A unified intrinsic functional expansion theory for solitary waves

A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120 down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokess formula, F2= tan , relating the wave speed (the Froude number F) and the logarithmic decrement of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokess basic term (singular in ), such that 2M is just somewhat beyond unity, i.e. 2M1. This fundamental criterion is fully validated by solutions for waves of various amplitude-to-water depth ratio =a/h, especially about 0.01, at which M=10 by the criterion. In this pursuit, the class of dwarf solitary waves, defined for waves with 0.01, is discovered as a group of problems more challenging than even the highest wave. For the highest wave, a new solution is determined here to give the maximum height hst=0.8331990, and speed Fhst=1.290890, accurate to the last significant figure, which seems to be a new record.

Subgraph Isomorphism Based Intrinsic Function Reduction in Decompilation

Program comprehension is one of the most important applications in decompilation. The more abstract the decompilation result the better it is understood. Intrinsic function is introduced by a compiler to reduce the overhead of a function call and is inlined in the code where it is called. When analyzing the decompiled code with lots of inlined intrinsic functions, reverse engineers may be confused by these detailed and repeated operations and lose the goal. In this paper, we propose a method based graph isomorphism to detect intrinsic function on the CFG (Control Flow Graph) of the target function first. Then we identify the boundary of the intrinsic function, determine the parameter and return value and reduce the intrinsic function to a single function call in the disassembled program. Experimental results show that our method is more efficient at reducing intrinsic functions than the state-of-art decompilers such as Hex-Rays, REC and RD (Retargetable Decompiler).

Weak Type Estimates for Intrinsic Square Functions on Weighted Morrey Spaces

In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.

QUATERNIONIC SLICE REGULAR FUNCTIONS AND QUATERNIONIC LAPLACE TRANSFORMS

The functions studied in the paper are the quaternion-valued functions of a quaternionic variable.It is shown that the left slice regular functions and right slice regular functions are related by a particular involution,and that the intrinsic slice regular functions play a central role in the theory of slice regular functions.The relation between left slice regular functions,right slice regular functions and intrinsic slice regular functions is revealed.As an application,the classical Laplace transform is generalized naturally to quaternions in two different ways,which transform a quaternion-valued function of a real variable to a left or right slice regular function.The usual properties of the classical Laplace transforms are generalized to quaternionic Laplace transforms.

Hilbert spectrum and intrinsic oscillation mode of dynamic response of a bilinear SDOF system: influence of harmonic excitation amplitude

Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.

Adaptive Variational Mode Decomposition for Bearing Fault Detection

Rolling element bearings are commonly used in rotary mechanical and electrical equipment. According to investigation, more than half of rotating machinery defects are related to bearing faults. However, reliable bearing fault detection still remains a challenging task, especially in industrial applications. The objective of this work is to propose an adaptive variational mode decomposition (AVMD) technique for non-stationary signal analysis and bearing fault detection. The AVMD includes several steps in processing: 1) Signal characteristics are analyzed to determine the signal center frequency and the related parameters. 2) The ensemble-kurtosis index is suggested to decompose the target signal and select the most representative intrinsic mode functions (IMFs). 3) The envelope spectrum analysis is performed using the selected IMFs to identify the characteristic features for bearing fault detection. The effectiveness of the proposed AVMD technique is examined by experimental tests under different bearing conditions, with the comparison of other related bearing fault techniques.

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.

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.

Grey Repairable System Analysis

In this paper, we systematically discuss the basic concepts of grey theory, particularly the grey differential equation and its mathematical foundation, which is essentially unknown in the reliability engineering community. Accordingly, we propose a small-sample based approach to estimate repair improvement effects by partitioning system stopping times into intrinsic functioning times and repair improvement times. An industrial data set is used for illustrative purposes in a stepwise manner.

Flow Regime Identification of Gas-liquid Two-phase Flow Based on HHT

A new method to identify flow regime in two-phase flow was presented, based on signal processing of differential pressure using Hilbert Huang transform （HHT）. Signals obtained from a Venturi meter were decomposed into different intrinsic mode functions （IMFs） with HHT, then the energy fraction of each intrinsic mode and the mean value of residual function were calculated, from which the rules of flow regime identification were summarized. Experiments were carried out on two-phase flow in the horizontal tubes with 50mm and 40mm inner diameter, while water flowrate was in the range of 1.3m^3.h^-1 to 10.5m^3.h^-1, oil flowrate was from 4.2m^3.h^-1 to 7.0m^3.h^-1 and gas flowrate from 0 to 15m^3.h^-1. The results show that the proposed rules have high precision for single phase, bubbly, and slug, plug flow regirne identification, which are independent of not only properties of two-phase fluid. In addition, the method can meet the need of industrial application because of its simple calculation.

