# Investigation of the Internal Structure of Hard-to-Reach Objects Using a Hybrid Algorithm on the Example of Walls

## TL;DR

This paper proposes a hybrid algorithm to examine the internal structure of walls using computed tomography with incomplete data.

## Contribution

A novel hybrid algorithm combining metaheuristic and numerical optimization methods is introduced for tomographic reconstruction with incomplete data.

## Key findings

- The hybrid algorithm effectively reconstructs internal structures from incomplete tomographic data.
- The proposed method outperforms classical approaches in terms of computational efficiency.
- Computational examples demonstrate the effectiveness of the hybrid algorithm in detecting anomalies in walls.

## Abstract

The article presents research on the application of computed tomography with an incomplete dataset to the problem of examining the internal structure of walls. The case of incomplete information in computed tomography often occurs in various applications, e.g., when examining large objects or when examining hard-to-reach objects. Algorithms dedicated to this type of problem can be used to detect anomalies (defects, cracks) in the walls, among other artifacts. Situations of this type may occur, for example, in old buildings, where special caution should be exercised. The approach presented in the article consists of a non-standard solution to the problem of reconstructing the internal structure of the tested object. The classical approach involves constructing an appropriate system of equations based on X-rays, the solution of which describes the structure. However, this approach has a drawback: solving such systems of equations is computationally very complex, because the algorithms used, combined with incomplete information, converge very slowly. In this article, we propose a different approach that eliminates this problem. To simulate the structure of the tested object, we use a hybrid algorithm that is a combination of a metaheuristic optimization algorithm (Group Teaching Optimization Algorithm) and a numerical optimization method (Hook-Jeeves method). In order to solve the considered inverse problem, a functional measuring the fit of the model to the measurement data is created. The hybrid algorithm presented in this paper was used to find the minimum of this functional. This paper also shows computational examples illustrating the effectiveness of the algorithms.