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This paper presents a fault diagnosis method for gearbox based on local mean decomposition (LMD), permutation entropy (PE) and extreme learning machine (ELM). LMD, a new self-adaptive time-frequency analysis method, is applied to decompose the vibration signal into a set of product functions (PFs). Then, PE values of the first five PFs (PF-PE) are calculated to characterize the complexity of the vibration signal. Finally, for the purpose of less time-consuming and higher accuracy, ELM is used to identify and classify of gearbox in different fault types. The experimental results demonstrate that the proposed method is effective in diagnosing and classifying different states of gearbox in short time.

Since the vibration signals of gearbox are non-linear and non-stationary, it is difficult to accurately evaluate the working conditions. Therefore, a fault feature extraction technique based on intrinsic characteristic-scale decomposition (ICD) and multi-scale entropy (MSE) is presented in this paper. The measured signals are firstly decomposed into a series of product components (PCs) by ICD. Secondly, the main product component is selected, and then MSE is used to extract the feature vectors from the selected PCs. Finally, the obtained feature vectors of gearbox with different scale factors are adopted as inputs of support vector machine (SVM) to fulfill the fault patterns identification. The superiority of the proposed technique is verified through comparing with three other methods.

Local mean decomposition (LMD) is a novel adaptive time-frequency analysis method, which is widely used in reciprocating compressor fault diagnosis. However, LMD decomposition results method is sensitive to noise. In order to eliminate influence of noise, cascaded bistable stochastic resonance (CBSR) is introduced and a new fault diagnosis method based on CBSR denoising and LMD is proposed in this paper. Firstly, CBSR is employed as the pretreatment to remove noise in vibration signals, and then the denoised signal is decomposed by LMD method. Finally, the fault frequency of reciprocating compressor is found through the envelope spectrum analysis of the first PF component. The effectiveness of the proposed method is verified by the simulation data and the practical reciprocating compressor fault diagnosis.

This paper proposes a new rolling bearing fault diagnosis method based on adaptive multiscale fuzzy entropy (AMFE) and support vector machine (SVM). Unlike existing multiscale Fuzzy entropy (MFE) algorithms, the scales of AMFE method are adaptively determined by using the robust Hermite-local mean decomposition (HLMD) method. AMFE method can be achieved by calculating the Fuzzy Entropy (FuzzyEn) of residual sums of the product functions (PFs) through consecutive removal of high-frequency components. Subsequently, the obtained fault features are fed into the multi-fault classifier SVM to automatically fulfill the fault patterns recognition. The experimental results show that the proposed method outperforms the traditional MFE method for the nonlinear and non-stationary signal analysis, which can be applied to recognize the different categories of rolling bearings.

Empirical mode decomposition (EMD), a self-adaptive time-frequency analysis methodology, is particularly suitable for processing the nonlinear and non-stationary time series, which can decompose a complicated signal into a series of intrinsic mode functions. Although it has the attractive features, the approach to construct the envelop-line in EMD has obvious shortcomings. A suggested improvement to EMD by adopting the optimized rational Hermite interpolation is proposed in this paper. In the proposed method, it adopts rational Hermite interpolation to compute the envelope-line, which has a shape controlling parameter compared with the cubic Hermite interpolation. In the meantime, one parameter determining criterion is introduced to guarantee the shape controlling parameter selection performs optimally. Besides the empirical envelope demodulation (EED) is introduced and utilized to analyze the IMFs derived from the improved EMD method. Hence, a new time-frequency method based on the optimized rational Hermite-based EMD combined with EED is proposed and the effectiveness was validated by the numerical simulations and an application to the reciprocating compressor fault diagnosis. The contributions of this paper are three aspects: Firstly, the definition of the best envelope is non-existent, some light is given about which envelope maybe better in this paper. Secondly, the optimal shape controlling parameter selection combined with rational Hermite interpolation is developed, leading to the significant performance enhancement. Thirdly, little research has been carried out on the fault diagnosis of the reciprocating compressor using EMD, the proposed method is a good start.