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Data-driven fault diagnosis methods have been widely used in the field of fault diagnosis of rotating machinery components. However, most of the current research methods mainly rely on a large amount of data generated by fixed-length data segmentation. The segmented data is usually a short-period small segment signal, and the actual long-period redundant signal cannot be directly used as a test sample for fault identification. In view of the above shortcomings, a new fault diagnosis method based on data probability density and one-dimensional convolutional neural network (DPD-1DCNN) is proposed. It has two characteristics: ①the density feature of the extracted signal resists the redundancy of the data; ②adapt redundant signals of different lengths as input to the diagnostic model. The method is verified on the planetary gearbox fault data generated by the DDS test bench, which not only ensures high diagnostic accuracy, but also enhances the adaptability of the diagnostic model.

Aiming at the problem of fault feature extraction and pattern recognition of planetary gearbox, a planetary gearbox fault diagnosis method combined honey badger algorithm(HBA) optimal improved complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN), hierarchical weighted permutation entropy(HWPE) and grey wolf algorithm(GWO) optimal support vector machine(SVM)was proposed. Firstly, HBA was used to optimize the white noise amplitude weight and noise adding times of ICEEMDAN, and HBA-ICEEMDAN decomposition was performed on the vibration signal of planetary gearbox to obtain several mode functions, and the components with larger correlation coefficients were selected for reconstruction. Then, sensitive feature values of reconstructed low noise signals were extracted by HWPE method to obtain fault feature vectors. Finally, GWO was used to optimize the penalty coefficient and kernel coefficient of SVM, and GWO-SVM multi fault classifier was trained to realize damage identification of planetary gearbox, and the experiments were carried out with the vibration data of planetary gearbox, and the effectiveness of the algorithm was verified. The research results show that the fault diagnosis method of planetary gearbox combining HBA-ICEEMDAN, HWPE and GWO-SVM can accurately identify typical single point faults and composite faults of planetary gearbox, with an identification accuracy rate of 98.15%. Comparing with other combination methods, the method has more advantages and effectiveness in fault diagnosis of planetary gearbox. [ABSTRACT FROM AUTHOR]

Aiming at the problems of low accuracy of fault diagnosis for the planetary gearbox of wind turbine and its multiple sources of vibration excitation, a method used to diagnosis the detect of the planetary gearbox was proposed, it was based on multi-channel fusion and multi-scale dynamic adaptive residual learning（MC-MSDARL）. Firstly, the proposed multi-scale dynamic adaptive convolution neural networks（MSDAC） was used to dynamically adjust the weights of convolution kernels at different scales to adaptively extract the local and global intrinsic features of single channel data. Secondly, in order to improve the learning ability of the model, the method combined MSDAC with residual learning. Finally, MC-MSDAR was used to fuse the multi-scale features of multi-channel data into a feature vector, and then it was inputted to SoftMax layer to achieve the identification and classification of the fault which was in the planetary gearbox. The research results show that the accuracy of fault diagnosis of planetary gearbox based on MC-MSDAR is 97%, which verifies the effectiveness of this method. When the results of MC-MSDAR is compared with the results implemented by other deep learning methods, the proposed MC-MSDAR has a better performance on generalization ability than other deep learning methods. [ABSTRACT FROM AUTHOR]

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Tooth break is a common fault which always occurs in the planetary gearboxes, and when it occurs, due to the influence of transmission path, the vibration signal collected by the sensor becomes complicated, which brings difficulties to fault diagnosis. Thus, in order to study the influence of transmission path on spectrum structure of planetary gearboxes with tooth break fault, the rigid-flexible coupling models with no fault, sun gear tooth break fault, planet gear tooth break fault and ring gear tooth break fault of planetary gearboxes are established on Adams, and the vibration signals of the box body are extracted and analyzed by simulation. The simulation results show that: in the time-domain, the change of the path will have an obvious amplitude modulation on the vibration signal which is measured at a fixed point of the box. What's more, in the spectrum diagram, the two sides of the meshing frequency will also produce side bands composed of different frequencies.This study can provide basis and reference for fault diagnosis of planetary gearboxes in the future.

