Issue 52

B. E. Sobrinho et alii, Frattura ed Integrità Strutturale, 52 (2020) 51-66; DOI: 10.3221/IGF-ESIS.52.05 52 and well-known technique used to detect damage in structures is based on Wavelet Transform, which can be applied using the damaged condition of the structure; see for example [2, 3, 4]. The inverse problem to find and to identify damage in a structure, as seen in [5], is solved by two different and independent approaches, one based on optimization (using a genetic algorithm) and the other one based on a parameter identification (using a neural network). In [6], it is pointed out that the optimization algorithms have a flexibility of implementation because the evaluation scheme customizes the algorithm for a specific purpose. This paper proposes a new methodology in the context of the Structural Health Monitoring Methods, using Differential Evolution to detect damage in steel beams on the basis of numerical and experimental results. O PTIMIZATION ALGORITHMS Differential Evolution Algorithms ccording to [7], the main goal of the optimization algorithms is to find the ideal solution for a given problem, whereas it can achieve the objectives that have been established with the least cost and / or maximum efficiency. The Differential Evolution (DE) method, proposed by [8], is a heuristic approach for minimizing possibly non- linear and non-differentiable continuous space functions. The DE method has been presented with a simple, but powerful numerical optimization algorithm for global optimal solution search and has been successfully applied in complex optimization problems. The DE method uses algorithms that are based on population of individuals. Each individual represents a search point in the space of potential solutions to a given problem and imitates nature principles to create optimization procedures. This method has selection procedures based on the individual fitness, crossover and mutation operators. Fig. 1 shows the flowchart of DE algorithms presented in [9]. The main procedure of DE includes four phases, such as initiation, mutation, crossover and selection. Figure 1: Differential Evolution (DE) method flowchart [9]. In [10], other mechanisms that can be used to finish the evolutionary process are referred: the processing time, the evaluations number of the objective function, the final value of the objective function and own user monitoring. It must be emphasized that it seems always to converge with a low computational effort using numerical evaluations of objective functions. The optimization problem The optimization algorithms involve well-defined mathematical formulations, in which a set of variables describes the system, called design variables. Both the objective function and project restrictions can have features of analyses or synthesis of design, for example, minimizing the mass of a structure in order to find a specified stress limit. As defined in [11], the optimization problem, or determining the minimum, is composed as follows:  Objective function: it is the mathematical function f(p) to be optimized;  Design variables: these are the independent variables that appear in the objective function; A Crossover Objective Function Evaluation Selection Convergence? Started Population (BEGINNING) Objective Function Evaluation Minimum Point (END) YES NO Diferential Mutation