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.

中文翻译：

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直升机燃气涡轮发动机飞行试验分析中的奇异值法

经验模型评估过程是实验飞行测试数据分析的核心业务。直升机发动机可用功率的准确和方便的飞行测试对于预测直升机的总体性能至关重要。估计飞行中直升机燃气涡轮发动机功率的常见做法包括将飞行测试数据简化为简单的单变量分析方法。虽然这种方法便于实际使用，但它经常导致对可用发动机功率的不切实际的预测。解决直升机可用功率问题的一种新方法是所谓的约束条件下的多变量多项式优化方法。在该方法中，由发动机无量纲参数构建的 18 个回归量用于定义经验多项式模型。本文旨在补充约束条件下的多变量多项式优化方法，并回答以下问题：哪种多变量多项式可以普遍用于表示直升机燃气轮机发动机的性能？从这个意义上说，分析了安装在不同直升机上的七种燃气涡轮发动机，每一种都提供了 512 个可能的多项式模型，用于可用功率计算。虽然传统的假设检验统计方法未能回答上述问题，即代表发动机性能的最佳一般经验模型是什么，但基于奇异值分解定理的替代方法被证明成功地提供了回答。而且，