In view of the problems of poor discrimination of fault feature vectors extracted in the process of fault diagnosis of planetary gearboxes and insufficient diagnosis success rate, a method based on Local Mean Decomposition（LMD） permutation entropy and BP neural network is proposed. Through the LMD decomposition of the original signal, the PF components containing the main information are obtained, and the permutation entropy values are calculated to construct the feature vector. The extracted feature vectors are used to train the BP neural network and complete the failure pattern recognition test. Taking the EMD permutation entropy method and the non-dimensional analysis method as the comparison groups, the experiment proves that the feature vectors extracted from different working conditions with this method are more distinguishable, and the fault diagnosis effect is better. Moreover, this method shows better comprehensive performance when the number of training groups changes.

The fault diagnosis method of planetary gearbox based on machine learning relies on the artificial selection of the eigenvectors. The quality of eigenvectors selection largely determines the accuracy of the diagnosis method. The convolutional neural network (CNN) can extract characteristics automatically. But it is difficult to accurately diagnose the fault from a single vibration signal when it is used for the planetary gearbox fault diagnosis. To solve the above problems, a fault diagnosis method of planetary gearbox based on multi-information fusion and CNN is proposed. The method performs data layer fusion on three-dimensional (horizontal radial direction, vertical radial direction and axial direction) vibration signals and sound signals of the planetary gearbox. The one-dimensional vibration signals and sound signals are integrated into two-dimensional signals in a parallel connection mode. The two-dimensional signals are used as the input of CNN. The multiple convolutional layers and maximum pooling layers are used for depth characteristic extraction and information filtering. Finally, the Softmax classifier is used to achieve fault classification. The fault diagnosis experiment platform of the planetary gearbox is built. The vibration signals and sound signals of normal and fault states of the planetary gearbox under different speed and load conditions are collected and input into CNN for training and verification. Four single-source information of horizontal radial vibration signal, vertical radial vibration signal, axial vibration signal and sound signal are selected under the same conditions and combined with CNN respectively for comparison. The experiment is used to verify the superiority of the fault diagnosis method for planetary gearbox based on multi-information fusion and CNN. The experimental results show that the fault identification accuracy of the two methods of axial vibration signal+CNN and sound signal+CNN is 74.07% and 75.13% respectively. The fault identification accuracy of the two methods of horizontal radial vibration signal+CNN and vertical radial vibration signal+CNN is 89.70% and 87.09% respectively. The method based on multi-information fusion and CNN has the fastest convergence speed and the highest fault identification accuracy, which is 93.33%.

Planetary gearboxes have the advantages of compact structure，high transmission efficiency，stable operation，etc.，and are widely used in heavy loads and key mechanical equipment. Since planetary gearbox often works in harsh environment，its key components are prone to tooth root crack fault damage and are not easy to be identified，easy to cause security risks. Compared with traditional transverse vibration signal，torsional vibration signal is not affected by the modulation of time-varying transmission path in theory，it has great advantages，so its frequency component is simple and it is easy to extract fault features. Taking torsional vibration signals as the analysis object，a windowed RMS time-domain synchronous averaging technique is proposed to realize the early tooth root crack fault diagnosis of planetary gearbox，and a fault simulation test bed is built to verify the effectiveness of the method.

Copyright of Journal of Mine Automation is the property of Industry & Mine Automation Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Planetary gearboxes are widely used in mechanical transmission systems due to their large transmission ratio and high transmission efficiency. In a planetary gearbox， the sun gear is usually set to float to balance the sharing of loads among planet gears. However， this floating set will result in the variation of pressure angle， overlap ratio and meshing phase in the meshing progress. In the previous studies， these parameters were reduced to constant. To study the influence of the dynamic parameters on the vibration response of planetary gearboxes under different operating conditions， a new lumped parameter model containing the time-varying pressure angle， time-varying overlap ratio and time-varying meshing phase is established. Based on this model， the vibration response mechanism of the sun gear is analyzed. Moreover， the comparison with the previous model is made and the rule of phase modulation caused by these dynamic parameters is revealed. By comparing the dynamic responses under different loads and rotation speeds， the phase modulation is studied in detail.

