A mathematical model and a heuristic procedure for the robust design problem with high-low tolerances

2001 ◽  
Vol 33 (12) ◽  
pp. 1121-1127 ◽  
Author(s):  
YAHYA FATHI ◽  
DANIEL PALKO
Keyword(s):  
Mathematical Model ◽  
Robust Design ◽  
Design Problem ◽  
Heuristic Procedure

A Mathematical Model for the Optimal Robust Design of Cause Selecting Control Charts

2022 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
SALIH OSMAN Duffuaa ◽  
Ahmed M. Ghaithan ◽  
Ahmed M. Attia
Keyword(s):  
Mathematical Model ◽  
Robust Design ◽  
Control Charts

A Model-Based Formulation of Robust Design

2005 ◽  
Vol 127 (3) ◽  
pp. 388-396 ◽  
Author(s):  
Khalid Al-Widyan ◽  
Jorge Angeles
Keyword(s):  
Covariance Matrix ◽  
Robust Design ◽  
Design Problem ◽  
Engineering Systems ◽  
Design Environment ◽  
Design Task ◽  
Model Based ◽  
Functional Relations ◽  
Design Variables ◽  
Environment Parameters

Laid down in this paper are the foundations on which the design of engineering systems, in the presence of an uncontrollable changing environment, can be based. The changes in environment conditions are accounted for by means of robustness. To this end, a theoretical framework as well as a general methodology for model-based robust design are proposed. Within this framework, all quantities involved in a design task are classified into three sets: the design variables (DV), grouped in vector x, which are to be assigned values as an outcome of the design task; the design-environment parameters (DEP), grouped in vector p, over which the designer has no control; and the performance functions (PF), grouped in vector f, representing the functional relations among performance, DV, and DEP. A distinction is made between global robust design and local robust design, this paper focusing on the latter. The robust design problem is formulated as the minimization of a norm of the covariance matrix of the variations in PF upon variations in the DEP, aka noise in the literature on robust design. Moreover, one pertinent concept is introduced: design isotropy. We show that isotropic designs lead to robustness, even in the absence of knowledge of the statistical properties of the variations of the DEP. To demonstrate our approach, a few examples are included.

Analytical Robust Design of a Gear Milling Machine Headstock

2010 ◽  
Vol 37-38 ◽  
pp. 162-165 ◽  
Author(s):  
Yong Liang Chen ◽  
Shuang Liu ◽  
Han Tao Wang ◽  
Pei Hua Gu
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Robust Design ◽  
Optimization Model ◽  
Functional Performance ◽  
Geometric Design ◽  
Design Parameters ◽  
Milling Machine ◽  
Robust Analysis ◽  
Rayleigh Method

Headstock is a key component of gear milling machine. The dynamic functional performance of the headstock is usually influenced by uncertainties of both geometric and non-geometric design parameters. A new mathematical model to represent relationships among first frequency and design parameters of the headstock were derived with Rayleigh method. Then, a larger-the-better and smaller-the-better robust analysis and optimization model was developed. The sensitivity analysis results show that height of the headstock makes a great impact on the first frequency. Through robust optimizations, the first frequency is scaled up by 3.35 percent while minimizing the variance of the first frequency.

Robust Mechanical Design Using Engineering Models

1995 ◽  
Vol 117 (B) ◽  
pp. 48-54 ◽  
Author(s):  
A. Parkinson
Keyword(s):  
Robust Design ◽  
Design Problem ◽  
Mechanical Design ◽  
Check Valve ◽  
Valve Design ◽  
Robust Designs ◽  
Linkage Design ◽  
Engineering Models ◽  
Transmitted Variation

This paper examines how engineering models can be used to develop robust designs—designs that can tolerate variation. Variation is defined in terms of tolerances which bracket the expected deviation of model variables and/or parameters. Several methods for robust design are discussed. The method of transmitted variation is explained in detail and illustrated on a linkage design problem and a check valve design problem.

scholarly journals A Heuristic Procedure for the Outbound Container Relocation Problem during Export Loading Operations

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Roberto Guerra-Olivares ◽  
Rosa G. González-Ramírez ◽  
Neale R. Smith
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Container Terminals ◽  
Heuristic Procedure ◽  
Container Handling ◽  
Loading Sequence ◽  
Travel Distances

During export ship loading operations, it is often necessary to perform relocation movements with containers that interfere with access to the desired container in the ship loading sequence. This paper presents a real-time heuristic procedure for the container relocation problem employing reachstacker vehicles as container handling equipment. The proposed heuristic searches for good relocation coordinates within a set of nearby bays. The heuristic has a parameter that determines how far from the original bay a container may be relocated. The tradeoff between reducing relocation movements and limiting vehicle travel distances is examined and the performance of the heuristic is compared with a common practice in the smaller container terminals in Chile and Mexico. Finally, a mathematical model for the container relocation problem is presented.

VNS Metaheuristics to Solve a Financial Portfolio Design Problem

2020 ◽  
pp. 148-164
Keyword(s):  
Mathematical Model ◽  
Simulated Annealing ◽  
Local Search ◽  
Design Problem ◽  
Quadratic Model ◽  
Financial Problem ◽  
Financial Portfolio ◽  
The Mathematical Model ◽  
Portfolio Design

This chapter introduces a VNS-based local search for solving efficiently a financial portfolio design problem described in Chapter 1 and modeled in Chapter 3. The mathematical model tackled is a 0-1 quadratic model. It is well known that exact solving approaches on large instances of this kind of model are costly. The authors have proposed local search approaches to solve the problem, and the efficiency of this type of method has been proved. This chapter shows that the matricial 0-1 model of the problem enables specialized VNS algorithms by taking into account the particular structure of the financial problem considered. First experiments show that VNS with simulated annealing is effective on non-trivial instances of the problem.

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