Measurement of Material Volume Fractions in a Microwave Resonant Cavity Sensor Using Convolutional Neural Network

TL;DR

This work tackles non-destructive, real-time determination of dielectric two-phase volume fractions inside a microwave resonant cavity by mapping broadband S-parameters to material fractions with a 1D-CNN. A Bruggeman-based simulation pipeline accompanies the CNN to model mixtures, while experimental validation with 21 salt–sand samples demonstrates strong predictive power, especially with data augmentation and selective preprocessing ($R^2$ up to $0.9994$ and $MAE$ around $5.7 imes10^{-3}$). The study finds that de-embedding and filtering offer limited or even negative benefits, suggesting the CNN can robustly learn from raw or lightly processed data. Overall, the approach enables rapid, low-cost, in-line sensing of material fractions in microwave systems, with implications for real-time material characterization.

Abstract

A non-destructive, real-time method for estimating the volume fraction of a dielectric mixture inside a resonant cavity is presented. A convolutional neural network (CNN)-based approach is used to estimate the fractional composition of two-phase dielectric mixtures inside a resonant cavity using scattering parameter (S-parameter) measurements. A rectangular cavity sensor with a strip feed structure is characterized using a vector network analyzer (VNA) from 0.01--20~GHz. The CNN is trained using both simulated and experimentally measured S-parameters and achieves high predictive accuracy even without de-embedding or filtering, demonstrating robustness to measurement imperfections. The simulation results achieve a coefficient of determination ($R^2$)=0.99 using $k$-fold cross-validation, while the experimental model using raw data achieves an $R^2=0.94$ with a mean absolute error (MAE) below 6\%. Data augmentation further improves the accuracy of the experimental prediction to above $R^2=0.998$ (MAE$<$0.72\%). The proposed method enables rapid, non-destructive, accurate, low-cost, and real-time estimation of material fractions, illustrating strong potential for sensing applications in microwave material characterization.

Figures (7)

• Figure 1: The CNN architecture consists of two 1D convolutional layers, interleaved with max-pooling layers, and two fully connected layers at the end. The input data is a 1D array of size 1002 × 8 per sample.
• Figure 2: The 3D sensor geometry used for the full-wave electromagnetic simulations in CST Studio Suite. The structure consists of a rectangular cavity with dimensions of 40 mm$\times$20 mm$\times$40 mm ($a \times b \times h$), featuring a centrally located aperture on the top surface measuring 20 mm$\times$2 mm ($d \times w$). A strip line of size 14 mm$\times$5 mm ($l \times s$) is positioned 1.9 mm above the cavity lid, oriented perpendicular to the longer side of the aperture shour
• Figure 3: The training and validation (a) losses and (b) MAEs of the CNN using simulated data averaged over five folds.
• Figure 4: Measurement setup for the binary material volume fraction sensor.
• Figure 5: (a) Solid lid (without aperture) used to de-embed the S-parameters up to the aperture edges. (b) Empty rectangular cavity with the perforated lid used for measuring the S-parameters of the empty sensor and the sensor loaded with the MUT.