PSI - Issue 52

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

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Dong Xiao et al. / Structural Integrity Procedia 00 (2023) 000–000

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Figure 3 illustrates the relaxation of the nonlinear constraint to a linear constraint. For example, when C = 2 , c l = 0 . 9 , c u = 1 . 1 , ˆ f d = 200 Hz , the loading frequency f l and unloading frequency f u are bounded in the range of [150 , 300] Hz . The nonlinear constraint in Equation 15, represented by the red area between two red arches, is re laxed to the linear constraint, depicted by the blue area between two blue lines. This relaxation slightly expands the design space but allows for easier and faster optimisation computations.

Fig. 3: Constraint of loading and unloading frequency

2.6. Adaptive impact location and peak force bound constraint

Traditional optimisation methods often fix the bounds of design variables, resulting in a fixed optimisation space. However, this fixed space may require a large number of samples to explore the entire design space, leading to slower convergence. To address this, in this study, local surrogates are employed to dynamically bound the design variables. To bound the impact location and impact peak force, it is necessary to extract features from the impact responses that are most closely related to these design variables. According to the findings in Sharif-Khodaei et al. [2012]; Seno et al. [2019], time of arrivals is highly correlated with the impact location. This correlation arises because the time taken for the wave to propagate depends on the distance it has to travel. Furthermore, Seno and Aliabadi [2021] has demonstrated that there is a positive linear relationship between the impact peak force and the maximal response amplitude. This finding suggests that the gradient of the peak force and maximal response amplitude remains relatively constant for a given impact location. These correlations provide valuable insights that can be used to e ff ectively constrain the impact location and impact peak force variables during the optimisation process. Therefore, two Kriging local surrogates are constructed to relate time of arrivals with impact locations and the force gradients based on the impact data in the impact pool. These surrogates provide estimates of the uncertainties associated with the impact location and the peak force of target impact. The impact location bounds, and the impact peak force bounds of target impact are determined using the three-sigma rule, ensuring a 99.7% confidence level. The local surrogates play a crucial role in bounding the design variables within the framework of e ffi cient global optimisation, commonly known as surrogate-assisted e ffi cient global optimisation Viana et al. [2013]; Haftka et al. [2016]. By integrating the local surrogate of impact location and impact peak force and the e ffi cient search strategy, the surrogate-assisted e ffi cient global optimisation method e ff ectively reduces the computational burden while ensuring precise and reliable impact identification. It provides a more e ffi cient approach to identify impacts in composite structures based on model-based methods.