Hilbert-Huang Transform Analysis Research Articles

Nonlinear Response Characterization of Post-Tensioned R.C. Bridges through Hilbert–Huang Transform Analysis

A novel methodology for the characterisation of the nonlinear behaviour of post-tensioned r.c. bridges, which exploits the response to heavy traffic travelling during operational conditions, is presented. This type of bridges shows a nonlinear elastic behaviour due to the partial opening of cracks under heavy loads whose entity is related to the intensity of the prestressing force. The properties of this response vary because of material relaxation or damage of the prestressing system. The study exploits the abilities of the Hilbert–Huang transform (HHT) to extract the instantaneous properties of the dynamic response, and a novel procedure to characterise the nonlinear elastic response is presented and investigated through theoretical applications on simplified dynamic systems. A frequency-amplitude correlation chart is proposed as a visual tool to retrieve useful information on the nonlinear response related to the instantaneous variation of the natural frequency with the response amplitude. With the aim of denoising and eliminating spurious contributions introduced by the local nature of the information extracted through the Hilbert spectral analysis, a probabilistic model is proposed for the result interpretation, through which the probability distribution of the instantaneous natural frequencies conditional to different levels of the response amplitude is provided and potential bridge’s response modifications and anomalous behaviours of the prestressing system can be detected. An extensive parametric analysis is performed to assess the influence of the most relevant parameters governing the problem and verify the effectiveness of the proposed strategy.

Non-Contact Impact Source Localization in Composite Symmetry Panels Based on A0 Mode of Lamb Waves

Traditional methods for detecting damage in engineering structures often use offline static damage detection. To enable the real-time and precise identification of dynamic damage while maintaining symmetry in engineering structures, this study primarily concentrates on isotropic plate structures widely employed in engineering. Moreover, fiberglass board composite plates were opted as a specific research object. By utilizing the weak S0 mode signals generated by low-frequency ultrasonic Lamb waves, the non-stationary A0 wave signals in the composite symmetry plate structure are collected using the non-contact SLDV (Scanning Laser Doppler Vibrometer) technique. The frequency characteristic parameters in the vibration signals are obtained through HHT (Hilbert–Huang Transform) analysis, followed by filtering and noise reduction. Finally, the circular trajectory intersection method is employed to accurately locate dynamic damage sources in plate structures with different material properties, thereby validating the positioning effect of contact sensors in detecting impacts caused by random impulses.

Non-destructive compaction quality evaluation of runway construction based on GPR data

ABSTRACT Assessing the compaction quality of rockfill materials is an essential link in the runway construction. However, traditional on-site limited sampling detection is not only time-consuming and labour-intensive, but also destructive. Common ground penetrating radar (GPR) calculates the relative permittivity of a material by measuring its thickness. Nonetheless, assessing the thickness of runway construction materials poses a significant challenge. To address this challenge, this paper focuses on the Hilbert -Huang transform (HHT) analysis of GPR signal of different compacting materials, and then replaces the traditional method of calculating the relative permittivity by measuring the thickness of materials. At the same time, taking the runway as an example, this work verified a crest factor (CF) index effectiveness in predicting the relative compaction of rockfill material through HHT analysis of GPR signals collected in the field, with an average error rate of 4.03%. Finally, Kriging interpolation method is used to estimate the compaction quality of any point, and the corresponding heat map of compaction quality evaluation is generated to determine the area of insufficient compaction in the construction process. Highlights The GPR method is used for non-destructive testing of the compaction quality of runway rockfill materials; Compaction quality evaluation by multiple indicators of GPR data signal processing. The influence of number of roller passes, materials mix ratios and different rockfill materials on the compaction quality of runway are analysed. The applicability of the GPR method is verified by runway construction tests.

Study on noise behavior of micro-textured composite coated cemented carbide surface grinding titanium alloy based on HHT analysis

In modern industrial production, noise can reflect the cutting state of the workpiece and tool to a certain extent, and the noise collection method cannot interfere with the complex processing environment. To further improve the cutting performance of coated cemented carbide micro-textured tools, this paper builds a friction and wear test platform for micro-textured cemented carbide pins with AlSiTiN-AlCrN coating and titanium alloy discs. Based on the test noise signal, the relationship between friction and wear and the noise of the workpiece was studied by the Hilbert–Huang transform (HHT). Through the change of noise in different periods, the micro-texture and coating life of cemented carbide pin under other processing parameters were analyzed. Based on the influence of the interaction between processing parameters and micro-texture diameter on the test results, the test parameters were optimized. The results show that the change of noise signal during the test presents a “V” curve with the grinding process, which mainly affects the noise through the shift of pin-disc friction form and the anti-wear effect of micro-texture. The interaction mainly affects the test results by affecting the micro-texture diameter, laser energy concentration, and the roughness of the inner wall of the pit. The optimized micro-texture geometry and preparation parameters are as follows: scanning times is 8, micro-texture diameter is 50 μm, scanning speed is 1500 mm/s, micro-texture spacing is 170 μm, and laser power is 40 W. The research content of this paper provides a reference for improving the surface properties of cemented carbide.

