Eliminating the phase deviation caused by object motion plays a vital role to obtain the precise phase map to recover the object shape with phase-shifting-profilometry. Pixel-by-pixel phase retrieval using the least-squares algorithm has been widely employed to eliminate the phase deviation caused by moving object. However, pixel-level operation can only eliminate phase deviation within a limited range, and will bring high computational burden. In this paper, we propose an image-level phase compensation method with stochastic gradient descent (SGD) algorithm to accelerate the phase deviation elimination. Since the iteration calculation is implemented at the image-level, the proposed method can accelerate the convergence significantly. Furthermore, since the proposed algorithm is able to correct the phase deviation within (−π,π), the algorithm can tolerate a greater motion range. In addition to simulation experiments, we consider 2-D motion of the object, and conduct a series of comparative experiments to validate the effectiveness of the proposed method in a larger motion range.

Unknown faults may occur in practical applications, necessitating an open-set classifier that can classify known classes as well as recognize unknown faults. The current deep open-set classification methods are implicit in optimizing the intra-or inter-class distances, which may result in performance degradation when the number of unknown classes far exceeds that of the known. In this study, the discriminative angle deep features for vibration signals are investigated. A novel normalized one-versus-all classification loss with center and contrastive regularization is proposed. The trained network can explicitly optimize deep features to ensure intra-class compactness and inter-class divergence. In this case, such discriminative features can be used for open-set fault classification. Furthermore, the effectiveness of the proposed method is verified using field-measured motor bearing and gear vibration signals. The results demonstrate the evident advantages of our proposed method over other approaches in practical fault diagnosis scenarios.

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