About Approximations

If an approximation is created in the Design Gateway and initialized before accessing the Runtime Gateway’s Visual Design tab (either in the Design Gateway or during execution), the approximation will be immediately available for viewing. Otherwise, the approximation must be initialized before Isight can display the visuals and internal data on the Visual Design tab.

Approximations work by building a simplified mathematical model for the selected component using multiple data points. The approximation data points can be obtained either by executing the approximated component multiple times or by reading a data file with previously analyzed points. The process of building the mathematical model using data points is called initialization. After an approximation is initialized, it can be evaluated and used at run time to replace the approximated component. Multiple approximations can be created, initialized, and viewed for any Isight component, but only one of them can be used at run time. To use an approximation at run time, you must activate it before submitting the model for execution.

When an approximation is created for a process component, the subflow of the component is approximated, such that when the process component executes the subflow, the active approximation is executed instead. If there are multiple components in the subflow (i.e., multiple simcodes, calculations, etc.), they are all replaced by one approximation.

You can create a user-defined approximation in which you can select the desired approximation algorithm (see Creating User-Defined Approximations). Alternatively, you can create an automatic approximation if you do not want to learn the details of the approximation techniques. By default, Isight uses a preconfigured RBF model when you create an automatic approximation (see Creating an Automatic Approximation). Finally, you can create an approximation based on a previously saved coefficient file (see Creating Approximations Using a Coefficient File).

Approximation Algorithms

The following four approximation algorithms (or techniques) are available in Isight:

RBF Model. A neural network-based approximation technique that includes radial and elliptical basis functions (see Creating a User-Defined Approximation Using the Radial Basis Functions (RBF) Technique).
Response Surface Model. A polynomial-based approximation technique (see Creating a User-Defined Approximation Using the Response Surface Model (RSM) Technique).
Kriging Model. An interpolation technique (see Creating a User-Defined Approximation Using the Kriging Model Technique).
Orthogonal Polynomial Model. A regression technique (see Creating a User-Defined Approximation Using the Orthogonal Polynomial Technique).

They are all available when creating a user-defined approximation. By default, Isight uses a preconfigured RBF model when you create an automatic approximation. For coefficient file approximations, Isight uses the algorithm found in the file.

Approximation Sampling Methods

You can configure the sampling method to be used when creating approximations.

The following approximation sampling methods are available in Isight:

Random Points. Isight generates the required number of points for the approximation.
Data File. Isight uses an existing file that contains data points.
DOE Matrix. Isight uses DOE to determine the set of points to evaluate.
Component History Data. Isight uses the history data of the selected component for the approximation. This method is available only if the model has already executed.

For more information, see Configuring the Sampling Methods.

If you select the DOE matrix sampling method, you can select from the following sampling techniques:

Sampling Technique	Description
Central Composite Design	A statistically based technique in which a 2-level full-factorial experiment is augmented with a center point and two additional points for each factor (called “star points”). Although Central Composite Design requires a significant number of design point evaluations, it is a popular technique for compiling data for response surface modeling because of the expanse of design space covered and the higher-order information obtained.
Data File	Provides a convenient way for you to define your own set of trials outside of Isight and still make use of Isight’s integration and automation capabilities. The design matrix can be defined by data imported from one or more files, allowing you to execute the DOE study (automatically evaluate all the design points) and analyze the results.
Fractional Factorial	A certain fractional subset (1/2, 1/4, 1/8, etc. for two-level factors and 1/3, 1/9, 1/27, etc. for three-level factors) of the full factorial experiment that is carefully selected to minimize aberrations in the experiment. Fractional factorial designs are available only when all factors have either two or three levels. Fractional factorial experiments are also useful when some factors are independent of each other or when certain interactions can be neglected.
Full-Factorial	Evaluates all combinations of all factors at all levels. Typically, the standard engineering practice is to systematically evaluate a grid of points requiring $n 1 \times n 2 \times n 3 \times \dots n i$ ( $i$ = # factors, $n_{i}$ = # levels for factor $i$ ) design point evaluations. This practice provides extensive information for accurate estimation of factor and interaction effects. However, it is often deemed cost-prohibitive because of the number of analyses required.
Latin Hypercube	A class of experimental designs that efficiently sample large design spaces. The design space for each factor is divided uniformly (the same number of divisions, $n$ , for all factors). These levels are randomly combined to specify $n$ points defining the design matrix (each level of a factor is studied only once).
Optimal Latin Hypercube	A modified Latin Hypercube where the combination of factor levels for each factor is optimized, rather than randomly combined. The design space for each factor is divided uniformly (the same number of divisions, $n$ , for all factors). These levels are randomly combined to generate a random Latin Hypercube as the initial DOE design matrix with $n$ points (each level of a factor studies only once). An optimization process is applied to this initial random Latin Hypercube design matrix. By swapping the order of two factor levels in a column of the matrix, a new matrix is generated and the new overall spacing of points is evaluated. The goal of this optimization process is to design a matrix in which the points are spread as evenly as possible within the design space defined by the lower and upper level of each factor.
Orthogonal Arrays	A specific type of fractional factorial experiment carefully selected to maintain orthogonality (independence) among the various factors and certain interactions. It is this orthogonality that allows for independent estimation of factor and interaction effects from the entire set of experimental results. Using orthogonal arrays for fractional factorial design reduces the analysis result resolution (i.e., factor effects are aliased with interaction effects as more factors are added to a given array); however, the significant reduction in the required number of experiments (cost) can often justify this loss in resolution as long as some of the interaction effects are assumed negligible. Isight’s automation of this procedure allows you to efficiently and effectively study the design space with little or no knowledge of orthogonal arrays.
Parameter Study	Can be used to refer to any study of design parameter; in Isight the term “Parameter Study” is used to refer to a true study of the sensitivity of the design to each factor independent of all other factors. Each factor is studied at all of its specified levels (values) while all other factors are held fixed at their baseline. Because interaction effects are varied independently, they are not accounted for when the effects of factors on responses are reported.

About Approximations

Approximation Algorithms

Approximation Sampling Methods

Approximation Component