The reliable operation of industrial equipment is imperative for ensuring both safety and enhanced production efficiency. Machine learning technology, particularly the Light Gradient Boosting Machine (LightGBM), has emerged as a valuable tool for achieving effective fault warning in industrial settings. Despite its success, the practical application of LightGBM encounters challenges in diverse scenarios, primarily stemming from the multitude of parameters that are intricate and challenging to ascertain, thus constraining computational efficiency and accuracy. In response to these challenges, we propose a novel innovative hybrid algorithm that integrates an Arithmetic Optimization Algorithm (AOA), Simulated Annealing (SA), and new search strategies. This amalgamation is designed to optimize LightGBM hyperparameters more effectively. Subsequently, we seamlessly integrate this hybrid algorithm with LightGBM to formulate a sophisticated fault warning system. Validation through industrial case studies demonstrates that our proposed algorithm consistently outperforms advanced methods in both prediction accuracy and generalization ability. In a real-world water pump application, the algorithm we proposed achieved a fault warning accuracy rate of 90%. Compared to three advanced algorithms, namely, Improved Social Engineering Optimizer-Backpropagation Network (ISEO-BP), Long Short-Term Memory-Convolutional Neural Network (LSTM-CNN), and Grey Wolf Optimizer-Light Gradient Boosting Machine (GWO-LightGBM), its Root Mean Square Error (RMSE) decreased by 7.14%, 17.84%, and 13.16%, respectively. At the same time, its R-Squared value increased by 2.15%, 7.02%, and 3.73%, respectively. Lastly, the method we proposed also holds a leading position in the success rate of a water pump fault warning. This accomplishment provides robust support for the timely detection of issues, thereby mitigating the risk of production interruptions.