As a representative deep learning network, Convolutional Neural Network (CNN) has been extensively used in bearing fault diagnosis and many good results have been reported. In Prognostics and Health Management (PHM) field, the CNN’s input size is usually designed as a 1D vector or 2D square matrix, and the convolution kernel size is also defined as a square shape like 3 × 3 and 5 × 5, which are directly adopted from the image recognition. Though satisfying results can be obtained, CNN with such parameter specifications is not optimal and efficient. To this end, this paper elaborated the physical characteristics of bearing acceleration signals to guide the CNN design. First, the fault period under different fault types and shaft rotation frequency were used to determine the size of CNN’s input. Next, an exponential function was involved in fitting the envelope of decaying acceleration signal during each fault period, and signal length within different decaying ratios was used to define the CNN’s kernel size. Finally, the designed CNN was validated with the Case Western Reserve University bearing dataset and Paderborn University bearing dataset. Results confirm that the physics-guided CNN (PGCNN) with rectangular input shape and rectangular convolution kernel works better than the baseline CNN with higher accuracy and smaller uncertainty. The feasibility of designing CNN parameters with physics-guided rules derived from bearing fault signal analysis has also been verified.

A locational error model for spatial features in vector-based geographical information systems (GIS) is proposed in this paper. Using error in points as the fundamental building block, a stochastic model is constructed to analyse point, line, and polygon errors within a unified framework, a departure from current practices which treat errors in point and line separately. The proposed model gives, as a special case, the epsilon band model a true probabilistic meaning. Moreover, the model can also be employed to derive accuracy standards and cartographic estimates in GIS.