A novel framework for spatiotemporal groundwater pumping process estimation based on data-driven approaches

Understanding the spatial and temporal distribution of pumping activities is crucial for effective water resource management. However, obtaining accurate pumping records is often challenging, particularly in areas without efficient groundwater withdrawal permit systems. In this study, we propose a novel approach for identifying pumping activities and estimating their associated pumping rates across space and time. Our data-driven approach integrates empirical orthogonal function (EOF) and Hilbert-Huang transform (HHT) analyses on first-differenced head data to extract high-frequency head variations that are closely related to pumping activities. The identified pumping-associated head variations are used to estimate the on-and-off times of local pumping stations and their associated pumping-rate time series. We test our approach using a hypothetical aquifer with designed pumping and real precipitation time series. Our results show that the EOF analysis is able to distinguish pumping locations where distinct temporal head variabilities are present. HHT analysis is then able to effectively remove noise from the EOF-identified pumping-associated head variations. Compared to the designed pumping data, our results demonstrate that our proposed method is able to produce accurate pumping estimates in terms of both spatial and temporal distribution and total amounts. While our approach does have limitations, such as delayed and boundary effects, our results suggest that it can be an effective tool for pumping estimation in areas with relatively abundant head observations across space and time, which is a common scenario in Taiwan.

Damage Modes Recognition of Wood Based on Acoustic Emission Technique and Hilbert–Huang Transform Analysis

Identifying the different damage modes of wood is of great significance for monitoring the occurrence, development, and evolution of wood material damage. This paper presents the research results of the application of acoustic emission (AE) technology to analyze and evaluate the mapping relationship between the damage pattern of wood in the fracture process and the AE signal. For the three-point bending specimen with pre-crack, the double cantilever beam specimen, the single fiber tensile specimen, and the uniaxial compression specimen, the bending tensile compression test and the AE monitoring were performed, respectively. After the post-processing and analysis of the recorded AE signal, the results show that the peak frequency of AE is an effective parameter for identifying different damage modes of wood. In this study, the empirical mode decomposition (EMD) of the AE signal can separate and extract a variety of damage modes contained in the AE signal. The Hilbert–Huang transform (HHT) of the AE signal can clearly describe the frequency distribution of intrinsic mode function (IMF) components in different damage stages on the time scale, and can calculate instantaneous energy accurately, which provides a basis for damage mode recognition and lays a foundation for further accurate evaluation of the wood damage process.

Multiscale Temporal Variations of Atmospheric Mercury Distinguished by the Hilbert-Huang Transform Analysis Reveals Multiple El Niño-Southern Oscillation Links.

Atmospheric mercury (Hg) cycling is sensitive to climate-driven changes, but links with various teleconnections remain unestablished. Here, we revealed the El Niño-Southern Oscillation (ENSO) influence on gaseous elemental mercury (GEM) concentrations recorded at a background station in East Asia using the Hilbert-Huang transform (HHT). The timing and magnitude of GEM intrinsic variations were clearly distinguished by ensemble empirical mode decomposition (EEMD), revealing the amplitude of the GEM concentration interannual variability (IAV) is greater than that for diurnal and seasonal variability. We show that changes in the annual cycle of GEM were modulated by significant IAVs at time scales of 2-7 years, highlighted by a robust GEM IAV-ENSO relationship of the associated intrinsic mode functions. With confirmation that ENSO modulates the GEM annual cycle, we then found that weaker GEM annual cycles may have resulted from El Niño-accelerated Hg evasion from the ocean. Furthermore, the relationship between ENSO and GEM is sensitive to extreme events (i.e., 2015-2016 El Niño), resulting in perturbation of the long-term trend and atmospheric Hg cycling. Future climate change will likely increase the number of extreme El Niño events and, hence, could alter atmospheric Hg cycling and influence the effectiveness evaluation of the Minamata Convention on Mercury.

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.

