Dimensionality reduction and visualization of structural reliability problems using polar features

A method for reducing the dimensionality of a structural reliability problem of many dimensions to only two independent dimensions is presented. Such a drastic reduction is achieved by means of a polar representation of a set of unclassified random numbers in the standard normal space. The most important feature of the proposed approach is that, due to the probabilistic properties of the nonlinear transformation applied, the safe and failure classes of samples are clearly distinguishable and occupy a standard position in a plot. On this basis it is possible to solve the reliability problem by means of a simple visually-aided selection of the relevant samples and discarding the rest. Also, the method permits to identify the samples in the safe domain that are on the verge of the failure domain, which constitute the so-called critical realizations or worst-case scenarios. Several benchmark examples demonstrate the simplicity and versatility of the proposed approach. Finally, some classical reliability methods are critically examined from the point of view of the proposed reliability plot.

► Reliability problems are nonlinearly transformed to two independent variables.
► The probability functions of the variables are derived.
► A bidimensional plot discriminating safe and unsafe samples is produced.
► The failure samples naturally accommodate in a standard sector.
► The method supersedes all methods based on the design point.