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.INDEX TERMS Prognostics and health management (PHM), condition monitoring, edge computing, bearing fault diagnosis, degradation assessment, perceptual hashing, wavelet packet transform, discrete cosine transform, symbolic aggregate approximation (SAX).
Anamorphic lenses, with different optical powers along the tangential plane and the sagittal plane, are calibrated in this paper. The imaging model for anamorphic lenses is introduced. Compared with the pinhole model, it has two more intrinsic parameters: the anamorphic distance and the anamorphic angle. The anamorphic lens has two optical centers: one is in the tangential plane and the other is in the sagittal plane. The distance between the two optical centers is the anamorphic distance. The anamorphic angle refers to the angle between the camera coordinates and the pixel coordinates in the CCD plane. Formulas determining the initial value of the anamorphic distance are provided. Two experiments are conducted for the anamorphic lens calibration. As a comparison, the anamorphic lens is calibrated using the anamorphic imaging model and the pinhole model, respectively. The calibration accuracy can be improved remarkably if the anamorphic imaging model is applied, and calibrated results for the anamorphic distance and the anamorphic angle are very stable for different positions of the calibration target, which shows the validity and effectiveness of the anamorphic imaging model for anamorphic lens calibration.
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