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The natural distribution of industrial data is imbalanced, which deteriorates the performance of intelligent fault diagnostic models. Although cost-sensitive learning is an effective method for solving the data imbalance problem, it suffers from the difficulty of setting optimal costs. Therefore, this paper proposes a strategy that considers the number distribution of samples, the convergence trend of classes, and the convergence trend of samples to calculate sample costs adaptively. Using costs to weigh the sample losses and applying them to different models and different loss functions, the diagnostic results under different sample sets show that the weighted losses can significantly improve the model's performance when using imbalanced data. By further analysing the training loss of the modified model, the angles between deep features, and the angles between deep features and classification weight vectors, it can be found that the dominance of majority classes in imbalanced data is suppressed in training, which is attributed to the loss of each class being coordinated by the proposed strategy. The comparison with various imbalanced learning methods demonstrates the advantages of the proposed method under conditions of large imbalance ratios and complex tasks. • A novel cost-adaptive calculation method is proposed. • The cost varies adaptively with the sample distribution, the sample convergence trend, and the category convergence trend. • By applying the sample cost to the loss function, the losses of each class are coordinated. • Results with different models, different loss functions, and different datasets show the flexibility of the proposed method. [ABSTRACT FROM AUTHOR]

Because the fault characteristic frequencies of a rolling bearing are submerged in strong noise when it fails early, the fault feature in the original signal is relatively weak to allow the diagnosis of the bearing. Consequently, the method to extract a weak fault feature is becoming a challenging research topic in fault diagnosis. Traditional diagnostic networks are typically trained by the time series or the frequency spectrum of the acquired discrete signal fragment, whereas the connection of the local fragments (quasi-periodicity) is neglected, resulting in low diagnostic accuracy for the bearing under strong noise conditions. To solve this problem, a novel weak fault feature extraction and diagnosis method, composed of two parts, is proposed in this paper. The first part is a multi-channel continuous wavelet transform (MCCWT), by which the original temporal signals can be more easily transformed into a new representation with several channels and fewer network parameter requirements than those required by the traditional methods. The second part is a convolution-feature-based recurrent neural network (CFRNN) that is based on a traditional recurrent neural network (RNN). In the latter, a recurrent unit combining several residual blocks and a long short term memory (LSTM) block is proposed to mine the temporal features and the local vibration characteristics simultaneously. The efficiency of the proposed diagnosis method is validated respectively by the datasets collected by simulating fault bearings with strong noise and using real fault bearings containing faults at an early stage. • The quasi-periodicity is considered in the proposed weak fault diagnosis method. • A multi-channel representation method is proposed to keep the details in signal. • Residual blocks were used to interpret the local time–frequency characteristics. • The efficiency was validated by simulated fault bearings and real fault bearings. [ABSTRACT FROM AUTHOR]

Imbalance is a typical characteristic of data in the field of intelligent fault diagnosis. As a data augmentation method that both balances data and extends information, the generative adversarial network has aroused widespread concern in the data imbalance problem. However, it still suffers from high difficulty in model training and poor quality of generated samples. To address this issue, this paper proposes a progressive generative adversarial network, which is a strategy able to gradually generate complex signals from low-frequency signals to wide-frequency signals. In the developed network, on the one hand, decomposing signals into different frequency bands explicitly reduces the difficulty of directly generating high-dimensional and wide-frequency signals. On the other hand, different generative models can focus on different frequency bands, avoiding the interference of high-energy signals on the fault feature frequencies. In order to achieve good generative performance, the generators and training method for the progressive generative adversarial network are elaborately designed. The correlation shortcut avoids information suppression due to the poor selection of noise amplitudes, and the focusing shortcut forces the body of the generator to focus on key feature bands. Ultimately, the superiority of the progressive generative network is verified by evaluating the quality of the generated samples on three datasets and applying the generated samples to solve the data imbalance problem. • A progressive generation framework is proposed to improve the quality of the generated signal. • The proposed generator retains the correlation between low and high frequencies. • The proposed generator can focus on specific frequency bands. • Model at each level is trained independently to avoid the accumulation of errors. [ABSTRACT FROM AUTHOR]

The performance of intelligent fault diagnosis models is often hindered by the lack of available samples, a common issue in both the few-shot learning and imbalanced learning problems. While data generation has been shown to be an effective strategy for addressing this issue, existing methods tend to focus solely on the similarity of the generated samples, overlooking their diversity. In this regard, a self-reasoning training strategy that enables the participation of highly reliable generated samples in the training process is proposed. By augmenting the training samples, the strategy provides the generation model with diverse input information, effectively enhancing the diversity of the samples generated by the model. To assess the reliability of the generated samples, Pearson correlation coefficient between the generated and real samples in the amplitude–frequency domain is utilized. To this end, an amplitude–frequency domain generation model is constructed. In order to avoid issues such as gradient disappearance and convergence degradation during the generation process in the amplitude–frequency domain, a phase-frequency domain generation model as well as a time domain discriminator model are developed. While the phase-frequency domain generation model enhances the diversity of the generated samples in that domain, the time domain discriminator model ensures sample similarity by correlating the amplitude–frequency domain generation model with the phase-frequency domain generation model. Through experiments, it is demonstrated that the proposed method can effectively address the overfitting problem of generative adversarial networks with few samples, improving the diversity of the generated samples. Moreover, the improvement in fault diagnosis performance achieved by the samples generated by the proposed method further underscores its potential and superiority in practical applications. • A self-reasoning training strategy is proposed. • A generation model driven by multi-domain information is developed. • The quality (similarity and diversity) of the generated samples is enhanced. [ABSTRACT FROM AUTHOR]