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Two Approaches to Design Optimization During Finite Element Analysis

Response Surface Optimization
June 13, 2014 By: Patrick Cunningham

Design optimization as part of a finite element analysis consists of input variables, constraints, and an objective. The aim of a design optimization is to determine values for the input variables that will meet the design objective, while staying within the constraints.

Input variables define the possible configurations of the design and may consist of any physical dimensions, loading and material coefficients that can vary in the design and manufacture of the part. The optimal design will consist of the best possible combination of design variables that meet the design goals.

Constraints are limits that the optimization algorithm must stay within when sampling the design points. Constraints apply to the output quantities like deformation and stress in a structural optimization and are used to guarantee that design requirements for strength and life are met by the optimum design.

The Objective in a structural optimization is typically to minimize weight since it often influences both cost and performance. When the analysis is run, an optimization algorithm samples design points within the range of the input variables, searching for the combination of minimal weight and acceptable strength.

There are many optimization methods to choose from - but they all share one thing; the need for analysis results that can be used to navigate through the possible design configurations to the optimum choice. Two approaches that can be used to generate the analysis results are as follows:

1) Direct Optimization uses actual analysis results that are solved sequentially during the optimization.  The optimization algorithm determines what the next design point should look like from the history of previous results.  The iterations continue until the design goal is met or a specified limit on the number of sample iterations is reached.   It is important to note here that the sample designs are chosen based on the current optimization goal.   If the optimization goal is changed, the sample data must be regenerated.

2) Response Surface Optimization requires that the design point results are generated before the optimization. The design point configurations are typically determined using Design of Experiments methods with the intent of characterizing the system response using a minimum number of actual analysis runs.  Response surface functions are fit to the analysis data and serve as a surrogate model of the design.  The optimization algorithm samples the surrogate model in search of the optimum design.

There are several advantages to the Response Surface approach:

  • The optimization run is significantly faster than the direct approach because it is sampling the surrogate model in place of solving each point deterministically.  
  • In a response surface optimization, the number of design points required is predetermined by the DOE method.
  • Knowing the design point definitions beforehand allows the response surface approach to take advantage of parallel computing.  With sufficient hardware and software resources the response surface design points can be solved simultaneously.  In the best case, the complete DOE can be computed in the same amount of time as a single design point.
  • The response surfaces can be used for multiple optimizations as they are not linked to a particular optimization goal.  

Clearly, the accuracy of the response surface result is a function of the data fitting of the response surfaces to the DOE design points.  In addition to using goodness of fit metrics during the response surface generation, it is always advisable to generate an actual result of the optimum design to complete the optimization.  Comparing the actual (solved) result to the surrogate model result will give confidence in the predictive quality of your response surfaces in the event that they will be reused for other goals.

I welcome feedback from those who have used optimization techniques as part of their engineering analysis process to help design better products!