4.3. Efficiency — Incremental Dynamic Analysis

Theoretical Background

For IDA, efficiency is quantified by the dispersion of IM capacities across records at a given damage state (Shome & Cornell, 1999).

Definition

Given the IM capacity \(C_i^{(r)}\) of record \(r\) for damage state \(i\), the efficiency is the logarithmic standard deviation of those capacities:

\[\beta_{D|IM} = \sqrt{ \frac{1}{N-1} \sum_{r=1}^{N} \bigl(\ln C_i^{(r)} - \overline{\ln C_i}\bigr)^2 }\]

where \(\overline{\ln C_i} = \frac{1}{N}\sum_{r=1}^{N} \ln C_i^{(r)}\).

A smaller dispersion indicates that records scaled to the same IM level produce similar structural capacities — i.e. the IM is a more efficient predictor of structural performance.