# Damage feature extraction

After an earthquake, the structural safety of all buildings in the affected region needs to be assessed. This is currently done by a visual inspection of each building. This approach is very time-consuming and requires a significant amount of expertise by the inspectors. A lack of the latter can lead to inaccurate assessments, which are often overly conservative in terms of safety but impacting negatively the expected resilience. In the future, the post-earthquake assessment process will be accelerated and objectified with the help of Artificial Intelligence (AI) and computer vision. Towards this end, it is necessary to detect and quantify damage in structural elements. The purpose of this study is to find a set of useful features–that can be extracted from images–correlating well with the level of damage to load-bearing walls. In general, a critical indicator of damage is the occurrence of cracks in walls. They are also used to understand the element behavior and damage severity.

### Fractal dimension

Fractal is a branch of the set theory in mathematics. In theory, fractals are objects that are self-similar over an infinite range of scales meaning that the pattern looks the same in large and small scales. However, in nature, objects are either not perfectly self-similar or their self-similarity only exists in a finite range of scales. As the value of the fractal dimension increases, the complexity and space-filling properties of the pattern increases. In Figure 1, both patterns show some degree of self-similarity.  The box fractal is obtained following a mathematical expression; and therefore, their exact fractal dimension can be obtained analytically. On the other hand, the crack pattern cannot be constructed through a mathematical operation. Consequently, their fractal dimension cannot be computed analytically. For such patterns, which are not mathematically fractal geometries, the box-counting method (BCM) is widely utilized to estimate their fractal dimensions. In our studies at EESD, we used the notion of fractal dimension to describe the complexity of the crack patterns and to build predictive models to estimate the damage level in structural elements (walls).

• Article:
• Stiffness and Strength Estimation of Damaged Unreinforced Masonry Walls Using Crack Pattern [journal link]
• Sensitivity analysis of fractal dimensions of crack maps on concrete and masonry walls [journal link]