Improvement of the Mirror Extending in Empirical Mode Decomposition Method and the Technology for Eliminating Frequency Mixing

The mirror extending approach proposed by Zhao and Huang in EMD method is improved in this paper. Mirror extending manner of data is kept unchanged, but the approach for determining envelopes is changed. When the end of data is obviously not extremum, the envelope is determined by the first inner extremum and the image value in the mirror, ignoring the value on the end. This improvement eliminates the frequency compression near the end and decreases the error. Meanwhile, tridiagonal equations are used and the calculation speed is much increased. The temporal process curve is more important in reflecting the real physical process and comparable with other phenomena. Frequency mixing in IMFs makes it impossible. A high frequency reconstruction (HFR) approach is proposed to eliminate common frequency mixing and reconstruct an IMF with all high frequency portions. By this approach, the IMFs without frequency mixing are obtained to express significative processes. The high frequency information restored in high frequency IMF can be extracted by general spectrum method. After obtaining IMFs by EMD method, some of the theoretical and technological issues still exist when using the IMFs. The consistency of IMFs with real physical process is discussed in detail. By virtue of the approach proposed in this paper, the EMD method can be widely used in various fields.

Regional features of the temperature trend in China based on Empirical Mode Decomposition

By the Empirical Mode Decomposition method, we analyzed the observed monthly average temperature in more than 700 stations from 1951-2001 over China. Simultaneously, the temperature variability of each station is calculated by this method, and classification chart of long term trend and temperature variability distributing chart of China are obtained, supported by GIS, 1 kmxl km resolution. The results show that： in recent 50 years, the temperature has increased by more than 0.4~C/10a in most parts of northern China, while in Southwest China and the middle and lower Yangtze Valley, the increase is not significant. The areas with a negative temperature change rate are distributed sporadically in Southwest China. Meanwhile, the temperature data from 1881 to 2001 in nine study regions in China are also analyzed, indicating that in the past 100 years, the temperature has been increasing all the way in Northeast China, North China, South China, Northwest China and Xinjiang and declining in Southwest China. An inverse ‘V-shaped’ trend is also found in Central China. But in Tibet the change is less significant.

Residual Fatigue Life Prediction of Ball Bearings Based on Paris Law and RMS

Paris law can reflect the failure mechanism of materials and is usually used to be a method to predict fatigue life or residual fatigue life.But the variable which can represent the health of machine is hardly measured on line.To a degree,the difficulty of on-line application restricts the scope of application of Paris law.The relationship between characteristic values of vibration signals and the variable in the Paris equation which can describe the health of machine is investigated by taking ball bearings as investigative objects.Based on 6205 deep groove ball bearings as a living example,historical lives and vibration signals are analyzed.The feasibility of describing that variable in the Paris equation by the characteristic value of vibration signals is inspected.After that vibration signals decomposed by empirical mode decomposition（EMD）,root mean square（RMS） of intrinsic mode function（IMF） involving fault characteristic frequency has a consistent trend with the diameter of flaws.Based on the trend,two improved Paris models are proposed and the scope of application of them is inspected.These two Paris Models are validated by fatigue residual life data from tests of rolling element bearings and vibration signals monitored in the process of operation of rolling element bearings.It shows that the first improved Paris Model is simple and plain and it can be easily applied in actual conditions.The trend of the fatigue residual life predicted by the second improved Paris model is close to the actual conditions and the result of the prediction is slightly greater than the truth.In conclusion,after the appearance of detectable faults,these improved models based on RMS can predict residual fatigue life on line and a new approach to predict residual fatigue life of ball bearings on line without disturbing the machine running is provided.

Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces

Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As an application,we prove that the dual space of H x(Rn)is the Campanato space associated with X.For any given a∈(0,1]and s∈Z+,using the atomic and the Littlewood—Paley function characterizations of H x(Rn),we also establish its 5-order intrinsic square function characterizations,respectively,in terms of the intrinsic Lusin-area function S a,s,the intrinsic g-function g a,s,and the intrinsic g*λ-function g*λ,a,s,whereλcoincides with the best known range.

An optimized design of seizure detection system using joint feature extraction of multichannel EEG signals

