The FORM node performs First Order Reliability Method (FORM) to compute the design point, beta index and from that, the probability of failure.
FORM approximates the limit state function by a linear function in standard-normal space using a first order Taylor expansion. For this approximation, the probability of failure can be computed analytically. The expansion point is the design point, for example the point on the limit state surface being closest to the origin in standard normal space. The distance of the design point to the origin of standard-normal space is called reliability index beta.
The closest point projection can be expressed as an optimization problem. FORM embeds a user-specified optimization algorithm into FORM. Currently only NLPQL is selectable. More optimization algorithms will be available in future versions. The optimization procedure tries to find the design point. From that, the probability of failure is computed. Note that the optimizer completely operates in standard-normal space. Requested designs are transformed to the design space by the FORM algorithm.
FORM is designed to find the probability of failure within a few steps. The number of steps is generally independent of the magnitude of the failure probability. FORM may be applied if the error due to the linearisation is negligible in the vicinity of the design point. The applicability of FORM is restricted by the capabilities of the selected optimization method, for example smoothness, convexity, differentiability, continuity in case of multiple safety margin functions, unique failure domains,and so on.
FORM can be used for multiple search runs examining multiple potential failure regions. If you specify start designs, each start design is used as starting point for a local optimization run. Additionally an initial Monte Carlo presampling can be specified, where the most suitable points are selected for local search runs. The maximum number of search runs is limited to the given setting. The presamples are scaled by the given factor in the standard normal space before they are considered in the selection. All found local failure points are listed in the postprocessing. Finally, the most dominant failure region is considered in the calculation of the reliability index and the failure probability.
In case of discrete distribution types, the values of the discrete parameters are kept constant during each local optimization run according to the start design values. If no start designs and no pre-samples are specified, all possible combinations of discrete states are analyzed in the local optimization runs.
Further information about methods of reliability analysis used in optiSLang can be found here.
Initialization Options
To access the options shown in the following table, double-click the FORM system on the Scenery pane and switch to the FORM tab.
| Option | Description | ||
|---|---|---|---|
| Used optimization algorithm | Selects the optimization method being used to find the design point. | ||
| Accuracy | |||
| Desired accuracy | Tolerance by which the Karush-Kuhn-Tucker optimality conditions are considered to be satisfied. For example, if the given tolerance is smaller than the accuracy of function values and gradients then NLPQL may not or may slowly converge. Check if the given tolerance is sufficiently small compared with the initial gradients. | ||
| Differentiation scheme | Method for computing numerical gradients. The higher the order of accuracy, the more accurate is the approximation of the numerical derivatives. On the other hand, the higher order derivatives may lead to a less robust iteration due to large noise and/or discontinuities. | ||
| Differentiation step size | Size of the differential interval is given by a relative value that denotes the interval length related to the bounds in percent. With decreasing differentiation step size, you generally obtain a more accurate approximation of the gradient. | ||
| Computational aspects | |||
| Maximum number of solver runs | Maximum allowed number of solver runs. Once the number of solver runs reaches this number, the iteration will be terminated. | ||
| Number of parallel line searches | Number L of parallel solver runs in line search. Set L=1 if a classical iterative line search is requested. L>1 means parallel line search. | ||
| Global search | |||
| Number of initial samples | Sets the number of presamples generated randomly in addition to the start designs. | ||
| Initial sampling scaling factor | Sets the scaling factor which scales the standard deviation of the initial presampling density in standard normal space. | ||
| Maximum number of optimization runs | Sets the maximum number of local optimization runs using the start designs and the presampling as starting points. For each run a single starting point is considered in the local optimizer. | ||
Additional Options
To access the options shown in the following table, in any tab, click .
| Option | Description |
|---|---|
| Limit maximum in parallel |
Controls the resource usage of nodes in the system. When the check box is cleared (default), a value is chosen to ensure the best possible utilization of the child nodes. When the check box is selected, set the value manually to specify how many designs are sent to child nodes, limiting the maximum degree of parallelism for all children. Ansys recommends keeping the check box clear. |
| Auto-save behavior |
Select one of the following options:
The project, including the database, is auto-saved (depending on defined interval) after calculating this node/system (either when the calculation succeeds or fails). By default, all parametric and algorithm systems have selected, all other nodes have selected. |