The Markov method is a common reliability assessment method. It is often used to describe the dynamic characteristics of a system, such as its repairability, fault sequence and multiple degradation states. However, the “curse of dimensionality”, which refers to the exponential growth of the system state space with the increase in system complexity, presents a challenge to reliability assessments for complex systems based on the Markov method. In response to this challenge, a novel reliability assessment method for complex systems based on non-homogeneous Markov processes is proposed. This method entails the decomposition of a complex system into multilevel subsystems, each with a relatively small state space, in accordance with the system function. The homogeneous Markov model or the non-homogeneous Markov model is established for each subsystem/system from bottom to top. In order to utilize the outcomes of the lower-level subsystem models as inputs to the upper-level subsystem model, an algorithm is proposed for converting the unavailability curve of a subsystem into its corresponding $2\times 2$ dynamic state transition probability matrix (STPM). The STPM is then employed as an input to the upper-level system’s non-homogeneous Markov model. A case study is presented using the reliability assessment of the Reactor Protection System (RPS) based on the proposed method, which is then compared with the models based on the other two contrast methods. This comparison verifies the effectiveness and accuracy of the proposed method.

Targeting the challenge of variable working conditions in bearing fault diagnosis, most of the fault diagnosis methods based on transfer learning focus on the transfer of knowledge, resulting in a poor diagnosis effect in the target domain. To solve the problem of transfer performance degradation, a multi-perception graph convolution transfer network (MPGCTN) is proposed. The MPGCTN is composed of a graph generation module, graph perception module, and domain discrimination module. In the graph generation module, a one-dimensional convolution neural network (1-D CNN) is used to extract features from the input, and then the structural features of samples are mined in the graph generation layer to construct the sample graph. In the following graph perception module, a multi-perception graph convolution network is designed to model the sample graph and learn the data structure information of the sample. Finally, in the domain discrimination module, the method is used to align the structural differences of the case graphs in different domains. Experimental results from experiments on Case Western Reserve University (CWRU) and Paderborn University (PU) bearing datasets show that the proposed method is effective and superior.