# Sobol Sequence

Sobol Sequence is a widely known low-discrepancy sequence of quasi-random sampling family. It is designed to equally spread-out points in a space by minimizing clumps and empty spaces.

This is a space filling DOE scheme which has the property of extensibility, which means the method can take an existing set of data in a space and add more data points to provide equal coverage. The number of runs is specified by the user.

## Usability Characteristics

• Use for exploring the entire design space and creating fitting functions to the exact output responses.
• To get a good quality fitting function, a minimum number of runs should be evaluated. (N+1) (N+2)/2 runs are needed to fit a second order polynomial, assuming that most output responses are close to a second order polynomial within the commonly used input variable ranges of ±10%. An additional number of runs equal to 10% is recommended to provide redundancy, which results in more reliable post-processing. As a result, this equation is recommended to calculate the number of runs needed or a minimum of 1.1*(N+1) (N+2)/2 runs.
• Add existing data to the inclusion matrix to use the extensibility feature. While any data can be used as an inclusion, the best performance can be expected when the inclusion is an existing data set from a Sobol Sequence DOE.
• Supports input variable constraints.

## Settings

In the Specifications step, Settings tab, change method settings.

Table 1.
Parameter Default Range Description
Number of Runs $\frac{1.1\left(N+1\right)\left(N+2\right)}{2}$ > 0 integer Number of new designs to be evaluated.
Sequence Offset 1

Integer

0 to ∞

Controls the starting offset for the Sobol Sequence. For example, a value of 101 starts the generated evaluation points from the 101st point of the Sobol Sequence.

Note: In the presence of input variable constraints, the algorithm may skip runs, resulting in internal sequence of Sobol Sequence to be different than the Sequence Offset defined by the user. Take note of duplicate runs prior to evaluation. If possible, the inclusion matrix method is recommended.
Scramble Off Off or On Scrambling is a randomization process to get more uniform distribution. It is useful especially when a small number of points is needed.
Seed 0

Integer

0 to ∞

Used for repeatability in random number generator and effective only if Scramble option is active.