Adaptive Fourier Decomposition Based Time-Frequency Analysis

The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition （AFD） offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects： instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.

Study on the Improvement of the Application of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise in Hydrology Based on RBFNN Data Extension Technology

The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult.Currently,some hydrologists employ the complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)method,a new time-frequency analysis method based on the empirical mode decomposition(EMD)algorithm,to decompose non-stationary raw data in order to obtain relatively stationary components for further study.However,the endpoint effect in CEEMDAN is often neglected,which can lead to decomposition errors that reduce the accuracy of the research results.In this study,we processed an original runoff sequence using the radial basis function neural network(RBFNN)technique to obtain the extension sequence before utilizing CEEMDAN decomposition.Then,we compared the decomposition results of the original sequence,RBFNN extension sequence,and standard sequence to investigate the influence of the endpoint effect and RBFNN extension on the CEEMDAN method.The results indicated that the RBFNN extension technique effectively reduced the error of medium and low frequency components caused by the endpoint effect.At both ends of the components,the extension sequence more accurately reflected the true fluctuation characteristics and variation trends.These advances are of great significance to the subsequent study of hydrology.Therefore,the CEEMDAN method,combined with an appropriate extension of the original runoff series,can more precisely determine multi-time scale characteristics,and provide a credible basis for the analysis of hydrologic time series and hydrological forecasting.

Quantitative detection of locomotive wheel polygonization under non-stationary conditions by adaptive chirp mode decomposition

Wheel polygonal wear is a common and severe defect,which seriously threatens the running safety and reliability of a railway vehicle especially a locomotive.Due to non-stationary running conditions(e.g.,traction and braking)of the locomotive,the passing frequencies of a polygonal wheel will exhibit time-varying behaviors,which makes it too difficult to effectively detect the wheel defect.Moreover,most existing methods only achieve qualitative fault diagnosis and they cannot accurately identify defect levels.To address these issues,this paper reports a novel quantitative method for fault detection of wheel polygonization under non-stationary conditions based on a recently proposed adaptive chirp mode decomposition(ACMD)approach.Firstly,a coarse-to-fine method based on the time–frequency ridge detection and ACMD is developed to accurately estimate a time-varying gear meshing frequency and thus obtain a wheel rotating frequency from a vibration acceleration signal of a motor.After the rotating frequency is obtained,signal resampling and order analysis techniques are applied to an acceleration signal of an axle box to identify harmonic orders related to polygonal wear.Finally,the ACMD is combined with an inertial algorithm to estimate polygonal wear amplitudes.Not only a dynamics simulation but a field test was carried out to show that the proposed method can effectively detect both harmonic orders and their amplitudes of the wheel polygonization under non-stationary conditions.

基于CEEMDAN-HT的永磁同步电机匝间短路振动信号故障特征提取研究

由于长时间处于高负荷运行状态,永磁同步电机(permanent magnet synchronous motor, PMSM)定子绕组线圈匝与匝之间的绝缘性能容易降低,导致出现匝间短路,此时电机的振动强度会发生改变。针对此现象,提出将自适应噪声完备经验模态分解(complete ensemble empirical mode decomposition with adaptive noise, CEEMDAN)与希尔伯特变换(Hilbert transform, HT)结合,构成一种CEEMDAN-HT非线性信号分析方法,并将其应用于提取振动信号故障特征。首先,利用CEEMDAN算法分解振动信号,得到一系列本征模态函数(intrinsic mode function, IMF),并将主元分析中的方差贡献率用于识别包含故障特征信息的IMF。其次,使用HT对方差贡献率较高的IMF进行分析,并以三维联合时频图呈现时间、瞬时频率与幅值,得到了主要故障特征。最后,使用ANSYS有限元软件建立了电机短路故障模型,并搭建了短路故障试验平台,通过对比有限元仿真结果与试验结果,对提出的方法进行了有效性和准确性验证。

Rolling Bearing Feature Frequency Extraction using Extreme Average Envelope Decomposition

