Monitoring Phase Increments in Fuel Supply Adjustment Based on Correlation Analysis of Indirect Measurement Data

Yenikieiev O. Yevsyukova F. Anatoliі B. Zakharenkov D. Martyniuk H. Zhaksigulova D.
February 2026 Modern Education and Computer Science Press

International Journal of Intelligent Systems and Applications
2026 #18 Issue 1 1 - 16 pp.

It is proposed to use correlation analysis methods to process indirect measurement data when monitoring the incremental сylindrical phase delays referenced to the first cylinder. A method is proposed for restoring the optimal parameters of stratified charge delivery to the combustion chambers of piston-type internal combustion engines. TThe conceptual framework for the development of software and hardware systems incorporating feedback control based on the state of the measurement signal, represented by crankshaft rotational irregularities, has been established. A deterministic mathematical model representing the torque transmission architecture of the powertrain is formulated as a mechanical system with three degrees of freedom, taking into account energy dissipation due to friction. The motions of the masses of the mathematical model are described by a deterministic system of linear differential equations. The parameters of these equations are normalised using the theorems and methods of similarity theory. The Laplace transform under zero initial conditions is applied to solve the resulting system of differential equations. Using the method of determinants and the Mathcad software environment, the information links between the cylinder torques and the signal of uneven rotation of the first crankshaft mass were established. In the Matlab software environment, special points were identified and a simplified representation of the torque transfer functions was obtained as a result of their analysis. A limited Fourier series using Mathcad software approximated the cylinder torques. A computational scheme was developed for simulating deterministic signals characterizing the rotational irregularity of the first crankshaft mass. The additive disturbance superimposed on the measurement signal is modeled as structured white noise with a frequency spectrum constrained to ten harmonic components. Within the computer modeling framework, the output signal generation utilizes an approach based on the regulation of information pathway lengths in neural network structures to define the gain coefficients corresponding to the aggregated torque amplitudes of individual cylinders. For the first time, an auxiliary algorithm was developed to monitor incremental phase delays of the cylinders relative to the reference (first) cylinder by calculating the mutual correlation function between the rotational irregularity signal of the first crankshaft mass and the torque output of the first cylinder. The software application for calculating the reciprocal correlation function is implemented in the program Mathcad. As a result of the analysis of the mutual correlation function graph, three distinct maxima were identified. The initial peak of the computed mutual correlation function corresponds to the phase associated with the nominal torque generation of the second combustion chamber. The second peak reflects the standard torque phase of the third chamber, while the third peak indicates the reference phase for the first combustion unit. Furthermore, the proportional values of these maxima align with the gain factors assigned to each cylinders torque in the computational summation scheme. The cross-correlation between the processed measurement signal and the torque signal of the first cylinder was evaluated under conditions of additive stochastic interference. Analysis of the correlation curve demonstrates that a measurement uncertainty of approximately 14% in the rotational non-uniformity of the primary crankshaft mass does not preclude the effective application of correlation analysis techniques for phase shift tracking in the fuel delivery timing across engine cylinders.

Hardware , Information Technology , Mathematical Model , Mutual Correlation Function , Non-uniformity of Rotation , Phase Increment , Software , Transfer Function , Uncertainty

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Mariupol State University, Department of System Analysis and Information Technologies, St. Preobrazhenska, 6/4, Kyiv, 03037, Ukraine
National Technical University «Kharkov Polytechnic Institute», Department of Technology of Mechanical Engineering and Metal-Cutting Machine Tools, 2, Kyrpychova str, Kharkiv, 61002, Ukraine
Private Higher Educational Establishment “European University”, Department of Computer Science and Software Engineering, Akademika Vernadskoho Blvd, 16V, Kyiv, 03115, Ukraine
Serikbayev East Kazakhstan Technical University, 19 D Serikbayev Str, Ust-Kamenogorsk, 070004, Kazakhstan
Faculty of Computer Science and Technology, National Aviation University, L. Guzara Avenue, 1, Kyiv, 03058, Ukraine
Department of System Analysis and Information Technologies, Mariupol State University, St. Preobrazhenska, 6/4, Kyiv, 03037, Ukraine

Mariupol State University
National Technical University «Kharkov Polytechnic Institute»
Private Higher Educational Establishment “European University”
Serikbayev East Kazakhstan Technical University
Faculty of Computer Science and Technology
Department of System Analysis and Information Technologies

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