Intra-wave Frequency Modulation Research Articles

Detekcija klimatskih kolebanja Hilbert-Huangovom metodom na podacima stoljetnog opservatorija Zagreb-Grič, Hrvatska

Advanced statistical methods are applied on long-term data sets from Zagreb-Grič centennial observatory in Croatia to address recent climate change and variabilities; annual averages are used. Hilbert-Huang transform (HHT), consisting of empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA), is an empirically based data-analysis method for extracting periodic components embedded within generally nonlinear and non-stationary data. The EMD splits the original series into a so-called intrinsic mode functions (IMFs). First, using the EMD algorithm, intrinsic mode functions (IMFs) are obtained. The analysis of low frequency IMFs indicates significant influence of the North-Atlantic Oscillation on the air temperature, cloudiness and precipitation series in the part of northern Croatia. For the considered climatic elements, the analysis revealed mild deviations in natural fluctuations of the analyzed signal for the last 30 to 40 years, which are most likely caused by anthropogenic activities. Next, HSA is applied to each IMF obtained for the series of annual averages of sea level air pressure. In order to validate this approach and the results, an associated Hilbert spectrum (HS) is compared with the continuous wavelet analysis, i.e., this is another corresponding checkup. The comparison shows significantly improved time and frequency resolution in favor of HS. Moreover, HS provides a unique capability of displaying intra-wave frequency modulation, i.e., changes in frequency that occur within one cycle of oscillation.

Structural rotor rub-impact diagnosis under intricate noise interferences based on targeted component extraction and stochastic resonance enhancement

Rub-impact is a common nonlinear fault of the rotor system, occurring in rotating machines with radial clearance between the rotor and the stator, which may lead to serious consequences. Since the vibration response of rotor rub-impact is shown as multicomponent with time-varying characteristics of undulatory instantaneous frequency, it is desired to exploit advanced signal processing methods for rub-related feature excavation and failure diagnosis under complex noise interferences, which is of crucial significance to ensure the stable and efficient operation of the whole unit. This paper concerns the processing of acceleration signals and proposes a novel intrawave frequency modulation detection approach for structural rotor rubbing diagnosis based upon targeted component extraction and stochastic resonance enhancement. First, the acquired vibratory acceleration signal is converted into displacement signal via a two-stage integration strategy. Next, to extract the rotating frequency component of high information clarity for further time–frequency analysis from the multicomponent signal, an especially designed improved variational mode decomposition method based on the modified target frequency index is put forward, and the instantaneous frequency of the objective component is estimated. Then, the optimum stochastic resonance is leveraged for intrawave frequency modulation enhancement. Finally, the rotor rub-related symptom can be distinctly revealed and the diagnostic procedure can be performed. The effectiveness and superiority of the proposed rotor rub-impact diagnosis approach are demonstrated through both simulations and experiments, indicating that it is suitable to be implemented in practical applications, with high noise-resistance ability, and can efficiently extract the potential characteristics of rotor rub-impact malfunction from multicomponent signals.

Study of Resonance Helical Magnetic Field (RHF) Effect In IR-T1 Tokamak Plasma Using Hilbert-Huang Transform

In the IR-T1 Tokamak the effect of a resonance helical magnetic field (RHF) on plasma confienment are presented using Hilbert-Huang Transform method.Mirnov coil data analyzed by Hilbert-Huang Transform (HHT) and decomposed to the main intrinsic mode functions(imfs) and their instantanous frequencies (IFs). We find that, HHT method can extract MHD activities with different amplitudes in the different times. Then, the IFs of these modes can be calculated by Hilbert Transform (HT). As a comparison of WT and HHT analysis the Hilbert spectrum has much better frequency definition. Amplitude modulation of Mironov oscillations in IR-T1 tokamak plasma generate intra-wave frequency modulation, In the Hilbert spectrum analysis this effect is small compared to the STFT and WT spectrums. In our study, Magnetic islands with frequency around 40 kHz can be seen in wavlet Transform(WT) and HHT results in ohmic and RHF discharges. The HHT results after application of l=2/n=1 resonant field show that, the amplitude of m=2 poloidal MHD mode are amplified and then suppressed for a few milliseconds after amplification. Similarly, the amplitude of the m=3 MHD mode are amplified and then strongly suppressed by the start of the l=3/n=1 resonant field.

