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

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and actual responses, the impact characteristics can be identified. As a result, this approach is commonly referred to as model-based methods for on-line impact identification. Extensive research has been conducted to develop enhanced model-based methods for on-line impact identifica tion. These research endeavors can be broadly classified into two categories: the refinement of more comprehensive mathematical models and the design of more e ffi cient optimisation algorithms. Regarding mathematical models, early studies focused on identifying impacts on beams based on the Bernoulli Euler beam theory Choi and Chang [1996], as well as on simple plates using Kirchho ff ’s thin plate theory Tracy and Chang [1998a,b]. In recent years, the Finite Element Method (FEM) Hu and Fukunaga [2005]; Hu et al. [2007]; Yan and Zhou [2009]; Sun et al. [2014] has gained popularity due to its versatility and applicability in simulating impacts on complex structures. Although the FEM allows for the simulation of impacts on a wide range of structures, it can be computationally expensive due to the need for fine meshes, small time steps, and complex contact and friction models. By adopting the FEM as the mathematical model, the FEM-based impact identification method considers the FEM as a black-box solver for simulating impacts. This black box establishes a relationship between impact characteristics and impact responses. To identify the impact characteristics of an impact with available local responses based on the FEM model, the impact identification turns out to be an optimisation problem. The objective function of this optimisation problem is the response di ff erence between simulated actual responses, while the design variables are the impact characteristics need to be identified. To solve this impact identification optimisation problem, various optimisation algorithms have been employed. And the e ffi ciency of optimisation algorithms is of great concern. Early optimisation methods such as the Newton-Raphson method Choi and Chang [1996], gradient method Tracy and Chang [1998a,b] were initially employed for impact identification in the last century. These methods heavily relied on the initial guess and tended to converge quickly to local optima. Quadratic programming optimisation Hu and Fukunaga [2005]; Hu et al. [2007] was also utilized, but it was found to be time-consuming as it required exploring all possible impact locations. Over the past 15 years, heuristic algorithms such as genetic algorithm Yan and Zhou [2009]; Sun et al. [2014], particle swarm optimisation algorithm El-Bakari et al. [2014] have been introduced into impact identification. However, these heuristic algorithms often necessitate a large number of impact response evaluations, making them computationally expensive and time-consuming. To address the computational e ffi ciency challenges associated with FEM-based impact identification, this study in troduces the surrogate-assisted e ffi cient global optimisation algorithm for impact identification minimization problem. This e ffi cient global optimisation algorithm involves constructing a Kriging surrogate that captures the relationships between impact location, impact force (design variables), and response di ff erences (objective function). Here, the combinations of impact location, impact force are referred to as samples. By adaptively sampling using generalized expected improvement criterion and simulating impacts corresponding to these enhanced samples, the Kriging surro gate is iteratively updated and the impact characteristics of the target impact can be iteratively identified. Furthermore, local surrogates for impact location and impact peak force are constructed to expedite convergence. These local surro gates, updated with the optimisation Kriging meta-model, e ff ectively confine the impact location and peak force within a feasible range. This constraint strategy results in a rapidly shrinking optimisation space, leading to fast convergence to the global optimum. The FEM model of a composite panel is established to validate the proposed impact identification method. The impact force history obtained from drop tower impact experiments serves as the input excitation for the FEM model. The results show that the proposed method accurately identifies the impact location and impact force history with less than 100 simulations, demonstrating its e ffi ciency and e ff ectiveness. Leveraging surrogate models and e ffi cient search strategies significantly reduces computational burden while ensuring precise and reliable impact identification. The rest of this paper is organized as follows: Section 2 introduces impact identification methods developed based on surrogate-assisted e ffi cient global optimisation. In Section 3, the FEM model is illustrated and validated with experiments. Section 4 displays the results of impact localisation and impact force estimation of the proposed method. And final conclusions are drawn in Section 5.