Hilbert-Huang变换及其在纱线故障诊断中的应用

阐述了Hilbert-Huang变换的基本原理,以实际的纱线信号为例,通过经验模态分解(EMD)将纱线信号分解成有限个固有模态函数(IMF),并求得纱线信号的Hilbert谱.结合分析纱线信号的波谱图和Hilbert谱图,判断出故障产生的原因.

The filtering characteristics of HHT and its application in acoustic log waveform signal processing

Array acoustic logging plays an important role in formation evaluation. Its data is a non-linear and non-stationary signal and array acoustic logging signals have time-varying spectrum characteristics. Traditional filtering methods are inadequate. We introduce a Hilbert- Huang transform （HHT） which makes full preservation of the non-linear and non-stationary characteristics and has great advantages in the acoustic signal filtering. Using the empirical mode decomposition （EMD） method, the acoustic log waveforms can be decomposed into a finite and often small number of intrinsic mode functions （IMF）. The results of applying HHT to real array acoustic logging signal filtering and de-noising are presented to illustrate the efficiency and power of this new method.

Random noise attenuation by f–x spatial projection-based complex empirical mode decomposition predictive filtering

The frequency–space（f–x） empirical mode decomposition（EMD） denoising method has two limitations when applied to nonstationary seismic data. First, subtracting the first intrinsic mode function（IMF） results in signal damage and limited denoising. Second, decomposing the real and imaginary parts of complex data may lead to inconsistent decomposition numbers. Thus, we propose a new method named f–x spatial projection-based complex empirical mode decomposition（CEMD） prediction filtering. The proposed approach directly decomposes complex seismic data into a series of complex IMFs（CIMFs） using the spatial projection-based CEMD algorithm and then applies f–x predictive filtering to the stationary CIMFs to improve the signal-to-noise ratio. Synthetic and real data examples were used to demonstrate the performance of the new method in random noise attenuation and seismic signal preservation.

Seismic attribute extraction based on HHT and its application in a marine carbonate area

The Hilbert-Huang transform（HHT） is a new analysis method suitable for nonlinear and non-stationary signals.It is very appropriate to seismic signals because they show both non-stationary and nonlinear characteristics.We first introduce the realization of HHT empirical mode decomposition（EMD） and then comparatively analyze three instantaneous frequency algorithms based on intrinsic mode functions（IMF） resulting from EMD,of which one uses the average instantaneous frequency of two sample intervals having higher resolution which can determine that the signal frequency components change with time.The method is used with 3-D poststack migrated seismic data of marine carbonate strata in southern China to effectively extract the three instantaneous attributes.The instantaneous phase attributes of the second intrinsic mode functions（IMF2） better describe the reef facies of the platform margin and the IMF2 instantaneous frequency attribute has better zoning.Combining analysis of the three IMF2 instantaneous seismic attributes and drilling data can identify the distribution of sedimentary facies well.

Reservoir detection based on EMD and correlation dimension

In hydrocarbon reservoirs, seismic waveforms become complex and the correlation dimension becomes smaller. Seismic waves are signals with a definite frequency bandwidth and the waveform is affected by all the frequency components in the band. The results will not define the reservoir well if we calculate correlation dimension directly. In this paper, we present a method that integrates empirical mode decomposition （EMD） and correlation dimension. EMD is used to decompose the seismic waves and calculate the correlation dimension of every intrinsic mode function （IMF） component of the decomposed wave. Comparing the results with reservoirs identified by known wells, the most effective IMF is chosen and used to predict the reservoir. The method is applied in the Triassic Zhongyou group in the XX area of the Tahe oil field with quite good results.

Seismic data denoising based on mixed time-frequency methods

Deconvolution denoising in the f-x domain has some defects when facing situations like complicated geology structure, coherent noise of steep dip angles, and uneven spatial sampling. To solve these problems, a new filtering method is proposed, which uses the generalized S transform which has good time-frequency concentration criterion to transform seismic data from the time-space to time-frequency-space domain （t-f-x）. Then in the t-f-x domain apply Empirical Mode Decomposition （EMD） on each frequency slice and clear the Intrinsic Mode Functions （IMFs） that noise dominates to suppress coherent and random noise. The model study shows that the high frequency component in the first IMF represents mainly noise, so clearing the first IMF can suppress noise. The EMD filtering method in the t-f-x domain after generalized S transform is equivalent to self-adaptive f-k filtering that depends on position, frequency, and truncation characteristics of high wave numbers. This filtering method takes local data time-frequency characteristic into consideration and is easy to perform. Compared with AR predictive filtering, the component that this method filters is highly localized and contains relatively fewer low wave numbers and the filter result does not show over-smoothing effects. Real data processing proves that the EMD filtering method in the t-f-x domain after generalized S transform can effectively suppress random and coherent noise of steep dips.

