PSI - Issue 19

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

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The stochastic simulation discussed here is based on the Monte Carlo method using Latin Hypercube Sampling. This approach is discussed in the following sections.

2.1. An introduction to the Monte Carlo method

The Monte Carlo simulation method is described in [RUB 16]. The basic approach calculates a large number of random values pertaining to each parameter in the analysis. The random values follow the specified probability distributions and are usually assumed to be independent of one another. The calculation of the random values is illustrated in Fig. 3.

Fig. 3. Overview of the Monte Carlo random number calculation method A pseudo-random number in the range (0,1) is calculated by the computer. This is based on a Uniform distribution where any value may be drawn from the range with equal probability. The Uniform distribution is then ‘Shaped’ using the Cumulative Density Function (CDF) ‘ ’ of the required distribution as illustrated in Fig. 3. The resulting output consists of a set of random values with the required statistical distribution. The following probability distributions are most commonly used: Gaussian-normal distribution

Log-normal distribution Exponential distribution Weibull distribution Uniform distribution Log-uniform distribution