We study the extension of canonical correlation from pairs of random vectors to the case where a data sample consists of pairs of square integrable stochastic processes. Basic questions concerning the definition and existence of functional canonical correlation are addressed and sufficient criteria for the existence of functional canonical correlation are presented. Various properties of functional canonical analysis are discussed. We consider a canonical decomposition, in which the original processes are approximated by means of their canonical components.
Minimum entropy deconvolution (MED) is widely used in the gearbox fault diagnosis because it can enhance the energy of the impact signal. However, it is sensitive to single abnormal impulsive oscillation. This is because it takes kurtosis as the objective function and solves the optimal filter by iteration. In addition, the filter length is not adaptive and needs to be determined artificially. This paper proposes a maximum kurtosis spectral entropy deconvolution (MKSED) method and applies it to bearing fault diagnosis. Considering that the kurtosis spectral entropy has the advantage of highlighting the continuous impact oscillation, the kurtosis spectral entropy is chosen as the objective function of deconvolution. At the same time, kurtosis spectral entropy is also used as the fitness function of improved local particle swarm optimization algorithm (LPSO), and the filter length is optimized by LPSO, which makes that MKSED adaptively determines the length of the filter while solving the deconvolution, so that it can accurately extract the continuous pulse signal. The results of the simulation signal analysis show that the proposed MKSED method is superior to MED, and the proposed method is applied to bearing fault diagnosis, which verifies its ability to extract continuous impact.
In industrial production, it is highly essential to extract faults in gearbox accurately. Specifically, in a strong noise environment, it is difficult to extract the fault features accurately. LMD (local mean decomposition) is widely used as an adaptive decomposition method in fault diagnosis. In order to improve the mode mixing of LMD, ELMD (ensemble Local Mean Decomposition) is proposed as local mode mixing exists in noisy environment, but white noise added in ELMD cannot be completely neutralized leading to the influence of increased white noise on PF (product function) component. This further leads to the increase in reconstruction errors. Therefore, this paper proposes a composite fault diagnosis method for gearboxes based on an improved ensemble local mean decomposition. The idea is to add white noise in pairs to optimize ELMD, defined as CELMD (Complementary Ensemble Local Mean Decomposition) then remove the decomposed high noise component by PE (Permutation Entropy) while applying the SG (Savitzky-Golay) filter to smooth out the low noise in PFs. The method is applied to both simulated signal and experimental signal, which overcomes mode mixing phenomenon and reduces reconstruction error. At the same time, this method avoids the occurrence of pseudocomponents and reduces the amount of calculation. Compared with LMD, ELMD, CELMD, and CELMDAN, it shows that improved ensemble local mean decomposition method is an effective method for extracting composite fault features.
In the era of big data, data-driven methods mainly based on deep learning have been widely used in the field of intelligent fault diagnosis. Traditional neural networks tend to be more subjective when classifying fault time-frequency graphs, such as pooling layer, and ignore the location relationship of features. The newly proposed neural network named capsules network takes into account the size and location of the image. Inspired by this, capsules network combined with the Xception module (XCN) is applied in intelligent fault diagnosis, so as to improve the classification accuracy of intelligent fault diagnosis. Firstly, the fault time-frequency graphs are obtained by wavelet time-frequency analysis. Then the time-frequency graphs data which are adjusted the pixel size are input into XCN for training. In order to accelerate the learning rate, the parameters which have bigger change are punished by cost function in the process of training. After the operation of dynamic routing, the length of the capsule is used to classify the types of faults and get the classification of loss. Then the longest capsule is used to reconstruct fault time-frequency graphs which are used to measure the reconstruction of loss. In order to determine the convergence condition, the three losses are combined through the weight coefficient. Finally, the proposed model and the traditional methods are, respectively, trained and tested under laboratory conditions and actual wind turbine gearbox conditions to verify the classification ability and reliable ability.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.