Effect of wheel polygonalization on the Degree of Non-linearity of dynamic response of high-speed vehicle system

Polygonalization of the wheel describes the growth of out-of-round profiles of the wheels of railway vehicle. This problem was identified in the 1980s but its mechanism is still not well understood. The wheel-rail disturbance formed by wheel polygonalization will accelerate the fatigue fracture of the key parts of rail vehicles and seriously threaten the safety of rail vehicle. This fact has led to significant efforts in detecting and diagnosing wheel polygonalization, in particular in setting the criteria for health monitoring. Currently, the time-domain feature parameters extraction method based on data statistics and frequency-domain feature parameters extraction method based on spectrum estimation are widely applied to detect wheel polygonalization. However, the basis of spectral estimation is the Fourier transform, which is not good at dealing with non-linear vibration systems (such as vehicle-track coupled system). Aiming at the wheel polygonalization problem existing in high-speed train, the non-linear extent of vibration response of vehicle system caused by wheel polygonalization is analyzed based on vehicle-track coupled dynamics and adaptive data analysis method. A typical high-speed train model is established according to the vehicle-track coupled dynamics theory. The wheel polygonalization model is introduced and vehicle system vibration response is calculated by numerical integration. The vibration response signal is decomposed by empirical mode decomposition (EMD) to produce the intrinsic mode functions (IMFs). By calculating the intra-wave frequency modulation of IMFs, that is, the difference between instantaneous and mean frequencies and amplitudes, the non-linearity of the dynamic response is quantified. Influences of wheel polygonalization on the non-linearity of steady-state and unsteady vibration responses of vehicle system are analyzed in detail. An objective criterion for wheel polygonalization health monitoring based on Degree of Non-linearity is proposed, which provides an effective tool for prognostics and health management of trains.

Study of MHD Activities in IR-T1 Tokamak Plasma Using Hilbert-Huang Transform

In the IR-T1 tokamak plasma, study of the MHD activities is presented by using the combination of singular value decomposition (SVD) and Hilbert-Huang transform (HHT). In this work, we have proposed the SVD+HHT method to study the MHD activity for mode number identification and time-frequency behavior. Also, we have used spatio-temporal structures of the Mirnov coil fluctuations in terms of correlation function to better identification of mode number and frequencies of dominant MHD modes. High correlation values of spatio-temporal wave-like structures in lifetime below 0.1 ms in the different poloidal separation were observed. It was shown that the main frequency rotation of the MHD activities is above 10 kHz. Spatio-temporal wave-like structures, with maximum value in poloidal separation 120 or 180 degrees, show that the wavelength of the MHD mode is related to m = 2 and m = 3. Also, there are small-scale structures, mostly contributed by high-frequency short wavelength fluctuating component in the bottom of the poloidal separation 90 degrees related to m = 4 or m = 5 mode numbers. These results have been compared with the SVD + HHT analysis results. In addition, amplitude modulation of Mirnov oscillations in IR-T1 tokamak plasma generates intra-wave frequency modulation. These amplitude variations of MHD oscillations cause a frequency fluctuation. Our results have indicated that in the Hilbert spectrum (HT) analysis, the intra-wave frequency modulation is small compared to the short-time Fourier transform (STFT) and wavelet transform (WT) spectrum.

Study on intra-wave frequency modulation phenomenon in detection of rub-impact fault

Abstract The rub-impact fault occurring in the rotating machinery can cause the periodically frequency modulation (FM) in its vibration response. Such kind of modulation mode has been named as intra-wave FM effect, which carries the intrinsic fault information of rubbing-related dynamic system. Assisted by a fast-modulated instantaneous frequency (IF) extraction method named M-VNCMD, the intra-wave FM phenomena arising in several simulated and real rubbing responses are revealed and investigated in detail in this paper. To be specific, the intra-wave FM response is firstly modeled as the sinusoidal modulation form according to the extracted fault features, and then expanded as a series of harmonics to establish the relationship between its modulation pattern and Fourier spectrum. The connection among the fault diagnosis criteria based on modulation patterns and Fourier spectrum is finally uncovered to demonstrate the superiority of diagnosing the rubbing fault depending on modulation features.

