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

Abstract

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.

A dimensionality reduction approach in helicopter level flight performance testing

“…This approach was proven more accurate (in excess of 300%) in the prediction of the available power of a helicopter under a wide range of atmospheric conditions, as compared to the conventional flight test method [12]. This multivariable approach was also used successfully in the prediction of the helicopter hover performance [13]. Taking this multivariable approach reduced the average prediction error by about 47% compared to the conventional flight test method for hover performance.…”

“…Arush et al [12][13][14] presented an alternative approach to helicopter performance flight testing, using multivariable polynomials as empirical models. This approach was proven more accurate (in excess of 300%) in the prediction of the available power of a helicopter under a wide range of atmospheric conditions, as compared to the conventional flight test method [12].…”

“…The proposed CVSDR method is aimed at addressing all identified drawbacks of the conventional method, specified as items (1) to (5) above, while providing an even more accurate prediction for power required in level flight. The CVSDR method is expanded to accommodate a more complicated helicopter performance problem than the hover performance [13]. Abstractly, the current paper can be regarded as a rigorous expansion of hover CVSDR method into a higher dimensional space of level-flight performance.…”

“…In this particular demonstration, the three repeating variables are the ambient static temperature (Ta), the helicopter gross weight (W ) and the main rotor disk area (Ad). The five ND products (ψ) are defined in Equation (13). According to Buckingham [20], the repeating variables should be raised to some arbitrary powers, those are denoted as a 1 , b 1 , c 1 ,.…”

“…. ., c 5 in Equation (13). As demonstrated hereinafter, these arbitrary powers are identified as those numeric values that make the ψ products non-dimensional.…”