PSI - Issue 19

A. Halfpenny et al. / Procedia Structural Integrity 19 (2019) 150–167 Author name / Structural Integrity Procedia 00 (2019) 000–000

154

5

Triangular distribution Beta distribution Discrete distribution 2.2. An introduction to ‘Latin Hypercube Sampling Latin Hypercube Sampling is described in [MCK 84] and [IMA 84]. It differs from the basic Monte Carlo technique in two ways: the random sampling method is modified in order to ensure that tests are more evenly distributed over the random interval the multi-variate sampling is based on a Latin Square A disadvantage of the basic Monte Carlo technique is it requires a large number of samples in order to ensure complete coverage of the random interval (especially at the edges of the distributions). Latin Hypercube Sampling improves on this by dividing the random interval into a number of ‘divisions’. A single sample is chosen at random from within each division. This ensures that points are specifically drawn from all parts of the distribution whilst still maintaining the required population distribution. The approach is illustrated in Fig. 4.

Fig. 4. Overview of Latin Hypercube Sampling random number calculation

Multi-variate sampling is based on a Latin Square. The definition of a Latin square is given by [WIK 18] as follows: “In combinatorics and in experimental design, a Latin Square is an n×n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. The name ‘Latin Square’ was inspired by mathematical papers by Leonhard Euler, who used Latin characters as symbols, but any set of symbols can be used.”