Aiming at the problems of low fault recognition rate， slow convergence speed and difficult parameter selection in the process of fault diagnosis of planetary gearbox based on BP neural network improved by optimization algorithm， a GA-ACO algorithm is proposed to optimize the parameters of neural network. The basic principle and main steps of GA-ACO-BP algorithm are given. At the same time， this method is applied to the fault diagnosis of planetary gearbox. Comparing the performance of ACO-BP neural network algorithm and GA-ACO-BP algorithm， the results show that the convergence speed of ACO Optimized BP neural network is slow and the recognition accuracy is not high， while GA-ACO-BP algorithm can accurately and quickly diagnose and identify the fault of planetary gearbox.

Copyright of Lubrication Engineering (0254-0150) is the property of Editorial Office of LUBRICATION ENGINEERING and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Traditional machine learning methods have disadvantages such as low recognition rate and complicated feature extraction operations in the planetary gearbox fault diagnosis. In order to improve the diagnosis efficiency of planetary gearboxes， a fault diagnosis method based on one-dimensional deep convolutional neural network （1-DCNN） is proposed， and the original signals are directly input to the network for diagnosis. The accuracy of diagnosing five kinds of fault signals of planetary gear of planetary gear box can reach 100%， and the diagnostic accuracy and efficiency are better than other commonly used algorithms.

Planetary gearboxes have one or several planet gears rotating around the sun gear while revolving along their axle. This unique gear structure results in the simultaneous meshing of the planet gear with both sun and ring gears. Because of the high transmission ratio and large bearing capacity of its compact structure, planetary gearboxes have been extensively used in a variety of industrial applications. Therefore, planetary gearbox fault diagnosis is essential to ensure safe and efficient industrial manufacturing. Acoustic signal analysis provides an effective and noninvasive method for detecting potential faults in the planetary gearbox. However, the theoretical foundation of planetary gearbox fault signatures in acoustic signals is ambiguous. In this work, the planetary gearbox acoustic signal model of the resonance frequency region under the nonstationary state is structured by amplitude and frequency modulation, and the gear fault characteristics of the acoustic signals are explicitly derived. Given that resonance frequency is independent of rotational speed, the resonance frequency can be distinguished from speed-related frequency components. This lays the foundation for extracting the gear fault characteristics of the resonance frequency region. Moreover, the planetary gearbox often runs under time-varying speed conditions, and the fault frequency components are time-varying. To overcome the limitations of the traditional time–frequency analysis method in limited time–frequency resolution or cross-term interferences, the appropriate time–frequency analysis method is essential. In this work, the high-order synchrosqueezing transform is exploited to identify the time-varying fault characteristics of the planetary gearbox acoustic signal. Owing to the step of squeezing the energy distributed along instantaneous frequency in frequency direction, time–frequency representation by synchrosqueezing transform achieves a high time–frequency resolution. The high-order interpretation of instantaneous frequency further improves the capability to capture the time–frequency details. The acoustic signal model and corresponding fault characteristics of the planetary gearbox in the resonance frequency region are verified by both numerical simulations and laboratory experiments. The gear defect within the planetary gearbox is successfully diagnosed via the high-order synchrosqueezing transform.

In order to solve the difficult problem of early fault feature extraction of planetary gearbox and consider that the planetary gearbox vibration signal is coupling and nonlinear，and the signal has multiple transmission paths，a planetary gearbox fault diagnosis method based on Local Mean Decomposition（LMD） and Sample Entropy and Extreme Learning Machine（ELM） is proposed.Firstly，the vibration signal is adaptively decomposed into a plurality of PF components by LMD，and the first four PF components including the main fault information are selected in combination with the correlation coefficient and the variance contribution rate.Secondly，the Sample Entropy of the signal is calculated to form a feature vector.Finally，the feature vector is input into ELM for fault classification.Experiments are carried out on the planetary gearbox test bench，compared with the probabilistic neural network classification algorithm，and compared with the feature vector based on Singular Value Decomposition （SVD）.The results verify the effectiveness of the proposed method.

