This paper proposes a new method named composite multiscale fluctuation dispersion entropy (CMFDE), which measures the complexity of time series under different scale factors and synthesizes the information of multiple coarse-grained sequences. A simulation validates that CMFDE could improve the stability of entropy estimation. Meanwhile, a fault recognition method for rolling bearings based on CMFDE, the minimum redundancy maximum relevancy (mRMR) method, and the k nearest neighbor (kNN) classifier (CMFDE-mRMR-kNN) is developed. For the CMFDE-mRMR-kNN method, the CMFDE method is introduced to extract the fault characteristics of the rolling bearings. Then, the sensitive features are obtained by utilizing the mRMR method. Finally, the kNN classifier is used to recognize the different conditions of the rolling bearings. The effectiveness of the proposed CMFDE-mRMR-kNN method is verified by analyzing the standard experimental dataset. The experimental results show that the proposed fault diagnosis method can effectively classify the conditions of rolling bearings.

In the fault monitoring of rotating machinery, the vibration signal of the bearing and gear in a complex operating environment has poor stationarity and high noise. How to accurately and efficiently identify various fault categories is a major challenge in rotary fault diagnosis. Most of the existing methods only analyze the single channel vibration signal and do not comprehensively consider the multi-channel vibration signal. Therefore, this paper presents Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy (RCMMFDE), a method which extracts the recognition information of multi-channel signals with different scale factors, and the refined composite analysis ensures the recognition stability. The simulation results show that this method has the characteristics of low sensitivity to signal length and strong anti-noise ability. At the same time, combined with Joint Mutual Information Maximisation (JMIM) and support vector machine (SVM), RCMMFDE-JMIM-SVM fault diagnosis method has been proposed. This method uses RCMMFDE to extract the state characteristics of the multiple vibration signals of the rotary machine, and then uses the JMIM method to extract the sensitive characteristics. Finally, different states of the rotary machine are classified by SVM. The validity of the method is verified by the composite gear fault data set and bearing fault data set. The diagnostic accuracy of the method is 99.25% and 100.00%. The experimental results show that RCMMFDE-JMIM-SVM can effectively recognize multiple signals.

In the fault monitoring of rolling bearings, there is always loud noise, leading to poor signal stationariness. How to accurately and efficiently identify the fault type of rolling bearings is a challenge. Based on multivariate multiscale sample entropy (mvMSE), this paper introduces the refined composite mvMSE (RCmvMSE) into the fault extraction of the rolling bearing. A rolling bearing fault-diagnosis method based on stacked auto encoder and RCmvMSE (SDAE-RCmvMSE) is proposed. In the actual environment, the fault-diagnosis method use the multichannel vibration signals of the bearing as the input of stacked denoising autoencoders (SDAEs) to filter the noise of the vibration signals. The features of denoise signals are extracted by RCmvMSE and the rolling bearing operation-state diagnosis is completed with a support-vector machine (SVM) model. The results show that in the original test data, the accuracy rates of SDAE-RCmvMSE, RCmvMSE, and commonplace features of vibration signals combined with SVM (CFVS-SVM) methods are 99.5%, 100%, and 96% respectively. In the data with noise, the accuracy rates of RCmvMSE and CFVS-SVM are 97.75% and 93.08%, respectively, but the accuracy of SDAE-RCmvMSE is still 100%.

In this paper, composite multiscale weighted permutation entropy (CMWPE) is proposed to evaluate the complexity of nonlinear time series, and the advantage of the CMWPE method is verified through analyzing the simulated signal. Meanwhile, considering the complex nonlinear dynamic characteristics of fault rolling bearing signal, a rolling bearing fault diagnosis approach based on CMWPE, joint mutual information (JMI) feature selection, and k-nearest-neighbor (KNN) classifier (CMWPE-JMI-KNN) is proposed. For CMWPE-JMI-KNN, CMWPE is utilized to extract the fault rolling bearing features, JMI is applied for sensitive features selection, and KNN classifier is employed for identifying different rolling bearing conditions. Finally, the proposed CMWPE-JMI-KNN approach is used to analyze the experimental dataset, the analysis results indicate the proposed approach could effectively identify different fault rolling bearing conditions.

The common staged patterns are always required during the cutting process for separating a set of rectangular items from rectangular plates in manufacturing industries. Two‐staged patterns can reduce cutting complexity at the expense of material utilization; three‐staged patterns do the opposite. Combining these two types of staged patterns may be a good balance for two contradictory objectives of material utilization and cutting complexity. A heuristic approach is proposed to solve the two‐dimensional rectangular cutting stock problem with a combination of two‐staged general patterns (2SGP) and three‐staged homogenous patterns (3SHP). Firstly, the 2SGP and 3SHP are constructed by using recursive techniques. The pattern with the larger value is selected as the candidate pattern. Then, the value of each item is corrected according to the current candidate pattern. A cutting plan accurately satisfying all items demand is obtained by using the sequential heuristic algorithm. Finally, the cutting plan with a minimum number of used plates is achieved by applying the iterative algorithm. The computational results indicate that the proposed heuristic approach is more effective in material utilization and cutting complexity than the two published algorithms with staged patterns.