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Motivated by the description of the C*-algebra of the affine automorphism group N 6 , 28 of the Siegel upper half-plane of degree 2 as an algebra of operator fields defined over the unitary dual N 6 , 28 ˆ of the group, we introduce a family of C*-algebras, which we call almost C 0 ( K ) , and we show that the C*-algebra of the group N 6 , 28 belongs to this class. [ABSTRACT FROM AUTHOR]

Abstract: The first part of this series of papers addressed the theory, numerical implementation and parameter investigations of two further explored Vold–Kalman-filtering order-tracking techniques. A proposed tunable weighting factor for effectively distinguishing and separating both close and crossing order components of signals measured from rotary machines was implemented and examined. Additionally, parameters influencing waveform-tracking performance were investigated. Here, in the second paper of the series, geometric analysis to interpret dynamic signatures using order-tracking schemes is first summarised. To justify the effectiveness of applying developed techniques in practical works, three experimental tasks are accomplished. One is the separation of two close orders arising from flexible coupler imbalancing and gear meshing of a transmission-element test bench. The second task is the investigation of the dynamic characteristics of an electric scooter with a planetary gear set and four stages of speed-reduction gears using the implemented order-tracking techniques. The interactions between order components and structure resonances can be decoupled and distinguished precisely. The third task shows the successful ranking for different signature components of passby noise generated from an electric scooter with CVT transmission. This demonstrates the superiority of the angular-displacement Vold–Kalman-filtering order-tracking technique for analysing and interpreting dynamic signals arising from the operation of rotary machines. [Copyright &y& Elsevier]

Abstract: The papers explore and present advanced order-tracking techniques using the Vold–Kalman filter with a weighting factor to distinguish and separate both close and cross-order components in signals measured from rotary machines. In the first part of this series of papers, theoretical formulation, numerical implementation, and parameter investigation are performed. Especially, a weighting-factor parameter is further examined and implemented to tune and attain variant tracking filter characteristics. Significant comparisons to other conventional order-tracking schemes such as the windowed Fourier transform and the resampling method are made to highlight superior characters of the implemented techniques. Additionally, comprehensive parameter investigations, such as weighting factor, acquired reference shaft speed and noise/unwanted signature effects on tracking results, are also performed for guidelines upon using these techniques. Engineering applications on the noise–vibration–harshness concerns associated with a laboratory transmission-component test-bench and two types of electrical scooters are stated in the second part of the papers. [Copyright &y& Elsevier]