Latin HyperCube

When sampling a design space of N variables, the range of each variable is divided into M equally probable intervals. M sample points are then placed to satisfy the Latin HyperCube requirements. As a result, all experiments have unique levels for each input variable and the number of sample points, M, is not a function of the number of input variables.

Figure 1.

Figure 2 shows a Latin HyperCube (left) and Hammersley (right) for 100 runs.

Figure 2.

• 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 recommend to calculate the number of runs needed or a minimum of 1.1*(N+1)(N+2)/2 runs.
• The structure of a Latin HyperCube run matrix ensures that the runs are orthogonal. Orthogonality is desirable because it is less likely to result in singularities when creating Least Squares Regression fits.
• Any data in the inclusion matrix is combined with the run data for post-processing. Any run matrix point which is already part of the inclusion data will not be rerun.

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