PSI - Issue 78

782 A. Romanazzi et al. / Procedia Structural Integrity 78 (2026) 777–784 Therefore, the time interval is updated, and the ARX fitting is conducted on the new data set after initialising the iteration orders to the minimum AR-order, X-order and time delay order as [ , , m in ] . In such scenario, the constraint given by the minimum length for admissible segment, , must be met as: ( = − ) ≤ (14) Alternatively, the data points considered are of the size of the and the ARX iteration stops when either the is satisfied or the orders limit [ , , ] is achieved, and then the ̂ is selected according to equation 12. At the final stage, frequency response analysis is conducted on the transfer function ̂ and the resonant frequency peak is identified in the Bode plot for each segment. 3. Validation of the algorithm on experimental dataset In order to validate the robustness of the proposed algorithm, data from shake table tests performed by Tomassetti at al. (2019) to investigate the put-of-plane behaviour of masonry wall are considered as benchmark. The mock-up consisted of a U-shape in plan wall, of which acceleration response was monitored by a set of 9 accelerometers placed on the mock-up and at the foundation. Therefore, a series of 18 incremental seismic signals (SI) and 3 additional low amplitude random excitations signals for dynamic identification (DI) were performed. For the sake of brevity, the evolution of the first frequency along the segmentation are illustrated in detail only for the seismic input 18, which is reported to be the dynamic test that caused moderate damage with the full development of crack pattern corresponding to collapse mechanism (DS3). As for the SISO system identification, the time series corresponding to the accelerometer at the foundation level (Acc_INPUT) is considered as input variable, and the signal at the top middle-section of the wall (Acc_OUTPUT) is selected as output variable. With regard to the ARX setting, the autoregressive, the exogenous and the time lag orders are set in the range (20, 43), (20, 43) and (0, 1), respectively, and a minimum NRMSE of 85% is demanded as good-fit requirement. The multiplier to establish the minimum length of the segment is set equal to 20. At first, the SISO seismic signals are analysed, and the pre- and post-seismic scenarios are selected a priori considering the normalized input ̅̅̅ with control on the maximum output acceleration. Afterwards, the algorithm iteratively seeks the ARX model of the pre-seismic scenario that best fits the data over the defined model order combinations. Therefore, frequency response analysis is conducted considering as transfer function the selected ̂ model with orders (23, 41, 1) and NRMSE of about 75%. From the Bode diagram reported in Fig. 3a, the first frequency is identified as 12.39 (T= 0.08 ), to which corresponds a minimum length of segments of 1.61 according to equation 9. Therefore, the segmentation is recursively applied on the remaining signal and the post-seismic scenario previously selected. Once that the segmentation is performed over the entire SISO signal, the outcomes from system identification are collected and summarise in Fig. 3b. According to Fig. 3b, considerable damage occurred around 3.5 of the seismic test, as the first frequency decreases from 12.37 in segment 2, to 7.38 in segment 3. At the post-seismic scenario, the observed frequency is 6.05 , which is validated by the dynamic identification DI02 (6.80 ) with a relative error of about 10%. Furthermore, the damage progression can be reliably estimated for the entire segmentation considering the evolution of the first frequency during the dynamic test, validating the capability of the algorithm to determine the non-linearity of the system along the non-stationary signal.