Improved random noise attenuation using f-x empirical mode decomposition and local similarity

Conventional f-x empirical mode decomposition（EMD） is an effective random noise attenuation method for use with seismic profiles mainly containing horizontal events.However,when a seismic event is not horizontal,the use of f-x EMD is harmful to most useful signals.Based on the framework of f-x EMD,this study proposes an improved denoising approach that retrieves lost useful signals by detecting effective signal points in a noise section using local similarity and then designing a weighting operator for retrieving signals.Compared with conventional f-x EMD,f-x predictive filtering,and f-x empirical mode decomposition predictive filtering,the new approach can preserve more useful signals and obtain a relatively cleaner denoised image.Synthetic and field data examples are shown as test performances of the proposed approach,thereby verifying the effectiveness of this method.

Application of time–frequency entropy from wake oscillation to gas–liquid flow pattern identification

Gas–liquid two-phase flow abounds in industrial processes and facilities. Identification of its flow pattern plays an essential role in the field of multiphase flow measurement. A bluff body was introduced in this study to recognize gas–liquid flow patterns by inducing fluid oscillation that enlarged differences between each flow pattern. Experiments with air–water mixtures were carried out in horizontal pipelines at ambient temperature and atmospheric pressure. Differential pressure signals from the bluff-body wake were obtained in bubble, bubble/plug transitional, plug, slug, and annular flows. Utilizing the adaptive ensemble empirical mode decomposition method and the Hilbert transform, the time–frequency entropy S of the differential pressure signals was obtained. By combining S and other flow parameters, such as the volumetric void fraction β, the dryness x, the ratio of density φ and the modified fluid coefficient ψ, a new flow pattern map was constructed which adopted S（1–x）φ and （1–β）ψ as the vertical and horizontal coordinates, respectively. The overall rate of classification of the map was verified to be 92.9% by the experimental data. It provides an effective and simple solution to the gas–liquid flow pattern identification problems.

EMD Based Multi-scale Model for High Resolution Image Fusion

High resolution image fusion is a significant focus in the field of image processing. A new image fusion model is presented based on the characteristic level of empirical mode decomposition （EMD）. The intensity hue saturation （IHS） transform of the multi-spectral image first gives the intensity image. Thereafter, the 2D EMD in terms of row-column extension of the 1D EMD model is used to decompose the detailed scale image and coarse scale image from the high-resolution band image and the intensity image. Finally, a fused intensity image is obtained by reconstruction with high frequency of the high-resolution image and low frequency of the intensity image and IHS inverse transform result in the fused image. After presenting the EMD principle, a multi-scale decomposition and reconstruction algorithm of 2D EMD is defined and a fusion technique scheme is advanced based on EMD. Panchromatic band and multi-spectral band 3,2,1 of Quickbird are used to assess the quality of the fusion algorithm. After selecting the appropriate intrinsic mode function （IMF） for the merger on the basis of EMD analysis on specific row （column） pixel gray value series, the fusion scheme gives a fused image, which is compared with generally used fusion algorithms （wavelet, IHS, Brovey）. The objectives of image fusion include enhancing the visibility of the image and improving the spatial resolution and the spectral information of the original images. To assess quality of an image after fusion, information entropy and standard deviation are applied to assess spatial details of the fused images and correlation coefficient, bias index and warping degree for measuring distortion between the original image and fused image in terms of spectral information. For the proposed fusion algorithm, better results are obtained when EMD algorithm is used to perform the fusion experience.

Magnetotelluric signal-noise separation method based on SVM–CEEMDWT

To better retain useful weak low-frequency magnetotelluric(MT)signals with strong interference during MT data processing,we propose a SVM-CEEMDWT based MT data signal-noise separation method,which extracts the weak MT signal affected by strong interference.First,the approximate entropy,fuzzy entropy,sample entropy,and Lempel-Ziv(LZ)complexity are extracted from the magnetotelluric data.Then,four robust parameters are used as the inputs to the support vector machine(SVM)to train the sample library and build a model based on the different complexity of signals.Based on this model,we can only consider time series with strong interference when using the complementary ensemble empirical mode decomposition(CEEMD)and wavelet threshold(WT)for noise suppression.Simulation results suggest that the SVM based on the robust parameters can distinguish the time periods with strong interference well before noise suppression.Compared with the CEEMD WT,the proposed SVM-CEEMDWT method retains more low-frequency low-variability information,and the apparent resistivity curve is smoother and more continuous.Moreover,the results better reflect the deep electrical structure in the field.