Experimental study on the intrawave frequency modulation characteristic of rotor rub and crack fault

Abstract Rub and crack are two important rotor faults. In this paper, the rub, crack and rub-crack coupled fault experiments are performed on a rotor test rig and the instantaneous frequency signatures of the faults are analyzed using Hilbert–Huang transform. The intrawave frequency modulation property of the rub and crack rotor is revealed through the response of Jeffcott rotor model and experiments. It is demonstrated that the intrawave frequency modulation produces extra harmonic components in FFT spectrum. The relationship between the FFT spectrum and the modulation frequency is supplied. The simulated and experimental analysis results show that the different composition of the modulation frequency can be the feature to detect the local rub, crack and crack-rub coupled rotor fault.

Experimental Investigation on the Extreme Waves Induced by Single Wave Packets in Finite Water Depth

Single Gaussian wave groups with different initial wave steepness e0 and width N are produced in laboratory in finite depth to study the nonlinear evolution, the extreme events and breaking. The results show that wave groups with larger e0 will evolve to be several envelope solitons (short wave groups). By analyzing geometric parameters, a break in the evolution of the wave elevation and asymmetric parameters after extreme wave may be an indicator for the inception of refocus and the maximal wave moving to the middle, namely, wave down-shift occurs. The analysis of the surface elevations with HHT (Hilbert-Huang Transform), which presents the concrete local variation of energy in time and frequency can be exhibited clearly, reveals that the higher frequency components play a major role in forming the extreme event and the contribution to the nonlinearity. Instantaneous energy and frequency in the vicinity of the extreme wave are also examined locally. For spilling breakers, the energy residing in the whole wave front dissipates much more due to breaking, while the energy in the rear of wave crest loses little, and the intra-wave frequency modulation increases as focus. It illustrates that the maximal first order instantaneous frequency f1 and the largest crest tend to emerge at the same time after extreme wave when significant energy dissipation happens, and vice versa. In addition, it shows that there is no obvious relation of the CDN (combined degree of nonlinearity) to the wave breaking for the single Gaussian wave group in finite water depth.

Extracting a shape function for a signal with intra-wave frequency modulation.

In this paper, we develop an effective and robust adaptive time-frequency analysis method for signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu (Wu 2013 Appl. Comput. Harmon. Anal. 35, 181-199. (doi:10.1016/j.acha.2012.08.008)). A shape function could be any smooth 2π-periodic function. Based on this model, we propose to solve an optimization problem to extract the shape function. By exploring the fact that the shape function is a periodic function with respect to its phase function, we can identify certain low-rank structure of the signal. This low-rank structure enables us to extract the shape function from the signal. Once the shape function is obtained, the instantaneous frequency with intra-wave modulation can be recovered from the shape function. We demonstrate the robustness and efficiency of our method by applying it to several synthetic and real signals. One important observation is that this approach is very stable to noise perturbation. By using the shape function approach, we can capture the intra-wave frequency modulation very well even for noise-polluted signals. In comparison, existing methods such as empirical mode decomposition/ensemble empirical mode decomposition seem to have difficulty in capturing the intra-wave modulation when the signal is polluted by noise.

Nonlinearity of abnormal waves by the Hilbert–Huang Transform method

The nonlinearity of full-scale abnormal wave data is studied by the Hilbert–Huang Transform method. The vertical asymmetry of abnormal waves is examined in relation to the level of the intra-wave frequency modulation of different Intrinsic Mode Functions. The Draupner New Year wave data time series is used as an example of a vertically asymmetric abnormal wave, while record 37 from the hurricane Camille dataset is chosen as an example of a vertically symmetric abnormal wave. A measure of intra-wave frequency modulation is proposed based on the instantaneous frequency variations within one single wave. The study of the variation of local frequency in the vicinity of abnormal waves demonstrates that a larger intra-wave frequency modulation is associated with a higher asymmetry of the wave profile.

An Adaptive Non-Linearity Detection Algorithm for Process Control Loops

Non-linearities are considered to be a major source of oscillations and poor performance in industrial control systems, as 20-30 % of loops are reported to be oscillating due to valve non-linearities (Srinivasan et al. (2005)). This fact has led to a significant effort aimed at the detection and diagnosis of non-linearities; in particular for valve non-linearities in the control loops. The current paper presents an adaptive algorithm, based on HHT (Hilbert Huang Transform), for non-linearity detection and isolation in process systems. The HHT is an adaptive data analysis technique that is applicable to non-linear and non-stationary time series. An index termed the Degree of Non-Linearity (DNL), based on intra-wave frequency modulation, is used to identify the presence of non-linearity in the signal generating system. The proposed method is shown to be more robust in differentiating between linear and nonlinear causes of oscillations when compared to existing methods, and can handle non-stationary effects.

