GA-based Damage Detection in Structures Using Frequency and Modal Strain-energy

In this study, an improved GA-based damage detection algorithm using a set of combined modal features that include natural frequency, mode shape, and modal strain energy is proposed. In order to achieve the objective, the following approaches are implemented. Firstly, a new GA-based damage detection algorithm is formulated for beam-type structures. A schematic of the GA-based damage detection algorithm is designed and objective functions using a set of modal features are selected for the algorithm. Modal features selected for the algorithm include frequency changes, modal strain-energy changes and frequency changes combined with modal strainenergy changes. Secondly, experimental modal tests are performed on free-free beams. Sensor locations are determined from numerical analyses. Modal features such as natural frequency, mode shape, and modal strain energy are experimentally measured before and after damage in the test beams. Finally, damage detection exercises are performed on the test beams to verify the feasibility of the proposed method. Experimental results show that the damage is detected with good accurate using proposed method. INTRODUCTION During the past several decades, a significant amount of research has been conducted in the area of nondestructive damage detection via changes in modal responses of a structure. These methods utilize modal features such as natural frequency, frequency response function, mode shape, and modal strain energy [8,17]. Research efforts have been mainly focused on developing appropriate techniques of sensing and monitoring, damage identification, and performance evaluation of damaged structures. Research works on damage detection techniques include Kalman filter method [7], modal strain energy-based damage index (DI) method [10, 18], genetic algorithm (GA)-based method [3,13-15], and artificial neural network (ANN)-based method [2,19]. Among those, GA-based damage detection methods have been studied to locate and assess structural damages via system identification (SID) using genetic optimization process. Compared to other optimization methods, the GA-based methods do not need any differential information on objective functions. Also, the accuracy of damage detection can be improved by statistical multi-points-search algorithm [5]. There exist several problems that should be overcome to develop a rigorous GA-based damage detection method. First, the computation process of the GA-based method requires relatively longer time-consumption for damage detection compared to other methods (i.e., DI method or ANN method). Second, its accuracy depends on the types of modal features that are selected for damage detection. Third, a baseline model should be created by an appropriate system identification process. The inaccuracy of the baseline model leads to faults in damage detection. There have been several research attempts in order to overcome the problems. Au et al. [1] proposed methods using a micro genetic algorithm that reduces the calculation time. Routolo et al. [16] improved the accuracy of GA-based damage detection by using an objective function that combined modal features such as natural frequencies, mode shapes, and mode curvatures. To reduce the effect of modeling error, Hao et al. [6] also proposed a GA-algorithm using the changes of natural frequencies and mode shapes between pristine and damaged states. In spite of those research efforts, however, the following research needs are remained to improve the accuracy of GA-based damage detection. First, a robust GA-algorithm should be developed to reduce the effect of model errors on damage detection process. Second, a set of modal features representing structural characteristics should be selected to discriminate damaged states from undamaged pristine state. Maia et al. [12] and Kim et al. [9] studied on the performance of modal features (such as natural frequency, mode shape, mode curvature, and modal strain energy) for damage detection accuracy in structures. They concluded that modal strain energy is more sensitive to damages in structures (e.g., beam and truss) than any other modal features. In this study, an improved GA-based damage detection algorithm using a set of combined modal features that include natural frequency and modal strain energy is proposed. In order to achieve the objective, the following approaches are implemented. Firstly, a new GA-based damage detection algorithm is formulated for beam-type structures. A schematic of the GA-based damage detection algorithm is designed and objective functions using a set of modal features are selected for the algorithm. Modal features selected for the algorithm include frequency changes, modal strain-energy changes and frequency changes combined with modal strain-energy changes. Secondly, experimental modal tests are performed on free-free beams. Sensor locations are determined from numerical analyses. Modal features such as natural frequency, mode shape, and modal strain energy are experimentally measured before and after damage in the test beams. Finally, damage detection exercises are performed on the test beams to verify the feasibility of the proposed method. GA-BASED DAMAGE DETECTION TECHNIQUE GA-Based Damage Detection Algorithm Structural damage is typically related to change in the structural physical parameters. In damage detection, damage is usually represented by an elemental stiffness reduction factor (SRF) in order to preserve the structural connectivity and reduce the unknown variables. The SRF is defined as the ratio of the elemental stiffness reduction to the initial stiffness. It ranges from 0 to 1, where 0 signifies no damage in the element and 1 means that the element loses its stiffness completely. The objective of damage detection is to derive the SRFs by which nonzero terms locate the damage and their magnitudes represent the damage severities [6]. In GA-based damage detection techniques, structural damage is estimated from model update process using damage-induced changes in modal features. As shown Fig. 1, an analytical model is continuously updated until the difference between experimental and analytical modal features is minimized. This process is defined as the minimization problem and it can be formulated as follows: Find α Minimize [ ] ) ( ) ( α α B A J − = (1) Subject to 0 ) ( < α g , 0 ) ( = α h where α is element’s SRF vector, ) (α J is objective function for damage detection, A is experimental modal feature extracted from the target structure, ) (α B is analytical modal feature calculated from the numerical model of the test structure, and ) (α g and ) (α h are equality and inequality constraints, respectively. In GA-based damage assessment, the accuracy of damage detection depends on the feasibility of modal features and a baseline analytical model that are selected for the test structure [11,16]. Also, the time consumed for damage detection process would be reduced by using optimization techniques [1,16]. In this study, micro GA is applied to minimize Eq. (1). Traditional genetic algorithms use large population to keep up the variety of genetic information; however, micro GA uses very small population that makes it efficient for searching optimum solution [1]. Fig. 2 schematizes the damage detection process using micro GA. Firstly, five (5) individual sets of stiffness reduction factors are assumed randomly and the population using the sets is initialized. Then the fitness that represents the maximized level of objective function is evaluated for each individual. Secondly, if all individuals are converged to a point, they are restarted and initialized. If they are not converged to a point and do not satisfy the end condition, they are updated by genetic operators such as reproduction, crossover, and mutation. The algorithm uses the elite strategy that reintroduces the best individual in the present generation when the best individual from the previous generation is lost in the present generation. These processes are repeated until the end condition is satisfied and damages are assessed from the optimized analytical model.