Optimization of Design Tolerances Through Response Surface Approximations

2002 ◽  
Vol 124 (3) ◽  
pp. 762-767 ◽  
Author(s):  
J. P. Jordaan ◽  
C. P. Ungerer
Keyword(s):  
Monte Carlo ◽  
Response Surface ◽  
Design Space ◽  
Analytical Relationship ◽  
Manufacturing Cost ◽  
Functional Requirements ◽  
Mechanical Assembly ◽  
Response Surface Approximations ◽  
Yield Values ◽  
Optimal Set

A methodology whereby the optimal set of design tolerances is assigned to the dimensions of a general mechanical assembly, is developed and tested. The manufacturing cost is minimized, while the design is constrained to a specified probability of meeting functional requirements, called the yield of the design. An analytical relationship for the assembly yield surface is generally unknown, and use is made of response surface approximations in the optimization algorithm. Yield values are determined at design space points through Monte Carlo simulations, seen as the response surface experiments. The methodology is benchmarked on example problems from the literature, and the optimum compares superior to published results.

Efficient Gradient-Based Tolerance Optimization Using Monte Carlo Simulation

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
R. Alan Bowman
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Manufacturing Cost ◽  
Optimization Approach ◽  
Functional Requirements ◽  
Mechanical Assembly ◽  
New Approach ◽  
Tolerance Optimization ◽  
Gradient Based ◽  
Derivatives Of

A gradient-based optimization approach is employed to select design tolerances for the component dimensions of a mechanical assembly to minimize manufacturing cost while achieving a desired probability of meeting functional requirements, known as the yield. Key to the feasibility of such an approach is to be able to use Monte Carlo simulation to make estimates of the derivatives of the yield with respect to the design tolerances quickly and accurately. A new approach for making these estimates is presented and is shown to be far faster and more accurate than previous approaches. Gradient-based optimization using the new approach for estimating the derivatives is applied to example problems from the literature. The solutions are superior to all previously published solutions and are obtained with very reasonable computer run times. Additional advantages of a gradient-based approach are described.

Crashworthiness Design Using Topology Optimization

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Neal M. Patel ◽  
Byung-Soo Kang ◽  
John E. Renaud ◽  
Andrés Tovar
Keyword(s):  
Topology Optimization ◽  
Design Space ◽  
Three Dimensional ◽  
Manufacturing Cost ◽  
Optimization Approach ◽  
Maximum Displacement ◽  
Efficient Manner ◽  
Response Surface Approximations ◽  
Cost Constraints ◽  
Crashworthiness Design

Crashworthiness design is an evolving discipline that combines vehicle crash simulation and design synthesis. The goal is to increase passenger safety subject to manufacturing cost constraints. The crashworthiness design process requires modeling of the complex interactions involved in a crash event. Current approaches utilize a parametrized optimization approach that requires response surface approximations of the design space. This is due to the expensive nature of numerical crash simulations and the high nonlinearity and noisiness in the design space. These methodologies usually require a significant effort to determine an initial design concept. In this paper, a heuristic approach to continuum-based topology optimization is developed for crashworthiness design. The methodology utilizes the cellular automata paradigm to generate three-dimensional design concepts. Furthermore, a constraint on maximum displacement is implemented to maintain a desired performance of the structures synthesized. Example design problems are used to demonstrate that the proposed methodology converges to a final topology in an efficient manner.

Decoupling the Design Sampling Region From the Trust Region in Approximate Optimization

2000 ◽  
Author(s):  
Victor M. Pérez ◽  
John E. Renaud
Keyword(s):  
Convergence Rate ◽  
Response Surface ◽  
Design Space ◽  
Trust Region ◽  
Good Representation ◽  
Approximate Representation ◽  
Design Problems ◽  
Computational Costs ◽  
Approximate Optimization ◽  
Response Surface Approximations

Abstract Response Surface Approximations (RSA’s) are widely used in the design community to provide designers with an approximate representation of a system. The use of RSA’s allow designers to query the system while avoiding the high computational costs associated with today’s advanced simulation codes. Sequential Approximate Optimization (SAO) methodologies have proved to be effective in managing the optimization of multi-disciplinary design problems. In SAO the sampling required to build the RSA’s often takes place within the same bounds as imposed on the current optimization iterate. This assures a good representation of the system in the region where it will be optimized. However it may restrict the approximation from extrapolating beyond the design space, and therefore improve the convergence rate of the algorithm. In this research a decoupling of the sampling region from the trust region is proposed.

