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Rotating machinery has been developed with high complexity and precision, and bearings and gears are crucial components in the machinery system. Deep learning has attracted considerable attention from researchers in this area. The convolutional neural network (CNN) is a typical deep learning model that has a strong capability for automatically extracting features from raw data. This capability minimizes dependence on expert knowledge during feature extraction and selection. In CNN, hyperparameters, such as activation functions, can directly influence the performance of the model. In this study, the improved rectified linear units (ReLU)-CNNs are proposed for machinery fault diagnosis. The model's input are raw vibration signals without feature extraction and selection. It is experimentally validated for fault diagnosis using bearing and gearbox datasets. Results show that the proposed method can obtain satisfactory accuracy with enhanced convergence speed. For both datasets, the proposed method gives better diagnosis accrues than the other compared models. The proposed model can take advantages of standard ReLU-CNN, and these advantages can overcome traditional activation functions' vanishing gradient problems. Meanwhile, the improved ReLU-CNN has a new property that makes it perform better than the standard ReLU-CNN.

In this paper, we have experimentally demonstrated a secure 100 Gb/s intensity-modulation and direct-detection transmission over 100 km standard single-mode fiber (SSMF) based on quantum noise stream cipher (QNSC) for the first time. The original 4-level pulse-amplitude modulation (PAM4) data is mapped to M-level data sequence randomly, and quantum noise such as the generated amplified spontaneous emission noise and the shot noise in the channel can mask these adjacent signal levels. The legitimate receiver needs to distinguish not M-level encrypted data but 4-level data with the shared key. In our scheme, a calculated detection failure probability of 98.72% is achieved. Apparently, more quantum noise contributes to higher security but the worse signal to noise ratio. To balance algorithm complexity, transmission performance and security performance, a sparse ℓ1 regularization based on recursive least square (RLS) algorithm is proposed and firstly used in Volterra equalizer. To eliminate the power fading induced by fiber dispersion, a dual-drive Mach-Zehnder modulator is used to achieve single-sideband modulation, and no dispersion compensation is required. By these means, 100 Gb/s PAM4-QNSC signal transmission over 100 km SSMF with the bit error rate (BER) below the 7% overhead hard-decision forward error correction threshold of 3.8 x 10-3 is achieved, and >59% complexity reduction of Volterra equalizer is realized. Moreover, the measured BER of 150 Gb/s PAM8-QNSC signal transmission over 50 km SSMF could go below the 20% overhead soft-decision forward error correction threshold of 2.0x10-2. The results validate that the proposed scheme is effective to realize low-cost, high-speed (>100 Gb/s), and secure optical fiber transmission in the data center.

Sparse representation is the important principle of unsupervised learning method. In order to accurately identify the fault condition of machines, the desired feature distribution should show population sparsity and lifetime sparsity. In this paper, to improve the accuracy and robustness of the classification, a novel fault diagnosis method named Cross-sparse Filtering (Cr-SF) is proposed based on the cross l1/2-norms of the feature matrix, which mean the population sparsity and lifetime sparsity terms. After the weights training process, a novel nonlinear activation function is used for feature extraction in the test process. Cr-SF can learn discriminative features from the raw data and accurately identify the fault condition. Rolling bearing fault and gear-box fault datasets are employed to validate the performance of the proposed method. The verification results confirm that Cr-SF is an effective tool for handling big data. The robustness and accuracy of the classification results using Cr-SF are comparable to convolutional networks with a much faster training process.

Tacholess order tracking techniques based on time-frequency (TF) ridge detection have been extensively used in bearing fault diagnosis under varying speed conditions for decades. However, the signal components of a fault bearing related to shaft rotational frequency (SRF) is difficult to be accurately extracted by these methods because of TF resolution limitation and strong noise interference. A new TF decomposing algorithm, that is, variational nonlinear chirp mode decomposition (VNCMD) is effective to extract the time-varying feature under limited TF resolution. However, its performance is influenced by prior knowledge of initial parameters. Besides, ridge information hidden in noise is difficult to be mined effectively, which increases the difficulty of ridge extraction. In this study, a feature isolation technology is proposed to enhance fault-related features and reduce the interference of noise and irrelevant components. Then inspired by the decomposing properties research on the convergence characteristics of VNCMD, an optimization tendency guiding mode decomposition (OTGMD) method is proposed to track the instantaneous frequency (IF) of fault-related mode, which can alleviate the personnel experience requirement and is not affected by the set of TF resolution. The proposed method mainly consists of three steps. First, SRF-related information is highlighted through low-pass filtering, and the dominant IF is achieved through ridge detection method. Subsequently, for the convenience of mode extraction, the fault characteristic is augmented through iterative envelope analysis. Then, the OTGMD optimization strategy is developed to gradually decompose the target mode on the basis of the above process. Finally, a stopping criterion based on characteristic frequency ratios (CFRs) is constructed to adaptively terminate the iteration process. Simulation and experiments demonstrate that the proposed method is effective and suitable for bearing fault diagnosis under varying speed conditions.

