•A normalized CNN is constructed for fault diagnosis of hydraulic piston pump.•Multiple signals are analyzed and used for intelligent fault diagnosis.•Bayesian algorithm is introduced for automatic selection of hyperparameters.•Severity level of different failure and changeable conditions are discussed.•The BNCNN presents high accuracy and stability by experimental verification. Hydraulic piston pump is known as one of the most critical parts in a typical hydraulic transmission system. It is imperative to probe into an accurate fault diagnosis method to guarantee the stability and reliability of the system. Due to the shortcomings of traditional methods, the development of artificial intelligence enlightens the intensive exploration for machinery fault diagnosis. In this research, a normalized convolutional neural network (NCNN) framework with batch normalization strategy is developed for feature extraction and fault identification. First, the batch normalization technology is introduced in the modeling to resolve the change of data distribution. Second, inspired by the intelligent algorithms, Bayesian algorithm is employed to automatically tune the model hyperparameters. The improved model is named BNCNN. Third, BNCNN is used for fault diagnosis based on synchrosqueesed wavelet transform. The experiments in a hydraulic piston pump are employed for the demonstration of the method. Moreover, the superior performance of the proposed method is validated by the contrastive analysis. The results reveal that BNCNN can accurately and steadily complete the fault classification of hydraulic pump.