Frequency Components Of Signal Research Articles

Order-difference of normalized square envelope spectrum and its applications in early chatter detection of roll grinder

Roll grinder is widely demanded in grinding the surface of rolls that will be used to mill steel strips for high-quality automobile outer panels. The grinding chatter generally leads to poor machining accuracy and massive economic losses. The significance of roll grinder vibration monitoring is to detect the early grinding chatter. However, in harsh working conditions, some chatter detection methods inevitably confuse the fault components and interference components in vibration signals and the chatter feature information cannot be extracted exactly. The dynamical model of roll grinder system reveals that the spectrums of vibration signals contain intrinsic frequency components and chatter frequency components under health and chatter conditions. Based on the analytical modelling, a new health index order-difference of normalized square envelope spectrum (ODNSES) is proposed to detect early chatter and evaluate the health degradation of the roll grinder. The normalized square envelope spectrum (SES) is used as the pretreatment of ODNSES to compare the frequency components in vibration signals under health and early chatter conditions. Furthermore, order-difference of normalized SES is proposed to suppress the noise interference and to enable ODNSES to characterize the grinding chatter process. The detailed simulation research is performed to verify three important properties of ODNSES. The experimental results show that ODNSES would not be interfered by background noise significantly and it is on average 29.12% more sensitivity to impulse amplitudes than classical health indexes. The testing results on actual roll grinder exhibit that ODNSES can detect the early chatter and quantify the abnormal vibration in the grinding process.

Time–frequency ridge characterisation of sleep stage transitions: Towards improving electroencephalogram annotations using an advanced visualisation technique

Manual sleep stage scoring of polysomnography recordings is an expensive and time-consuming process, further complicated by inconsistent sleep stage agreement among sleep experts (clinicians and sleep technologists). Hence, development of automated sleep scoring algorithms are an emerging topic of interest. Automation typically mimics the clinical decision path by implementing a series of predefined rules, such as the American Academy of Sleep Medicine’s (AASM) scoring manual. Recently, data driven methods have emerged using machine or deep learning. Both manual and automated methods of scoring have known limitations; primarily, unacceptable variation in agreement between different scorers and algorithms. Within the literature, electroencephalogram (EEG) frequency is an important feature considered by both sleep experts and automated approaches for classifying sleep stages.This study presents a novel approach to sleep stage analysis, by developing a methodology to precisely determine the temporal location of sleep stage transitions. The current gold standard fails to identify such transitional changes, which leads to poor inter-scorer reliability. Therefore, development and implementation of such methodologies is a crucial, but overlooked, step in improving the consistency of scoring within sleep studies. In this work, EEG time–frequency ridge analysis was used to characterise the dominant frequency component of EEG signals in time, at the point of sleep stage transition. An in-depth analysis of N3 → N2 and N2 → N3 transitions in the 2018 PhysioNet challenge “You Snooze, You Win” and the Wisconsin Sleep Cohort (WSC) datasets (n = 994, n = 742; approximately 13,888 h of sleep data) showed consistent time–frequency patterns at the point of transition, from one sleep stage to another. This methodology allows simple and ‘interpretable’ features to be generated in future work, to precisely identify the temporal location of sleep stage transitions with the aim of improving inter-scorer reliability.

High-frequency SSVEP-BCI system for detecting intermodulation frequency components using task-discriminant component analysis

Recently, steady-state visual evoked potential (SSVEP)-based brain-computer interface (BCI) has significantly progressed and is moving from the laboratory to practical application. However, the system performance and comfort of SSVEP-BCIs still need to be improved. In this study, five flicker frequencies (i.e., 30–34 Hz with an interval of 1 Hz) and eight scaling frequencies (i.e., 0.4–1.8 Hz with an interval of 0.2 Hz) were adopted to jointly encode forty visual stimulus targets using evoked intermodulation (IM) frequency components. Both luminance and shape changes are implemented by sinusoidal sampling stimulus coding methods. High-frequency flicker frequencies and green visual stimuli were chosen to improve the comfort of the proposed system. An extended version of a training algorithm named task-discriminant component analysis (TDCA) was proposed to detect the IM components of SSVEP signals. The average recognition accuracy of eleven subjects is 96.82 ± 0.01 % in the offline experiments for a data length of 5 s. Online validation experiments was constructed from the optimized parameters of offline analysis, and the average accuracy and ITR were 94.37 ± 1.17 % and 113.47 ± 2.60 bits/min, respectively. Furthermore, ten subjects who participated in the validation part also completed the online free-spell task successfully. These results showed that it is feasible to expand the number of stimulus targets by using IM frequency components of SSVEP signals for target coding, and that the system performance is superior.

