PSI - Issue 66

Umberto De Maio et al. / Procedia Structural Integrity 66 (2024) 502–510 Author name / Structural Integrity Procedia 00 (2025) 000–000

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the final feature extraction stage following the classification into three categories: global , local , and combined . This demonstrates how CNNs can take a complex input, like the critical mode shape, and reduce it to a meaningful classification for specific tasks such as detecting local or global instabilities in structural analysis.

Fig. 1. A convolutional neural network (CNN) architecture used for classification tasks, particularly for analyzing the first mode shape in structural or vibrational analysis.

2.3. Genetic algorithm for the optimization procedure Genetic Algorithm (GA) is a search and optimization technique based on natural selection and genetics principles. It finds reasonable solutions to complex optimization problems by successively evolving a population of candidate solutions. Every solution also called an individual in GA, is characterized by a set of parameters known as genes. The quality or fitness of every individual is measured by a fitness function, which calculates the degree to which that individual satisfies the objective of the problem. Then, this population of solution strings evolves over generations through several operations: selection, crossover, and mutation. In the specific context adopted in this work, the genetic algorithm is employed to optimize the geometrical parameters of the proposed microstructure, which influence the critical buckling deformation of a representative volume element (RVE). The algorithm starts by generating a population of 50 random candidate solutions. These candidates represent different combinations of the key geometrical parameters within predefined ranges. Each candidate solution is evaluated based on the cost function, which employs a MATLAB instance to call a COMSOL model and compute the linear buckling for the microstructure. The CNN network classifies the buckling mode shape as either local , global, or combined . If the mode shape is not classified as local, a penalty factor is introduced to the cost function to optimize the geometry toward solutions characterized by Global or Combined buckling mode shapes. The main reason for this choice is that when a structure experiences global buckling, the instability tends to involve large portions of the structure, often requiring an increase in the representative volume element (RVE) size, leading to a significant increase in the computational effort. After evaluating the fitness of the initial population, the algorithm selects the best-performing solutions. These solutions are then used to produce a new generation of candidates via crossover, where the characteristics of two parent solutions are combined to form offspring. This process simulates the biological reproduction of traits from parents to offspring. In addition, mutations are introduced to avoid premature convergence to local optima, which involves making small random changes to some candidate solutions. This increases the diversity of the population and allows the algorithm to explore new areas of the solution space. The GA iterates for a set number of generations or until specific convergence criteria are met. These criteria include a lack of fitness over several generations (stall generations) or reaching a predefined maximum number of generations (in this case, 100).