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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]