Aircraft Overloads Restoration by Measuring its Velocity and Orientation Angles Based on the Nonlinear Programming Method

Abstract

The paper considers application of the nonlinear programming method in solving the signal restoration problem. It assumes that the input signal could be represented as a weighted sum of elements of the given basis, after that the expansion coefficients are determined by the numerical optimization methods from the condition of the best fit to the system outputs. The problem of restoring overloads of an aircraft is solved, when the orientation angles and velocity projections in the normal coordinate system are known. Chebyshev polynomials and Hermite splines are compared as the basis for signals representation. The paper lists advantages and disadvantages of both the approaches to numerical solution of the selected problem. A modified Newton method is applied to determine the expansion coefficients. It assesses the influence of various types of measurement errors on the solution accuracy. Errors in assessing velocity projections distributed according to the normal law, constant errors in the velocities and yaw angles, as well as in the overloads boundary conditions are considered. The proposed method is not affected by constant errors in the velocity projections, and errors in the overloads boundary conditions provide a limited effect on the solution accuracy concentrated mainly at the beginning and end of the section. The solution quality deteriorates when introducing random noise into the velocity projections and constant errors into the yaw angle making it possible to compare selected methods of the signal approximation. The numerical experiment showed that the Chebyshev polynomials in the general case allow achieving a more accurate signal approximation than the cubic splines, despite the smaller number of parameters

Please cite this article in English as:

Korsun O.N., Korolev A.Yu., Stulovskiy A.V. Aircraft overloads restoration by measuring its velocity and orientation angles based on the nonlinear programming method. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2025, no. 3 (152), pp. 105--120 (in Russ.). EDN: NSQNYJ

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