In the intelligent diagnosis of planetary gearbox faults,the issue of "difficult extraction"of the vibration signal characteristics,the"quality difference"of the constructed eigenvector set and the"low precision"of the fault classification model based on the extreme learning machine. Put forward a state identification method for a planetary gearbox solar wheel for how to capture sensitive transient impact feature in the vibration signal and construct a high-dimensional eigenvector set and improve the fault classification accuracy of the extreme learning machine. Firstly,the vibration signals are respectively solved by fast kurtosis diagram and variational mode decomposition and several intrinsic mode function matching the center frequency fωcorresponding to the maximum kurtosis value are selected,find the value of improve multi-scale permutation entropy to construct the highdimensional eigenvector set. Secondly,the de-noising automatic encoder is used to make the input weight and threshold of the implicit learning node of the extreme learning machine satisfy the orthogonal condition to realize the layering of its hidden layers.Finally,the above eigenvector set is used as the input of the hierarchical extreme learning machine,and the fault classification model of the planetary gearbox solar wheel is established through training. The results show that the proposed method achieves the effective extraction of sensitive transient impact feature in the vibration signal of the solar wheel and the high quality construction of the eigenvector set,and also improves the classification accuracy of the intelligent diagnosis model.

The shuffled frog leaping algorithm（ SFLA） is a swarm intelligent optimization algorithm that combines competitive evolutionary strategy and limited random search. It has been applied to various optimization problems. This paper analyzed the advantages of the SFLA for global optimization problems,and established optimization BP neural network algorithm model（ SFLA-BP） based on SFLA,and carried on the simulation study. The planetary gearbox was taken as an engineering example,and its nonlinear characteristic was presented because of transmission path of fault vibration signals complicated and their coupling with each others. The kernel principal component analysis（ KPCA） was used to extract the time domain and frequency domain sensitive features,and the feature dimensions were reduced from 27 to 9. A neural network fault diagnosis system with 9-14-4 structure was established. This paper makes full use of the advantage of the global search of SFLA to realize fault diagnosis of planetary gear with different wear levels. The diagnosis results show that the SFLA-BP model has a smaller overall output error compared with BP neural network,and the diagnostic accuracy increases by 12. 5 %,and has achieved a more accurate identification effect on different degrees damage faults.

Aiming at the problem that the fault information of the planetary gearbox was difficult to quantified and measured under the compli cated working conditions, a fault diagnosis method of the planetary gearbox based on the harmonic effective index (HEI) to quantify the fault information was proposed. Firstly, the signal is analysed and processed, the RCMDE value of FSWT frequency sliced signal was calculated, the frequency band with more fault features was selected for signal reconstruction; MOMEDA was used to extract the fault impulse component of the reconstructed signal accurately. Then the fault information contained in the vibration signal was quantified by establishing the harmonic effective index (HEI), the fault diagnosis of planetary gearbox was realized. And the test data of the planetary gearbox tooth surface wear fail ure was used for verification. The research results show that the method can extract the fault characteristics in the vibration signal of the plane tary gearbox; the planetary gear fault characteristic frequency f, -7.03 Hz and its multiplication frequency nf, can be clearly observed in the frequency spectrum of the processed signal. The HEI value of f, in the experimental data is 3.47 x 10 which can be used as an effective in dex to measure the degree of failure of the planetary gearbox. [ABSTRACT FROM AUTHOR]

According to the nonlinear and non-stationary of the planetary gearbox vibration signal fault characteristics is difficult to extract and the problem of low classification accuracy Gaussian kernel extreme learning machine based on random generation kernel parameters， a method for identifying the state of planetary gearboxes with enhence multi-scale permutation entropy （EMPE） and nuclear-polarized Gaussian kernel extreme learning machine （KELM） is proposed. Firstly， noise reduction of vibration signals of planetary gearbox planetary gears by morphological average filtering and using EMPE to obtain permutation entropy values at multiple scales to constructing eigenvector set. Secondly， kernel parameter σ of Gaussian kernel extreme learning machine is optimized by kernel polarization. Finally， using the EMPE eigenvector set as input， the planetary gear state identification model is constructed by the training of KP-KELM algorithm. The experiment results show that， compared with the fault classification model based on SVM and KELM， the EMPE and KP-KELM planetary gear fault diagnosis method has higher classification accuracy and stronger generalization ability.

