A Generalized Process for Optimal Threshold Setting in HUMS

Abstract

Monitoring the health of a helicopter drive train enhances flight safety and reduces operating costs. Health and usage management systems (HUMS) monitor the drive train by using accelerometers to measure component vibration. Algorithms process the time domain vibration data into various condition indicators (CI), which are used to determine component health via thresholding. For the rotating machinery, a standard set of CI are shaft order one, two and three (i.e. 1, 2 or 3 times the shaft RPM). Shaft order one (SOI) is indicative of an unbalance, where as higher shaft order can be used to detect a bent shaft or misalignment condition. In the case of bearings, CIs are envelope spectrum or cepstrum analysis of the ball, cage, inner race and outer race frequencies. There are a number of standard CI used for gear analysis, such as line elimination and resynthesis, side band modulation, gear misalignment, etc. In general, some method is used to set thresholds for these CIs: when the threshold is exceeded, maintenance is recommended. The HUMS system must balance the risk of setting the threshold too high such that a component may fail in flight versus the risk of setting the threshold too low, which results in additional maintenance cost. This paper covers a generalized process of optimally setting threshold for CI and fusing the information into an Health Indicator. It can be shown that the distributions of CI for shaft magnitude and bearing envelop energy are Rayleigh distribution. The normalized distance functions for these CIs are a Nakagami distribution with mu (shape parameter) of n (number of CI) and Omega (scale parameter) of 2 x 1/(2-pi/2) x mu. For gear CIs, which are considered as Gaussian, the normalized distance function is again Nakagami, but with a mu of nil and Omega of n. Given the theoretical mu and Omega, a threshold for any set of CI can be generated resulting in system probability of false alarm (PFA). This is an optimal decision rule for detecting a component which is no longer nominal. The normalized distance distribution is a function of the component CI sample statistic. Procedures are developed to calculate the unbiased statistic: covariance for Rayleigh based CIs and mean value/covariance for Gaussian based CIs. In the cases where the population of components is not nominal (e.g. mass imbalances which violate the Rayleigh assumption) tools are presented to control this. For gear, normalizing transforms can be used to ensure the CIs are more Gaussian. Example data from utility helicopters are given.