# Generic Tool for Design of Experiments (GT DoE)

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 approximation model trained on different experimental designs: random and special design generated with GT DoE.

In the case of random design, we take measurements at random points to build the approximation model. One can see that this experimental design may be unsuitable for model building. Experimental design Approximation 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 approximation model has high accuracy and reliably approximates the original function. Experimental design Approximation model

## 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: 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 DoE for RSM RSM model

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

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