Rolling bearings, as critical components of rotating machinery, significantly influence equipment reliability and operational efficiency. Accurate fault diagnosis is therefore crucial for maintaining industrial production safety and continuity. This paper presents a new fault diagnosis method based on FCEEMD multi-complexity low-dimensional features and directed acyclic graph LSTSVM. The Fast Complementary Ensemble Empirical Mode Decomposition (FCEEMD) method is applied to decompose vibration signals, effectively reducing background noise. Nonlinear complexity features are then extracted, including sample entropy (SE), permutation entropy (PE), dispersion entropy (DE), Gini coefficient, the square envelope Gini coefficient (SEGI), and the square envelope spectral Gini coefficient (SESGI), enhancing the capture of the signal complexity. In addition, 16 time-domain and 13 frequency-domain features are used to characterize the signal, forming a high-dimensional feature matrix. Robust unsupervised feature selection with local preservation (RULSP) is employed to identify low-dimensional sensitive features. Finally, a multi-classifier based on DAG LSTSVM is constructed using the directed acyclic graph (DAG) strategy, improving fault diagnosis precision. Experiments on both laboratory bearing faults and industrial check valve faults demonstrate nearly 100% diagnostic accuracy, highlighting the method’s effectiveness and potential.