Victor Noster Kürschner

Accurate classification of two-phase gas-liquid flows is essential for reliable monitoring and control in industrial systems. Although several optical and machine-learning studies have been reported, most still focus on single wavelengths or isolated feature domains, lacking an integrated methodology that links sensor physics, feature extraction, and machine learning. This study addresses this gap by proposing the Multi-Feature Multi-Domain (MFMD) framework and its derived Optimal Feature and Method Selection (OFMS) guideline, providing a unified methodology to achieve high accuracy and model parsimony. The methodology was experimentally validated in horizontal air–water flows (five patterns: bubble, plug, slug, stratified, and wavy) using collimated near-infrared (NIR) sensors operating at 850, 980, and 1310 nm, selected for their distinct absorption sensitivities to interfacial, hybrid, and volumetric characteristics. Features were extracted from the time (Probability Density Function, PDF), frequency (Power Spectral Density, PSD), and time-frequency (Discrete Wavelet Transform, DWT) domains. This multi-domain feature set was processed by comparing feature selection (Recursive Feature Elimination, RFE) with transformation methods (Linear Discriminant Analysis, LDA, and Principal Component Analysis, PCA). Classification was performed using Support Vector Machine (SVM), k-Nearest Neighbors (kNN), Random Forest (RF), and Artificial Neural Networks (ANN). Results demonstrate that multi-wavelength fusion is essential for reliable flow discrimination. The RFE-based approach achieved 100% accuracy when combining all data sources, while supervised LDA significantly outperformed PCA by enhancing class separability. The resulting OFMS guideline consolidates these findings into a practical tool for selecting the most effective feature–classifier strategy, whether prioritizing maximum accuracy or a more parsimonious machine learning model.

Extended Kalman Filters (EKFs) are widely employed for attitude estimation using Magnetic and Inertial Measurement Units (MIMUs) in battery-powered sensing systems. In such applications, energy availability influences system operation, yet battery state information is commonly treated by external supervisory mechanisms rather than being integrated into the estimation process. This work presents an EKF-based formulation in which the battery State of Charge (SOC) is explicitly included as a state variable, allowing joint estimation of attitude and energy state within a single filtering framework. SOC dynamics are modeled using a low-complexity estimator based on terminal voltage and current measurements, while attitude estimation is performed using a Simplified Extended Kalman Filter (SEKF) tailored for embedded MIMU-based applications. The proposed approach was evaluated through numerical simulations under constant and time-varying load profiles representative of low-power electronic devices. The results indicate that the inclusion of SOC estimation does not affect the attitude estimation performance of the original SEKF, while SOC estimation errors remain below 8% for the evaluated load conditions with power consumption of approximately 0.1 W, consistent with wearable and small autonomous electronic platforms. By incorporating energy state estimation directly into the filtering structure, rather than treating it as an external supervisory task, the proposed formulation offers a unified estimation approach suitable for embedded MIMU-based systems with limited computational and energy resources.