PSI - Issue 44

Fabrizio Paolacci et al. / Procedia Structural Integrity 44 (2023) 307–314 Fabrizio Paolacci et al. / Structural Integrity Procedia 00 (2022) 000–000

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outline of the procedure is briefly showed in the following section, which includes the definition of the objective function, and a new search algorithm. 3. A search algorithm for natural records selection The input signal are selected from a given database of natural records. A first selection of n R > n S records is made according to a range of magnitude, distance from the fault (R jb) distance) and ground type. Because of some response spectra could deviate excessively from the mean target spectrum, even if the mean spectrum is close to the target, it is possible to apply a constraint in the selection to reject them. This is useful to discard samples with a very small probability of occurrence. Considering that usually two components of each ground motion record are needed, the procedure allows to find set of records so that the mean response spectrum of both the components match the median and the 84% fractile spectrum. Given the target mean S 0 (T) and percentile S 1 (T) spectra, we find the n-tuple of ground records: {a gkx (t), a gky (t)}, (k=1,2,…,n S ), whose spectral ordinates S kx (T j ) and S ky (T j ), evaluated for the periods T j , are such that: d 0r = K lS rm L T j M -lS 0 L T j MK =min , d 1r = K lS rm L T j M + ∆ lS r L T j M -lS 1 L T j MK =min (5) where | ∙ | indicates the vector norm (here the quadratic norm), lS=logS , r=x, y, and: lS rm L T j M = 1 n S ∑ lS kr ( T ) n S k=1 , ∆ lS r L T j M = O ∑ P lS kr L T j M -lS rm L T j MQ 2 n S k=1 n S -1 (6) The problem is multi-objective that can be reduced by assuming: d = α max { d 0x , d 0y }+ β max{ d 1x , d 1y }=min (7) where α and β are weighting factors. Among the n R records extracted from the database, a set of n S must be selected. The optimal solution could be obtained by calculating the value of e for the combinations of n R elements in groups of n S , and then choosing the one that minimize ϵ ; nevertheless, the number of the combinations is very high and the calculation take too much time. The developed algorithm is thus based on the following steps: 1. The maximum number S of combination that we are willing to calculate is set. 2. The ground motions response spectra are sorted in ascending order of the deviation K UV L W M − 7 L W MK 3. The number of elements in each group is set: = 2 . 4. The maximum number of records ; ≤ [ is evaluated so that P ; Q ≲ S . 5. The first ; records, and the relevant response spectra, are selected among those sorted. 6. The values of for the P ; Q combinations are evaluated. 7. The combinations are sorted in ascending order of and the records are sorted according to the order of appearance in the combinations. 8. Set = + 1 and go to step 4 until ≤ _ . Clearly, this solution is approximate, even though it is deemed sufficiently accurate. By increasing the number of combinations n c , the accuracy improves, even not decisively, while the computational time increases considerably. A significant improvement can be obtained, after the records selection, by applying a scale factors s k close to 1 for both x and y components. The optimal solution can be found with an ordinary optimization algorithm available in Matlab©, consisting in minimizing the quantity d of the Eq. (7), which is obtained by substituting in Eq. (5) and (6) kr with r , respectively. The procedure has been implemented in the software SCoReS (Spectrum Compatible seismic Records Selection) developed in the Matlab environment. By assuming = 5 × 106, the selection of the 5 groups of