Robust Optimal Design for Worst-Case Tolerances

1994 ◽  
Vol 116 (4) ◽  
pp. 1019-1025 ◽  
Author(s):  
G. Emch ◽  
A. Parkinson
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Worst Case ◽  
New Approach ◽  
Robust Designs ◽  
Design Variables ◽  
Robust Optimal Design ◽  
Programming Techniques ◽  
Engineering Models ◽  
Analytical Tools

Engineering models can and should be used to understand the effects of variability on a design. When variability is ignored, brittle designs can result that will not function properly or that will fail in service. By contrast, robust designs function properly even when subjected to off-nominal conditions. There is a need for better analytical tools to help engineers develop robust designs. In this paper we present a new approach for developing designs that are robust to variability induced by worst-case tolerances. An advantage of this approach is that tolerances may be placed on any or all model inputs, whether design variables or parameters. The method adapts nonlinear programming techniques in order to determine how a design should be modified to account for variability. We tested the method under relatively severe conditions on 13 problems, with excellent results. Using this approach, a designer can account for the effects of worst-case tolerances, making it possible to build robustness into an engineering design.

Using Engineering Models to Control Variability: Feasibility Robustness for Worst-Case Tolerances

1993 ◽  
Author(s):  
Gary Emch ◽  
Alan Parkinson
Keyword(s):  
Nonlinear Programming ◽  
Engineering Design ◽  
Test Cases ◽  
Worst Case ◽  
Robust Designs ◽  
Feasibility Robustness ◽  
Programming Techniques ◽  
Engineering Models ◽  
Analytical Tools ◽  
General Method

Abstract Engineering models can and should be used to understand the effects of variability on a design. When variability is ignored, brittle designs can result that fail in service. By contrast, robust designs function properly even when subjected to off-nominal conditions. There is a need for better analytical tools to help engineers develop robust designs. In this paper we present a general method for developing designs that are robust to variability induced by worst-case tolerances. The method adapts nonlinear programming techniques in order to determine how a design should be modified to account for variability. We show how this can be done with second order, or even exact, worst-case tolerance models. Results are given for 13 test cases that span a variety of problems. The method enables a designer to understand and account for the effects of worst-case tolerances, making it possible to build robustness into an engineering design.

A General Approach for Robust Optimal Design

1993 ◽  
Vol 115 (1) ◽  
pp. 74-80 ◽  
Author(s):  
A. Parkinson ◽  
C. Sorensen ◽  
N. Pourhassan
Keyword(s):  
Statistical Analysis ◽  
Optimal Design ◽  
Design Optimization ◽  
Design Problem ◽  
Optimization Process ◽  
Worst Case ◽  
Rigorous Approach ◽  
Design Variables ◽  
Robust Optimal Design ◽  
And Control

This paper describes a general, rigorous approach for robust optimal design. The method allows a designer to explicitly consider and control, as an integrated part of the optimization process, the effects of variability in design variables and parameters on a design. Variability is defined in terms of tolerances which bracket the variation of fluctuating quantities. A designer can apply tolerances to any model input and can analyze how the tolerances affect the design using either a worst case or statistical analysis. As part of design optimization, the designer can apply the method to find an optimum that will remain feasible when subject to variation, and/or the designer can minimize or constrain the effects of tolerances as one of the objectives or constraints of the design problem.

Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design

1988 ◽  
Author(s):  
P. Y. Papalambros
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Design Problems ◽  
Local Optima ◽  
Solution Strategies ◽  
Active Constraints ◽  
Active Sets ◽  
Trade Offs ◽  
Design Variables ◽  
Monotonicity Analysis

Abstract Solution strategies for optimal design problems in nonlinear programming formulations may require verification of optimality for constraint-bound points. These points are candidate solutions where the number of active constraints is equal to the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs and it would be desirable to identify them early, or exclude them in a strategy using active sets. Potential constrained-bound solutions are usually identified based on the principles of monotonicity analysis. This article discusses some cases where these points are in fact global or local optima.

scholarly journals Field-based optimal-design of an electric motor: a new sensitivity formulation

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 924-928 ◽  
Author(s):  
Paolo Di Barba ◽  
Maria Evelina Mognaschi ◽  
David Alister Lowther ◽  
Sławomir Wiak
Keyword(s):  
Optimal Design ◽  
Electric Motor ◽  
Pareto Front ◽  
Switched Reluctance Motor ◽  
Design Criteria ◽  
New Approach ◽  
Switched Reluctance ◽  
Reluctance Motor ◽  
Robust Optimal Design

