DERİN ÖĞRENME KULLANILARAK GENİŞ BANT DİELEKTRİK VERİLERDEN COLE–COLE PARAMETRELERİNİN İTERATİF OLMAYAN TAHMİNİ

Öz

Bu çalışmada, geniş bant dielektrik verilerini ε′(ω) ve ε″(ω) kullanarak tek-kutuplu Cole–Cole dispersiyon modeli parametrelerini (Δε, ε∞, τ, α, σ) iteratif olmayan, doğrudan tahmin eden derin öğrenme tabanlı bir ters model önerilmiştir. 0.5–20 GHz bandında 401 frekans noktasında Cole–Cole denklemi kullanılarak 10⁶ örnekten oluşan sentetik bir veri kümesi üretilmiş ve MATLAB ortamında çok katmanlı algılayıcı (MLP) mimarisi bu veri seti ile eğitilmiştir. Model, farklı bant genişliği ve örnekleme çözünürlüğüne sahip deneysel ölçümler (0.1 M NaCl çözeltisi, kan/kas/deri doku benzeri örnekler, butanol ve monopropilen glikol) üzerinde test edilmiştir. Tahmin edilen Cole–Cole parametreleri ile yeniden oluşturulan dielektrik yanıtlar üç noktalı (multi-point) kalibrasyon ile iyileştirilmiştir. Bu süreç sonunda orijinale veriler ile yeniden oluşturulan dielektrik özellikler için RMSE değerleri ε′ için 1.26’nın ve ε″ için 1.06’nın altında elde edilmiştir. Elde edilen sonuçlar, literatürde yaygın olarak kullanılan iteratif yöntemlerle karşılaştırıldığında, önerilen derin öğrenme tabanlı yaklaşımın Cole–Cole parametrelerini milisaniye mertebesinde, yüksek doğruluk ve tutarlılık ile tahmin edebildiğini ortaya koymaktadır.

Anahtar Kelimeler

• Dielektrik Özellikler
• Cole–Cole Modeli
• Makine Öğrenmesi
• Mikrodalga Ölçümleri
• Doku Benzeri Fantomlar
• Ters Modelleme

Proje Numarası

TÜBİTAK 125E412, İTÜ BAP MGA-2025-46879

NON-ITERATIVE ESTIMATION OF COLE–COLE PARAMETERS FROM BROADBAND DIELECTRIC DATA USING DEEP LEARNING

Öz

In this study, a deep learning–based inverse model is proposed to directly and non-iteratively estimate the parameters of the single-pole Cole–Cole dispersion model (Δε, ε∞, τ, α, σ) using broadband dielectric data ε′(ω) and ε″(ω). A synthetic dataset consisting of 10⁶ samples was generated using the Cole–Cole equation over 401 frequency points in the 0.5–20 GHz band, and a multilayer perceptron (MLP) architecture was trained on this dataset in the MATLAB environment. The trained model was evaluated on experimental measurements with varying bandwidths and sampling resolutions, including a 0.1 M NaCl solution, tissue-mimicking samples (blood, muscle, and skin), butanol, and monopropylene glycol. The dielectric responses reconstructed from the estimated Cole–Cole parameters were further refined using a three-point (multi-point) calibration. As a result of this process, root mean square error (RMSE) values below 1.26 for ε′ and 1.06 for ε″ were achieved between the original and reconstructed dielectric properties. The results demonstrate that, compared to the iterative methods commonly used in the literature, the proposed deep learning–based approach can estimate Cole–Cole parameters with high accuracy and consistency on a millisecond timescale.

Anahtar Kelimeler

• Cole–Cole Model
• Dielectric Properties
• Inverse Modeling
• Machine Learning
• Microwave Measurements
• Tissue-Mimicking Phantoms

Proje Numarası

TÜBİTAK 125E412, İTÜ BAP MGA-2025-46879

Teşekkür

This study was funded by the Scientific Research Unit (BAP) of Istanbul Technical University, Project No. MGA-2025-46879 and by the Scientific and Technological Research Council of Turkey (TUBITAK) under Grant Number 123E578. The author thanks TUBITAK for their support.

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