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The measurement of instantaneous angular speed is being increasingly investigated for its use in a wide range of condition monitoring and prognostic applications. Central to many measurement techniques are incremental shaft encoders recording the arrival times of shaft angular increments. The conventional approach to processing these signals assumes that the angular increments are equidistant. This assumption is generally incorrect when working with toothed wheels and especially zebra tape encoders and has been shown to introduce errors in the estimated shaft speed. There are some proposed methods in literature that aim to compensate for this geometric irregularity. Some of the methods require the shaft speed to be perfectly constant for calibration, something rarely achieved in practice. Other methods assume the shaft speed to be nearly constant with minor deviations. Therefore existing methods cannot calibrate the entire shaft encoder geometry for arbitrary shaft speeds.The present article presents a method to calculate the shaft encoder geometry for arbitrary shaft speed profiles. The method uses Bayesian linear regression to calculate the encoder increment distances. The method is derived and then tested against simulated and laboratory experiments. The results indicate that the proposed method is capable of accurately determining the shaft encoder geometry for any shaft speed profile.1 The term 'zero-crossing time' is sometimes used exclusively to indicate the exact time a signal changes sign, like a sine wave passing through 0 V. For the purposes of this article and related literature [6], the term 'zero-crossing time' is used to indicate the exact time a signal has passed a prescribed threshold value (2.5 V in the case of TTL signals).

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Blade tip timing (BTT) is a noncontact method for measuring turbomachinery blade vibration. Proximity sensors are mounted circumferentially around the turbomachine casing and used to measure the tip displacements of blades during operation. Tip deflection data processing is nontrivial due to complications such as aliasing and high levels of noise. Specialized BTT algorithms have been developed to extract the utmost amount of information from the signals. The effectiveness of these algorithms is, however, influenced by the circumferential spacing between the proximity sensors. If the spacing is suboptimal, an algorithm can fail to measure dangerous blade vibration. This paper presents a novel optimization approach that determines the optimal spacing between proximity sensors.