# Structural Damage Identification Using a Modified Directional Bat Algorithm
## 1 Introduction
[PERSON] et al. [26] proposed a Gauss tree seed algorithm to identify the structural damage of simply supported beam and truss structures based on the objective function composed of the absolute error of acceleration response. [PERSON] et al. [27] proposed a damage identification method of a bird mating optimizer, which used the bird mating optimizer to identify the structural damage based on the objective function composed of frequency and acceleration. Although most of the above-mentioned SIOAs have achieved good success in solving constrained optimization problems of structural damage identification, there are still problems like large population and too many iterations, which lead to complex calculation and long calculation time, especially when using structural response data as the error objective function. The bat algorithm (BA) is a random search algorithm proposed by [PERSON] [28], which simulates bats in nature using sonar to detect prey and avoid obstacles. It consists of three parts: global search, local search and parameter update. BA has been widely used in different fields because of its few parameters, fast convergence and feasibility [29]. However, the standard BA is a kind of searching mechanism close to the current optimal solution, which makes it easy to fall into the problem of local optimal solution, resulting in it being unable to find the optimal solution of the objective function. To solve this limitation, many researchers have improved the standard BA by enhancing the search ability and population diversity. [PERSON] et al. [30] modified the global search formula of the standard BA through Levy flight to enhance the search ability of the algorithm, and they used it to solve the logistics planning problem. [PERSON] et al. [31] combined BA with an iterative local search algorithm to enhance the diversity of population, add stochastic inertia weight to adjust search step length and balance search mode by linear updating pulse rate and loudness. [PERSON] et al. [32] combined the improved time factor, Gaussian mutation factor and Cauchy mutation factor with BA to improve the performance of BA in the optimization problem, and they applied them to the problem of low-velocity impact localization. [PERSON] et al. [33] proposed an adaptive BA to optimize the observation matrix, and they designed a dynamic adjustment strategy of the optimal radius to improve its global convergence ability. In addition to the above bat variants, there are many other variants, such as Island Bat [34], directional Bat algorithm (DBA) [35], Hybrid Bat algorithm [36], Enhanced Bat [37], Novel chaotic Bat [38], Chaotic bat swarm optimization [39] and so on. It can be seen that many improved BAs have made some progress in different fields, but the above methods are not well applied to the problem of structural damage identification. For the problem of structural damage identification, the BA needs to be improved to find out the location and degree of structural damage accurately under the condition of small population and few iterations. In this paper, a modified directional bat algorithm (MDBA) has been proposed, which combines the individual optimal updating mechanism, elimination strategy and DBA, and it is applied to the optimization problem of structural damage identification. The beam-type bridge model and truss-type bridge model are used for numerical simulation. The structural damage is expressed by linear reduction of element stiffness, and the error objective function is constructed by structural modal information. Under the condition of low population and few iterations, the MDBA is compared with the differential evolution algorithm (DE), particle swarm optimization algorithm (PSO), shuffled frog leaping algorithm (SFLA) and several variants of BA. Furthermore, the robustness of the algorithm is tested by using different degrees of noise. The results show that the MDBA can be used as an efficient application tool to solve the problem of structural damage identification. The remainder of this paper is as follows.