Approximations

You use approximations to visualize the behavior of your data (data trends) and to predict new values of your output parameters based on a specified combination of values of your input parameters, where that combination does not already exist in your data set.

See Also
A Graphical View of Your Approximations
A Quality View of Your Approximations
Exporting an Approximation
Adding the Alternative Created by an Approximation
Measure of Fit
The Response Surface Approximation Model
The Radial Base Function Model
The Universal Kriging Model

For each output parameter, Results Analytics uses the selected approximation technique to predict the value of the output variable.

Response Surface Model (RSM)
The response surface model (default) uses a polynomial combination of vectors representing the input parameters. The order of the polynomial regression model depends on the number of data points in your data set. By default, Results Analytics uses a polynomial with up to tenth-order uni-variate terms and fifth-order cross terms for the model. However, if the number of data points is small, Results Analytics chooses the order of the terms based on the number of parameters and the number of alternatives.

The response surface model uses simple equations that quickly and easily fit the data; however, it is valid only for simple smooth functions (linear functions with limited noise) or in local regions. In addition, the length of time to fit an approximation is dependent on the number of points, and the response surface model can be slow if you have a large number of data points. To increase performance, you can limit the maximum number of data points that will be used by the approximation, and you can reduce the polynomial order of the terms.

Radial Basis Function (RBF)
The radial basis function model is a type of neural network employing a hidden layer of radial units and an output layer of linear units. The radial basis function model has a short initialization time and is generally faster than the response surface model for a large number of data points. In addition, the radial basis function model is preferable when you know all of the inputs to be independent and when all of the inputs are of equal importance. The radial basis function model is also preferable to the response surface model when your data are nonlinear and when the data fall into specified categories, such as strings defining the model or the manufacturing type.
Universal Kriging

The Universal Kriging model is an interpolation method that converts partial observations of a spatial field to predictions of that field at unobserved locations. The model is useful in predicting temporally and spatially correlated data and typically creates a good approximation in cases with a small number of data points.

The Kriging model is very flexible and allows you to choose between a wide range of correlation functions for building the model. Depending on your choice of the correlation function, the model can either honor the data (providing an exact interpolation of the data) or smooth the data (providing an inexact interpolation).

Depending on the number of input parameters, the number of design points, and the number of responses (outputs) of the Kriging model, the process of building the model can be very time consuming. As the size of the matrices increases, the amount of CPU power required for manipulating the matrices grows exponentially. Therefore, generating a good Kriging model that uses many design points can take a substantial amount of time even after all the data points are analyzed.

If the value of an input parameter is missing for some data points, Results Analytics does not use the input parameter in the calculation of the approximation. However, if you exclude the data points with missing values, Results Analytics restores the input parameter and recalculates the approximation.

When you enter the Predict page for the first time, click Create New Approximations to calculate predicted values of the output parameters using the default settings. Results Analytics provides two views of the data predicted by the approximation technique:

Profiler
The Profiler view displays the calculated approximation curves of each dependent variable (output parameter) versus each independent variable (input parameter). Results Analytics also provides a summary view of the quality of the regression analysis.
Measure
The Measure view displays a detailed, quantitative view of the quality of the regression analysis.
Optimize
The Optimize view allows optimization of the approximation model, and displays history plots of the optimization run.

You can adjust the approximation options and the value of the input parameters and view the predicted value of the output parameters along with a measure of the relative quality of the fit. When you are satisfied with the quality of the approximation, you can add the input and output parameters as a new data point in your data set. In addition, you can export the approximation in a variety of forms that can be used by other applications. For example, you can export an approximation into a Process Composer workflow as a substitute, or surrogate, for a time-consuming simulation. Similarly, you can export an approximation into an FMU (Functional Mock-up Unit) that can be imported into the Dymola Behavior Modeling app.

Approximations are stored along with the data set in an analysis case.