PSI - Issue 52

Dong Xiao et al. / Procedia Structural Integrity 52 (2024) 667–678 Dong Xiao et al. / Structural Integrity Procedia 00 (2023) 000–000

676

10

4.2. Optimisation convergence

Impacts I1-I4 were identified using model-based methods with surrogate-assisted e ffi cient global optimisation. The objective function, which measures the relative response error, was minimized iteratively by infill sampling and simulating the impacts corresponding to the infilled samples. The convergence of the objective function for impacts I1-I4 is depicted in Figure 8.

Fig. 8: Target function convergence

Fig. 9: Impact location convergence

The results show that initially, as simulating more impacts, the response error decreases significantly. As the number of impact simulations reaches 60, the relative response error for all four impacts is reduced to less than one-tenth. Further infill sampling and impact simulations continue to reduce the relative response error, although the rate of reduction varies depending on the impact. In the following subsections, the identification of impact location and impact force is presented. It is observed that when the relative response error is smaller than one-tenth, the identified impact location and impact force exhibit a considerable level of accuracy. This confirms the e ff ectiveness and e ffi ciency of the surrogate-assisted e ffi cient global optimisation method in accurately identifying the impact characteristics. Figure 9 displays the convergence of impact locations for the four impacts. It can be observed that the impact location converges rapidly during the optimisation process. When the number of impact simulations reaches 60, the localisation errors for all four impacts are reduced to less than 3 mm . After achieving a localisation error smaller than 5 mm , the optimisation algorithm shifts its focus towards exploring the impact force space. Consequently, the localisation error exhibits small fluctuations following the initial sharp drop in localisation error. Furthermore, it can be concluded that the slower reduction in relative response error observed for impact I3 between impacts 20 and 60, as shown in Figure 8, can be partially attributed to the slower convergence of the impact location. 4.3. Impact localisation Figure 10 illustrates the convergence of the impact duration, while Figure 11 depicts the convergence of the peak force for the identified impacts. The impact duration is controlled by the loading frequency f l and unloading frequency f u . While the peak force parameter p max controls the severity of the impact. It can be observed that during the first 60 impact simulations, the simulated impacts are designed to explore the impact frequencies and peak force spaces. By the time 60 impact simulations are reached, the impact duration con verges to the range of [13 , 14] ms , which corresponds to the actual impact duration 13 . 2 ms . Simultaneously, the peak force converges to the range of [1890 , 1950] N , which is in close agreement with the actual peak force 2105 N . 4.4. Impact force identification