The vibration signal contains a wealth of sensitive information which reflects the running status of the equipment. It is one of the most important steps for precise diagnosis to decompose the signal and extracts the effective information properly. The traditional classical adaptive signal decomposition method, such as EMD, exists the problems of mode mixing, low decomposition accuracy etc. Aiming at those problems, EAED（extreme average envelope decomposition） method is presented based on EMD. EAED method has three advantages. Firstly, it is completed through midpoint envelopment method rather than using maximum and minimum envelopment respectively as used in EMD. Therefore, the average variability of the signal can be described accurately. Secondly, in order to reduce the envelope errors during the signal decomposition, replacing two envelopes with one envelope strategy is presented. Thirdly, the similar triangle principle is utilized to calculate the time of extreme average points accurately. Thus, the influence of sampling frequency on the calculation results can be significantly reduced. Experimental results show that EAED could separate out single frequency components from a complex signal gradually. EAED could not only isolate three kinds of typical bearing fault characteristic of vibration frequency components but also has fewer decomposition layers. EAED replaces quadratic enveloping to an envelope which ensuring to isolate the fault characteristic frequency under the condition of less decomposition layers. Therefore, the precision of signal decomposition is improved.

Parametric adaptive time-frequency representation based on time-sheared Gabor atoms

A localized parametric time-sheared Gabor atom is derived by convolving a linear frequency modulated factor, modulating in frequency and translating in time to a dilated Gaussian function, which is the generalization of Gabor atom and is more delicate for matching most of the signals encountered in practice, especially for those having frequency dispersion characteristics. The time-frequency distribution of this atom concentrates in its time center and frequency center along energy curve, with the curve being oblique to a certain extent along the time axis. A novel parametric adaptive time-frequency distribution based on a set of the derived atoms is then proposed using a adaptive signal subspace decomposition method in frequency domain, which is non-negative time-frequency energy distribution and free of cross-term interference for multicomponent signals. The results of numerical simulation manifest the effectiveness of the approach in time-frequency representation and signal de-noising processing.

Missing interpolation model for wind power data based on the improved CEEMDAN method and generative adversarial interpolation network

Randomness and fluctuations in wind power output may cause changes in important parameters(e.g.,grid frequency and voltage),which in turn affect the stable operation of a power system.However,owing to external factors(such as weather),there are often various anomalies in wind power data,such as missing numerical values and unreasonable data.This significantly affects the accuracy of wind power generation predictions and operational decisions.Therefore,developing and applying reliable wind power interpolation methods is important for promoting the sustainable development of the wind power industry.In this study,the causes of abnormal data in wind power generation were first analyzed from a practical perspective.Second,an improved complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN)method with a generative adversarial interpolation network(GAIN)network was proposed to preprocess wind power generation and interpolate missing wind power generation sub-components.Finally,a complete wind power generation time series was reconstructed.Compared to traditional methods,the proposed ICEEMDAN-GAIN combination interpolation model has a higher interpolation accuracy and can effectively reduce the error impact caused by wind power generation sequence fluctuations.

A Fault Feature Extraction Model in Synchronous Generator under Stator Inter-Turn Short Circuit Based on ACMD and DEO3S

This paper proposed a new diagnosis model for the stator inter-turn short circuit fault in synchronous generators.Different from the past methods focused on the current or voltage signals to diagnose the electrical fault,the sta-tor vibration signal analysis based on ACMD(adaptive chirp mode decomposition)and DEO3S(demodulation energy operator of symmetrical differencing)was adopted to extract the fault feature.Firstly,FT(Fourier trans-form)is applied to the vibration signal to obtain the instantaneous frequency,and PE(permutation entropy)is calculated to select the proper weighting coefficients.Then,the signal is decomposed by ACMD,with the instan-taneous frequency and weighting coefficient acquired in the former step to obtain the optimal mode.Finally,DEO3S is operated to get the envelope spectrum which is able to strengthen the characteristic frequencies of the stator inter-turn short circuit fault.The study on the simulating signal and the real experiment data indicates the effectiveness of the proposed method for the stator inter-turn short circuit fault in synchronous generators.In addition,the comparison with other methods shows the superiority of the proposed model.

A Sparse Kernel Approximate Method for Fractional Boundary Value Problems

In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.

Prediction of seawater pH by bidirectional gated recurrent neural network with attention under phase space reconstruction:case study of the coastal waters of Beihai,China

Marine life is very sensitive to changes in pH.Even slight changes can cause ecosystems to collapse.Therefore,understanding the future pH of seawater is of great significance for the protection of the marine environment.At present,the monitoring method of seawater pH has been matured.However,how to accurately predict future changes has been lacking effective solutions.Based on this,the model of bidirectional gated recurrent neural network with multi-headed self-attention based on improved complete ensemble empirical mode decomposition with adaptive noise combined with phase space reconstruction(ICPBGA)is proposed to achieve seawater pH prediction.To verify the validity of this model,pH data of two monitoring sites in the coastal sea area of Beihai,China are selected to verify the effect.At the same time,the ICPBGA model is compared with other excellent models for predicting chaotic time series,and root mean square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE),and coefficient of determination(R2)are used as performance evaluation indicators.The R2 of the ICPBGA model at Sites 1 and 2 are above 0.9,and the prediction errors are also the smallest.The results show that the ICPBGA model has a wide range of applicability and the most satisfactory prediction effect.The prediction method in this paper can be further expanded and used to predict other marine environmental indicators.

MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES

Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries consisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary dimensions.

A novel feature extraction method for ship-radiated noise

To improve the feature extraction of ship-radiated noise in a complex ocean environment,a novel feature extraction method for ship-radiated noise based on complete ensemble empirical mode decomposition with adaptive selective noise(CEEMDASN) and refined composite multiscale fluctuation-based dispersion entropy(RCMFDE) is proposed.CEEMDASN is proposed in this paper which takes into account the high frequency intermittent components when decomposing the signal.In addition,RCMFDE is also proposed in this paper which refines the preprocessing process of the original signal based on composite multi-scale theory.Firstly,the original signal is decomposed into several intrinsic mode functions(IMFs)by CEEMDASN.Energy distribution ratio(EDR) and average energy distribution ratio(AEDR) of all IMF components are calculated.Then,the IMF with the minimum difference between EDR and AEDR(MEDR)is selected as characteristic IMF.The RCMFDE of characteristic IMF is estimated as the feature vectors of ship-radiated noise.Finally,these feature vectors are sent to self-organizing map(SOM) for classifying and identifying.The proposed method is applied to the feature extraction of ship-radiated noise.The result shows its effectiveness and universality.

Unintentional modulation microstructure enlargement

Radio frequency fingerprinting(RFF)is a technology that identifies the specific emitter of a received electromagnetic signal by external measurement of the minuscule hardware-level,device-specific imperfections.The RFF-related information is mainly in the form of unintentional modulation(UIM),which is subtle enough to be effectively imperceptible and is submerged in the intentional modulation(IM).It is necessary to minimize the influence of the IM and expand the slight differences between emitters for successful RFF.This paper proposes a UIM microstructure enlargement(UMME)method based on feature-level adaptive signal decomposition(ASD),accompanied by autocorrelation and cross-correlation analysis.The common IM part is evaluated by analyzing a newly-defined benchmark feature.Three different indexes are used to quantify the similarity,distance,and dependency of the RFF features from different devices.Experiments are conducted based on the real-world signals transmitted from 20 of the same type of radar in the same working mode.The visual image qualitatively shows the magnification of feature differences;different indicators quantitatively describe the changes in features.Compared with the original RFF feature,recognition results based on the Gaussian mixture model(GMM)classifier further validate the effectiveness of the proposed algorithm.

ANALYTIC PHASE RETRIEVAL BASED ON INTENSITY MEASUREMENTS

This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f(a)and certain n-intensity measurements|<f,E_(a1…an)>|,where a_(1)…a_(n)∈D,and E_(a1…an)is the n-th term of the Gram-Schmidt orthogonalization of the Szego kernels k_(a1),k_(an),or their multiple forms.Three schemes are presented.The first two schemes each directly obtain all the function values f(z).In the first one we use Nevanlinna’s inner and outer function factorization which merely requires the 1-intensity measurements equivalent to know the modulus|f(z)|.In the second scheme we do not use deep complex analysis,but require some 2-and 3-intensity measurements.The third scheme,as an application of AFD,gives sparse representation of f(z)converging quickly in the energy sense,depending on consecutively selected maximal n-intensity measurements|<f,E_(a1…an)>|.

Diagnosis of multiple faults using a double parallel two-hidden-layer extreme learning machine

