Identification of gases by noise spectrum parameters based on the Einstein-Smoluchowski equation

Abstract

In this work, a mathematical model based on the Einstein–Smoluchowski stochastic equation describing the output voltage of gas sensors is presented. The Ornstein–Uhlenbeck stochastic process was used to analyze the noise spectrum of laser gas sensors, as a result of which it was proved that the output signal has the form of a Lorentz spectrum. The model allows us to determine the frequency spectrum of the output voltage, taking into account the diffusion and relaxation processes of the gas. Experimental studies have shown changes in time series and correlation parameters for various gases (air, methane, ethanol, ammonia). The proposed model can serve as a basis for creating digital twins of sensors and developing self-calibration systems.

The analytical approach establishes a relationship between stochastic fluctuations caused by molecular diffusion and the measurable spectral characteristics of the sensor output. Characteristic parameters of the Lorentzian spectrum, including spectral density, relaxation time, and correlation properties, were evaluated for different gaseous media. Comparative analysis demonstrates that each gas exhibits distinct noise signatures determined by its physical and diffusion properties, enabling reliable discrimination without introducing additional sensing elements. The proposed methodology improves the understanding of fluctuation-induced processes in laser gas sensors and provides a theoretical framework for noise-based gas identification. The obtained results may contribute to the development of intelligent gas sensing systems, real-time signal processing algorithms, and adaptive monitoring platforms for environmental, industrial, and safety applications.