Transfer learning based models have been employed for intelligent fault diagnosis under different working conditions. However, an actual and important problem is neglected in existing intelligent fault diagnosis methods, which is that target domain mechanical fault datasets are always highly imbalanced with abundant normal condition mechanical samples but a paucity of samples from rare fault conditions. To solve this actual problem, this paper proposed a novel adaptive cross-domain feature extraction (ACFE) method which can automatically extract similar features between different feature spaces. ACFE wants to obtain more information for determining the category of each training target sample, so it avoids the distribution adaptation and is suitable for the imbalanced problem. Specifically, high dimensional distance through kernel method is employed for ensuring the strong identify ability first. Then, for automatically extracting cross-domain feature, we calculate the posterior probability of category of each target domain training sample based on high dimensional distance, and employ entropy loss to capture the cross-domain information. Besides, we propose the guide loss to avoid the features of a category overall falling into false category caused by imbalanced dataset. Based on ACFE, the intelligent fault diagnosis method for dealing with the imbalanced target dataset is described. To verify the effectiveness, we carry out two specially designed experiments, and the results shows that, comparing with related method, the proposed method achieve a superior performance.

The problem of insufficient datasets has long been a hot topic in the field of prognosis and health management of rotary machines. Generative adversarial network (GAN) and other data augmentation algorithms can solve the problem of insufficient samples. However, the premise of the above method is the signal collected at a constant speed rather than at large speed fluctuation. To deal with data augmentation under large speed fluctuation, this article proposes an effective deep learning method, namely, domain adaptive efficient sub-pixel network (DAESPN). The core idea of DAESPN is to enhance the resolution of the original sample for data augmentation. The DAESPN framework is implemented as follows: after the data passes through the fully connected neural network, the multi-feature maps of the four channels are outputted. A group of high resolution (HR) features is obtained through the sub-pixel fully connected layer. In addition, maximum mean discrepancy (MMD) and mean square error (MSE) are used to construct the loss function of the model. Experimental results of gearbox and bearing datasets show that the DAESPN model has strong feasibility to carry out data augmentation for fault diagnosis of rotating machines under speed fluctuation condition. In addition, the feature learning process of DAESPN is visually displayed and analyzed.

Variational mode decomposition (VMD) has been widely applied to the field of machinery fault diagnosis due to its good time-frequency decomposition capability. However, the performance of the VMD for extraction of fault transient components is dependent on proper parameters in the method and is not satisfactory under noisy conditions. This paper proposes a new method, termed multi-bandwidth mode manifold (Triple M, TM), to extract the real fault transient components for fault diagnosis of rolling bearings. The new TM method unites multiple fault-related modes with different bandwidths by a nonlinear manifold learning algorithm. The modes with large bandwidths contain more fault-related information while those with small bandwidths contain less fault-unrelated components and noise. The advantages of different fault-related modes are fully used by the proposed method, leading to clear fault transients that facilitates the bearing fault detection. First, an efficiency-improved VMD method named recycling VMD (RVMD) is performed on the bearing signal repeatedly with different parameter values to obtain the fault-related modes with different bandwidths, i.e., the multi-bandwidth modes. Then, the manifold learning algorithm is carried out to extract the intrinsic manifold structure of bearing fault transient components from the multi-bandwidth modes. Finally, the bearing fault type is identified from the extracted feature with clear fault transients. The enhanced performance of the proposed method over the traditional methods is validated by a simulation analysis and two experimental applications of bearing defect identifications.

Currently, most of the vibration signal analysis methods for bearing fault diagnosis under varying speed conditions are based on the resampling technology with shaft rotational frequency (SRF). However, the SRF obtained by a fixed tachometer or time-frequency (TF) ridge detection reduces measuring flexibility or introduces errors inevitably. In this paper, a multi-band feature extraction method using coarse TF ridge-guided variational nonlinear chirp mode decomposition (VNCMD) is proposed for bearing fault diagnosis under varying speed conditions. Specifically, the proposed method is conducted as follows. First, the low-frequency component (LFC) and resonance component are extracted by the low-pass filtering and the fast kurtogram method, respectively, to alleviate the noise interference. Second, the coarse TF ridges are identified by a tractable ridge estimation method that is based on the TF representation for preliminary selection of the initial instantaneous frequency. Third, the coarse TF ridge-guided VNCMD is constructed to track the SRF and instantaneous fault characteristic frequency (IFCF) from the envelope signals of the LFC and the resonance component, respectively. Finally, the characteristic frequency ratio is computed on the basis of the values of SRF and IFCF to determine the fault type of ball bearing without resampling. The simulation studies and experimental verifications confirm that the proposed method can accurately locate bearing defect types and outperforms some existing methods.

