High data throughput during real-time vibration monitoring can easily lead to network congestion, insufficient data storage space, heavy computing burden, and high communication costs. As a new computing paradigm, edge computing is deemed to be a good solution to these problems. In this paper, perceptual hashing is proposed as an edge computing form, aiming not only to reduce the data dimensionality but also to extract and represent the machine condition information. A sub-band coding method based on wavelet packet transform, two-dimensional discrete cosine transform, and symbolic aggregate approximation is developed for perceptual vibration hashing. When the sub-band coding method is implemented on a monitoring terminal, the acquired kilobyte-long vibration signal can be transformed into a machine condition hash occupying only a few bytes. Therefore, the efficiency of condition monitoring can benefit from the compactness of the machine condition hash, while comparable diagnostic and prognostic results can still be achieved. The effectiveness of the developed method is verified with two benchmark bearing datasets. Considerations on practical condition monitoring applications are also presented.

This paper provided thin lens aberrations for anamorphic lenses, including the central thin lens aberrations, the central Lagrange invariant shift, the central conjugate shift, and the central pupil shift. Based on thin lens theory and the paraxial lens module, the aberration of the anamorphic lens system can be easily corrected. The central Lagrange invariant shift can be used for aberration correction for an anamorphic zoom lens system. In order to make a concise expression for the central conjugate shift, eight aberration coefficients are introduced: ${\overline{D}}_{3x}$, ${\overline{D}}_{5x}$, ${\overline{D}}_{6x}$, ${\overline{D}}_{10x}$, ${\overline{D}}_{11y}$, ${\overline{D}}_{12x}$, ${\overline{D}}_{15x}$, and ${\overline{D}}_{16y}$. Similarly, four aberration coefficients are introduced for the central pupil shift: $D_{11x}$, ${\overline{D}}_{11x}$, $D_{16x}$, and ${\overline{D}}_{16x}$. A simulation is conducted that proves numerically the validity of the thin lens aberrations for an anamorphic lens system.

If the stop lies on the right of the anamorphic lenses, the entrance pupils in the tangential plane and the sagittal plane might not coincide with each other. In this condition, the anamorphic ratio will change according to the position of the object, which is not preferred in filming and machine vision. In view of this, a systematic approach for the paraxial design of anamorphic lenses with common entrance pupils is provided. Two basic types of anamorphic attachment are presented: basic anamorphic attachment and basic anamorphic zoom attachment. The anamorphic ratio can be changed by changing the interval distances between lens components if anamorphic zoom attachments are adopted. Formulas defining the interval distances between lens elements, the object position, the stop position, and the anamorphic ratio are derived. Illustrating figures and examples are also provided for each lens type.