The design point $\mathbf{u}^*$ obtained in FORM can be directly exploited for sensitivity analysis – without any additional model calls. Specifically, the directional cosines of $\mathbf{u}^*$, which are referred to as FORM $\alpha$-factors $[\alpha_1,\ldots,\alpha_M]$, are used as sensitivity metric. The FORM $\alpha$-factors are very easy to evaluate, as they only require a normalization of the vector of the design point $\mathbf{u}^*$:
$$
\alpha_i = \frac{u_i}{\|\mathbf{u}^*\|} = \frac{u_i}{\beta_\mathrm{FORM}}\,.
$$
Interpretation
Linear limit-state function ins $\mathbf{U}$-space
The squares of the $\alpha$-factors ($\alpha_1^2,\ldots,\alpha_M^2$) indicate the relative contribution ($\sum_{i=1}^M \alpha_i^2 = 1$) of the corresponding elements of $\mathbf{U}$ to the total variance of the linearized limit-state function (where $\mathbf{U}$ is the vector $\mathbf{X}$ of uncertain model parameters transformed to standard Normal space).
Thus, if the limit-state function is actually linear (in standard Normal space), then the squared FORM $\alpha$-factors provide a global sensitivity measure: What is the relative contribution of $U_i$ to the total variance? If the elements of $\mathbf{X}$ are statistically independent, the $\alpha$-factors can be directly used as sensitivity metric for $\mathbf{X}$. Thus, for the linearized limit-state function, the $\alpha$-factors can be interpreted as variance-based sensitivity measures [Papaioannou and Straub, 2021]. The $\alpha$-factors equal the first-order Sobol' indices AND the total-effect indices of the limit-state function. For sensitivity with respect to the probability of failure, the ranking obtained with the $\alpha$-factors corresponds to the ranking of the first-order Sobol' indices and to the ranking of the total-effect indices [Papaioannou and Straub, 2021].
Non-linear limit-state functions
For the general case (i.e., considering also non-linear limit-state functions), the $\alpha_i$ provides a local sensitivity measure: It quantifies the sensitivity of the limit-state function at $\mathbf{u}^*$ for changes in the normalized variable $U_i$. The $\alpha_i$ have an important practical interpretation: If the absolute value of $\alpha_i$, $|\alpha_i|$ is small, the uncertainty about $X_i$ has a small impact on the reliability. Conversely, if $|\alpha_i|$ is large, the uncertainty about $X_i$ has a strong influence on the reliability.
[Papaioannou and Straub, 2021] show that if FORM provides a reasonable approximation to the actual probability of failure, then the relation between FORM and the Sobol indices (which strictly only holds for linear limit-state functions in $\mathbf{U}$-space) can be used to approximate the Sobol indices of the non-linear problem.
Statistically dependent input variables
The discussion above is only valid for statistically independent uncertain model parameters $\mathbf{X}$ (of dimension $M$). In case the variables in $\mathbf{X}$ are statistically dependent, a one-to-one mapping between $X_i$ (in original space) and $U_i$ (in standard Normal space) does no longer exist, for all $i\in\{1,\ldots,M\}$. In this case, the coefficient $\alpha_i$ can no longer be used as a sensitivity measure for $X_i$. For a discussion of the case with statistically dependent components of $\mathbf{X}$, the reader is referred to [Papaioannou, 2012, Section 4.3.3].
References
[Papaioannou, 2012] Papaioannou, Iason. Non-intrusive Finite Element Reliability Analysis Methods. Dissertation, Technische Universität München, 2012.
[Papaioannou and Straub, 2021] Papaioannou, Iason; Staub, Daniel. Variance-based reliability sensitivity analysis and the FORM $\alpha$-factors. Reliability Engineering & System Safety. Volume 210, 2021.
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