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.