Entropy-based methods have gained widespread adoption in fault diagnosis owing to their superior classification capabilities, particularly diversity entropy (DE) which demonstrates exceptional consistency, robust noise immunity, and computational efficiency. However, DE exhibits limitations in characterizing continuous degradation trends due to its poor monotonicity on the continuous health monitoring. To address this issue, this article proposed a novel method called vector DE (VDE) for the continuous health monitoring of rolling bearing. First, in the proposed VDE, a magnitude entropy is proposed to converts the probabilistic state information of the global amplitude information into entropy value, which could improve the monotonicity while retaining the original frequency sensitivity. Second, the characteristic properties and the root cause of the poor monotonicity have been explored: the original DE only calculates the angles of orbits in the phase space, ignoring that the global amplitude reduces amplitude sensitivity which leads to poor monotonicity. Lastly, the effectiveness of the proposed VDE has been verified in the continuous health monitoring of rolling bearing through the experimental run-to-failure bearing signals.
LiXLeiXJiangL, et al. A new strategy: remaining useful life prediction of wind power bearings based on deep learning under data missing conditions. Mathematics2024; 12: 2119.
2.
ZhouPYuXYangY, et al. Fault-induced gear meshing modulation sideband extraction and evaluation for fault diagnosis of planetary gearboxes. Sci China Technol Sci2025; 68: 1120305.
LeiYLiuHLiN, et al. Condition monitoring and fault diagnosis of industrial robots: a review. Sci China Technol Sci2025; 68: 1110301.
5.
WangYLiuFXiF, et al. Data driven comprehensive performance evaluation of aeroengines: a network dynamic approach. Engineering2025; 46: 292–305.
6.
LiYBaiXLiuC, et al. A self-supervised assisted label-efficient method for online remaining useful life prediction. Measurement2025; 242: 115902.
7.
NiuMJiangHYaoR.Adaptive multiscale wavelet-guided periodic sparse representation for bearing incipient fault feature extraction. Sci China Technol Sci2024; 67: 3585–3596.
8.
ShuangLShenXZhouJ, et al. Bearings remaining useful life prediction across equipment-operating conditions based on multisource-multitarget domain adaptation. Measurement2024; 236: 115026.
9.
WangYChenXZhangS, et al. A review of modelling and data analysis methods for accelerated test. J Reliab Sci Eng2025; 1: 012002.
10.
LiXLiSWeiD, et al. Dynamics simulation-driven fault diagnosis of rolling bearings using security transfer support matrix machine. Reliab Eng Syst Saf2024; 243: 109882.
11.
ZhangYJiJCRenZ, et al. Digital twin-driven partial domain adaptation network for intelligent fault diagnosis of rolling bearing. Reliab Eng Syst Saf2023; 234: 109186.
12.
SiSLvCCaiZ, et al. Fractional core-based collapse mechanism and structural optimization in complex systems. Sci China Inf Sci2023; 66: 192202.
13.
DingLJiJLiY, et al. A novel weak feature extraction method for rotating machinery: link dispersion entropy. IEEE Trans Instrum Meas2023; 72: 1–12.
14.
ZhongTQinCShiG, et al. A residual denoising and multiscale attention-based weighted domain adaptation network for tunnel boring machine main bearing fault diagnosis. Sci China Technol Sci2024; 67: 2594–2618.
15.
NomanKLiYWenG, et al. Continuous monitoring of rolling element bearing health by nonlinear weighted squared envelope-based fuzzy entropy. Struct Health Monit2024; 23: 40–56.
16.
NomanKLiYWangS.Continuous health monitoring of rolling element bearing based on nonlinear oscillatory sample entropy. IEEE Trans Instrum Meas2022; 71: 1–14.
17.
LiOLeiJQinC, et al. A novel multi-channel CNN-LSTM and transformer-based network for diesel engine misfire diagnosis under different noise conditions. Sci China Technol Sci2024; 67: 2965–2967.
18.
ShannonCE.A mathematical theory of communication. Bell Syst Tech J1948; 27: 379–423.
19.
PincusSM.Approximate entropy as a measure of system complexity. Proc Natl Acad Sci1991; 88: 2297–2301.
20.
RichmanJSMoormanJR.Physiological time-series analysis using approximate entropy and sample entropy. Am J Physiol Heart Circ Physiol2000; 278: H2039–H2049.
21.
ChenWWangZXieH, et al. Characterization of surface EMG signal based on fuzzy entropy. IEEE Trans Neural Syst Rehabil Eng2007; 15: 266–272.
22.
BandtCPompeB.Permutation entropy: a natural complexity measure for time series. Phys Rev Lett2002; 88: 174102.
23.
ZhuangDLiuHZhengH, et al. The IBA-ISMO method for rolling bearing fault diagnosis based on VMD-sample entropy. Sensors2023; 23: 991.
24.
PanYChenYFeiX, et al. Intelligent Fault diagnosis for rotating mechanical systems: an improved multiscale fuzzy entropy and support vector machine algorithm. Algorithms2024; 17: 588.
25.
MaPLiangWZhangH, et al. Multiscale permutation entropy based on natural visibility graph and its application to rolling bearing fault diagnosis. Struct Health Monit Int J2025; 24: 313–326.
26.
WangXSiSLiY.Multiscale diversity entropy: a novel dynamical measure for fault diagnosis of rotating machinery. IEEE Trans Ind Inform2021; 17: 5419–5429.
27.
HouBWangDWangY, et al. Adaptive weighted signal preprocessing technique for machine health monitoring. IEEE Trans Instrum Meas2021; 70: 1–11.
28.
NomanKHouBWangD, et al. Weighted squared envelope diversity entropy as a nonlinear dynamic prognostic measure of rolling element bearing. Nonlinear Dyn2023; 111: 6605–6620.
29.
MaCFengKWangX, et al. Condition-adaptive permutation entropy: a novel dynamic complexity-based health indicator for bearing health monitoring. IEEE Trans Reliab2024; 74: 2394–2407.
30.
WangBLeiYLiN, et al. A hybrid prognostics approach for estimating remaining useful life of rolling element bearings. IEEE Trans Reliab2020; 69: 401–412.
31.
BaiRLiYNomanK, et al. Diversity entropy-based Bayesian deep learning method for uncertainty quantification of remaining useful life prediction in rolling bearings. J Vib Control2023; 29: 5053–5066.
32.
PatrickNRafaelGKamalM, et al. PRONOSTIA: an experimental platform for bearings accelerated life test. In: Proceedings of the IEEE international conference on prognostics and health management, Denver, CO, USA, 18–21 June 2012, pp. 1–8. Denver, CO: IEEE.
