Applications of sampling Kantorovich operators to thermographic images for seismic engineering

TL;DR

This paper applies multivariate sampling Kantorovich operators to thermographic images in seismic engineering, enabling reconstruction and analysis of building behavior under seismic stress using MATLAB algorithms.

Contribution

It introduces a novel application of sampling Kantorovich operators in seismic engineering for thermographic image reconstruction and structural analysis.

Findings

Successful reconstruction of thermographic images of buildings.

Comparison of structural behavior models under seismic action.

Use of Orlicz spaces for non-continuous signal reconstruction.

Abstract

In this paper, we present some applications of the multivariate sampling Kantorovich operators $S_w$ to seismic engineering. The mathematical theory of these operators, both in the space of continuous functions and in Orlicz spaces, show how it is possible to approximate/reconstruct multivariate signals, such as images. In particular, to obtain applications for thermographic images a mathematical algorithm is developed using MATLAB and matrix calculus. The setting of Orlicz spaces is important since allow us to reconstruct not necessarily continuous signals by means of $S_w$. The reconstruction of thermographic images of buildings by our sampling Kantorovich algorithm allow us to obtain models for the simulation of the behavior of structures under seismic action. We analyze a real world case study in term of structural analysis and we compare the behavior of the building under seismic action using various models.