Deep belief network (DBN) is one of the most representative deep learning model. However, it has a disadvantage that the network structure and parameters are basically determined by experiences. In this paper, an improved quantum-inspired differential evolution, namely MSIQDE algorithm based on making use of merits of Mexh wavelet function, standard normal distribution, adaptive quantum state update and quantum non-gate mutation is proposed to avoid premature convergence and improve global search ability. Then the MSIQDE with global optimization ability is used to optimize the parameters of the DBN to construct an optimal DBN model, which is further applied to propose a new fault classification, namely MSIQDEDBN method. Finally, the vibration data of rolling bearings from the Case Western Reserve University and a real-world engineering application are carried out to verify the performance of the MSIQDE-DBN method. The experimental results show that the MSIQDE takes on better optimization performance and the MSIQDE-DBN can obtain higher classification accuracy than the other comparison methods.

Quantum-inspired differential evolution (QDE) is an evolutionary algorithm, which can effectively solve complex optimization problems. However, sometimes, it easily leads to premature convergence and low search ability and falls to local optima. To overcome these problems, based on the MSIQDE (improved QDE with multistrategies) algorithm, an enhanced MSIQDE algorithm based on mixing multiple strategies, namely, EMMSIQDE is proposed in this article. In the EMMSIQDE, a new differential mutation strategy of a difference vector is proposed to enhance the search ability and descent ability. Then, a new multipopulation mutation evolution mechanism is designed to ensure the relative independence of each subpopulation and the population diversity. The feasible solution space transformation strategy is used to achieve the optimal solution by mapping the quantum chromosome from a unit space to solution space. Finally, some multidimensional unimodal and multimodal functions are selected to demonstrate the optimization performance of EMMSIQDE. The results demonstrate that the EMMSIQDE is significantly better than the DE, QDE, QGA, and MSIQDE, and has better optimization ability, scalability, efficiency, and stability.

Bearing fault diagnosis is of significance to ensure the safe and reliable operation of a motor. Deep learning provides a powerful ability to extract the features of raw data automatically. A convolutional deep belief network (CDBN) is an effective deep learning method. In this article, a novel vibration amplitude spectrum imaging feature extraction method using continuous wavelet transform and image conversion is proposed, which can extract the image features with two-dimensional and eliminate the effect of handcrafted features under low signal-to-noise ratio conditions, different operating conditions, and data segmentation. Then, a novel CDBN with Gaussian distribution is constructed to learn the representative features for bearing fault classification. The proposed method is tested on motor bearing dataset with four and ten classifications. The results have been compared with other methods. The experiment results show that the proposed method has achieved significant improvements and is more effective than the traditional methods.