The detection of seizure onset and events using electroencephalogram(EEG) signals are important tasks in epilepsy research.The literature available on seizure detection has discussed the implementation of advanced signal processing algorithms using tools accessed over the cloud.However,seizure monitoring application needs near sensor processing due to privacy and latency issues.In this paper,a real time seizure detection system has been implemented using an embedded system.The proposed system is based on ensemble empirical mode decomposition(EEMD) and tunable-Q wavelet transform(TQWT) algorithms.The analysis and classification of non-stationary EEG signals require the wavelet transform with high Q-factor.However,direct use of TQWT increases the computational complexity of feature extraction from multivariate EEG signals.In this paper,the first step is to process the signal by using EEMD to obtain 8 intrinsic mode functions(IMFs).The Kraskov(KraEn),sample(SampEn),and permutation(PermEn) entropy features of IMFs are extracted and based on optimum values,and 4 IMFs are decomposed using TQWT.Secondly,centered correntropy(CenCorrEn) features of the 1^(st)and 16^(th) sub-band of TQWT have been used as classifier inputs.The performance of multilayer perceptron neural networks(MLPNN),least squares support vector machine(LSSVM),and random forest(RF) classifiers has been tested on the multichannel EEG data recorded from a local hospital.The RF classifier has produced the highest accuracy of 96.2% in classifying the signals.The proposed scheme has been employed in developing an embedded seizure detection system to assist neurologists in making seizure diagnostic decisions.

GEARBOX FAULTDIAGNOSIS BASED ON EMPIRICAL MODE DECOMPOSITION

Time synchronous averaging of vibration data is a fundament technique forgearbox diagnosis. Currently, this technique relies on hardware tachometer to give phase synchronousinformation. Empirical mode decomposition (EMD) is introduced to replace time synchronous averagingof gearbox vibration signal. With it, any complicated dataset can be decomposed into a finite andoften small number of intrinsic mode functions (IMF). The key problem is how to assure thatvibration signals deduced by gear defects could be sifted out by EMD. The characteristic vibrationsignals of gear defects are proved IMFs, which makes it possible to utilize EMD for the diagnosis ofgearbox faults. The method is validated by data from recordings of the vibration of a single-stagespiral bevel gearbox with fatigue pitting. The results show EMD is powerful to extractcharacteristic information from noisy vibration signals.

Intelligent Islanding Detection of Multi-distributed Generation Using Artificial Neural Network Based on Intrinsic Mode Function Feature

The integration of distributed energy resources(DERs) into distribution networks is becoming increasingly important, as it supports the continued adoption of renewable power generation, combined heat and power plants, and storage systems. Nevertheless, inadvertent islanding operation is one of the major protection issues in distribution networks connected to DERs. This study proposes an intelligent islanding detection method(IIDM) using an intrinsic mode function(IMF)feature-based grey wolf optimized artificial neural network(GWO-ANN). In the proposed IIDM, the modal voltage signal is pre-processed by variational mode decomposition followed by Hilbert transform on each IMF to derive highly involved features. Then, the energy and standard deviation of IMFs are employed to train/test the GWO-ANN model for identifying the islanding operations from other non-islanding events. To evaluate the performance of the proposed IIDM, various islanding and non-islanding conditions such as faults, voltage sag, linear and nonlinear load and switching, are considered as the training and testing datasets. Moreover, the proposed IIDM is evaluated under noise conditions for the measured voltage signal. The simulation results demonstrate that the proposed IIDM is capable of differentiating between islanding and non-islanding events without any sensitivity under noise conditions in the test signal.

A method for extracting human gait series from accelerometer signals based on the ensemble empirical mode decomposition

In this paper, the ensemble empirical mode decomposition （EEMD） is applied to analyse accelerometer signals collected during normal human walking. First, the self-adaptive feature of EEMD is utilised to decompose the ac- celerometer signals, thus sifting out several intrinsic mode functions （IMFs） at disparate scales. Then, gait series can be extracted through peak detection from the eigen IMF that best represents gait rhythmicity. Compared with the method based on the empirical mode decomposition （EMD）, the EEMD-based method has the following advantages： it remarkably improves the detection rate of peak values hidden in the original accelerometer signal, even when the signal is severely contaminated by the intermittent noises; this method effectively prevents the phenomenon of mode mixing found in the process of EMD. And a reasonable selection of parameters for the stop-filtering criteria can improve the calculation speed of the EEMD-based method. Meanwhile, the endpoint effect can be suppressed by using the auto regressive and moving average model to extend a short-time series in dual directions. The results suggest that EEMD is a powerful tool for extraction of gait rhythmicity and it also provides valuable clues for extracting eigen rhythm of other physiological signals.

Anchoring Bolt Detection Based on Morphological Filtering and Variational Modal Decomposition

The pull test is a damaging detection method that fails to measure the actual length of a bolt.Thus,the ultrasonic echo is an important non?destructive testing method for bolt quality detection.In this research,the variational modal decomposition(VMD)method is introduced into the bolt detection signal analysis.On the basis of morphological filtering(MF)and the VMD method,a VMD?combined MF principle is established into a bolt detection signal analysis method(MF?VMD).MF?VMD is used to analyze the vibration and actual bolt detection signals of the simulation.Results show that MF?VMD effectively separates intrinsic mode function,even under strong interference.In comparison with conventional VMD method,the proposed method can remove noise interference.An intrinsic mode function of the field detection signal can be effectively identified by reflecting the signal at the bottom of the bolt.