A method for constraining the end effect of EMD based on sequential similarity detection and adaptive filter

Aimed at the problem of the end effect when using empirical mode decomposition(EMD),a method for constraining the end effect of EMD is proposed based on sequential similarity detection and adaptive filter.The method divides the signal into many wavelets,and it changes the initial wavelet length to select the best initial wavelet that has the minimum error and maximum number of matching seed wavelets,and the wavelet slopes are used for pre-matching and secondary matching to speed up the matching speed.Then,folded self-adaptive threshold is used to select multiple seed wavelets,and finally the end waveform is predicted and expanded according to the adaptive filter method.The proposed method is used to analyze the non-stationary nonlinear simulation signal and experimental signal,and it is compared with the mirror extension and RBF extension methods.The orthogonality index and similarity index of the EMD results of the extended signal after the proposed method are better than those of the other methods.The results show that the proposed method can better constrain the end effect,and has certain validity,accuracy and stability in solving the end effect problem.

Effective forecast of Northeast Pacific sea surface temperature based on a complementary ensemble empirical mode decomposition–support vector machine method

The sea surface temperature （SST） has substantial impacts on the climate; however, due to its highly nonlinear nature, evidently non-periodic and strongly stochastic properties, it is rather difficult to predict SST. Here, the authors combine the complementary ensemble empirical mode decomposition （CEEMD） and support vector machine （SVM） methods to predict SST. Extensive tests from several different aspects are presented to validate the effectiveness of the CEEMD-SVM method. The results suggest that the new method works well in forecasting Northeast Pacific SST at a 12-month lead time, with an average absolute error of approximately 0.3℃ and a correlation coefficient of 0.85. Moreover, no spring predictability barrier is observed in our experiments.

Combined filter method for weakening GNSS multipath error

A filter method that combines ensemble empirical modal decomposition(EEMD)and wavelet analysis methods was proposed to separate and correct the global navigation satellite system(GNSS)multipath error more effectively.In this method,the GNSS signal is first decomposed into several intrinsic mode functions(IMFs)and a residual through EEMD.Then,the IMFs and residual are classified into noise terms,mixed terms,and useful terms according to a combined classification criterion.Finally,the mixed term denoised by wavelet and the useful term are reconstructed to obtain the multipath error and thus enable an error correction model to be built.The measurement data provided by the Curtin GNSS Research Center were used for processing and analysis.Results show that the proposed method can separate multipath error from GNSS data to a great extent,thereby effectively addressing the defects of EEMD and wavelet methods on multipath error weakening.The error correction model established with the separated multipath error has a higher accuracy and provides a certain reference value for research on related signal processing.

Noise-assisted MEMD based relevant IMFs identification and EEG classification

Noise-assisted multivariate empirical mode decomposition(NA-MEMD) is suitable to analyze multichannel electroencephalography(EEG) signals of non-stationarity and non-linearity natures due to the fact that it can provide a highly localized time-frequency representation.For a finite set of multivariate intrinsic mode functions(IMFs) decomposed by NA-MEMD,it still raises the question on how to identify IMFs that contain the information of inertest in an efficient way,and conventional approaches address it by use of prior knowledge.In this work,a novel identification method of relevant IMFs without prior information was proposed based on NA-MEMD and Jensen-Shannon distance(JSD) measure.A criterion of effective factor based on JSD was applied to select significant IMF scales.At each decomposition scale,three kinds of JSDs associated with the effective factor were evaluated:between IMF components from data and themselves,between IMF components from noise and themselves,and between IMF components from data and noise.The efficacy of the proposed method has been demonstrated by both computer simulations and motor imagery EEG data from BCI competition IV datasets.

Dynamic unbalance detection of cardan shaft in high-speed train based on EMD-SVD-NHT

Contrary to the aliasing defect between the adjacent intrinsic model functions(IMFs) existing in empirical model decomposition(EMD), a new method of detecting dynamic unbalance with cardan shaft in high-speed train was proposed by applying the combination between EMD, Hankel matrix, singular value decomposition(SVD) and normalized Hilbert transform(NHT). The vibration signals of gimbal installed base were decomposed through EMD to get different IMFs. The Hankel matrix constructed through the single IMF was orthogonally executed through SVD. The critical singular values were selected to reconstruct vibration signs on the basis of the key stack of singular values. Instantaneous frequencys(IFs) of reconstructed vibration signs were applied to detect dynamic unbalance with shaft and eliminated clutter spectrum caused by the aliasing defect between the adjacent IMFs, which highlighted the failure characteristics. The method was verified by test data in the unbalance condition of dynamic cardan shaft. The results show that the method effectively detects the fault vibration characteristics caused by cardan shaft dynamic unbalance and extracts the nature vibration features. With comparison to the traditional EMD-NHT, clarity and failure characterization force are significantly improved.

