Axial piston pumps are critical components of hydraulic systems due to their compact design and high volumetric efficiency, making them widely used. However, they are prone to failure in harsh environments characterized by high pressure and heavy loads over extended periods. Therefore, detecting abnormal behavior in axial piston pumps is of significant importance. Traditional detection methods often rely on vibration signals from the pump casings; however, these signals are susceptible to external environmental interference. In contrast, pressure signals exhibit greater stability. In this study, we propose a novel anomaly detection method for axial piston pumps, referred to as DTW-RCK-IF, which combines dynamic time warping (DTW) for data segmentation, a random convolutional kernel (RCK) for feature extraction, and isolation forest (IF) for anomaly detection using pressure signals. The model is trained using normal operating data to enable the effective detection of abnormal states. First, the DTW algorithm is employed to segment the raw data, ensuring a high degree of similarity between the segmented data. Next, the random convolutional kernel approach is used in a convolutional neural network for feature extraction, resulting in features that are representative of normal operating conditions. Finally, the isolation forest algorithm calculates the anomaly scores for anomaly detection. Experimental simulations on axial piston pumps demonstrate that, compared with vibration signals, the DTW-RCK-IF approach using pressure signals yields superior results in detecting abnormal data, with an average F1 score of 98.79% and a good fault warning effect. Validation using the publicly available CWRU-bearing and XJTU-SY-bearing full-life datasets further confirms the effectiveness of this method, with average F1 scores of 99.35% and 99.73%, respectively, highlighting its broad applicability and potential for widespread use.