Internal heat source in the vadose zone: A comprehensive exploration through theoretical spectral analysis and practical application into thermal diffusivity and hydraulic flux in a Quaternary soil water layer

AbstractThis groundbreaking study introduces a scientifically robust method for assessing internal heat generation in shallow, unsaturated aquifers, highlighting the intricate interplay between internal heat, thermal diffusivity, and hydraulic flux. The research pioneers a novel approach employing time‐frequency spectral analysis to address challenges posed by conventional methods that rely solely on prescribed thermal diffusivity and hydraulic flux for evaluating internal heat over time. Rooted in a solid theoretical framework supported by meticulous temperature and heat flux observations, the method adeptly incorporates the concept of an unknown internal heat. The study systematically explores three distinct boundary conditions, showcasing versatility: one with fixed temperatures at the inlet and outlet, another with known temperature at the inlet and no heat flux at the outlet, and a third with a prescribed inlet temperature and constrained outlet heat flux. The estimation of internal heat, coupled with prescribed thermal diffusivity and hydraulic flux, harnesses in‐situ temperature and heat flux spectra through an innovative inverse stochastic spectral approach. A notable feature of this research lies in its ability to strategically handle various parameters, including prescribed thermal diffusivity, hydraulic flux, variations in target depth, significant frequency components, and boundary conditions. The variation assessment findings emphasize the diverse range when predicting internal heat generation based on prescribed thermal diffusivity and hydraulic flux. This study facilitates the determination of potential internal heat magnitudes at different depths and provides profound insights into in‐situ conditions within the vadose zone.

Graph features based classification of bronchial and pleural rub sound signals: the potential of complex network unwrapped.

The study presents a novel technique for lung auscultation based on graph theory, emphasizing the potential of graph parameters in distinguishing lung sounds and supporting earlier detection of various respiratory pathologies. The frequency spread and the component magnitudes are revealed from the analysis of eighty-five bronchial (BS) and pleural rub (PS) lung sounds employing the power spectral density (PSD) plot and wavelet scalogram. The low-frequency spread, and persistence of the high-intensity frequency components are visible in BS sounds emanating from the uniform cross-sectional area of the trachea. The frictional rub between the pleurae causes a higher frequency spread of low-intensity intermittent frequency components in PS signals. From the complex networks of BS and PS, the extracted graph features are - graph density ([Formula: see text], transitivity ([Formula: see text], degree centrality ([Formula: see text]), betweenness centrality ([Formula: see text], eigenvector centrality ([Formula: see text]), and graph entropy (En). The high values of [Formula: see text] and [Formula: see text] show a strong correlation between distinct segments of the BS signal originating from a consistent cross-sectional tracheal diameter and, hence, the generation of high-intense low-spread frequency components. An intermittent low-intense and a relatively greater frequency spread in PS signal appear as high [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] values. With these complex network parameters as input attributes, the supervised machine learning techniques- discriminant analyses, support vector machines, k-nearest neighbors, and neural network pattern recognition (PRNN)- classify the signals with more than 90% accuracy, with PRNN having 25 neurons in the hidden layer achieving the highest (98.82%).

Narrow band-pass filtered canonical correlation analysis for frequency identification in SSVEP signals

Steady-state visual evoked potentials (SSVEP) are generated in the parieto-occipital regions, accompanied by background noise and artifacts. A strong pre-processing method is required to reduce this background noise and artifacts. This study proposed a narrow band-pass filtered canonical correlation analysis (NBPFCCA) to recognize frequency components in SSVEP signals. The proposed method is tested on the publicly available 40 stimulus frequencies dataset recorded from 35 subjects and 4 class in-house dataset acquired from 10 subjects. The performance of the proposed NBPFCCA method is compared with the standard canonical correlation analysis (CCA) and the filter bank CCA (FBCCA). The mean frequency detection accuracy of the standard CCA is 86.21% for the benchmark dataset, and it is improved to 95.58% in the proposed method. Results indicate that the proposed method significantly outperforms the standard canonical correlation analysis with an increase of 9.37% and 17% in frequency recognition accuracy of the benchmark and in-house datasets, respectively.

