Physics-Informed Two-Stage Learning Framework for Engine Ignition Frequency and RPM Estimation

Abstract

Accurate estimation of the ignition frequency (f0) of internal combustion engines is essential for non-invasive rotational speed (RPM) monitoring and condition diagnosis. In practice, domain shifts caused by sensor placement, vehicle-specific resonances, and environmental noise can distort the harmonic structure of f0, leading to multiple plausible spectral peaks within short analysis windows. A physics-informed, two-stage machine-learning framework is developed to estimate the ignition frequency of four-stroke engines using synchronized sound and vibration measurements. A nonlinear product signal (xprod(t) = xsound(t) xvib(t)) is introduced to emphasize ignition events jointly detected by both sensors, providing an additional representation for joint analysis of ignition-related components. Features are extracted from multiple signal representations, including the FFT, Envelope FFT, Cepstrum, Autocorrelation (ACF), and Envelope–ACF, and combined into a unified feature space capturing harmonic consistency, periodicity, and peak morphology. The framework consists of two learning stages. Stage 1 classifies global engine characteristics, including the cylinder count and ignition-frequency class. Stage 2 ranks local frequency candidates using a LightGBM-based LambdaMART ranker to identify the ignition frequency f0. Generalization performance is evaluated using Leave-One-Source-Out (LOSO) and Leave- One-Vehicle-Out (LOVO) protocols. Results show a mean LOSO accuracy of 95.5% for cylinder classification and a Top-1 accuracy of 84% within a ±5 Hz tolerance for candidate ranking, with mean frequency errors below 2 Hz (≈60 rpm). The model demonstrates consistent generalization behavior on unseen vehicles, indicating robustness to domain shifts across sensors and operating conditions. The proposed approach therefore provides an interpretable and practically applicable solution for non-invasive RPM estimation and establishes a foundation for real-time diagnostic applications on embedded automotive systems.