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Efficient and accurate diagnosis of rotating machinery in the petrochemical industry is crucial for ensuring normal machinery operation. However, the nonlinear and non-stationary vibration signals generated by machinery in harsh environments pose significant challenges in distinguishing fault signals from normal ones. Although several fault diagnosis methods based on mutual dimensionless indicators (MDI) have been proposed, they often fail to achieve effective and accurate health monitoring. Hence, this paper proposes a BP-Incremental Broad Learning System (BP-INBLS) model based on the combined synergistic of two modules, to address the existing challenges. Firstly, a new mutual dimensionless indicator (VMDI) with high sensitivity and low overlap is refactored. Secondly, leveraging the advantages of incremental learning algorithms, a novel Broad Learning System (BLS) model for quickly identifying different fault types is constructed. Finally, the proposed method is validated using multiple datasets and verified through a comparative analysis with a published method based on dimensionless indicators (DI). The results demonstrate the effectiveness of the proposed method in fault diagnosis. [ABSTRACT FROM AUTHOR]