Multi-Regression Analysis to Enhance the Predictability of the Seismic Response of Buildings

Several methodologies for assessing seismic risk extract information from the statistical relationship between the intensity of ground motions and the structural response. The first group is represented by intensity measures (IMs) whilst the latter by engineering demand parameters (EDPs). The higher the correlation between them, the lesser the uncertainty in estimating seismic damage in structures. In general, IMs are composed by either a single (scalar-based IMs) or a group of features of both the ground motion and the structure (vector-valued IMs); the latter category provides higher efficiency to explain EDPs when compared to the first one. This paper explores how to find new vector-valued IMs, which are highly correlated with EDPs, by means of multi-regression analysis. To do so, probabilistic nonlinear dynamic analyses have been performed by considering a seven-story reinforced concrete building as a testbed. At a first stage, 30 scalar-based IMs have been correlated with 4 EDPs (i.e., 120 groups of IM-EDP pairs have been studied). Afterwards, the structural responses have been classified as elastic, inelastic and a combination of both. It has been analyzed how efficiency behaves when making these classifications. Then, 435 vector-valued IMs have been created to enhance the predictability of the scalar EDPs (i.e., 1740 groups of IM-EDP pairs have been analyzed). Again, the most efficient IMs have been identified. Sufficiency, which is another statistical property desired in IMs, has also been examined. Results show that the efficiency and sufficiency to predict the structural response increase when considering vector-valued IMs. This sophistication has important consequences in terms of design or assessment of civil structures.