As a critical and fragile rotary supporting component in mechanical equipment, fault diagnosis of rolling bearing has been a hot issue. A rolling bearing fault diagnosis technique based on fined-grained multi-scale symbolic entropy and whale optimization algorithm-multiclass support vector machine (abbreviated as FGMSE-WOA-MSVM) is proposed in this paper. Firstly, the vibration signals are decomposed with fine-grained multi-scale decomposition, and the symbolic entropy of the sub-signals at different analysis scales are extracted and constructed as the multi-dimension fault feature vector. In order to address the problem of sensitive parameters for MSVM model, whale optimization algorithm (abbreviated as WOA) is introduced to optimize the penalty factor and kernel function parameters to construct the optimal WOA-MSVM model. Finally, Instance analysis is carried out with bearing fault dataset from Jiangnan University to verify the parameters influence and the effectiveness on the unbalanced sample set. The results show that compared with different feature vector inputs and learning models such as k-Nearest Neighbor (abbreviated as KNN), Decision Tree (abbreviated as DT), Random Forest (RF), etc., the proposed technique can achieve an accuracy rate of 99.33%, besides, the computation speed is fast and the diagnosis efficiency is high which means its potential value for engineering application.

In active heave compensation, in order to realize the smooth control of the heave compensation platform, it is necessary to use the ship motion measurement system to accurately obtain the ship displacement signal, invert the ship displacement signal, and then control the expansion and contraction of the electric cylinder so that the compensation platform remains horizontal. The ship displacement measurement system generally adopts the second integral of the acceleration sensor to obtain the ship displacement signal. During the acquisition process of the ship displacement signal, the quadratic integration process of the acceleration, and the communication process of the output control command, there is a processing lag which makes the error accumulate, resulting in a delay in the measurement of the ship motion. In order to collect the ship motion more accurately and control the heave compensation platform more precisely, this paper proposes a ship motion prediction method based on a variable step-variable sampling frequency characteristic LSTM (Long Short-Term Memory) neural network. First, we use the autocorrelation function algorithm to calculate the inherent delay of the lag in the process of signal acquisition by the measurement system. Secondly, the LSTM neural network is used to predict the inherent delay step of the lagging ship displacement signal. During the prediction process, it is found that the difference in the sampling frequency of the displacement signal will lead to a change in the step of the inherent delay—experiment in the laboratory to verify. By controlling the motion platform to simulate the motion of the ship and using the ship motion measurement system and the laser sensor system to measure the displacement signal of the motion platform synchronously, it is verified that the ship motion measurement system does have an inherent delay. Thirdly, on a sailing ship, ship displacement signals are collected by setting multiple sets of ship motion measurement systems. Finally, multiple sets of sampling frequency and multiple steps are set, and the ship motion is predicted based on the variable step-variable sampling frequency LSTM neural network. It is verified that the prediction accuracy is related to the sampling frequency of the signal collector and the prediction step of the LSTM neural network, which improves the prediction accuracy of the model and the timeliness of ship motion acquisition.

Deep learning can be applied in the field of fault diagnosis without an accurate mechanism model. However, the accurate diagnosis of minor faults using deep learning is limited by the training sample size. In the case that only a small number of noise-polluted samples is available, it is crucial to design a new learning mechanism for the training of deep neural networks to make it more powerful in feature representation. The new learning mechanism for deep neural networks model is accomplished by designing a new loss function such that accurate feature representation driven by consistency of trend features and accurate fault classification driven by consistency of fault direction both can be secured. In such a way, a more robust and more reliable fault diagnosis model using deep neural networks can be established to effectively discriminate those faults with equal or similar membership values of fault classifiers, which is unavailable for traditional methods. Validation for gearbox fault diagnosis shows that 100 training samples polluted with strong noise are adequate for the proposed method to successfully train deep neural networks to achieve satisfactory fault diagnosis accuracy, while more than 1500 training samples are required for traditional methods to achieve comparative fault diagnosis accuracy.

Federated learning is an effective means to combine model information from different clients to achieve joint optimization when the model of a single client is insufficient. In the case when there is an inter-client data imbalance, it is significant to design an imbalanced federation aggregation strategy to aggregate model information so that each client can benefit from the federation global model. However, the existing method has failed to achieve an efficient federation strategy in the case when there is an imbalance mode mismatch between clients. This paper aims to design a federated learning method guided by intra-client imbalance degree to ensure that each client can receive the maximum benefit from the federation model. The degree of intra-client imbalance, measured by gain of a class-by-class model update on the federation model based on a small balanced dataset, is used to guide the designing of federation strategy. An experimental validation for the benchmark dataset of rolling bearing shows that a 23.33% improvement of fault diagnosis accuracy can be achieved in the case when the degree of imbalance mode mismatch between clients is prominent.