Abstract: As a core component of China's energy structure, coal has long played an irreplaceable role in many fields such as power production, industrial heating and residential life, among which coal-fired boilers are the key equipment for coal utilization, and their performance and efficiency directly affect the effective use of energy and the effectiveness of environmental protection. With the promotion of the global goal of "carbon peak and carbon neutrality", boiler technology continues to innovate and develop, and the system structure becomes more and more complex, making it more susceptible to various factors such as fuel quality, air supply, furnace design, and operating condition adjustment during operation, which in turn leads to the problem of combustion instability. Unstable combustion will not only lead to a decrease in the thermal efficiency of the boiler and an increase in energy consumption, but also may lead to safety accidents and pose a threat to personal safety and the environment. Therefore, it is necessary to identify the instability of boiler combustion in time and take targeted solutions. In order to comprehensively understand the research status and development trend of combustion stability discrimination methods and promote the safe and efficient operation of boiler systems, this paper deeply analyzes the basic principles of combustion instability, including the definition of combustion stability, the factors affecting combustion stability, and the discrimination indicators of combustion stability. The combustion stability discrimination method based on index identification can intuitively reflect the combustion stability status by analyzing the characteristics of specific physical signals. Combined with artificial intelligence technology, the method of judging combustion stability has the advantages of high accuracy, strong real-time and strong adaptability, and through the training of neural networks and other models, the complex laws in the combustion process are automatically learned from a large amount of data, so as to realize intelligent combustion stability discrimination and prediction. The numerical simulation method for determining combustion stability has the advantages of low cost, high efficiency and good repeatability, and the mathematical model and simulation platform of the combustion process are constructed to simulate the combustion process under different working conditions, and the influencing factors and changes of combustion stability are analyzed.