A fault diagnosis method combining one-dimensional convolutional neural network (1D-CNN) and Kolmogorov Arnold Network (KAN) is proposed for faults such as fouling in the superheater tubes and radiation heating surfaces of small ship booster boilers. This method first extracts features from the original signal through convolutional layers, and then inputs the extracted features into the KAN model for classification. Evaluation metrics such as confusion matrix, accuracy, and F1 score are introduced for model evaluation. Through comparative experiments, it is found that the diagnostic accuracy of this method can reach over 99%, which is better than diagnostic models such as CNN, MLP, and CNN-MLP; Further verification of its robustness was carried out by randomly injecting Gaussian noise, which enables precise localization of six induced causes of overheating and tube bursting faults in ship booster boilers.