The influence of coupling nonlinearities on the dynamic behavior of a beam-plate system

Considering the wide application of beam-plate systems in engineering, this work studies the dynamic behavior of the beam-plate system connected by coupling nonlinearities. The governing equations of the beam-plate system are derived and then solved by employing the Galerkin truncation method (GTM). The correctness and stability of dynamic responses of the beam-plate system with coupling nonlinearities are studied, where a four-truncation number of the beam combined with a six-truncation number of the plate can guarantee the stability of the system's dynamic responses. Then, the influence of coupling nonlinearities on the dynamic behavior of the beam-plate system is studied. By analyzing the numerical results, the dynamic behavior of the beam-plate system with coupling nonlinearities can be effectively controlled by adjusting the parameters of coupling nonlinearities in a reasonable range. Complicated responses of the beam-plate system are motivated by coupling nonlinearities, where the working state of complex responses is quasi-periodic. The employment of coupling nonlinearities provides a possible way to control the frequency components of the vibration signal belonging to the beam-plate system. A reasonable use of coupling nonlinearities plays a positive effect on the vibration control of the beam-plate system.

Advancements in wideband source localization with an acoustic vector sensor line array

A method is presented for localizing wideband acoustic sources using an array of acoustic vector sensors (AVS). The method focuses on leveraging the lack of correlation between acoustic pressure and particle velocity in the underwater environmental noise field. Coherent processing is introduced in the signal processing stage to suppress noise components in the observed data. By employing a focused transform that maps various frequency components of the wideband signal into the same signal subspace, an asymptotically unbiased Direction of Arrival (DOA) estimation is achieved using a multidimensional subspace method. A concise expression for the Cramér-Rao Bound (CRB) on the estimation errors is provided within the framework of the wideband multi-vector-sensor model. The performance of the proposed method for localizing sources is assessed through simulation and experimental data analysis. The research indicates that coherent processing effectively suppresses isotropic components in background noise, the proposed method achieves a lower estimation error, closer to the CRB, compared to the scalar array counterpart under identical signal-to-noise ratio (SNR) conditions.

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Design of spatiotemporal variability index for climatic variables

Spatiotemporal signals are currently gaining wide popularity owing to their richness in terms of information content from both spatial and temporal aspects. Climatic studies involve the usage of such signals from different spatial locations to understand the climatic conditions, anomalies and for prediction of similar climatic zones. Measurement of the complex inter-relationships in the spatiotemporal processes is of vital importance in this regard. The predominant frequency components associated with annual, semi-annual, and quarterly seasonal variations exhibit interchangeability across spatial and temporal dimensions, thereby contributing significantly to the variability within the spatiotemporal region under investigation. Employing frequency domain analysis enables the examination of these crucial seasonal components, even amidst noise, provided effective frequency domain-based techniques are employed. This paper is based on the measurement of the variability of spatiotemporal climatic variables considered from different geographic zones using multivariate variational mode decomposition. The main advantage of the proposed index lies in the ability to measure the variability of the signals acquired from either spatially close or far-off locations on Earth. Also, the index harnesses the hidden frequency components in the spatiotemporal signals under test by comparing the aligned periodic components across different zones. The correctness of the proposed index is tested through exhaustive simulation studies and also against the weather measurements like the Earth skin temperature, humidity and precipitation acquired from spatially close and far-off locations over a period of 40 years.

Vibration control on coupled unit-plant structure of pumped storage power station during sudden load-up process

