Model Browser User's Guide

Creating a Space Filling Design

Space-filling designs should be used when there is little or no information about the underlying effects of factors on responses. For example, they are most useful when you are faced with a new type of engine, with little knowledge of the operating envelope. These designs do not assume a particular model form. The aim is to spread the points as evenly as possible around the operating space. These designs literally fill out the n-dimensional space with points that are in some way regularly spaced. These designs can be especially useful in conjunction with nonparametric models such as radial basis function (a type of neural network).

1. Add a new design by clicking the  button in the toolbar or select File -> New.
2. Select the node in the tree by clicking. An empty Design Table appears if you have not yet chosen a design. Otherwise, if this is a new child node the display remains the same, because child nodes inherit all the parent design's properties.
3. Select Design -> Space Filling -> Design Browser, or click the  Space Filling Design button on the toolbar.
4. A dialog appears if there are already points from the previous design. You must choose between replacing and adding to those points or keeping only fixed points from the design. The default is replacement of the current points with a new design. Click OK to proceed, or Cancel to change your mind.

The Space Filling Design Browser appears.

Note    As with the Classical Design Browser, you can select the three types of design you can preview in the Space Filling Design Browser from the Design -> Space Filling menu in situations when you already know the type of space-filling design you want.

Space Filling Design Styles

In the Design drop-down menu you can see the three design styles available:

• Latin Hypercube Sampling
• Lattice
• Stratified Latin Hypercube

Latin Hypercube Sampling

Latin Hypercube Sampling (LHS) are sets of design points that, for an N point design, project onto N different levels in each factor. Here the points are generated randomly. You choose a particular Latin Hypercube by trying several such sets of randomly generated points and choosing the one that best satisfies user-specified criteria.

Lattice

Lattice designs project onto N different levels per factor for N points. The points are not randomly generated but are produced by an algorithm that uses a prime number per factor. If good prime numbers are chosen, the lattice spreads points evenly throughout the design volume. A poor choice of prime numbers results in highly visible lines or planes in the design projections. If all the design points are clustered into one or two planes, it is likely that you cannot estimate all the effects in a more complex model. When design points are projected onto any axes, there are a large number of factor levels.

For a small number of trials (relative to the number of factors) LHS designs are preferred to Lattice designs. This is because of the way Lattice designs are generated. Lattice designs use prime numbers to generate each successive sampling for each factor in a different place. No two factors can have the same generator, because in such cases the lattice points all fall on the main diagonal of that particular pairwise projection, creating the visible lines or planes described above. When the number of points is small relative to the number of factors, the choice of generators is restricted and this can lead to Lattice designs with poor projection properties in some pairwise dimensions, in which the points lie on diagonals or double or triple diagonals. This means that Latin Hypercube designs are a better choice for these cases.

Stratified Latin Hypercube

Stratified Latin Hypercubes separate the normal hypercube into N different levels on user-specified factors. This can be useful for situations where the preferred number of levels for certain factors might be known; more detail might be required to model the behavior of some factors than others. They can also be useful when certain factors can only be run at given levels.

The preceding example shows the different properties of a poor lattice (left) and a good lattice (right), with a similar number of points.The poorly chosen prime number produces highly visible planes and does not cover the space well. An example of an LHS design of the same size is shown for comparison.

Creating a Classical Design

Setting Up a Space Filling Design