Nonlinearity and non-stationarity analysis of dynamic response of vehicle–track coupling system enhanced by Huang transform

A method is proposed to analysis the nonlinearity and non-stationarity of dynamic response of high speed vehicle–track coupling system, to understand the properties of signal and its underlying physical meaning. First, a space coupling model of high speed vehicle–track system is built according to the theory of coupling dynamics of vehicle–track system. Then, the dynamic response of vehicle–track system is processed by Ensemble Empirical Mode Decomposition (EEMD) to generate the intrinsic mode functions (IMFs). Next, the “Direct Quadrature” (DQ) method is used to calculate the local instantaneous frequency and instantaneous amplitude of the IMFs, the generalized zero-crossing method and the full wave zero-crossing method are applied to calculate the mean local frequency of the IMFs. Finally, the index and degree of nonlinearity and non-stationarity based on intra-wave frequency modulation (the deviation of the instantaneous frequency from the generalized zero-crossing frequency) and inter-wave frequency modulation (the deviation of the instantaneous frequency from the full wave zero-crossing frequency), are defined to quantify the nonlinearity and non-stationarity of dynamic response. The usefulness and capability of the proposed method are displayed through two cases, which are considered general enough to be the representatives of nonlinear and non-stationary dynamic response of vehicle–track coupling system.

Loudspeaker Nonlinear Distortion Signal Instantaneous Frequency Measurement and Analysis

Loudspeaker is a strongly nonlinear system which is associated with several situations such as electronic, magnetic, mechanical and acoustic. Recently, most of the methods used to measure and analysis loudspeaker are based on the FFT. Unfortunately, traditional Fourier transform based signal analysis method usually causes meaningless results when it is used to analysis non-stationary and nonlinear signal. In this paper, we use Hilbert-Huang transform (HHT) to review the instantaneous frequency of loudspeaker output. Experiments demonstrate that the distortion of loudspeaker can be recognized as intrawave frequency modulation caused by wave profile deformation. Then a novel nonlinear distortion measurement method is proposed which can reveal more accurate and physical meaningful characteristic of loudspeaker.

A Stochastic Approach for Evaluating the Nonlinear Dynamics of Vertical Motion Recorded at the IWTH25 Site for the 2008 Mw 6.9 Iwate-Miyagi Inland Earthquake

The vertical accelerogram recorded at the IWTH25 site located just above the earthquake fault of the 2008 M w 6.9 Iwate–Miyagi inland earthquake showed nonlinear dynamics because of intrawave frequency modulation with a maximum amplitude close to 4 g , due to the nonlinear response of the near-surface layer at the site. In the present paper, a stochastic second-order model is proposed to explain these observations. The dynamics of the model are determined by the configuration of three pairs of complex conjugated poles in the z -transform domain, and the dynamics of these poles are interpreted in terms of the instantaneous frequency of the recorded acceleration signal. The results of simulations using the proposed model show overall agreement with the recorded accelerogram, including its maximum amplitude and its time of appearance. The physical mechanism producing the displacement waveform is found to be analogous to a ball bouncing on a vibrating surface. From the simulated and recorded seismograms, it was apparent that at least two consecutive high bounces are required to produce extremely high accelerations of close to 4 g .

Misalignment diagnosis of rotating machinery through vibration analysis via the hybridEEMD and EMD approach