Multiscale Features of the Near-Hermean Environment as Derived Through the Hilbert-Huang Transform

The interaction between the interplanetary medium and planetary environments gives rise to different phenomena on several temporal and spatial scales. Here, we propose for the first time, the application of the Hilbert-Huang Transform (HHT) to characterize both the local and global properties of Mercury's environment as seen during two Mercury Surface, Space Environment, Geochemistry and Ranging (MESSENGER) flybys. In particular, we compute the energy-time-frequency distribution of the observed magnetic field components and the reconstruction of these signals at large, magnetohydrodynamics (MHD) and kinetic scales through the empirical mode decomposition. We show that the HHT analysis allows to capture and reproduce some interesting features of the Hermean environment such as flux transfer events (FTEs), Kelvin-Helmholtz vortices, and ultralow frequency (ULF) wave activity. Moreover, our findings support the ion kinetic nature of the Hermean plasma structures, the characterization of the magnetosheath by anisotropic ion-kinetic intermittent fluctuations, superimposed to both MHD fluctuations and large-scale field structure. Our approach has proven to be very promising for characterizing the structure and dynamics of planetary magnetic field at different scales, for identifying the boundaries, and for discriminating the different scale-dependent features of global and local source processes that can be used for modeling purposes.

Research on vibration effect of tunnel blasting based on an improved Hilbert–Huang transform

Through a tunnel-blasting project, the effect of tunnel-blasting vibration has been analyzed from the perspective of vibration energy transfer. The non-linear regression method was used to obtain the prediction equation for blast vibration velocity based on the field blast vibration data. Then, the maximum charge per delay of the blasting construction of the tunnel was obtained through the formula inversion. Based on the traditional Hilbert transform, a novel Hilbert–Huang transform (HHT) analysis method considering Complete Ensemble Empirical Mode Decomposition with Adaptive Noise decomposition (CEEMDAN) and wavelet packet threshold de-noising method has been proposed, the feasibility of which was verified using the field blast vibration signals. It has been proved that the improved HHT analysis method can be used to analyze the influence of the different blasting vibration parameters on the regular distribution of vibration energy. In addition, the dimensional analysis method was used to establish the blasting vibration energy prediction model. The results of this research show that the improved HHT analysis method can solve the problem of modal aliasing caused by the traditional decomposition method, and can obtain the purified main modal components, which improves the adaptability of HHT analysis. In addition, with the increase of the distance between blast area and the maximum charge per delay, the high-frequency energy of the blasting signal gradually weakens, while the dominant energy frequency band diverts to the low-frequency band. The methods and conclusions of this research can provide a certain reference for the controlled blasting construction in similar cases.

Identification of the typical frequency range associated with subsurface gas zones: a study using Hilbert-Huang transform and wavelet analysis

Frequency attributes embedded in nonlinear geophysical signals such as well-log data or seismic data can provide vital clues in the effective characterization of the subsurface reservoir. Therefore, it is always important to recognize suitable mathematical techniques that need to be employed to extract such vital information from the nonlinear geophysical data. Several nonlinear mathematical techniques include wavelet analysis, fractal and multifractal analyses, and the fully data-adaptive Hilbert-Huang transform (HHT) technique. In the present study, we employ the HHT and the wavelet analysis techniques to seismic data of the Dutch sector of southern North Sea. We use a small portion of the seismic data, consisting of inline section 133 and time slice section 520 ms of the F3 block, to extract the instantaneous frequency associated with the subsurface gas zone. HHT constitutes two independent techniques, namely, the empirical mode decomposition (EMD) technique and the Hilbert spectral analysis (HSA). While the EMD technique facilitates to decompose the data into different signals of varied frequencies, called intrinsic mode functions (IMFs), the HSA helps to determine the instantaneous amplitudes and frequencies of the IMFs. EMD technique, together with HSA, has delineated a low-frequency spectral signature, believed to be a subsurface gas zone in the chosen data, corroborating the results of earlier studies of the same data sets. The instantaneous frequency range of the gas zone estimated by HSA was validated with the two-dimensional continuous wavelet transform (CWT) of the data sets using a suitable frequency range of Morlet wavelet. Results of the combined HHT and CWT analyses confirmed that the subsurface gas zone could be well identified in the frequency range 14–18 Hz. Results have direct implications in situ, in the sense that, by performing CWT analysis of seismic data using a Morlet wavelet in the frequency range 14–18 Hz, one can easily identify the location of subsurface gas zones.

