The underdetermined blind source separation (UBSS) has been considered to be a novel signal processing technique, which can separate the fault source signals from their mixtures. The mixing matrix estimation is a major step in the UBSS, this paper focuses on boosting the accuracy level of the estimated mixing matrix in the underdetermined case. Since the traditional clustering algorithms may not capture the signal characteristics well and secure a satisfactory estimation of the mixing matrix, an effective twostage clustering algorithm is proposed to estimate the mixing matrix through a combination of hierarchical clustering and K-means. More specifically, first, the sum of frequency points energy in the time-frequency (TF) domain is calculated to estimate the number of source signals before clustering, and the initial clustering centers are obtained with a hierarchical clustering algorithm. Second, after eliminating outliers deviating from the initial clustering centers with the cosine distance, the new clustering centers are obtained by recalculating the mean value of each sub-cluster. Finally, the new clustering centers are set as the initial clustering centers of the K-means algorithm to estimate the mixing matrix. Extensive simulations and experiments show that the proposed method can effectively separate the source signals and ensure an estimate of the mixing matrix that is substantially more accurate than the K-means algorithm alone.

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In order to effectively extract the key feature information hidden in the original vibration signal, this paper proposes a fault feature extraction method combining adaptive uniform phase local mean decomposition (AUPLMD) and refined time-shift multiscale weighted permutation entropy (RTSMWPE). The proposed method focuses on two aspects: solving the serious modal aliasing problem of local mean decomposition (LMD) and the dependence of permutation entropy on the length of the original time series. First, by adding a sine wave with a uniform phase as a masking signal, adaptively selecting the amplitude of the added sine wave, the optimal decomposition result is screened by the orthogonality and the signal is reconstructed based on the kurtosis value to remove the signal noise. Secondly, in the RTSMWPE method, the fault feature extraction is realized by considering the signal amplitude information and replacing the traditional coarse-grained multi-scale method with a time-shifted multi-scale method. Finally, the proposed method is applied to the analysis of the experimental data of the reciprocating compressor valve; the analysis results demonstrate the effectiveness of the proposed method.

In this paper, the equivalent velocity of head model based on HIC value is studied. Firstly, based on the existing pedestrian model, a large number of experimental simulation and statistical analysis have been completed after modification, and the functional relationship between HIC value and vehicle pedestrian contact speed has been obtained. Then, a separate head model is established according to the contact characteristics of the original dummy model, and the functional relationship between the HIC value and the collision speed when the head hits the windscreen is obtained by simulation, and the equivalent velocity relationship between the collision speed of the head model and the human-vehicle contact speed is deduced. Finally, according to the existing finite element head model and the coupling calculation method, the simulation results under the coupling calculation condition are explored. The equivalent velocity relation proposed in this paper has guiding significance to the value of collision velocity in the head collision model and also promotes the development of research on human-vehicle collision accidents.

The accuracy and stability of the envelope estimation function are enduring issues throughout the research process of LMD. This paper presents double interpolation and mutation interval reconstruction local mean decomposition (DIMIRLMD) to improve the stability of the demodulation process and the accuracy of PF components. DIMIRLMD first proposes a mutation interval reconstruction envelope algorithm using extreme symmetry points to suppress the demodulation mutation phenomenon, which disturbs the stability of the demodulation process, and then selects the optimal PF component from a double interpolation PF component library based on the index of orthogonality (IO) for a better hierarchical property. DIMIRLMD was employed to analyze the simulation signal and vibration signal of a reciprocating compressor in an oversized bearing clearance state, and the results illustrate its performances are more excellent than those of three other LMD methods. Furthermore, the envelope frequency spectrum obtained from the proposed LMD presents a clear double rotation fault frequency and lower noise disturbance.