PSI - Issue 64

Vera Rillo et al. / Procedia Structural Integrity 64 (2024) 700–707 Rillo et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 2. (a) First vertical mode of the central span ; (b) Torsional mode of the central span; (c) Vertical mode of lateral spans; (d) Vertical mode of all spans; (e) Second vertical mode of the central span ; (f) Torsional mode of the lateral spans.

3.3. Definition of the Optimal Sensor configuration

The extraction of the modal parameters, from the acceleration time histories extracted from SAP2000 (Computers and Structures, 2016), was carried out by using the Frequency Domain Decomposition (FDD) method available in the commercial software ARTeMIS (SVS, 2019). In the FDD method the spectral density matrix is decomposed by Singular Value Decomposition (SVD) to obtain frequency values and mode shapes (Brincker et al., 2001). The natural frequencies and the modal shapes identified via FDD method are summarized in Figure 3. In order to design the layout of the monitoring system, it is necessary to carry out an analysis concerning the optimal sensors position. The aim is to identify the optimal sensor configuration in terms of the number and position of sensors. In this paper, the authors assumed that the optimal configuration is the one yielding dynamic characteristics as similar as possible to those obtained with the starting scenario including 24 sensors, with the fewest number of sensors. Generally, the OSP techniques are characterized by a first step, during which the most significant sensors are ranked, followed by a second step regarding the optimization of the configuration. Therefore, after exporting the modal shape vectors and the relative frequencies for each target mode, i.e., the six modes obtained through the simulation of the ambient vibration test, for the first step the three OSP methods, described in section 2, were applied in order to rank the most significant sensors for identifying the dynamic characteristics of the bridge. As second step, the adopted procedure involved the deactivation in ARTeMIS (SVS, 2019) of the sensor occupying the last position in the ranking and the reapplication the OSP method under examination. This process was repeated 23 times for the three derived rankings (EFI, EVP, and ADPR) until reaching the configuration with 2 sensors. The data of interest needed to be processed in this second step of optimization are the frequencies and modal shapes for each mode of vibration at each scenario. An optimal criterion based on the Modal Assurance Criterion (MAC) between the modal shapes obtained with the starting scenario including 24 sensors and that ones regarding all the analyzed scenarios obtained deactivating one sensor at time was chosen. However, it is well known that the MAC number is applicable between matrices of the same dimensions. Therefore, as suggested in Rillo et al. (2024), for the 23 scenarios in which