The versatile regulatory capacity of pumped storage power station (PSPS) stems from the reversible pumped turbine unit switching between multiple operating conditions. Nevertheless, the unit and plant structure experience heightened vibrations owing to the intricate interplay of hydraulic, electrical, and mechanical excitations during transition processes, and the vibration responses fluctuate as operating conditions shift, posing a significant challenge to the safety and high quality operation of power station. To tackle the practical engineering issue, this paper delves into the sudden load-up scenario in power generation situation of pumped turbine, leveraging a finite element model encompassing the coupled hydraulic-mechanical-electrical-structural system (HMES) of PSPS and a mathematical model of unit shaft system, the impacts of dynamic loads induced by various vibration source on the unit and plant structure during transient condition, are meticulously analyzed and discussed through numerical simulations. Additionally, the magnetorheological damper (MRD), is incorporated into the PSPS to explore the effectiveness of MRD in controlling transient vibration in the interconnected unit-plant structure. The results indicate that the system parameters and associated load excitations undergo rapid fluctuations during the load-up process, bringing about noticeable oscillations in vibration amplitudes of rotor and turbine. The floors and fan hood of plant are the most vulnerable areas in terms of structural strength, with associated displacement amplitudes being most noticeable. The incorporation of MRD proves to be highly effective in mitigating the unsteady vibrations in both the unit and the plant structure during load-up course, as well as optimizing the motion patterns of rotor and turbine, promoting a notable reduction in frequency amplitudes of spectrum. Moreover, the maximal transient displacement amplitude of unit is significantly diminished, with the rotor experiencing a decrease of approximately 79%, while the amplitude of turbine declines by 16%. The displacement fluctuation ranges of the plant structure are observably diminished, and the complex frequency components of vibration signal are efficiently controlled. The transient vibration characteristics of the coupled unit-plant structure and the damping behavior of MRD during the transition process are unveiled by the research findings in this paper, which can offer valuable insights for the stability assessment and the research on vibration management of HMES for PSPS under the unsteady operation conditions.

The origins of frequency-difference and frequency-sum beamforming

Beamforming the signals recorded by an array enables the determination of sound source location(s) or the arrival directions of ray paths between a sound source and the receiving array. Frequency-difference and frequency-sum beamforming are beamforming techniques that provide out-of-band information from in-band signal frequencies. Interestingly, the out-of-band frequencies can be chosen by the user, within limits set by the signal recordings, to achieve desired properties of the beamformed output, such as: increased resolution, reduced sidelobes, or greater robustness to random scattering. Both techniques are general and are not limited to any particular acoustic environment, frequency range, or array geometry. Frequency-sum beamforming, generates higher-frequency information from lower frequency signal components, enhancing beamforming results in scenarios with random scattering between the source and the receivers. However, it is limited by artifacts arising from cross-terms when multiple source signals are present in the same bandwidth. Conversely, frequency-difference beamforming manufactures lower-frequency information from higher frequency signal components, effectively mitigating the impact of spatial aliasing in situations where the receiving array is sparse. This presentation delves into the origins of frequency-difference and frequency-sum beamforming, presents the fundamental mathematics underlying their algorithms, and showcases their performance via simulations and experimental results. [Work supported by ONR.]

Auditory-inspired adaptive frequency tracking

One of the best frequency trackers to date is the human (mammalian) auditory system, which has evolved through millions of years of resolving classification problems. It is a versatile, elegant and powerful sound processing unit. It excels in detecting, estimating, and classifying multiple targets simultaneously even in noisy environments. Hence, mimicking even some features of the auditory system could be beneficial in developing superior frequency tracking and classification algorithms. An auditory inspired adaptive synchrony capture filterbank (SCFB) signal processing architecture for tracking signal frequency components was proposed in a related paper [JASA-2013]. The SCFB architecture consists of a fixed array of traditional, passive linear, gammatone filters in cascade with a bank of three adaptively tunable bandpass filters that form a frequency-discriminator-loop (FDL). The SCFB exhibits many desirable properties for processing speech, music, and other complex sounds. In recent work [Dec2021], the algorithm was modified using adaptive tuning parameters, and a generalized way to determine/suppress voiced and unvoiced (silent) regions. This modified algorithm estimates frequencies with higher accuracy even in the presence of closely spaced input tones. Preliminary analysis with synthetic, human speech and humpback/whale-call signals demonstrates that the revised algorithm performs well. This talk will focus on follow-on work.

Sensorimotor content of multi-unit activity recorded in the paramedian lobule of the cerebellum using carbon fiber microelectrode arrays.