Multiple faults are easily confused with single faults.In order to identify multiple faults more accurately,a highly efficient learning method is proposed based on a double parallel two-hidden-layer extreme learning machine,called DPTELM.The DPT-ELM method is a variant of an extreme learning machine(ELM).There are some issues with ELM.First,achieving a high accuracy requires too many hidden nodes;second,the direct connection between the input layer and the output layer is ignored.Accordingly,to deal with the above-mentioned problems,DPT-ELM extends the single-hidden-layer ELM to a two-hidden-layer ELM,which can achieve a desired performance with fewer hidden nodes.In addition,a direct connection is built between the input layer and the output layer.Since the input layer weights and the thresholds of the two hidden layers are determined randomly,this simplifies the improved model and shortens the calculation time.Additionally,to improve the signal to noise ratio(SNR),an adaptive waveform decomposition(AWD)algorithm is used to denoise the vibration signal.Then,the denoised signal is used to extract the eigenvalues by the time-domain and frequency-domain methods.Finally,the eigenvalues are input to the DPT-ELM classifier.In this paper,two groups of rolling bearing data at different speeds,which were collected from a real experimental platform,are used to test the method.Each set of data includes three single fault states,two complex fault states and a healthy state.The experimental results demonstrate that the DPT-ELM method achieves fast learning speed and a high accuracy.Moreover,based on 10-fold cross-validation,it proves to be an effective method to improve the accuracy with fewer hidden nodes.

A hybrid approach based on complete ensemble empirical mode decomposition with adaptive noise for multi-step-ahead solar radiation forecasting

Accurate measurements of solar radiation are required to ensure that power and energy systems continue to function effectively and securely.On the other hand,estimating it is extremely challenging due to the non-stationary behaviour and randomness of its components.In this research,a novel hybrid forecasting model,namely complete ensemble empirical mode decomposition with adaptive noise-Gaussian process regression(CEEMDAN-GPR),has been developed for daily global solar radiation prediction.The non-stationary global solar radiation series is transformed by CEEMDAN into regular subsets.After that,the GPR model uses these subsets as inputs to perform its prediction.According to the results of this research,the performance of the developed hybrid model is superior to two widely used hybrid models for solar radiation forecasting,namely wavelet-GPR and wavelet packet-GPR,in terms of mean square error,root mean square error,coefficient of determination and relative root mean square error values,which reached 3.23 MJ/m^(2)/day,1.80 MJ/m^(2)/day,95.56%,and 8.80%,respectively(for one-step forward forecasting).The proposed hybrid model can be used to ensure the safe and reliable operation of the electricity system.

Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations

With wave-particle decomposition,a unified gas-kinetic wave-particle(UGKWP)method has been developed for multiscale flow simulations.With the variation of the cell Knudsen number,the UGKWP method captures the transport process in all flow regimes without the kinetic solver’s constraint on the numerical mesh size and time step being determined by the kinetic particle mean free path and particle collision time.In the current UGKWP method,the cell Knudsen number,which is defined as the ratio of particle collision time to numerical time step,is used to distribute the components in the wave-particle decomposition.The adaptation of particles in the UGKWP method is mainly for the capturing of the non-equilibrium transport.In this aspect,the cell Knudsen number alone is not enough to identify the non-equilibrium state.For example,in the equilibrium flow regime with a Maxwellian distribution function,even at a large cell Knudsen number,the flow evolution can be still modelled by the Navier-Stokes solver.More specifically,in the near space environment both the hypersonic flow around a space vehicle and the plume flow from a satellite nozzle will encounter a far field rarefied equilibrium flow in a large computational domain.In the background dilute equilibrium region,the large particle collision time and a uniform small numerical time step can result in a large local cell Knudsen number and make the UGKWP method track a huge number of particles for the far field background flow in the original approach.But,in this region the analytical wave representation can be legitimately used in the UGKWP method to capture the nearly equilibrium flow evolution.Therefore,to further improve the efficiency of the UGKWP method for multiscale flow simulations,an adaptive UGKWP(AUGKWP)method is developed with the introduction of an additional local flow variable gradient-dependent Knudsen number.As a result,the wave-particle decomposition in the UGKWP method is determined by both the cell and gradient Knudsen numbers,and the use of particles in the UGKWP method is solely to capture the non-equilibrium flow transport.The current AUGKWP method becomes much more efficient than the previous one with the cell Knudsen number only in the determination of wave-particle composition.Many numerical tests,including Sod shock tube,normal shock structure,hypersonic flow around cylinder,flow around reentry capsule,and an unsteady nozzle plume flow,have been conducted to validate the accuracy and efficiency of the AUGKWP method.Compared with the original UGKWP method,the AUGKWP method achieves the same accuracy,but has advantages in memory reduction and computational efficiency in the simulation for flows with the co-existing of multiple regimes.

