The rolling bearing fault signals are complex time series with complex dynamic characteristics and non-uniform periodicity due to the influence of random interference, such as random impulse noise and equipment vibration. This will affect the accuracy of the diagnostis method. This paper analyses the characteristics of bearing fault signals and discussed the basic ideas of current diagnosis methods. In order to decrease the computational complexity in time series analysis process and reduce the influence of random interference in subsequent feature extraction, this paper proposes a rolling bearing fault diagnosis method base on periodic sparse attention and LSTM (PSAL) for non-uniform bearing vibration signals. According to the periodic characteristics of bearing fault, a periodic sparse attention network is proposed to decrease the time consumption in the process of reducing the influence of random interference and enhancing the feature. Then, LSTM is used to extract long-term dependence features in the fault signals. Finally, two sets of rolling bearing datasets are adopted to verify the validity and superiority of the proposed method by comparing with other methods.

Unsupervised domain adaptation is widely used for fault diagnosis under variable working conditions. However, loss oscillation and slow convergence, which are caused by the dynamically varying alignment of targets during domain adaptation, are ignored. Therefore, in this article, a Gaussian mixture variational-based transformer domain adaptation (GMVTDA) fault diagnosis method is proposed. A feature extractor based on transformer layers is designed to capture long-term dependence information and local features. Subsequently, a domain alignment term is proposed to project the features learned from both working conditions into the common assistance distribution and make them follow the same distribution after the alignment process. In addition, considering that fault diagnosis is a multiclassification process, a Gaussian mixture is utilized to build the common assistance distribution. Ultimately, the proposed GMVTDA is applied to bearing fault diagnosis under variable working conditions, and the experimental results prove its effectiveness.

Lack of massive-labeled samples may cause the performance degradation of intelligent bearing fault diagnosis methods under variable working conditions. Unsupervised domain adaptation (UDA)-based methods can effectively alleviate this problem by decreasing the distribution discrepancy between two dataset. However, most current UDA-based methods focus only on minimizing the marginal distribution. The influence of misclassification of samples near the classification boundaries is ignored. This may lead to the result that even though the marginal distributions are aligned well, the diagnosis accuracy is not ideal enough. On account of this, an unsupervised contrastive domain adaptation network (UCDAN) for bearing fault diagnosis under variable working conditions is proposed. A deep convolution feature extractor is constructed to extract high-level features. At the same time, a domain-adversarial total loss function based on the strategy of minimizing the domain distribution discrepancy is designed to obtain domain-shared discriminant features for aligning the marginal distribution. Moreover, a contrastive estimation term is designed to quantize the similarity of data distribution and maximize the consistency between the samples from the same health conditions. Thereby reducing the probability of samples being misclassified near or on the boundary and improving diagnosis performance. And information entropy is used to avoid most samples are assigned to the same cluster. The effectiveness of UCDAN is confirmed by examining various fault diagnosis situations with domain discrepancies across the source and target conditions, using experimental data from two bearing systems.

This brief is concerned with the design of the disturbance observer (DOB) in the presence of uncertain delay. The stability, robustness, and output performance of the DOB-based control system are studied. First, the zero exclusion criterion is used to study the stability of the characteristic equation with uncertain delay, and a method is proposed to determine the range of the uncertain delay that a given DOB-based control system can tolerate. The effect of the DOB on the stability is analyzed, and some guidelines are proposed to design a DOB-based control system for a process with a given range of uncertain delay. In addition, the disturbance rejection performance and robustness are analyzed. As a result, the method to design a DOB-based control system satisfying multiple objectives in the presence of uncertain delay and disturbance is proposed. Simulation examples show the effectiveness and merits of the proposed method, and the method is successfully used to control the fuel flow of a glass furnace.