The cerebellum takes in a great deal of sensory information from the periphery and descending signals from the cerebral cortices. It has been debated whether the paramedian lobule (PML) in the rat and its paravermal regions that project to the interpositus nucleus (IPN) are primarily involved in motor execution or motor planning. Studies that have relied on single spike recordings in behaving animals have led to conflicting conclusions regarding this issue. In this study, we tried a different approach and investigated the correlation of field potentials and multi-unit signals recorded with multi-electrode arrays from the PML cortex along with the forelimb electromyography (EMG) signals in rats during behavior. Linear regression was performed to predict the EMG signal envelopes using the PML activity for various time shifts (±25, ±50, ±100, and ± 400 ms) between the two signals to determine a causal relation. The highest correlations (~0.5 on average) between the neural and EMG envelopes were observed for zero and small (±25 ms) time shifts and decreased with larger time shifts in both directions, suggesting that paravermal PML is involved both in processing of sensory signals and motor execution in the context of forelimb reaching behavior. EMG envelopes were predicted with higher success rates when neural signals from multiple phases of the behavior were utilized for regression. The forelimb extension phase was the most difficult to predict while the releasing of the bar phase prediction was the most successful. The high frequency (>300 Hz) components of the neural signal, reflecting multi-unit activity, had a higher contribution to the EMG prediction than did the lower frequency components, corresponding to local field potentials. The results of this study suggest that the paravermal PML in the rat cerebellum is primarily involved in the execution of forelimb movements rather than the planning aspect and that the PML is more active at the initiation and termination of the behavior, rather than the progression.

Fault diagnosis of tooth surface spalling based on variational mode decomposition and maximum correlation kurtosis method

As the early fault features of tooth surface spalling are very weak and difficult to extract because of random noise and other types of signal interference, a method that combines maximum correlation kurtosis uncoiling and variational mode decomposition is proposed herein. First, a series of modes are obtained by variational mode decomposition, and the kurtosis criterion is applied to select the modes containing rich fault information for reconstruction and noise reduction. Second, the maximum correlation kurtosis deconvolution method is used to enhance the selected signals. Finally, the fault features are extracted by envelope demodulation of the reconstructed signal. The effectiveness of the proposed method is verified by analysis, and the different frequency components of the vibration signals of tooth surface spalling faults are shown to be separated accurately.

High-Precision Inertial Sensor Charge Ground Measurement Method Based on Phase-Sensitive Demodulation

Inertial sensors are the key payloads in space gravitational wave detection missions, and they need to ensure that the test mass (TM), which serves as the inertial reference, freely floats in the spacecraft without contact, so that the TM is not disturbed by the satellite platform and the cosmic environment. Space gravitational wave detection missions require that the residual acceleration of the TM should be less than 3×10−15ms−2Hz−1/2. However, the TM with charges will interact with surrounding conductors and magnetic fields, introducing acceleration noise such as electrostatic force and Lorentz force. Therefore, it is necessary to carry out charge management on the TM, in which the high-precision measurement of charge is crucial. Space gravitational wave detection missions require a residual charge measurement accuracy of 3×10−13C for the TM. In this paper, we design a high-precision inertial sensor charge measurement method based on phase-sensitive demodulation (PSD). By establishing a torsion pendulum rotation model based on the force modulation method, the characteristics of the TM torsion angle signal are analyzed. The PSD is used to extract the amplitude of the specific frequency signal component containing the charge information, and then to calculate the value of the accumulated charges. The method is compared with the Butterworth band-pass filtering method, and the simulation results show that the method has a higher measurement accuracy, shorter settling time, and stronger anti-interference ability, meeting the TM residual charge measurement accuracy index requirement.

An emotion recognition method based on EWT-3D–CNN–BiLSTM-GRU-AT model

This has become a significant study area in recent years because of its use in brain-machine interaction (BMI). The robustness problem of emotion classification is one of the most basic approaches for improving the quality of emotion recognition systems. One of the two main branches of these approaches deals with the problem by extracting the features using manual engineering and the other is the famous artificial intelligence approach, which infers features of EEG data. This study proposes a novel method that considers the characteristic behavior of EEG recordings and based on the artificial intelligence method. The EEG signal is a noisy signal with a non-stationary and non-linear form. Using the Empirical Wavelet Transform (EWT) signal decomposition method, the signal's frequency components are obtained. Then, frequency-based features, linear and non-linear features are extracted. The resulting frequency-based, linear, and nonlinear features are mapped to the 2-D axis according to the positions of the EEG electrodes. By merging this 2-D images, 3-D images are constructed. In this way, the multichannel brain frequency of EEG recordings, spatial and temporal relationship are combined. Lastly, 3-D deep learning framework was constructed, which was combined with convolutional neural network (CNN), bidirectional long-short term memory (BiLSTM) and gated recurrent unit (GRU) with self-attention (AT). This model is named EWT-3D–CNN–BiLSTM-GRU-AT. As a result, we have created framework comprising handcrafted features generated and cascaded from state-of-the-art deep learning models. The framework is evaluated on the DEAP recordings based on the person-independent approach. The experimental findings demonstrate that the developed model can achieve classification accuracies of 90.57 % and 90.59 % for valence and arousal axes, respectively, for the DEAP database. Compared with existing cutting-edge emotion classification models, the proposed framework exhibits superior results for classifying human emotions.

