The hydraulic pump plays a very important role in the safe and stable operation of the hydraulic system. Once it fails, it will cause immeasurable losses to the entire hydraulic system. But in practice, because hydraulic pump often works under strong noise background, the fault characteristics of its vibration signals are often very weak and difficult to extract. To solve this problem, this paper proposes an effective time series dynamic feature extraction method, which is based on the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and composite multi-scale basic scale entropy (CMBSE). On this basis, a new hydraulic pump fault diagnosis method is proposed by combining tdistributed stochastic neighbor embedding (t-SNE) and whale optimization algorithm kernel extreme learning machine (WOA-KELM). First, CEEMDAN is used to decompose the fault signals of the hydraulic pump, and CMBSE is used to quantify the decomposed IMF components to obtain the fault characteristics of the different states of the hydraulic pump, and then use t-SNE to visualize the dimensionality reduction, and finally input into the WOA-KELM-based fault classifier for state identification. The experimental results show that this method can effectively extract the weak signal features under strong noise background, and has broad application prospects for hydraulic pump fault diagnosis.