ALGORITHMIC METHODS FOR RECOVERING THE FREQUENCY DEPENDENCE OF THE COMPLEX PERMITTIVITY OF INHOMOGENEOUS MATERIALS USING THE TIME-DOMAIN REFLECTOMETRY (TDR/TDS) METHOD

Abstract

The paper addresses a highly relevant problem in computer engineering: the automated non-destructive testing of inhomogeneous materials using Time Domain Reflectometry (TDR)–based dielectric spectroscopy. Rapid and reliable material characterization is essential in industrial quality control, civil infrastructure monitoring, energy systems, and advanced manufacturing, where internal defects or structural inhomogeneities must be detected without damaging the object under test.

A comparative analysis of measurement hardware platforms is conducted, with particular attention to the practical limitations of laboratory-grade instruments such as Vector Network Analyzer systems. While VNAs provide high accuracy across broad frequency ranges, their cost, size, and operational complexity restrict large-scale or embedded deployment. In contrast, TDR systems combined with modern Digital Signal Processing (DSP) techniques offer a compact, energy-efficient, and cost-effective alternative. The study substantiates that, when supported by advanced computational methods, TDR-based solutions can achieve competitive accuracy while remaining suitable for real-time and field applications.

The core focus of the work is the development of algorithmic methods for solving the ill-posed inverse problem of reconstructing the Complex Dielectric Permittivity (CDP) spectrum from time-domain reflection data. Since small measurement noise can lead to significant spectral distortions, robust regularization and stabilization strategies are essential. The paper analyzes signal pre-processing techniques, including adaptive filtering, baseline correction, and windowing transformations, aimed at suppressing multiple reflections and parasitic distortions. Particular attention is given to the Reflection-Decoupled Analysis (RDA) method, which enables improved separation of overlapping reflection components and enhances the reliability of spectral reconstruction.

A modular computational pipeline architecture is proposed, integrating electromagnetic modeling, inverse problem solvers, and parameter identification blocks. The framework incorporates physical relaxation models, specifically the Havriliak–Negami model, to ensure physically consistent approximation of dispersive behavior. Additionally, effective medium theories are applied to account for composite and heterogeneous material structures.

To improve convergence speed and estimation accuracy, a hybrid inversion strategy is introduced. It combines global optimization methods or neural network–based parameter initialization with the Levenberg–Marquardt algorithm for local refinement. This approach reduces sensitivity to initial conditions and mitigates the risk of convergence to local minima.

The experimental and simulation results demonstrate the feasibility of developing high-precision embedded dielectric spectroscopy systems for continuous material monitoring. The proposed methodology provides a scalable foundation for intelligent, real-time diagnostic platforms in next-generation engineering applications.