Arnoldi mode decomposition: A subspace sparse constrained method for periodic pulse extraction

To accurately detect early mechanical faults, a novel fault feature extraction method named Arnoldi mode decomposition (AMD) is proposed in this paper. First, AMD method constructs a numerically stable operator based on the output variance, projects the large-scale matrix formed from the signal onto a Krylov subspace via the Arnoldi process, and builds a set of low-dimensional orthogonal bases. The multi-parameter coupled filter optimization problem is then projected into the subspace for refined solution. Second, by exploiting the numerical stability of the orthogonal bases and the low-dimensional approximation capability of the Krylov subspace, numerical errors are effectively suppressed, thereby enhancing the stability of the feature extraction process. Finally, a nonlinear optimization is performed within the subspace using the reweighted kurtosis (RK) as the criterion, and a subspace sparse constraint strategy is adopted to update the filter along as few critical directions as possible, suppressing noise components and improving interpretability. Simulation signals and experimental bearing fault data demonstrate that the proposed AMD significantly improves the extraction ability of weak fault impulses, feature distinctiveness, and numerical stability, while maintaining low computational cost.