Метод визначення невимірюваних параметрів газотурбінних двигунів з урахуванням зміни технічного стану

The subject of this study is the estimation of non-measurable parameters of a gas turbine engine's operating process based on a limited set of measured parameters. The relevance of this research arises from the practical impossibility of measuring several critical engine parameters under operating conditions, such as thrust, turbine inlet gas temperature, among others, which are essential for control and diagnostics tasks. These parameters must be continuously estimated using only limited available data. This requires the use of a mathematical model of the engine's operating process, with consideration of measurement noise, the restricted set of measured parameters, and the influence of the engine’s technical condition. The proposed approach does not require the estimation of the full vector of internal health parameters. Instead, it focuses on the direct estimation of non-measurable quantities, which reduces computational complexity and prevents error accumulation during calculation. The objective of the study is to develop a method that minimizes the estimation error of the target non-measurable parameter under the conditions of limited measurements, multicollinearity in the mathematical model, and varying measurement accuracy. To achieve this, matrix algebra methods are employed, including pseudoinverse matrices, singular value decomposition (SVD), and weighted least squares (WLS). The following results have been obtained: a formulation of the optimal estimation problem for engine parameters at steady-state modes; an analytical solution representing the target transformation matrix as a product of matrices, where each factor separately accounts for the relation between measured and non-measurable parameters and the influence of measurement noise; and a demonstration that the proposed method provides high numerical stability. The scientific novelty lies in formulating the problem in a way that avoids estimating the full state vector and in applying a condition number minimization procedure by discarding small singular values. The practical value of the method lies in its applicability to both direct control algorithms based on non-measurable parameters, and onboard estimation and diagnostic algorithms that operate effectively with limited measurement data and under constrained computational resources.