Hybrid Algorithm for Automated Primary Analysis of Broadband Dielectric Spectra of Heterogeneous Materials

Abstract

Broadband dielectric spectroscopy (BDS) provides the measurement of frequency-dependent complex permittivity ε*(ω) that encodes multiple relaxation mechanisms and charge-transport phenomena in heterogeneous materials. However, the superposition of dipolar relaxation, interfacial (Maxwell–Wagner) polarization, electrode polarization and measurement noise makes the primary analysis of BDS data non-trivial and labor-intensive. The paper proposes a hybrid pipeline that combines physics-aware preprocessing, distribution-of-relaxation-times (DRT) estimation via Tikhonov regularization, and lightweight learning-based interpretation using a one-dimensional convolutional neural network (1D-CNN) trained on physics-informed synthetic spectra. First, singular spectrum analysis (SSA) and baseline correction are employed to suppress noise and low-frequency artifacts while preserving the overall spectral shape. Then a non-negative DRT profile is recovered from ε′(ω) and ε″(ω) by solving a discretized Fredholm equation of the first kind with smoothness regularization. The resulting DRT summarizes latent relaxation modes without explicit model-order selection. Next, physically interpretable features such as the number of peaks, their positions and widths, low-frequency conduction indicators and heuristics for Maxwell–Wagner polarization are extracted from both spectra and DRT. These features, together with the standardized spectra, are fed into a compact 1D-CNN that infers high-level meta-parameters including the number of overlapping relaxations, the presence of interfacial polarization and the presence of conduction tails. Numerical experiments covering a wide range of signal-to-noise ratios demonstrate robust denoising (ΔSNR ≈ 8...12 dB), accurate DRT recovery (median Wasserstein distance < 0.08) and reliable meta-parameter prediction (macro-F1 ≈ 0.91). A reference Python implementation is suggested, providing a command-line interface and a REST microservice suitable for integration into laboratory workflows. The proposed approach minimizes a priori model assumptions while preserving interpretability, which makes it a suitable primary-analysis engine for BDS studies of composites, porous media, soils, polymer electrolytes and other heterogeneous systems.