Generic Tool for Design of Experiments (GT DoE)

Design of Experiments (DoE) is an important starting point for most data analysis and optimization tasks

Design of Experiments (DoE)  is a method of choosing the values of parameters varied in a series of experiments or measurements.

Suppose that we have a model described by a few independent parameters. For each assignment of values to these parameters, we can determine through an experiment the properties of the resulting instance of the model. The question is: which assignments to choose if we want to perform multiple experiments and to maximize the obtained knowledge of the overall model, simultaneously saving time and costs of computations? This is the task solved by GT DoE.

There are different mathematical methods implemented in GT DoE; they provide optimal DoE's for different tasks in a wide range of applications.

To illustrate the usage of GT DoE, consider some noisy function shown on the picture and try to approximate it with a quadratic surrogate model trained on different experimental designs: random and special design generated with GT DoE. GT DoE
  Experimental design Surrogate model
In the case of random design, we take measurements at random points to build the surrogate model. One can see that this experimental design may be unsuitable for model building. GT DoE  GT DoE
  Experimental design Surrogate model
In this case, the experimental design is generated with DoE for RSM, a special technique of GT DoE. As one can see, the corresponding surrogate model has high accuracy and reliably approximates the original function. GT DoE GT DoE

 

 

This Generic Tool provides state-of-the-art algorithms for generating various types of DoE

Space-filling DoE techniques

 The techniques provide the most uniform filling of the design space for a special number of samples or generates sequences reasonably uniformly distributed when terminated at any point.

Support the generation of

  • Random, Full-factorial, Fractional Factorial, Latin Hypercubes, Optimal Latin Hypercubes designs for a specified number of points;
  • Halton, Sobol, Faure sequences.

Uniformity in the design space is one of the most important properties of Space-filling DoE. For example, to compare uniformity properties of different designs, look at a random design and “more uniform” Sobol sequence:

Space-filling DoE techniques  Space-filling DoE techniques 
 Random design  Sobol sequence

 

 Optimal Designs for Response Surface Model (DoE for RSM)

The technique provides optimal designs for the GT Approx Response Surface Model (RSM). These designs minimize either

  • the variance of the model parameter estimates, or
  • the variance of the model prediction.

An example of optimal DoE for RSM in two-dimensional design space for the case of seven design points and RSM model:

 

  Optimal Designs for Response Surface Model 
  Optimal DoE for RSM  RSM model

 

Adaptive DoE techniques

Adaptive DoE is a method which iteratively adds points, minimizing an uncertainty of the GT Approx Gaussian Processes (GP) model, to the training set. This method allows to control process of surrogate modeling via adaptive sampling plan which benefits most to the quality of the approximation.

Adaptive DoE techniques:

(1) start with generating initial design by one of space-filling techniques  for the original function;  Adaptive DoE techniques (2) construct approximation based on this initial sample;  Adaptive DoE techniques (3) enrich sample iteratively adding points in order to provide best possible improvement of approximation quality.  Adaptive DoE techniques