Transformers are indispensable critical equipment in power systems, and their fault prediction and diagnostic technologies hold significant importance for electrical grids. Regarding transformer fault prediction, the detection and analysis of dissolved gases in oil have emerged as an effective and widely applied method. This study investigates the mechanisms of transformer faults in relation to the generation of dissolved gases in oil and their composition. It utilizes the Random Forest algorithm and Particle Swarm Optimization (PSO-RF) to construct a transformer fault prediction model based on dissolved gas components in oil. The model is validated and analyzed using real-world datasets. Experimental results demonstrate that the PSO-RF prediction model performs exceptionally well on the test set, accurately predicting low-energy discharge, high-energy discharge, and overheating faults across different temperature ranges. This validates the close relationship between dissolved gas components in oil and transformer fault types, as well as the effectiveness and practicality of the proposed prediction method.