# Structural Damage Identification Using a Modified Directional Bat Algorithm
## 1 Introduction  
Due to the diversity of loads and the complexity of working environment, civil engineering structures often suffer various damages during service, such as concrete cracking, steel yield and so on. Structural damage could cause the change of structural physical characteristics (stiffness, mass, damping, etc.) and cause the variation of modal characteristics (natural frequency, modal shape, etc.). These damages also affect the safety of the structure to a certain extent, so it is very important to find the damage of the structure in time. [PERSON] et al. [1] gave an introduction to various methods for structural damage identification using vibration response data and vibration characteristics, such as acceleration response, natural frequency, vibration mode and flexibility. However, these measurement data are often affected by environmental factors, experimental errors and other uncertain factors, which lead to their failure to truly reflect the status of the structure. Therefore, how to use the structural health identification technology to evaluate the reliability, integrity and safety of the structure is particularly important [2]. In recent years, with the development of the computer, the combination of the swarm intelligence optimization algorithm (SIOA) and structural damage identification has become a popular direction in the field of structural health monitoring (SHM). SIOA transforms a complex structural damage identification into a constrained optimization problem. There are many kinds of SIOA, such as the classical genetic algorithm (GA) [3], particle swarm optimization (PSO) [4], differential evolution algorithm (DE) [5, 6], simulatedannealing algorithm (SA) [7], ant colony optimization (ACO) [8] and so on. In recent years, many new algorithms have emerged, such as the whale optimization algorithm (WOA) [9], bat algorithm (BA) [10], ant lion optimizer (ALO) [11], shuffled frog leaping algorithm (SFLA) [12], cuckoo algorithm (CS) [13], grey wolf optimizer (GWO) [14], fruit fly optimization algorithm (FOA) [15; 16], backtracking search algorithm (BSA) [17; 18] and so on. Swarm intelligence algorithms have been applied to a variety of problems. For example, SFLA algorithms have been used for the traveling salesman problem and maximum power point tracking problems and so on [19; 20]. Each algorithm has its own characteristics and shortcomings. For example, the GA algorithm is easy to implement and has a fast convergence speed, but it lacks global search ability. The PSO algorithm has simple structure and fast convergence speed, and it is easy to fall into a local optimal solution. The ACO algorithm has strong global search ability, is easy to combine with other evolutionary algorithms, has low convergence speed, is easy to fall into a local optimal solution and so on. Many BIOAs have been employed in structural damage identification. [PERSON] et al. [21] proposed a hybrid ant lion optimizer. Based on the damage identification objective function of modal parameters, the numerical simulation of a two-story rigid frame structure and plane truss structure was carried out, and the effectiveness and feasibility of the method were verified. [PERSON] et al. [22] used the Jaya algorithm to determine the damage location and damage degree of truss and frame structures based on multi damage location assurance criteria and modal flexibility changes. [PERSON] et al. [23] compared the accuracy of the GA algorithm and Bat algorithm through the objective function composed of a measured frequency response function and calculated frequency response function. The substructure, strain energy and SIOA were used to identify the damage of a large spatial structure [24; 25], in which the substructure was used to divide the large spatial structure, the strain energy was used to locate the structural damage, and SIOA was used to quantify the structural damage. It is worth noting that in addition to the above modal parameters, the objective function can also be constructed by using the structural response data.