AbstractIn this paper, a new approach to robust optimal design is proposed. The idea is to consider the sensitivity by means of two auxiliary criteria A and D, related to the magnitude and isotropy of the sensitivity, respectively. The optimal design of a switched-reluctance motor is considered as a case study: since the case study exhibits two design criteria, the relevant Pareto front is approximated by means of evolutionary computing.

scholarly journals Robust Optimal Design of Beams Subject to Uncertain Loads

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Ismail Kucuk ◽  
Sarp Adali ◽  
Ibrahim Sadek
Keyword(s):  
Optimal Design ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
Optimal Designs ◽  
Transverse Load ◽  
Cross Sectional ◽  
Worst Case ◽  
Operational Conditions ◽  
Robust Optimal Design ◽  
Optimal Area

Optimality conditions are derived for the robust optimal design of beams subject to a combination of uncertain and deterministic transverse and boundary loads using a variational min-max approach. The potential energy of the beam is maximized to compute the worst case loading and minimized to determine the optimal cross-sectional shape which results in coupled nonlinear differential equations for the unknown functions except for the case of a variable width beam. The uncertain component of the transverse load acting on the beam is not known a priori resulting in load uncertainty subject only to an norm constraint. Similarly the optimal area function is subject to a volume constraint leading to an isoperimetric variational problem. The min-max approach leads to robust optimal designs which are not susceptible to unexpected load variations as it occurs under operational conditions. The solution methodology is illustrated for the variable width beam by obtaining analytical results for several cases. The efficiency of the optimal designs is computed with respect to a uniform beam under worst case loading taking the maximum deflection as the quantity for comparison. It is observed that the optimal shapes are more than 70% efficient for the examples given in this study.

A Deterministic and Probabilistic Approach for Robust Optimal Design of a 6-DOF Haptic Device

2013 ◽  
Author(s):  
Aftab Ahmad ◽  
Kjell Andersson ◽  
Ulf Sellgren
Keyword(s):  
Monte Carlo ◽  
Optimal Design ◽  
Probabilistic Approach ◽  
Design Parameters ◽  
Optimization Approach ◽  
Performance Indices ◽  
Uncertain Variables ◽  
Global Indices ◽  
Design Variables ◽  
Robust Optimal Design

This work suggests a two-stage approach for robust optimal design of 6-DOF haptic devices based on a sequence of deterministic and probabilistic analyses with a multi-objective genetic algorithm and the Monte-Carlo method. The presented model-based design robust optimization approach consider simultaneously the kinematic, dynamic, and kinetostatic characteristics of the device in both a constant and a dexterous workspace in order to find a set of optimal design parameter values for structural configuration and dimensioning. Design evaluation is carried out based on local and global indices, like workspace volume, quasi-static torque requirements for the actuators, kinematic isotropy, dynamic isotropy, stiffness isotropy, and natural frequencies of the device. These indices were defined based on focused kinematic, dynamic, and stiffness models. A novel procedure to evaluate local indices at a singularity-free point in the dexterous workspace is presented. The deterministic optimization approach neglects the effects from variations of design variables, e.g. due to tolerances. A Monte-Carlo simulation was carried out to obtain the response variation of the design indices when independent design parameters are simultaneously regarded as uncertain variables. It has been observed that numerical evaluation of performance indices depends of the type of workspace used during optimization. To verify the effectiveness of the proposed procedure, the performance indices were evaluated and compared in constant orientation and in dexterous workspace.

Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design

1993 ◽  
Vol 115 (3) ◽  
pp. 374-379
Author(s):  
P. Y. Papalambros
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Active Set ◽  
Design Problems ◽  
Local Optima ◽  
Active Set Strategy ◽  
Active Constraints ◽  
Trade Offs ◽  
Design Variables ◽  
Monotonicity Analysis

Early preliminary models for optimal design problems in nonlinear programming formulations often have solutions that are constraint-bound points, i.e., the number of active constraints equals the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs, and it is desirable to identify them early in order to revise the model or to exclude the points from an active set strategy. Application of monotonicity analysis can quickly identify constraint-bound candidate solutions but not always prove their optimality. This article discusses some conditions under which these points are in fact global or local optima.

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