A singular values approach in helicopter gas turbine engines flight testing analysis

The process of empirical models evaluation is at the core business of experimental flight-testing data analysis. Accurate and convenient flight-testing of helicopter engine(s) available power is crucial for predicting the total helicopter performance. Common practice in estimation of in-flight helicopter gas turbine engine power consists of a reduction of flight-test data into simplistic single-variable analysis approach. While such an approach is convenient for practical use, it often results in unrealistic predictions of the available engine(s) power. A novel approach for the helicopter available power problem is the so-called Multivariable Polynomial Optimization under Constraints method. In this method, 18 regressors, constructed from the engine non-dimensional parameters, are used to define empirical polynomial models. This paper is intended to complement the Multivariable Polynomial Optimization under Constraints method and answer the question of which multivariable polynomial can be generally used in representing helicopter gas-turbine engine performance? In this sense, a variety of seven gas-turbine engines installed on different helicopters are analyzed, each one giving 512 possible polynomial models to be used for available-power calculations. While conventional statistical methods of hypothesis-testing failed in providing the answer to the question stated above of which the best general empirical model for representing engine performance is, an alternative approach based on the Singular-Value-Decomposition theorem, was proven successful in providing the answer. Moreover, this approach presented in the paper yielded a short list of 10 simple and convenient multivariable polynomials, best representing the performance of all seven engines analyzed as a group.

Unified integrals involving product of multivariable polynomials and generalized Bessel functions

The aim of this paper is to evaluate two integral formulas involving a finite product of the generalized Bessel function of the first kind and multivariable polynomial functions which results are expressed in terms of the generalized Lauricella functions. The major results presented here are of general character and easily reducible to unique and well-known integral formulae.

Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion

The power systems usually include a number of nonlinear receivers. Nonlinear receivers are the source of disturbances generated to the power system in the form of higher harmonics. The level of these disturbances describes the total harmonic distortion coefficient THD. Its value depends on many factors. One of them are the deformation and change in RMS value of supply voltage. A modern LED luminaire is a nonlinear receiver as well. The paper presents the results of the analysis of the influence of change in RMS value of supply voltage and the level of dimming of the tested luminaire on the value of the current THD. The analysis was made using a mathematical model based on multivariable polynomial fitting.

Helicopter gas turbine engine performance analysis: A multivariable approach

Helicopter performance relies heavily on the available output power of the engine(s) installed. A simplistic single-variable analysis approach is often used within the flight-testing community to reduce flight-test data in order to predict the available output power under various atmospheric conditions. This simplistic approach often results in unrealistic predictions. This paper proposes a novel method for analyzing flight-test data of a helicopter gas turbine engine. The so-called “Multivariable Polynomial Optimization under Constraints” method is capable of providing an improved estimation of the engine maximum available power. The Multivariable Polynomial Optimization under Constraints method relies on optimization of a multivariable polynomial model subjected to equalities and inequalities constraints. The Karush–Khun–Tucker optimization method is used with the engine operating limitations serving as inequalities constraints. The proposed Multivariable Polynomial Optimization under Constraints method is applied to a set of flight-test data of a Rolls Royce/Allison MTU250-C20 gas turbine, installed on an MBB BO-105 M helicopter. It is shown that the Multivariable Polynomial Optimization under Constraints method can predict the engine output power under a wider range of atmospheric conditions and that the standard deviation of the output power estimation error is reduced from 13 hp in the single-variable method to only 4.3 hp using the Multivariable Polynomial Optimization under Constraints method (over 300% improvement).