Bevel-helical gear units B3 Selection and ordering data continued Low spee B3-SH-22B

Flender/Flender Gear Units/Bevel-helical gear units B3

odes which may arise in signal sequences which have been generated under time-varying operating conditions. Individual mixture components may represent various, unobserved (latent) operating conditions. GMM models are fairly simple to implement, given that sufcient data are available for optimisation by means of expectation maximisation, and given that the length of the vector of random variables (length of the signal segment) does not give rise to very large dimensionalities. probability density distributions may be used to generate metric of similarity based on the natural logarithm of the likelihood of the observed sample [1]1. In this paper the negative natural logarithm of the likelihood (NLL) is used as measure of discrepancy. Dividing the signal into segments The time domain vibration signal is resampled at constant increments of the shaft angular position. Signal resampling is implemented with piecewise-cubic interpolation and is based on one pulse per shaft rotation tachometer reference signal. The resampled signal is subsequently cut into short signal segments by means of block windows. The window length and the extent to which the windows overlap inuence the resolution and sensitivity of the resulting NLL discrepancy signal. Longer window lengths offer more contextual information, however long window length also increases the dimensionality of the reference density distribution. High dimensional density distributions as estimated with GMMs are more subject to local minima during optimisation and also to data overtting, which may result in poor generalisation [1]. Long windows also result in increased smearing (reduced temporal resolution) of the NLL discrepancy signal. 1Please note that while probability and likelihood are related they are not interchangeable concepts. likelihood value is obtained from density distribution function when it is evaluated for specic realisation of continuous variable (or vector of variables). probability is obtaine