In order to solve the problem of high failure rate in the operation of planetary power shift gearbox for engineering vehicles， a dynamics simulation model of planetary gearbox is established based on the dynamics transmission theory， and the rotational speed， torque and transmission efficiency of planetary transmission components are analyzed. The ADAMS and Matlab simulation software are used to establish the virtual prototype joint simulation model of the gearbox， the dynamic performance of the gearbox under the forward working condition of the vehicle is simulated， and the transmission efficiency and power flow direction of the planetary gearbox are analyzed. The test results show that the speed change of the gearbox before and after gear shifting is relatively gentle， which shows that the new dynamic gear shifting strategy can reduce the gear shifting time of the gearbox and improve the dynamic response of the gearbox effectively during the operation of the engineering vehicle. The research results have practical significance for condition monitoring and power shift strategy formulation of planetary gearbox.

When the planetary gear transmission system fails， its signal transmission is coupled with each other， and the nonlinear characteristic is presented， which makes the fault type and damage degree of the planetary gear to be difficultly recognized. The optimization mathematical model of the kernel function scale parameter is constructed by means of Fisher criterion（FC） discriminate function in pattern recognition， and the improved particle swarm optimization method is applied to the optimization to fully improve the analysis performance of the kernel principal component analysis（KPCA） for nonlinear problem. It is applied to the identification and diagnosis of wear damage degree of planetary gear. The results of example analysis show that the intelligently optimized KPCA based on PSO-FC have improve the structure distribution of data in the feature space and achieved the good scale clustering effect in planetary gear wear damage degree recognition. It can effectively solve the identify problems of complex fuzzy damage boundary and damage degree in the mechanical transmission.

In order to solve the difficulty in fault feature extraction of the planetary gearbox vibration signal,a comprehensive fault diagnosis method based on empirical mode decomposition（ EMD）,singularity value decomposition（ SVD） and probabilistic neural networks（ PNN） is proposed. Firstly,with the EMD method,de-noised vibration signals are decomposed into a finite number of intrinsic mode functions （IMF）. Secondly,some IMF components are selected according to the criterion of correlation coefficient and variance contribution ratio,and singular value sequences regarded as eigenvectors are obtained with the method of SVD. Lastly,the eigenvectors serve as import of PNN so that faults of the planetary gearbox are recognized. Experiments are conducted on the planetary gearbox fault diagnosis test-bed and comparison is carried out with eigenvectors made of energy entropy,which fully validates the effectiveness of the proposed methodology.

Aiming at the problem of complex modulation characteristics of vibration signals of the planetary gearbox make the state identification model low accuracy,a state identification method for key components of planetary gearbox based on combinations of ensemble local mean decomposition（ ELMD） energy entropy and artificial fish swarm algorithm finding support vector machine（ AFSA-SVM） optimal kernel function coefficient is proposed. To begin,a number of narrow-band product function（ PF） from vibration signals are obtained by ELMD with after morphological average filter. Then the high dimensional feature vector set is built by calculating the energy entropy of the above PF. At last,the fault diagnosis model is developed based on AFSA-SVM algorithm,in which the extracted fault features are employed as inputs. The experimental results show that the proposed method can show the fault component of the original signal with effectively. It has the state identification accurate of the model is greatly improved.