The objective of this research is to investigate the feasibility of utilizing the hybrid methodof ensemble empirical mode decomposition (EEMD) and pure empirical modedecomposition (EMD) to efficiently decompose the complicated vibration signals ofrotating machinery into a finite number of intrinsic mode functions (IMFs), so that thefault characteristics of the misaligned shaft can be examined in the time–frequency Hilbertspectrum as well as the marginal Hilbert spectrum. The intrawave frequency modulation(FM) phenomenon, which indicates the nonlinear vibration behavior of a misaligned shaft,can be observed in the time–frequency Hilbert spectrum through the Hilbert–Huangtransform (HHT) technique. The fault characteristic of shaft misalignment isalso featured in terms of the amplitude modulation (AM) phenomenon in theinformation-containing IMF components that are extracted by the significance test.Through performing the envelope analysis on the information-containing IMF, the marginalHilbert spectrum of the envelope signal of this IMF component exhibits thatthe level of shaft misalignment is presented by the level of AM in the IMF. Atest bed of a rotor-bearing system is performed experimentally to illustrate boththe parallel and angular shaft misalignment conditions as well as the healthycondition. The analysis results show that the proposed approach is capable ofdiagnosing the misaligned fault of the shaft in rotating machinery and providinga more meaningful physical insight compared with the conventional methods.

DETECTION AND QUANTIFICATION OF CONTROL VALVE NONLINEARITIES USING HILBERT–HUANG TRANSFORM

Two of the most important sources of degradation of control loop performance are (i) valve stiction and (ii) tight controller tuning, both of which lead to oscillations in closed–loop outputs. A factor that distinguishes these two sources is the nonlinear signature of the valve stiction; a tightly tuned controller produces oscillations due to a linear source. Detection and isolation of nonlinear fault sources is essential to correctly determine the cause of poor loop performance of control loops. Despite a rich research activity in this area, there is hardly a method which can isolate the simultaneous effects of these two sources. Moreover, the traditional spectral analysis based on Fourier Transforms is largely restricted by the assumption of stationarity in the data to detect and quantify valve nonlinearities. In this work, Hilbert–Huang Transform (HHT) is used to (i) detect valve nonlinearities and (ii) isolate linear and nonlinear fault sources. The key characteristic of HHT is that it represents nonlinearities as intra-wave frequency modulations allowing it to distinguish it from linearities which do not exhibit such modulations. The advantages of HHT-based methods are that (i) nonlinearities translate to a unique signature (ii) nonstationarities in data can be handled in a natural way. It is observed that nonlinearity is captured by a Intrinsic Mode Functions (IMF) obtained from the Empirical Mode Decomposition (EMD) of the process output. The Hilbert–Huang spectrum of these IMFs exhibits intra-wave frequency modulation. The power spectrum of the IMFs shows the presence of harmonics which is used to characterize the valve stiction nonlinearity. Subsequent to detection, quantification is done using the power spectrum of the IMFs. The proposed method is sensitive enough to detect low levels of valve stiction nonlinearities. Results from simulation using one-parameter valve stiction model are presented in support of the proposed methodology. The results demonstrate the advantage and potential of the HHT-based method.

Analysis of Abnormal Wave Records by the Hilbert–Huang Transform Method

AbstractThe Hilbert–Huang transform method is used in this work to analyze wave records from the North Sea, which include abnormal waves. The analysis of the characteristics of abnormal waves is based on the local decomposition of wave data by using the intrinsic mode functions. The variations of amplitude of intrinsic mode functions around the time of the occurrence of abnormal waves are examined in order to investigate the contribution of different intrinsic mode functions on the abnormal waves’ profile, in an attempt to find relationships between them. The changes of local frequency of each intrinsic mode function in the vicinity of abnormal waves are examined. The essential nonlinearity of abnormal waves is considered as intrawave frequency modulation, a variation of the instantaneous frequency within one oscillation cycle. The Hilbert spectrum is used as a detector of abnormal waves.

Empirical mode decomposition and tissue harmonic imaging

Empirical mode decomposition (EMD) is a relatively new technique used in the analysis of nonlinear and nonstationary time series. Previous signal-processing methods used for medical ultrasound have been based on the assumption of a linear time-invariant system. More recently, the technique of tissue harmonic imaging (THI) has become prevalent. This technique relies on the nonlinear propagation of the sound wave through the medium to disperse the signal energy into the harmonic frequencies of the transmitted signal. In this paper, results are presented from using EMD to process received ultrasound echo signals that have passed through nonlinear media. The Hilbert spectrum is used to demonstrate an interpretation of the physical process underlying THI that is based on the concept of intrawave frequency modulation, rather then the spreading of signal energy into harmonic frequencies. The technique of EMD is shown to be able to produce superior results to the bandpass filtering method of THI, even when the band width of the transducer was such that the second harmonic would be suppressed. (E-mail: bmd@ee.ed.ac.uk)