Fragility module

Fragility module

After the definition of the relationship between structural response and ground shaking intensity (see Figure 6), fragility functions are derived using the cloud analysis approach. Two regression algorithms have been implemented in the toolkit. In the first option, a simple linear regression is used, in which all data points are equally used for the best-fit curve. In the second case, displacements deemed excessively high are treated differently through a censored regression analysis. Censored regression analysis requires the definition of a threshold (i.e. maximum displacement or acceleration). This threshold is defined by a censoring factor defined as the ratio between the maximum admissible EDP and the threshold for last damage state considered (e.g., complete damage). For example, a censoring factor equal to 1.5 means that EDPs 1.5 times above the threshold for the last damage state will be treated differently. If the user has not explicitly accounted for the building-to-building variability (i.e. only one capacity curve has been provided per building class), it is possible to increase the uncertainty to account for this source of variability. The VMTK performs this adjustment by adding to the dispersion of the record-to-record variability the contribution of the building-to-building variability provided by the user (introduced in the GUI through its sigma).

Inputs

Alongside with the IMLs and EDPs files computed in the structural response module, the user must provide a damage model csv file. This file should be formatted as a column array containing the EDPs thresholds for each damage state (being either displacements of accelerations).

Outputs

When performing fragility assessment the VMTK will output to the directory specified by the used a csv file containing in the first column the intensity measure level and the subsequent columns their respective probability of exceeding the damage states.