Multi-scale prediction of MEMS gyroscope random drift based on EMD-SVR

To improve the prediction accuracy of micro-electromechanical systems(MEMS)gyroscope random drift series,a multi-scale prediction model based on empirical mode decomposition(EMD)and support vector regression(SVR)is proposed.Firstly,EMD is employed to decompose the raw drift series into a finite number of intrinsic mode functions(IMFs)with the frequency descending successively.Secondly,according to the time-frequency characteristic of each IMF,the corresponding SVR prediction model is established based on phase space reconstruction.Finally,the prediction results are obtained by adding up the prediction results of all IMFs with equal weight.The experimental results demonstrate the validity of the proposed model in random drift prediction of MEMS gyroscope.Compared with a single SVR model,the proposed model has higher prediction precision,which can provide the basis for drift error compensation of MEMS gyroscope.

Vibration-based feature extraction of determining dynamic characteristic for engine block low vibration design

In order to maintain vibration performances within the limits of the design, a vibration-based feature extraction method for dynamic characteristic using empirical mode decomposition （EMD） and wavelet analysis was proposed. The proposed method was verified experimentally and numerically by implementing the scheme on engine block. In the implementation process, the following steps were identified to be important： 1） EMD technique in order to solve the feature extraction of vibration signals; 2） Vibration measurement for the purpose of confirming the structural weak regions of engine block in experiment; 3） Finite element modeling for the purpose of determining dynamic characteristic in time region and frequency region to affirm the comparability of response character corresponding to improvement schemes; 4） Adopting a feature index oflMF for structural improvement based on EMD and wavelet analysis. The obtained results show that IMF of signal is more sensitive to response character corresponding to improvement schemes. Finally, examination of the results confirms that the proposed vibration-based feature extraction method is very robust, and focuses on the relative merits of modification and full-scale structural optimization of engine, together with the creation of new low-vibration designs.

Single Trial Detection of Visual Evoked Potential by Using EMD and Wavelet Filtering Method

Empirical mode decomposition(EMD) is a new signal decomposition method, which could decompose the non-stationary signal into several single-component intrinsic mode functions (IMFs) and each IMF has some physical meanings. This paper studies the single trial extraction of visual evoked potential by combining EMD and wavelet threshold filter. Experimental results showed that the EMD based method can separate the noise out of the event related potentials (ERPs) and effectively extract the weak ERPs in strong background noise, which manifested as the waveform characteristics and root mean square error (RMSE).

Sparse time-frequency representation of nonlinear and nonstationary data Dedicated to Professor Shi Zhong-Ci on the Occasion of his 80th Birthday

Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications. In this paper, we review two data-driven time-frequency analysis methods that we introduced recently to study trend and instantaneous frequency of nonlinear and nonstationary data. These methods are inspired by the empirical mode decomposition method （EMD） and the recently developed compressed （compressive） sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a（t） cos（0（t））}, where a is assumed to be less oscillatory than cos（θ（t）） and θ ＇≥ 0. This problem can be formulated as a nonlinear ι0 optimization problem. We have proposed two methods to solve this nonlinear optimization problem. The first one is based on nonlinear basis pursuit and the second one is based on nonlinear matching pursuit. Convergence analysis has been carried out for the nonlinear matching pursuit method. Some numerical experiments are given to demonstrate the effectiveness of the proposed methods.

On-line chatter detection using servo motor current signal in turning

Chatter often poses limiting factors on the achievable productivity and is very harmful to machining processes. In order to avoid effectively the harm of cutting chatter,a method of cutting state monitoring based on feed motor current signal is proposed for chatter identification before it has been fully developed. A new data analysis technique,the empirical mode decomposition(EMD),is used to decompose motor current signal into many intrinsic mode functions(IMF) . Some IMF's energy and kurtosis regularly change during the development of the chatter. These IMFs can reflect subtle mutations in current signal. Therefore,the energy index and kurtosis index are used for chatter detection based on those IMFs. Acceleration signal of tool as reference is used to compare with the results from current signal. A support vector machine(SVM) is designed for pattern classification based on the feature vector constituted by energy index and kurtosis index. The intelligent chatter detection system composed of the feature extraction and the SVM has an accuracy rate of above 95% for the identification of cutting state after being trained by experimental data. The results show that it is feasible to monitor and predict the emergence of chatter behavior in machining by using motor current signal.