Weighted squared envelope nonlinear Gini index and its application to rotating machinery condition monitoring

Abstract Sparsity measures are effective tools for rotating machinery condition monitoring. However, under complex operating conditions, existing sparsity measures often exhibit significant fluctuations, making it difficult to accurately detect early faults and monotonically represent the degradation processes. To tackle these challenges, a novel health indicator named the weighted squared envelope nonlinear Gini index is proposed in this paper. Firstly, by introducing a nonlinearly increasing weight sequence inspired by the sigmoid function and the quadratic function-based quasi-arithmetic mean, a novel sparsity measure, the nonlinear Gini index, is developed based on the ratio of different quasi-arithmetic means framework. Building upon this foundation, the weighted squared envelope nonlinear Gini index is further constructed for condition monitoring by incorporating the weighted squared envelope into the nonlinear Gini index. When applied to two bearing run-to-failure datasets, the proposed health indicator shows improved sensitivity to early fault features and is able to depict the degradation processes monotonically, demonstrating notable advantages in condition monitoring.