In this paper, a ball mill gear reducer was regarded as the research object. Based on the HMM pattern recognition theory, DHMM methods that were used in fault diagnosis had been researched. The vibration signal was required a series transformations which are feature extraction, normalization, scalarization and quantization to get the sequence collections. Then the quantified sequence collections were trained to get the DHMM parameter, or the Viterbi Algorithm which was used for the quantified sequence collections to calculate the maximum probability, thereby the DHMM fault models library was established or the type of fault was recognized. Experiments of five kinds of fault model diagnosis were carried out in this article.

Deep neural networks (DNNs) with long-range dependence (LRD) have attracted more and more attention recently. However, LRD of DNNs is proposed from the view on gradient disappearance in training, which lacks theory analysis. In order to prove LRD of foggy images, the Hurst parameters of over 1,000 foggy images in SOTS are computed and discussed. Then, the Residual Dense Block Group (RDBG), which has additional long skips among two Residual Dense Blocks to fit LRD of foggy images, is proposed. The Residual Dense Block Group can significantly improve the details of dehazing image in dense fog and reduce the artifacts of dehazing image.