Multidisciplinary Analysis and Optimization of Discrete Problems Using Response Surface Methods

1997 ◽  
Vol 119 (4) ◽  
pp. 427-433 ◽  
Author(s):  
J. C. Korngold ◽  
G. A. Gabriele
Keyword(s):  
Response Surface ◽  
Product Life Cycle ◽  
Design Space ◽  
Local Response ◽  
Global Approximation ◽  
Response Surface Approximations ◽  
Sensitivity Equations ◽  
Multidisciplinary Analysis ◽  
Design And Manufacturing ◽  
Discrete Problems

The objective of this paper is to present a new algorithm to efficiently optimize multidisciplinary, coupled nonhierarchic systems with discrete variables. The algorithm decomposes the system into contributing disciplines, and uses designed experiments within the disciplines to build local response surface approximations to the discipline analysis. First and second order Global Sensitivity Equations are formulated and approximated by experimental data to build approximations to the global design space. The global approximation is optimized using branch and bound or simulated annealing. Convergence is rapid for systems with near quadratic behavior. The algorithm is demonstrated on a unique multidisciplinary learning tool, the Design and Manufacturing Learning Environment. This environment provides multimedia simulation for product life cycle disciplines, including design, manufacturing, marketing, and sales.

Crashworthiness Design Using a Hybrid Cellular Automaton Algorithm

2006 ◽  
Author(s):  
Neal M. Patel ◽  
Byung-Soo Kang ◽  
John E. Renaud
Keyword(s):  
Design Space ◽  
Manufacturing Cost ◽  
Optimization Approach ◽  
Concept Design ◽  
Design Synthesis ◽  
Response Surface Approximations ◽  
Complex Interactions ◽  
Cost Constraints ◽  
Passenger Safety ◽  
Crashworthiness Design

Crashworthiness design is an evolving discipline that combines vehicle crash simulation and design synthesis. The goal is to increase passenger safety subject to manufacturing cost constraints. The crashworthiness design process requires the modeling of the complex interactions involved in a crash event. Current approaches utilize a parameterized optimization approach that requires response surface approximations of the design space. This is due to the expensive nature of numerical crash simulations and the high nonlinearity and noisiness in the design space. These methodologies usually require a significant design effort to determine an initial design. In this research, a non-gradient approach to topology optimization is developed for crashworthiness design. The methodology utilizes the cellular automata paradigm to generate a concept design.

High-Speed Civil Transport Design Space Exploration Using Aerodynamic Response Surface Approximations

2002 ◽  
Vol 39 (2) ◽  
pp. 215-220 ◽  
Author(s):  
Chuck A. Baker ◽  
Bernard Grossman ◽  
Raphael T. Haftka ◽  
William H. Mason ◽  
Layne T. Watson
Keyword(s):  
Response Surface ◽  
High Speed ◽  
Design Space Exploration ◽  
Design Space ◽  
Space Exploration ◽  
Response Surface Approximations

Using Response Surface Approximations to Cover Holes in the Design Space: Conceptual Design of a Missile

2002 ◽  
Vol 2 (3) ◽  
pp. 224-231 ◽  
Author(s):  
M. Alexandra Scho¨nning ◽  
Jamal F. Nayfeh ◽  
P. Richard Zarda
Keyword(s):  
Response Surface ◽  
Conceptual Design ◽  
Design Of Experiment ◽  
Design Problem ◽  
Design Space ◽  
Multidisciplinary Optimization ◽  
Design Problems ◽  
Response Surface Approximations ◽  
Type Design ◽  
Practical Engineering

The objective of this paper is to demonstrate an innovative and practical technique in which multidisciplinary optimization can be carried out while there exist points in the design space for which a response cannot be evaluated. It will also be demonstrated how design of experiment and response surface approximations are used to eliminate other complications associated with optimization of large-scaled designs. A multidisciplinary highly coupled air-to-air sparrow like missile design problem will be introduced to demonstrate the practical side of design optimization. The intention here is to provide practical engineering recommendations to others attempting to optimize industrial type design problems.

Multidisciplinary Analysis and Optimization of Discrete Problems Using Response Surface Methods

1995 ◽  
Author(s):  
Jacob C. Korngold ◽  
Gary A. Gabriele
Keyword(s):  
Response Surface ◽  
Product Life Cycle ◽  
Design Space ◽  
Local Response ◽  
Global Approximation ◽  
Response Surface Approximations ◽  
Sensitivity Equations ◽  
Multidisciplinary Analysis ◽  
Design And Manufacturing ◽  
Discrete Problems

Abstract The objective of this paper is to present a new algorithm to efficiently optimize multidisciplinary, coupled non-hierarchic systems with discrete variables. The algorithm decomposes the system into contributing disciplines, and uses designed experiments within the disciplines to build local response surface approximations to the discipline analysis. First and second order Global Sensitivity Equations are formulated and approximated by experimental data to build approximations to the global design space. The global approximation is optimized using branch and bound or simulated annealing. Convergence is rapid for systems with near quadratic behavior. The algorithm is demonstrated on a unique multidisciplinary learning tool, the Design and Manufacturing Learning Environment. This environment provides multimedia simulation for product life cycle disciplines, including design, manufacturing, marketing, and sales.

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