In this article, the problem of distributed generalized Nash equilibrium (GNE) seeking in noncooperative games is investigated via multiagent networks, where each player aims to minimize his or her own cost function with a nonsmooth term. Each player’s cost function and feasible action set in the noncooperative game are both determined by actions of others who may not be neighbors, as well as his/her own action. Particularly, feasible action sets are constrained by private convex inequalities and shared linear equations. Each player can only have access to his or her own cost function, private constraint, and a local block of shared constraints, and can only communicate with his or her neighbours via a digraph. To address this problem, a novel continuous-time distributed primal–dual algorithm involving Clarke’s generalized gradient is proposed based on consensus algorithms and the primal–dual algorithm. Under mild assumptions on cost functions and graph, we prove that players’ actions asymptotically converge to a GNE. Finally, a simulation is presented to demonstrate the effectiveness of our theoretical results.

For the rotating machinery system, it is a challenge to explore fault detection and diagnosis for multiple-faults condition, which simultaneously contains faulty bearing components and faulty gear components. In the study, a fault feature separation and extraction approach is proposed for the bearing-gear fault condition through combining empirical mode decomposition (EMD), Hilbert transform (HT), principal component analysis (PCA), independent component analysis (ICA) techniques. Firstly, EMD is implemented to decompose the single sensor signal to obtain multiple sub-band signals termed as the intrinsic mode functions (IMFs). Secondly, the most relevant IMFs to bearing and gear fault features are selected to construct multiple-channels model with the help of the simulated bearing and gear fault signals. Thirdly, HT is utilized to compute marginal Hilbert spectrum (MHS) for each IMF in multiple-channels model, to construct an MHS matrix. Finally, some statistically independent components are obtained by decomposing the MHS matrix with PCA and ICA, and multiple fault features are identified from these components. The experimental application of the proposed method is put into a bearing-belt-gearbox union machinery system to evaluate its validity. The experimental analysis results indicate that the proposed method is effective to separate and extract a bearing fault and a gear fault for two types of compound bearing-gear fault conditions.

The prediction of remaining useful life (RUL) is one of the important measures to ensure the safety and reliability of mechanical equipment. Aiming at the low accuracy of residual life prediction caused by difficulty in feature extraction from high data redundancy in the monitoring process of rotating machinery, an RUL prediction method based on data feature distribution and spatial attention residual network (SARN) is proposed. In the proposed method, multi-sensor data is segmented utilizing distribution feature difference analysis, so as to highlight the degradation characteristics in the sample sequence. Combined with the proposed SARN based on a spatial attention mechanism and residual network, more extensive and complementary features can be extracted. It not only focuses on the importance screening of feature information from all input data, but also realizes the mapping between global sample features and labels, to improve the accuracy of RUL prediction. Finally, the method is verified by the experiments on PHM2012 and C-MAPSS datasets. The results indicate that, compared with the CNNLSTM method on C-MAPSS dataset, the proposed method has an average reduction of 14.37% in MAE index, and an average increase of 22.59% in R2 index. This shows that the proposed method has satisfied RUL prediction performance for rotating machinery.