Hybrid Deep Learning Model for Short-Term Wind Speed Forecasting Based on Time Series Decomposition and Gated Recurrent Unit

Accurate wind speed prediction has been becoming an indispensable technology in system security,wind energy utilization,and power grid dispatching in recent years.However,it is an arduous task to predict wind speed due to its variable and random characteristics.For the objective to enhance the performance of forecasting short-term wind speed,this work puts forward a hybrid deep learning model mixing time series decomposition algorithm and gated recurrent unit(GRU).The time series decomposition algorithm combines the following two parts:(1)the complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),and(2)wavelet packet decomposition(WPD).Firstly,the normalized wind speed time series(WSTS)are handled by CEEMDAN to gain pure fixed-frequency components and a residual signal.The WPD algorithm conducts the second-order decomposition to the first component that contains complex and high frequency signal of raw WSTS.Finally,GRU networks are established for all the relevant components of the signals,and the predicted wind speeds are obtained by superimposing the prediction of each component.Results from two case studies,adopting wind data from laboratory and wind farm,respectively,suggest that the related trend of the WSTS can be separated effectively by the proposed time series decomposition algorithm,and the accuracy of short-time wind speed prediction can be heightened significantly mixing the time series decomposition algorithm and GRU networks.

一种基于CEEMDAN-改进小波阈值的OTDR信号去噪算法

为了解决光时域反射仪(optical time domain reflectometer,OTDR)中背向散射信号受噪声干扰严重问题,本文提出了一种基于自适应噪声完备集合经验模态分解(complete ensemble empirical mode decomposition with adaptive noise,CEEMDAN)和改进小波阈值的OTDR信号去噪算法,利用CEEMDAN分解算法具有的抗模态混叠现象和降低重构误差等优点,将信号分解为若干IMF分量,根据相关系数的分析方法,找到噪声占主导的本征模态函数(intrinsic mode function,IMF)分量和信号占主导的IMF分量的临界点,去除噪声占主导的IMF分量,并将改进的小波阈值去噪方法对信号占主导的IMF分量进行去噪,最后重构信号。结果表明,本文提出的方法与传统的硬阈值方法、CEEMDAN-硬阈值方法和改进的小波阈值方法相比,能更好地抑制噪声,并达到更好的去噪效果,突显OTDR事件特征,更易于事件的检测。

Positive-instantaneous frequency and approximation

Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical importance,although the involved concept itself is paradoxical.The desire and practice of uniqueness of such frequency representation(decomposition)raise the related topics in approximation.During approximately the last two decades there has formulated a signal decomposition and reconstruction method rooted in harmonic and complex analysis giving rise to the desired signal representations.The method decomposes any signal into a few basic signals that possess positive instantaneous frequencies.The theory has profound relations to classical mathematics and can be generalized to signals defined in higher dimensional manifolds with vector and matrix values,and in particular,promotes kernel approximation for multi-variate functions.This article mainly serves as a survey.It also gives two important technical proofs of which one for a general convergence result(Theorem 3.4),and the other for necessity of multiple kernel(Lemma 3.7).Expositorily,for a given real-valued signal f one can associate it with a Hardy space function F whose real part coincides with f.Such function F has the form F=f+iHf,where H stands for the Hilbert transformation of the context.We develop fast converging expansions of F in orthogonal terms of the form F=∑k=1^(∞)c_(k)B_(k),where B_(k)'s are also Hardy space functions but with the additional properties B_(k)(t)=ρ_(k)(t)e^(iθ_(k)(t)),ρk≥0,θ′_(k)(t)≥0,a.e.The original real-valued function f is accordingly expanded f=∑k=1^(∞)ρ_(k)(t)cosθ_(k)(t)which,besides the properties ofρ_(k)andθ_(k)given above,also satisfies H(ρ_(k)cosθ_(k))(t)ρ_(k)(t)sinρ_(k)(t).Real-valued functions f(t)=ρ(t)cosθ(t)that satisfy the conditionρ≥0,θ′(t)≥0,H(ρcosθ)(t)=ρ(t)sinθ(t)are called mono-components.If f is a mono-component,then the phase derivativeθ′(t)is defined to be instantaneous frequency of f.The above described positive-instantaneous frequency expansion is a generalization of the Fourier series expansion.Mono-components are crucial to understand the concept instantaneous frequency.We will present several most important mono-component function classes.Decompositions of signals into mono-components are called adaptive Fourier decompositions(AFDs).Wc note that some scopes of the studies on the ID mono-components and AFDs can be extended to vector-valued or even matrix-valued signals defined on higher dimensional manifolds.We finally provide an account of related studies in pure and applied mathematics.