Probability-based Crossover and Mutation in Genetic Algorithms for Vibration-based Damage Detection in Plates

Abstract

Damage occurred in a structure cause reduce stiffness of the structure. Theoretically, once the stiffness is varied, the vibration characteristics - natural frequencies and mode shapes - of the structure are consequently changed. Therefore, the vibration-based damage detection can be formulated to an optimization problem in which an objective function numerically calculated from the difference between the experimental vibration characteristics and those of predicted damage where this paper employs experimental vibration characteristics that are approximated from the numerical calculation from the actual damage. The damage detection in plates is used as test cases in which a genetic algorithm (GA), a population-based derivative-free approach, is the solution search in the formulated optimization problems. There are 2 test cases of damage detection in plates to be investigated. The first case has one damaged region consisting of 4 damaged elements and the second case has five separately damaged elements. To enhance of performance of GA, this paper proposes a probability-based crossover and mutation embedded in GA. By this proposed idea each decision variable is assigned a probability to be performed GA operators - crossover and mutation. Unlike normal GA which applies the GA operators on all decision variables, by the probability-based crossover and mutation, only some decision variables to be performed the GA operators to avoid the unnecessary variables to be applied by the operators. After simulation runs, solutions obtained from the GA with probability-based crossover and mutation are better than those obtained from the normal GA for both 2 test cases. These results show that the probability-based crossover and mutation can enhance the performance of GA in damage detection in plates.