Авіаційно-космічна техніка та технологія (Aug 2020)
ESTIMATION OF POWER OF TREND CRITERIA
Abstract
An approach to the selection and comparison of the criteria that are used in the analysis of time series of registration parameters of the technical camp of power and power plants based on gas turbine engines is proposed. The approach is based on established important characteristics of trending criteria, namely the power of such criteria, which are considered as criteria for distinguishing complex hypotheses. For analysis, we propose a statistical model for generating data in the form of a combination of deterministic trends and random components. A deterministic component is considered as a linear approximation of its expansion in a Taylor series. This assumption is justified by the need to show a trend in the shortest period of time at which the trend component allows a linear approximation. A random compound is taken as a sample of a general population of independent random variables that have a normal distribution. For analysis, the most common trend criteria were selected: Student's criterion for equality of means; Fisher dispersion ratio criterion; correlation criterion and its varieties. The supporting hypothesis has the form of belonging of a time series to a sample from the general set of independent random variables, and an alternative is belonging to a sample with a linear trend. Trend statistics of the relevant criteria generated on a moving or sectional disjoint analysis window of a given dimension. The trend development parameter was selected as the ratio of the trend growth during the analysis to the standard deviation of the random component. For the considered trend criteria, the obtained dependences of their power on the trend development parameter and the probability of an error of the first kind (erroneous alarm), as well as the operational characteristics of the criteria. The analysis was performed by the methods of analytical estimates and statistical modeling. It has been established that in the case of an alternative, the statistics of the correlation criterion and the Fisher criterion are quickly normalized, and student statistics do not change their type. A comparison of trending power criteria with equal values of the probability of an error of the first kind allows us to establish the advantage of the Student criterion, and the correlation criterion has the worst performance. Obtaining indicators of the power of trend criteria are important for applied applications since it allows you to establish the probability of the second kind of error (skipping a trend).
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