Variational mode decomposition (VMD) is widely used in the condition monitoring and fault diagnosis of rotary machinery for its unique advantages. An adaptive parameter optimized VMD (APOVMD) is proposed in order to adaptively determine the suitable decomposed parameters and further enhance its performance. The traditional singular value decomposition (SVD) method cannot effectively select the reconstructed order, which often leads to unsatisfactory results for signal reconstruction. Thus, a singular kurtosis difference spectrum method is proposed to accurately determine the effective reconstructed order for signal noise reduction. In addition, because the fault signal of the planetary gearbox at the early fault stage is weak and susceptible to ambient noise and other signal interference, the fault feature information is difficult to extract. To address this issue, a novel method for early fault feature extraction of planetary gearbox based on APOVMD and singular kurtosis difference spectrum is proposed in this paper. First, the APOVMD is applied to decompose the planetary gearbox vibration signal into a series of band-limited intrinsic mode functions adaptively and non-recursively. Second, the sensitive component is selected from the IMFS according to the cosine similarity index. Third, the Hankel matrix is constructed for the sensitive component in the phase space and decomposed by SVD. Here, the effective reconstructed order is automatically selected by the singular kurtosis difference spectrum method for noise reduction. Finally, the Hilbert envelope spectrum analysis is carried out on the reconstructed signal, and the fault characteristic frequency information of planetary gearbox can be accurately extracted from the envelope spectrum to realize the fault identification and location. The results of simulation studies and actual experimental data analysis demonstrate that the proposed method has superior ability to extract the early weak fault characteristics of the planetary gearbox compared with the VMD-SVD and EEMD-SVD methods, and the validity and feasibility of the presented method are proved. INDEX TERMS Planetary gearbox, adaptive parameter optimized VMD, singular kurtosis difference spectrum, cosine similarity, early fault diagnosis.

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PurposeThis study aimed to explore the effect of exercise and cold exposure on insulin sensitivity and the level of serum free fatty acids (FFA) in diet-induced obese rats.MethodsSixty-four diet-induced obese rats were randomly assigned to eight groups: room temperature–sedentary, room temperature–exercise, acute cold exposure–sedentary, acute cold exposure–exercise, intermittent cold exposure–sedentary, intermittent cold exposure–exercise, sustained cold exposure–sedentary, and sustained cold exposure–exercise. After the interventions, the homeostatic model assessment for insulin resistance (HOMA-IR) values, the level of serum FFA, subcutaneous fat ratio (SFR) and visceral fat ratio, enzyme activities of adipose triglyceride lipase, and lipoprotein lipase (LPL) in inguinal adipose tissue, and protein expression of PGC1-α and p38 MAPK in skeletal muscle were investigated.ResultsWe found that exercise (P = 0.0136) and cold exposure (P < 0.0001) reduced HOMA-IR values independently. Exercise reduced serum FFA (P = 0.0041), whereas cold exposure did not affect them. Moreover, the HOMA-IR values were positively correlated with the serum FFA levels (r = 0.32, P = 0.01). SFR or visceral fat ratio was coordinately reduced by the interaction (for SFR, P = 0.0015) or opposing main effects between or of cold exposure and exercise, supporting the reduction of serum FFA. However, cold exposure or exercise increased the activity of adipose triglyceride lipase and LPL independently or interactively (for LPL, P = 0.0143), suggesting an increase in serum FFA. Finally, cold exposure and exercise enhanced protein expression of PGC1-α and p38 MAPK independently or interactively (for p38 MAPK, P = 0.0226), suggesting increased uptake and oxidation of serum FFA in muscle.ConclusionsThese results suggest that the combination of exercise and cold exposure may result in more serum FFA utilization than production and thus lead to reduced serum FFA and increased insulin sensitivity.