In today’s rapidly evolving manufacturing landscape with the advent of intelligent technologies, ensuring smooth equipment operation and fostering stable business growth rely heavily on accurate early fault detection and timely maintenance. Machine learning techniques have proven to be effective in detecting faults in modern production processes. Among various machine learning algorithms, the Backpropagation (BP) neural network is a commonly used model for fault detection. However, due to the intricacies of the BP neural network training process and the challenges posed by local minima, it has certain limitations in practical applications, which hinder its ability to meet efficiency and accuracy requirements in real-world scenarios. This paper aims to optimize BP networks and develop more effective fault warning methods. The primary contribution of this research is the proposal of a novel hybrid algorithm that combines a random wandering strategy within the main loop of an equilibrium optimizer (EO), a local search operator inspired by simulated annealing, and an adaptive learning strategy within the BP neural network. Through analysis and comparison of multiple sets of experimental data, the algorithm demonstrates exceptional accuracy and stability in fault warning tasks, effectively predicting the future operation of equipment and systems. This innovative approach not only overcomes the limitations of traditional BP neural networks, but also provides an efficient and reliable solution for fault detection and early warning in practical applications.