## Reliability Assessment

The SVM-based EDSD approach was further specialized to the case of reliability assessment through the so-called "generalized max-min" sample (Lacaze and Missoum, 2013). The basic idea stems from the recognition that surrogates need to be be more accurate in high probability density regions. For this purpose, the generalized max-min includes information on the probability density functions where as the traditional max-min sample of EDSD only include information on the spatial distribution of samples. The advantage of the generalized max-min over traditional techniques becomes more pronounced as the number of dimensions increases. Consider this 10D limit state (in a standard normal space) defined as:

$\frac{\sum_{i=1}^{10}\log X_i}{2}+12\leq0$

A comparison of the convergence of the generalized max-min, (in series and parallel) and the traditional max-min are depicted on Figure 1.

Figure 1: Convergence of the 10D example

The next step naturally was to consider correlated variables. As the generalized max-min take into account the joint PDF $\mathbf{f}_{\mathbf{X}}$ , dealing with correlated variables is supposedly not any different as uncorrelated variables. In order to motivate this assertion, consider Movie 1 and Movie 2 where traditional max-min samples and generalized one are sequentially added along a given limit state for a correlated bi-dimensional standard normal distribution ( $\rho=0.7$ ).

 Movie 1: Sequential addition of Max-Min samples Movie 2: Sequential addition of Generalized Max-Min samples

## References:

A generalized “max-min” sample for surrogate update,Structural and Multidisciplinary Optimization, 2013, pp. 1-5.

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