# Genetic Aggregation is default response surface

The Genetic Aggregation response surface automates the process of selecting, configuring, and generating the type of response surface best suited to each output parameter in your problem. From the different types of response surface available (Full 2nd order Polynomial, Non-Parametric Regression, Kriging, and Moving Least Squares), GARS automatically builds the response surface type that is the most appropriate approach for each output, (Figure 1).

Figure 1. GARS with auto- refinement gives the best fit possible for each output

Automatic refinement is available when you select at least one output parameter for refinement in the “Tolerances” table and specify a tolerance value for it. Once begun, the auto-refinement process handles design point failures and continues until one of the stopping criteria has been met (Figure 2).

Figure 2. GARS Automatic Refinement

Automatic Refinement adds design points until response surface accuracy meets user requirements (Figure 3).

Figure 3. Genetic Aggregation Refinement Options

Genetic Aggregation takes more time than classical response surfaces such as Full 2nd order Polynomial, Non-Parametric Regression, or Kriging because of multiple solves of response surfaces and the cross-validation process. In general GARS is more reliable than the classical response surface meta-models.

The GA response surface's selection of the best response surface is based on a genetic algorithm generating populations of different response surfaces solved in parallel.

The fitness function of each response surface is used to determine which one will yield the best approach; it takes into account both the accuracy of the response surface on the design points and the stability of the response surface (cross-validation), (Figure 4).

The GA response surface can be a single response surface or a combination of several different response surfaces (obtained by a crossover operation during the genetic algorithm).

Figure 4. GARS Goodness of fit

The Genetic Aggregation Convergence Curves chart enables you to monitor the automatic refinement process of the Genetic Aggregation response surface for one or more selected output parameters. It is available only when the Response Surface Type is set to Genetic Aggregation and at least one output parameter is selected for auto-refinement, (Figure 5).

The chart is automatically generated and dynamically updated as the Genetic Aggregation refinement runs. To view the Genetic Aggregation Convergence Curves chart, select one of the following nodes in the Outline view:

· Refinement

· Tolerances

· Refinement Points

The X-axis displays the number of refinement points, while the Y-axis displays the ratio between the Maximum Predicted Error and the Tolerance for each output parameter.

Each output parameter marked for auto-refinement is represented by a separate curve corresponding to this ratio, which is calculated for each output parameter to refine and at each iteration. Anything below the Convergence Threshold curve is in the convergence region, indicated by a shaded blue area on the chart.

For example: Before the first refinement point is run, if output P3 has a Tolerance of 0.2[g] and a Maximum Predicted Error of 0.3[g], then it has a ratio of 0.3/0.2=1.5. If the ratio is equal to 1.5, then we know that the Maximum Predicted Error is 1.5 times larger than the Tolerance.

The auto-refinement process can generate one point or several points per iteration. The objective is to reach a Convergence Threshold of less than or equal to 1 for all outputs used in the auto-refinement process, at which point all the convergence curves are in the area below the Convergence Threshold. The refinement process stops when either the Maximum Number of Refinement Points has been reached or when the Convergence Threshold objective has been met.

Figure 5. Refinement Convergence Chart

ANSYS DesignXplorer does include a variety of other response surface methods, and more can be added to our open platform via ACT. Each of these methods is advanced and it would take an expert user to understand them all fully. Fortunately, one does not need that level of understanding to use DX effectively.

Generally speaking, 2nd order polynomial RS algorithm can be used for simple cases (often mechanical analysis are simple enough), but always check goodness of fit. Kriging is a bit more advanced because it is flexible and self-adjusting with an automatic refinement feature, and it shouldn't be used for noisy data. Kriging would require to run verification points to get more realistic goodness of the fit. Non-parametric regression does a much better job of filtering out noisy data, but takes more design points to work well. Neural network is good for highly non-linear data, but is less accurate for most other situations. All of these (and other hidden methods and settings) are effectively replaced by the new Genetic Aggregation Response Surface Method (GARS) for most users.

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