MHD Mode Identification from Mirnov Coils Signals in Tokamak Via Combination of Singular Value Decomposition and Hilbert–Huang Transform Analysis Methods

In this work, we investigate how to study the MHD activities in Tokamak plasma via the combination of singular value decomposition (SVD) and Hilbert–Huang transform (HHT) methods. We apply this approach to the Mirnov coil signal fluctuations analysis without any filtering technique. First, the principal axes (PAs) of a pick-up Mirnov signals are extracted by SVD analysis. Next, the harmonics of dominants PAs is obtained by empirical mode decomposition (EMD) analysis. Moreover, the time–frequency behavior of Mirnov signals are extracted by HHT. The proposed technique is employed to analyze Mirnov coils signals for mode type and frequency identification, especially in multimode MHD activities. We obtained Spatial–temporal structures of the Mirnov coils fluctuations in terms of correlation functions to better identification of mode number and frequencies of dominant MHD modes. We also present the results of this method applied to IR-T1 and Golem Tokamaks Mirnov coils signals. Consequently, satisfying results from SVD + HHT analysis method and spatial–temporal structures for IR-T1 and Golem Tokamaks Mirnov data observed.

Application of arc-shaped electrostatic sensors for monitoring the flow behaviour at top and bottom section of a pneumatic conveying pipeline

Measurement of particle’s charge in the pneumatic conveying systems can be used to monitor the flow behaviour (stable or unstable) in dilute phase pneumatic conveying. The particle’s charge can be measured by inductive electrostatic sensors and converted into a time-domain signal, which is called an electrostatic signal. However, with popular ring-shaped sensors, limited information can be obtained on electrostatic signals. Arc-shaped electrostatic sensors have some advantages on measuring particle’s charge at different locations such as the top or bottom of the pipe. To get enough information about the flow behaviour, the electrostatic signal needs to be processed by using different data analysis techniques.In this study, electrostatic signals are recorded at the top and bottom section of the pipe at varied conveying air velocity and at a constant solid feed rate. These different air velocities result in a stable dilute flow and unstable dune flow in the pipeline. The electrostatic signals of stable and unstable flows are analysed by using Fast Fourier Transform (FFT) and Hilbert-Huang Transform (HHT) techniques for real-time monitoring of flow behaviour in a pilot pneumatic conveyor.The results show that HHT analysis is far better than FFT for distinguishing between stable dilute and unstable dune flow. Where FFT only capture the difference in the flow behaviour with only top electrostatic sensor’s signal but HHT work with both top and bottom sensor’s signals. HHT does not only distinguish between stable and unstable flows but also shows the consistency in the results of the 80 ​s, 10 ​s and 5 ​s of the data analysis, which is the main requirement for any technique to be used for real-time monitoring systems. This clearly represents a huge benefit for control and monitoring in the pneumatic conveying systems.

Spectral analysis of sea surface elevations produced by big storms: The case of hurricane Wilma

Hurricane Wilma was the most extreme hydro-meteorological event ever to occur in the Caribbean Sea. During its occurrence, the sea surface elevation was recorded close to Puerto Morelos, Quintana Roo, Mexico. The equipment used which features both, acoustical and pressure sensors to measure the water depth, was deployed approximately at a depth of 20 m so it gathered invaluable information that helps understanding the nature of this cyclone and provided unique data related to the hurricane from which various different analyses can be performed. Wavelet and Hilbert Huang Transform (HHT) spectra are the frequency domain analysis techniques presented in this paper. Together with the well-known and elsewhere reported simultaneous appearance of Sea and Swell waves, several other sea surface oscillations were produced by the cyclone. These wave dynamics were found in the results of the wavelet and HHT analyses of the free sea surface elevations time series before, during and after the hurricane passed the observation point (a total of 13 days). The wavelet analysis showed the time evolution of the energy distribution over an important range of frequencies. Two main features can be highlighted: the large number of wave periods recorded when the eye of the cyclone was close to the measuring point and the occurrence of a very long wave, with a period of around 109 h containing great energy. In turn, the HHT analysis showed its robustness, being capable of detecting long oscillations within time series shorter than the oscillation itself.

Hilbert-Huang Transform Analysis of Machining Stability in Ball-Nose End-Milling of Curved Surface

This paper investigates the machining stability in ball-end-milling of curved surface in which the inclination of tool continuously changes. Initially, the influence of inclination angle is geometrically investigated on the parameters such as immersion angle and cutting velocity. Then, the paper presents the stability lobe diagrams of the process. Curved surface milling is simulated by slot milling on a cylindrical workpiece using a ball-end-mill to obtain the cutting force and vibration, which are used for fast-Fourier transform and Hilbert-Huang transform (HHT) analyses. Experimental results show that the cutting force increases, and the stability becomes worse with the inclination angle, while the machining errors decrease with the inclination. The vibration analysis showed that the HHT can detect the transition from stable to unstable during milling of curved surface in the time-frequency plots.

