A new finite element method, which is the characteristic-based operator-splitting (CBOS) algorithm, is developed to solve Navier-Stokes (N-S) equations. In each time step, the equations are split into the diffusive pa...A new finite element method, which is the characteristic-based operator-splitting (CBOS) algorithm, is developed to solve Navier-Stokes (N-S) equations. In each time step, the equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm. For the diffusive part, the temporal discretization is performed by the backward difference method which yields an implicit scheme and the spatial discretization is performed by the standard Galerkin method. The convective part can be discretized using the characteristic Galerkin method and solved explicitly. The driven square flow and backward-facing step flow are conducted to validate the model. It is shown that the numerical results agree well with the standard solutions or existing experimental data, and the present model has high accuracy and good stability. It provides a prospective research method for solving N-S equations.展开更多
The local defect in rotating machine always gives rise to repetitive transients in the collected vibration signal. However, the transient signature is prone to be contaminated by strong background noises, thus it is a...The local defect in rotating machine always gives rise to repetitive transients in the collected vibration signal. However, the transient signature is prone to be contaminated by strong background noises, thus it is a challenging task to detect the weak transients for machine fault diagnosis. In this paper, a novel adaptive tunable Q-factor wavelet transform(TQWT) filter based feature extraction method is proposed to detect repetitive transients. The emerging TQWT possesses distinct advantages over the classical constant-Q wavelet transforms, whose Q-factor can be tuned to match the oscillatory behavior of different signals, but the parameter selection for TQWT heavily relies on prior knowledge. Within our adaptive TQWT filter algorithm, the automatic optimization techniques for three TQWT parameters are implemented to achieve an optimal TQWT basis that matches the transient components. Specifically, the decomposition level is selected according to a center frequency ratio based stopping criterion, and the Q-factor and redundancy are optimized based on the minimum energy-weighted normalized wavelet entropy.Then, the adaptive TQWT decomposition can be achieved in a sparse way and result in subband signals at various wavelet scales.Further, the optimum subband signal which carries transient feature information, is identified using a normalized energy to bandwidth ratio index. Finally, the single branch reconstruction signal from the optimum subband is obtained with transient signatures via inverse TQWT, and the frequency of repetitive transients is detected using Hilbert envelope demodulation. It has been verified via numerical simulation that the proposed adaptive TQWT filter based feature extraction method can adaptively select TQWT parameters and the optimum subband for repetitive transient detection without prior knowledge. The proposed method is also applied to faulty bearing vibration signals and its effectiveness is validated.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 41072235, 50809008)the Hong Kong Research Grants Council (Grant No. HKU 7171/06E)+1 种基金the National Basic Research Program of China ("973" Project) (Grant No. 2007CB209400)the Natural Science Foundation of LiaoNing Province of China (Grant No. 20102006)
文摘A new finite element method, which is the characteristic-based operator-splitting (CBOS) algorithm, is developed to solve Navier-Stokes (N-S) equations. In each time step, the equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm. For the diffusive part, the temporal discretization is performed by the backward difference method which yields an implicit scheme and the spatial discretization is performed by the standard Galerkin method. The convective part can be discretized using the characteristic Galerkin method and solved explicitly. The driven square flow and backward-facing step flow are conducted to validate the model. It is shown that the numerical results agree well with the standard solutions or existing experimental data, and the present model has high accuracy and good stability. It provides a prospective research method for solving N-S equations.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51335006 & 51605244)
文摘The local defect in rotating machine always gives rise to repetitive transients in the collected vibration signal. However, the transient signature is prone to be contaminated by strong background noises, thus it is a challenging task to detect the weak transients for machine fault diagnosis. In this paper, a novel adaptive tunable Q-factor wavelet transform(TQWT) filter based feature extraction method is proposed to detect repetitive transients. The emerging TQWT possesses distinct advantages over the classical constant-Q wavelet transforms, whose Q-factor can be tuned to match the oscillatory behavior of different signals, but the parameter selection for TQWT heavily relies on prior knowledge. Within our adaptive TQWT filter algorithm, the automatic optimization techniques for three TQWT parameters are implemented to achieve an optimal TQWT basis that matches the transient components. Specifically, the decomposition level is selected according to a center frequency ratio based stopping criterion, and the Q-factor and redundancy are optimized based on the minimum energy-weighted normalized wavelet entropy.Then, the adaptive TQWT decomposition can be achieved in a sparse way and result in subband signals at various wavelet scales.Further, the optimum subband signal which carries transient feature information, is identified using a normalized energy to bandwidth ratio index. Finally, the single branch reconstruction signal from the optimum subband is obtained with transient signatures via inverse TQWT, and the frequency of repetitive transients is detected using Hilbert envelope demodulation. It has been verified via numerical simulation that the proposed adaptive TQWT filter based feature extraction method can adaptively select TQWT parameters and the optimum subband for repetitive transient detection without prior knowledge. The proposed method is also applied to faulty bearing vibration signals and its effectiveness is validated.
