PSI - Issue 84

Alberto Barontini et al. / Procedia Structural Integrity 84 (2026) 352–359

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generated for each one of the 36 bars and each one of the variables. The first four vibration modes are selected as targets for the optimisation, and four uniaxial sensors are to be placed at optimal locations. The FE model, the modal analysis, and all subsequent sensor network optimisation algorithms were implemented in MATLAB to ensure consistent and streamlined control of the formulations at each step. For the following analyses, a realisation obtained using the mean values of the uncertain parameters is adopted as the reference model. The target mode shapes of the reference model are shown in Figure 1. These are characterised as mainly bending with a horizontal translational component due to the boundary conditions on the right end.

Fig. 1. Target mode shape.

Fig. 2. Sample MAC values for target mode shape.

The modal assurance criterion (MAC) values for the same modes, computed by comparing each sampled model with the reference model, are presented in Figure 2. Overall, the variation in the mode shapes appears to be negligible, with slightly larger discrepancies observed for the fourth mode; however, in all cases the MAC values remain above 0.9. The results of the optimisation are presented in Table 1 and visually shown in Figure 3. As the only investigated method that treats sensor location as a stochastic variable, A3 is discussed first. Although the variability in the mode shapes is limited (Figure 2), different realisations lead to a wide range of sensor configurations, as closely spaced candidate locations may carry comparable information. Only location 29 is selected in more than 65% of the samples. An inspection of the SA matrix shows that the locations with the highest probability of selection conditional on the inclusion of location 29 are 6, 16, and 26. The resulting sensor layout is well distributed, with three sensors positioned along the vertical direction, two near the extremities and one closer to the centre, and a single sensor along the horizontal direction. The global probability of selection and the probability of selection conditional on the inclusion of location 29 are shown in Figure 4(a,b), while the SA matrix is visualised in Figure 4(c) using colour maps to highlight stronger affinities. Here, each row represents the probability of selection of the DOFs in the columns conditional on the instrumentation of the corresponding DOF. Consequently, blue rows highlight DOFs that are never instrumented.