Seismic damage potential described by intensity parameters based on Hilbert-Huang Transform analysis and fundamental frequency of structures

This study aims to present new frequency-related seismic intensity parameters (SIPs) based on the Hilbert-Huang Transform (HHT) analysis. The proposed procedure is utilized for the processing of several seismic accelerograms. Thus, the entire evaluated Hilbert Spectrum (HS) of each considered seismic velocity time-history is investigated first, and then, a delimited area of the same HS around a specific frequency is explored, for the proposition of new SIPs. A first application of the suggested new parameters is to reveal the interrelation between them and the structural damage of a reinforced concrete frame structure. The index of Park and Ang describes the structural damage. The fundamental frequency of the structure is considered as the mentioned specific frequency. Two statistical methods, namely correlation analysis and multiple linear regression analysis, are used to identify the relationship between the considered SIPs and the corresponding structural damage. The results confirm that the new proposed HHT-based parameters are effective descriptors of the seismic damage potential and helpful tools for forecasting the seismic damages on buildings.

Antral contraction rate estimation from dynamic antral scintigraphy using Hilbert-Huang transform

Conventional analysis of the gastric antral contraction rate (ACR) utilizes the Fourier transform (FT) which does not effectively capture the non-stationary property of dynamic antral scintigraphy (DAS). In this study, we showed that application of Hilbert-Huang transform (HHT) on DAS yielded better estimates of ACR. Specifically, the time activity curves were extracted from the DAS data of 18 healthy volunteers and subjected to FT and HHT analyses. Comparison of the mean, standard deviation (SD), and root mean square error (RMSE) of ACR estimated by both methods showed that the proposed HHT method yielded significantly smaller SD (p<0.00001), smaller relative SD (13.3% versus 53.7%) and RMSE (0.72 cpm versus 1.59 cpm). Moreover, the HHT method also achieved lower relative SD of the frequency values from the intrinsic mode functions. Overall results indicated that the HHT method outperformed the conventional FT method in estimating the ACR from DAS. We anticipate that our approach will lead to development of effective noninvasive diagnoses of gastrointestinal tract diseases using DAS.

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.

Ionospheric Es layer scintillation characteristics studied with Hilbert-Huang transform

A coincident event of daytime ionospheric Es layer scintillation observations is analyzed with the Hilbert-Huang transform (HHT) to study its layer structure. One of the coincident observations is made by a radio beacon passing through the Es layer at a slant angle received by the SCINDA (Scintillation Decision Aide) receivers located at southern Taiwan. The data indicates that the Es layer consists of scattering blocks of ∼ 650 to 970 m in size as revealed in the dominant components of the HHT analysis. The time shift in the two spaced receiving antennas implies that the daytime E region westward drift is about 36 m/s. On the other hand, the same Es layer is observed by the radio occultation (RO) experiment with the L1 signal from the Global Positioning System (GPS) satellites to the FORMOSAT-3/Constellation-Observing-System-for-Meteorology (FS-3/COSMIC) satellites. The GPS L1 signal passes through the Es layer horizontally. The observed signal variations reveal a dense slab structure that blocks the L1 signal to cause a diffraction pattern. The slab thickness in the vertical direction is about 780 m. The HHT analyses of the coincident observations thus conclude that the observed daytime Es layer has a vertical dense slab structure and patches of scattering blocks in the horizontal structure.

Evaluation of HHT approach for estimating agricultural drought trend and frequency based on modified soil water deficit index (MSWDI)

Accurate estimation of the agricultural drought trend and frequency is important to water resources planning and management. In this study, an effective analysis tool, the Hilbert–Huang Transform (HHT) method, was introduced to estimate the agricultural drought trend and frequency based on modified soil water deficit index (MSWDI). The results indicate that (1) based on HHT multiscale decomposition, the MSWDI of four stations has two intra-annual fluctuations, three intra-decadal fluctuations with periodicities between 1 and 6 years, and two inter-decadal fluctuations; (2) the main periodicities obtained from wavelet analysis can also be detected by HHT analysis. Furthermore, the HHT analysis decomposed more time scale patterns than wavelets; (3) the residue of HHT showed a decreasing trend during the 1960s–1980s but an increasing one since the 1980s for the drought index MSWDI series at most of the stations in the Songnen Plain (SNP). It is consistent with the result of Mann–Kendall and Spearman’s Rho; (4) the drought temporal distribution analysis showed that the relative high drought probability was identified during the initial stage of crop growth. It can be concluded that the HHT analysis is an effective approach to examine multiple time scales of frequencies and trend of agricultural drought from its multiscale decomposition and time–frequency characterization, which can not only be applied for other time series but also have the functions combining the wavelet analysis and non-parameter trend tests. The results of this study could also help and be used to improve the drought prediction and expand the application of HHT method in climatology.