimal set.

Optimal Approximation of Real Values Using Rational Numbers With Application to the Kinematic Design of Gearboxes

1993 ◽  
Author(s):  
Leonard P. Pomrehn ◽  
Panos Y. Papalambros
Keyword(s):  
Design Problem ◽  
Rational Numbers ◽  
Optimal Approximation ◽  
Pareto Optimal ◽  
Individual Stage ◽  
Gear Teeth ◽  
Kinematic Design ◽  
Pareto Optimal Set ◽  
Reducing Gear ◽  
Optimal Set

Abstract This article proposes a method for optimally approximating real values with rational numbers. Such requirements arise in the design of various types of gear sets, where integer numbers of gear teeth force individual stage ratios to assume rational values. The kinematic design of an 18-speed gearbox, taken from the literature, is analyzed and solved using the proposed method. The method, called sequential exhaustion, sequentially considers each stage of the gearbox design, exhaustively examining each stage. Examination of 94 solutions leads to a pareto-optimal set containing 11 solutions. Further, although the layout of the gearbox is predefined for the kinematic design problem, certain solutions of the problem exhibit “non-reducing” gear pairs, revealing previously unforeseen changes in the gearbox layout.

The Skewboid Method: A Simple and Effective Approach to Pareto Relaxation and Filtering

2012 ◽  
Author(s):  
Matthew I. Campbell
Keyword(s):  
Pareto Optimality ◽  
Population Based ◽  
Pareto Optimal ◽  
Large Set ◽  
Number Of Solutions ◽  
Target Number ◽  
Relaxation Methods ◽  
Pareto Optimal Set ◽  
Optimal Set ◽  
Adjustment Parameter

The concept of Pareto optimality is the default method for pruning a large set of candidate solutions in a multi-objective problem to a manageable, balanced, and rational set of solutions. While the Pareto optimality approach is simple and sound, it may select too many or too few solutions for the decision-maker’s needs or the needs of optimization process (e.g. the number of survivors selected in a population-based optimization). This inability to achieve a target number of solutions to keep has caused a number of researchers to devise methods to either remove some of the non-dominated solutions via Pareto filtering or to retain some dominated solutions via Pareto relaxation. Both filtering and relaxation methods tend to introduce many new adjustment parameters that a decision-maker (DM) must specify. In the presented Skewboid method, only a single parameter is defined for both relaxing the Pareto optimality condition (values between −1 and 0) and filtering more solutions from the Pareto optimal set (values between 0 and 1). This parameter can be correlated with a desired number of solutions so that this number of solutions is input instead of an unintuitive adjustment parameter. A mathematically sound derivation of the Skewboid method is presented followed by illustrative examples of its use. The paper concludes with a discussion of the method in comparison to similar methods in the literature.

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