Mechanical fault diagnosis is essential in ensuring the safety of production and economic development. In the field of fault diagnosis, deep learning has been extensively used due to its excellent feature learning ability. However, it still suffers from several issues; for example, 1) simultaneous requirements of features from multiple aspects, including sparsity and robustness, are hardly met due to the limited feature learning ability of a single model, and 2) most methods deal with preprocessed signals instead of original time domain signals because of the noise interference and deficiency of a single model. To solve these problems, this study proposes a new deep fusion network for fault feature learning, which combines two types of deep learning models, namely, sparse autoencoder and contractive autoencoder, which are respectively applied to enhance features' sparsity and robustness and thereby guarantee the representativeness of extracted features and gain strong anti-interference ability. Consequently, fault diagnosis with original time domain signals can be realized. Bearing and gearbox fault diagnosis experiments are conducted to verify the performance of the presented network. Results show that the diagnosis accuracies for two cases are higher than those of networks based on single contractive autoencoder and sparse autoencoder. These results demonstrate that the proposed fusion network has superior feature learning ability relative to single model networks and can deal with original time domain signals by simultaneously enhancing features' sparsity and robustness.

To perform bearing fault diagnosis under variable speeds, the optimal resonant frequency (ORF) band selection and diagnosis strategy are pivotal. Indexes, such as kurtosis, crest factor (CF) and smoothness index (SI), are extensively used for guiding ORF selection. Due to that each index has unique advantages, the hybrid of such indexes has been developed. However, applications of the current index hybrid method are impeded by problems of: 1) ineffectiveness for signal corrupted by impulsive noises and 2) equal segmentation of frequency band with human intervention. This paper, therefore, firstly proposes a dual-guidance based scheme with an embedded tunable Q-factor wavelet transform (TQWT) to address the problems. The so-called dual-guidance scheme contains two guidance procedures: 1) the SI guided pre-process for obtaining weight vectors and 2) the index hybrid output guided scheme for ORF selection. The embedded TQWT is used for frequency band segmentation and sub-band signal acquisition without subjective interventions. With the proposed scheme, the ORF band can be determined for bearing fault feature extraction. Then, an algorithm for multiple instantaneous frequency (IF) ridge identification is exploited based on the peak search algorithm for diagnosis. To tackle the difficulty that, at each time instance, the amplitudes of IF ridges of interest do not always dominate the time frequency representation (TFR), a starting point search tactic with a synchronization step is explored. A diagnosis vector can subsequently be obtained by calculating the average ratios of the identified ridges and bearing fault diagnosis can then be done by matching the elements of the diagnosis vector with fault characteristic coefficient (FCC). Comparisons are performed to illustrate the superiority of the proposed method. The experimental analyses are also conducted to validate the proposed method for bearing fault diagnosis under variable speeds.

As a breakthrough in the field of machine fault diagnosis, deep learning has great potential to extract more abstract and discriminative features automatically without much prior knowledge compared with other methods, such as the signal processing and analysis-based methods and machine learning methods with shallow architectures. One of the most important aspects in measuring the extracted features is whether they can explore more information of the inputs and avoid redundancy to be representative. Thus, a stacked sparse autoencoder (SAE)-based machine fault diagnosis method is proposed in this paper. The penalty term of the SAE can help mine essential information and avoid redundancy. To help the constructed diagnosis network further mine more abstract and representative high-level features, the collected non-stationary and transient signals are preprocessed with ensemble empirical mode decomposition and autoregressive (AR) models to obtain AR parameters, which are extracted based on the intrinsic mode functions (IMFs) and regarded as the low-level features for the inputs of the proposed diagnosis network. Only the first four IMFs are considered, because fault information is mainly reflected in high-frequency IMFs. Experiments and comparisons are complemented to validate the superiority of the presented diagnosis network. Results fully demonstrate that the stacked SAE-based diagnosis method can extract more discriminative high-level features and has a better performance in rotating machinery fault diagnosis compared with the traditional machine learning methods with shallow architectures.