## 1 Introduction  
Static and dynamic loads, as well as the wear process of a structure, can cause various types of structural damage. Damage, such as cracks and pores, causes a decrease in the mass and stiffness of mechanical structures, resulting in changes in their properties the latter being the main cause of failure in structural systems. This can be avoided by prior identification of damage present in the structure, and the service life of the structure can be extended by repairing the damages in time. In recent years, special attention has been given to methods that can detect damage at an early stage. [PERSON] et al. [1] proposed the use of inverse problems as a basic strategy for damage detection and identification in Structural Health Monitoring (SHM). [PERSON] et al. [2] presented an efficient multi-stage optimization damage detection method for truss and frame structures equipped with a limited number of sensors. In this approach, a Finite Element (FE) model was developed to simulate the response of the actual structure. [PERSON] et al. [3] applied metaheuristic sunflower optimization, the artificial neural networks and the response surface method to solve the inverse problem of crack identification. The crack was modeled as a thin elliptical hole in a rectangular layered plate using the finite element method. The methods yielded various approaches to solve the problem, and provided reliable identification of the shape, size and position of a crack ranging in size from 3 to 30 mm. [PERSON] et al. [4] conducted multi-scale global identification. To solve the identification problem, task global optimization methods (evolutionary algorithm), finite element method commercial software, the response surface approach and the numerical homogenization algorithm were combined. [PERSON] et al. [5] used eigenfrequency sensitivity analysis to detect defects in beams. The effectiveness of the boundary element method (BEM) was compared with that of the finite element method (FEM). [PERSON] et al. [6] analyzed the static bending and buckling of bi-directional, functionally graded (BFG) plates with porosity using a new, first-order shear deformation theory (FSDT) based on the mixed finite element method (FEM). [PERSON] et al. [7] studied the linear and nonlinear solutions of a sigmoid functional-gradient nanoplate (S-FGM) with porous effects. Numerical size-dependent solutions were obtained using strain gradient theory and an isogeometric finite-element formulation. Please note that the application of the FEM and the BEM is one of the effective approaches for solving the direct problem and detecting structural damage. The inverse problem of determining the location and size of the damage was modeled using methods such as: (1) methods based on artificial neural networks [8; 9; 10; 11; 12]; (2) multiple loading methods [13; 14; 15; 16] and (3) methods based on topological optimization approaches [17; 18; 19; 20; 21; 22; 23; 24]. The topological derivative representing the sensitivity for an arbitrary shape, which is functional with respect to the generation of an infinitesimal singular domain perturbation, such as inclusion, was introduced by [PERSON] et al. [17], and its development was found [18]. [PERSON] et al. [19] developed a robust and accurate approach based on the innovative coupling of peridynamics (PD) (a meshless method) and topology optimization (TO) to determine the optimum topology of load-bearing structures. [PERSON] [20] considered the topological derivative in a limited-aperture inverse scattering problem for noniterative imaging of thin inhomogeneity. [PERSON] et al. [21] established a topological sensitivity framework for far field detection of diametrically small electromagnetic inclusions. [PERSON] et al. [22] studied the use of steady and time-harmonic thermograms for structural health monitoring of thin plates.