Issue 29

E. Grande et alii, Frattura ed Integrità Strutturale, 29 (2014) 325-333; DOI: 10.3221/IGF-ESIS.29.28 327 fusion of the information derived separately from the MSECR and rdi indices, while the MDF approach is an innovative procedure using only of the indexes rdi and MSECR in a multi-stage data fusion (Fig. 1). In the case of the DF approach, modal strain energy change ratios (MSECR) and rdi are evaluated by accounting all the available modes of vibration and assumed as two separate sources of information (S 1 rdi and S 2 MSE ). Then, the obtained MSECR and rdi are converted in local decisions m 1 (S 1 ), m 2 (S 2 ) and involved in DF process which provides the BPAs which can be assumed as indices able to detect the damage location. Regarding the MDF approach, the procedure is developed by considering the rdi index and the MSECR index separately. The main differences with respect to the DF procedure consists in the fact that the sources are composed by the same index (MSECR or rdi) and each source differ from the others by the number of accounted modes of vibrations. Indeed, considering n identified modes of vibration for both the undamaged and damaged state of the system, a group of n first- level sources, denoted as S i with i = 1,…, n , is defined by considering different sets of undamaged/damaged couples of mode shapes , i d i i         , according to the scheme reported in Fig. 1.b and Fig. 1.c. For each first-level source S i , it is possible to evaluate the rdi and the MSECR of the jth element (j = 1…N ), named rdi j [Si] and MSECR j [Si] . The local decision m i (Si) associated to the i th first-level source Si for both the use of rdi and MSECR are, then, obtained:       1 1 i i S j i i N S k k j N rdi m S rdi                  (7)       1 1 i i S j i i N S k k j N MSECR m S MSECR                  (8) A second group of n-1 second-level sources, denoted as i S , is introduced and, for each i S , the corresponding local decisions   i m S are obtained from subsequent data-fusion operations according to the scheme shown in Fig. 1. a) b) c) Figure 1 : Schematization of the proposed data fusion procedures for the optimization of the damage detection: a) DF fusion technique; b) DF technique based on the rdi indicator; c) MDF technique based on the MSECR j indicator.