Copyright of Journal of Southeast University / Dongnan Daxue Xuebao is the property of Journal of Southeast University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Vibration Engineering is the property of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Due to the effect of the modulation part, the energy diffuses around the surrounding area of dominating frequencies and diminishes the readability of the time-frequency representation when short-time Fourier transform (STFT) is used to process nonstationary signals. However, when the instantaneous frequency slowly changes or is constant, the effect is small and can even be neglected. Thus, the time-frequency representations have high-energy concentration. Based on this feature, a novel method called iterative generalized short-time Fourier transform (IG-STFT) was proposed, which improved the readability of the time-frequency representation. First, the stationary mono-components are separated using iterative generalized demodulation. Then, the time-frequency representations of each mono-component are acquired using STFT. Finally, the time-frequency representation of the original signal is obtained according to the analysis results of STFT and the phase function. The analysis results of a planetary gearbox simulation signal and experimental signals verify the effectiveness of this method for analyzing nonstationary signals and diagnosing gear faults.

A novel dynamic co-simulation methodology is presented to establish a mechanical-electricalhydraulic integrated dynamic model of marching tank for studying the nonlinear vibration of marching tank under high mobility conditions. A property hydraulic subsystem model is established in Amesim, a tank mechanical system model, in which several nonlinear factors, such as barrel flexibility, are considered, is builded using RecurDyn, and a control system model is also builded using MATLAB/Simulink. A calculation program of the three-dimensional road roughness considering the coherence of left and right tracks was created using the sinusoid superposition method. The calculated results show that the muzzle vibration amplitude is larger than that of cradle because of barrel’s flexibility. When the road roughness is small and the running speed is low, the muzzle bends downward relative to the cradle. With the increase in road roughness and running speed, the stability of hull and cradle is getting worse, and the stabilizer cannot guarantee the stabilization accuracy. The difference of elevation angular displacement between muzzle and cradle caused by barrel’s flexibility is significantly reduced. Therefore, the influence of barrel’s flexibility on the firing accuracy cannot be solved by static correction simply, and the driving condition should be considered. [ABSTRACT FROM AUTHOR]

A fault diagnosis classification model based on WGAN-CNN is proposed for few fault data of planetary gearbox and the imbalanced samples of each state in actual operation. The proposed model is a combination of Wasserstein generative adversarial network(WGAN), a sample generation model, a convolutional neural network (CNN), and a sample classification model. The model is used to oversample the spectral signals of fault data and expand the number of fault samples, thus classifying the fault states better. UCI artificial datasets were used to compare WGAN generation model and classical oversampling methods, and verified on a planetary gearbox fault test rig. The results show that the imbalanced samples seriously affect the classification results, and the WGAN-CNN model can well expand the fault sample datasets and improve the diagnostic accuracy in the case of rare fault samples. [ABSTRACT FROM AUTHOR]

For the nonlinearity and unstability of planetary gearbox vibration,as well as the weak fault feature during its operation,the quantum theory is introduced into calculation of information entropy,and a new feature extraction method-linear quantum information entropy( LQE) is proposed. The basic concepts of quantum theory and the linear quantum bit expression of vibration signals are introduced,and a multi-qubit system for vibration signals is established. Then a linear quantum information entropy algorithm is proposed based on the expression of multi-qubit signals. A planetary gearbox fault simulation test is performed,and the linear quantum information entropy of five state vibration signals collected by the test is solved. The calculated result of linear quantum information entropy is compared with the calculated results of time-frequency entropy( TFE),permutation entropy( PE) and sample entropy( SE). The result indicates that the linear quantum information entropy can be used effectively to extract the operating characteristics of planetary gearboxes. [ABSTRACT FROM AUTHOR]

A fault feature extraction method based on parameter optimized variational mode decomposition（VMD）and partial mean of multi-scale entropy is proposed for the extraction of planetary gearbox fault features. The particle swarm optimization（PSO） is used to optimize VMD parameters to overcome the drawback of subjectively selecting the parameters, and the signal is processed by parameter-optimized VMD. The effective components are selected by mutual information to reconstruct signal. Multi-scale entropy can be used to analyze the complexity of signal under different scale factors, and partial mean can be used to reflect the mean value and variation trend of data. Based on multi-scale entropy, the partial mean of multi-scale entropy is used to measure the operating states of planetary gearbox, thus extracting the fault features. The processed results of planetary gearbox experimental data show that the proposed method can be more effective for planetary gearbox fault extraction. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Vibration Engineering is the property of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Vibration Engineering is the property of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)