TY - JOUR
T1 - A full generalization of the Gini index for bearing condition monitoring
AU - Chen, Bingyan
AU - Song, Dongli
AU - Gu, Fengshou
AU - Zhang, Weihua
AU - Cheng, Yao
AU - Ball, Andrew
AU - Bevan, Adam
AU - Gu, James Xi
N1 - Funding Information:
This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFB3400704-02), the National Natural Science Foundation of China (Grant No. 52275133 ), the open project of State Key Laboratory of Traction Power, Southwest Jiaotong University, China (Grant No. TPL2210), the China Scholarship Council (Grant No. 202107000033) and the Science and Technology Project of Hunan Province, China (Grant No. 2021GK4014). The authors would like to thank CIMS and XJTU-SY for the free download of the bearing experimental datasets, and the editor and reviewers for their valuable suggestions on the paper.
Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2023/4/1
Y1 - 2023/4/1
N2 - The classic Gini index (GI) is generalized recently by using nonlinear weight sequences as sparsity measures for sparse quantification and machine condition monitoring. The generalized GIs with different weight parameters are more robust to random transients. However, they show insufficient performance in discriminating repetitive transients under noise contamination. To overcome this shortage, this paper proposes a two-parameter generalization method to tune not only the weight parameter but also the norm order, allowing for a full generalization of the classic GI to quantify transient features and leading to new statistical indicators which are named fully generalized GIs (FGGIs). Mathematical derivations show that FGGIs satisfy at least four of the six typical attributes of sparsity measures and that those with weight parameter equal to one satisfy at least five sparse attributes, proving that they are a new family of sparsity measures. Numerical simulations demonstrate that FGGIs can monotonically evaluate the sparseness of the signals and that the FGGIs with appropriate parameters exhibit improved performance in resisting random transient interferences and discriminating noise-contaminated repetitive transients compared to traditional sparsity measures. The performance of FGGIs in the condition monitoring of rolling element bearings is validated using two different run-to-failure experiment datasets, including a gradual failure and a sudden failure. The results show that increasing the norm order can improve the capability of FGGIs to characterize transient fault features, allowing more accurate trending of bearing health conditions, and therefore achieving better condition monitoring performance than the traditional sparsity measures.
AB - The classic Gini index (GI) is generalized recently by using nonlinear weight sequences as sparsity measures for sparse quantification and machine condition monitoring. The generalized GIs with different weight parameters are more robust to random transients. However, they show insufficient performance in discriminating repetitive transients under noise contamination. To overcome this shortage, this paper proposes a two-parameter generalization method to tune not only the weight parameter but also the norm order, allowing for a full generalization of the classic GI to quantify transient features and leading to new statistical indicators which are named fully generalized GIs (FGGIs). Mathematical derivations show that FGGIs satisfy at least four of the six typical attributes of sparsity measures and that those with weight parameter equal to one satisfy at least five sparse attributes, proving that they are a new family of sparsity measures. Numerical simulations demonstrate that FGGIs can monotonically evaluate the sparseness of the signals and that the FGGIs with appropriate parameters exhibit improved performance in resisting random transient interferences and discriminating noise-contaminated repetitive transients compared to traditional sparsity measures. The performance of FGGIs in the condition monitoring of rolling element bearings is validated using two different run-to-failure experiment datasets, including a gradual failure and a sudden failure. The results show that increasing the norm order can improve the capability of FGGIs to characterize transient fault features, allowing more accurate trending of bearing health conditions, and therefore achieving better condition monitoring performance than the traditional sparsity measures.
KW - Gini index
KW - generalized Gini indices
KW - fully generalized Gini indices
KW - sparsity measures
KW - condition monitoring
KW - rolling element bearings
KW - Condition monitoring
KW - Generalized Gini indices
KW - Rolling element bearings
KW - Sparsity measures
KW - Fully generalized Gini indices
UR - http://www.scopus.com/inward/record.url?scp=85145578356&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2022.109998
DO - 10.1016/j.ymssp.2022.109998
M3 - Article
VL - 188
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 109998
ER -