Dissolved gas‐in‐oil analysis (DGA) is a powerful method to diagnose and detect transformer faults. It is of profound significance for the accurate and rapid determination of the fault of the transformer and the stability of the power. In different transformer faults, the concentration of dissolved gases in oil is also inconsistent. Commonly used gases include hydrogen (H₂), methane (CH₄), acetylene (C₂H₂), ethane (C₂H₆), and ethylene (C₂H₄). This paper first combines BP neural network with improved Adaboost algorithm, then combines PNN neural network to form a series diagnosis model for transformer fault, and finally combines dissolved gas‐in‐oil analysis to diagnose transformer fault. The experimental results show that the accuracy of the series diagnosis model proposed in this paper is greatly improved compared with BP neural network, GA‐BP neural network, PNN neural network, and BP‐Adaboost.

Extended logical Petri nets are proposed to improve logical Petri nets, and the related firing rules and state reachability graph are introduced. Their attributes, place arrival time, and priority function are defined for each token, batch processing wait time and transition firing duration are defined for each logical input/output transition, and firing duration is defined for each ordinary transition. Their token removal and generation functions are defined to operate the attributes and arrival time of tokens in places. A state in their reachability graph is redefined. They are used to model an e-commerce system. The reachability, time cost superiority of tokens with different priorities, and fairness of the resulting model are analyzed and correct end-states are illustrated.

B2C is a commercial retail model of e-commerce for selling products and services directly to consumers. To solve the credit risk issues in B2C e-commerce, in this paper, a credit risk game mechanism is proposed based on game theory and logical Petri nets theory. First, by combining logical Petri nets with game theory, a theoretical modeling method called the logical game Petri nets is proposed. To characterize the utility that each body gained during the competition processes using the least square method, utility functions that describe the relationships between enterprises in different business modes are derived; next, a logical game Petri net model to specify the interactions among different bodies in the enterprise competition module is constructed. To analyze the behavior of the competition module, a reachable marking graph for this logical game Petri net model is established. According to this reachable graph, a utility matrix is subsequently designed to obtain the maximum expected utility for the bodies; finally, through analysis of the logical game Petri nets model for the enterprise competition module, the local optimal utility, as well as the global optimal utility of the individuals and groups, can be guaranteed.