EMERGENCY MODES MODELING IN A COMPLEX LOAD NODE: HIGH-FREQUENCY COMPONENTS OF SIGNALS

The purpose of the study is to show the features of the occurrence of high–frequency components in current and voltage signals in various elements of the electrical complex by the example of modeling emergency modes in power lines and a complex load node and to analyze their mutual influence.
 
 Materials and methods. The signals of currents and voltages during transients in a power line and the load node with a three-winding transformer were modeled using the author’s software. The calculations are based on the method of synthetic circuits (Dommel’s algorithm). The main attention is paid to the occurrence of high-frequency components of current and voltage during short circuits and switching.
 
 Results. Modeling of the three-phase short circuit in a 110 kV transmission line when it is divided into P-sections demonstrates how significantly the level of high-frequency components differs in each of the three phases. This is manifested primarily in voltage signals. In a complex load node with a 110/35/10 kV transformer, short circuits and switching on the 35 kV side significantly affect the currents and voltages on the 10 kV side. It is shown that a higher level of high-frequency components of current signals corresponds to energy recovery modes in case of imbalance and run-out of the powerful asynchronous motor on the 10 kV side. The possibility of using the obtained results for the classification of faults in electrical systems is discussed.
 
 Conclusions. The level and spectral composition of the currents and voltages high-frequency components in transient modes depends on the initial phase and is of interest for the faults analysis and classification. The nature of these oscillations is determined by the resonant frequencies of the electrical circuits that occur during switching and short circuits.

An adaptive cepstrum feature representation method with variable frame length and variable filter banks for acoustic emission signals

Acoustic emission technology is widely employed in defect detection, structural health monitoring, fault diagnosis, and other applications due to its benefits of non-contact, real-time, sensitivity, and flexibility. To implement efficient and timely intelligent monitoring, it is crucial to promptly and precisely gather the time-varying properties in the non-stationary acoustic emission signals. The current work proposes an adaptive cepstrum feature representation method that combines variable frame length and variable filter bank. The variable frame length is implemented based on the spectral distribution correlation, and the optimal frame length and frame rate are selected by iterative operations. The variable filter bank, on the other hand, characterizes the local measure features of variable frame length signals by setting dynamic weight distributions. The proposed adaptive cepstrum algorithm can be used as an auxiliary tool to initially analyze complex non-stationary signals, and thus effectively identify the time-varying and frequency components in acoustic emission signals. The superiority of the proposed method has been confirmed on simulation data. Furthermore, the practical performance of the proposed method is evaluated and illustrated based on the burst signal from laser shock peening processing and the mixed signal from pipeline leakage. The proposed method can be extended to other broadband signals and can be used for feature pre-processing before deep learning network modeling to improve recognition accuracy due to its high time–frequency resolution.

Application of Variational Mode decomposition in GPR Detection of Oil Contaminated Soil

In this article, Ground penetrating radar (GPR) is used to investigate the contaminated soil by oil pollutants in oilfield operation area. Time frequency analysis method is applied to GPR data to reveal the changes of GPR signal frequency components with time variation, which is very important for data interpretation. We use variational mode decomposition (VMD) for time frequency analysis. It can decompose radar signal into several quasi-orthogonal intrinsic mode functions (IMFs) with limited bandwidth, and has strong robustness and local decomposition ability. We apply the VMD on field data acquired in the area with waste liquid contaminated soil in oilfield. The decomposed IMFs from GPR data shows that the signals from the contaminated soil is characterized by the strong energy and low frequency. Then the instantaneous attribute analysis of the IMF is carried out to delineate the scope and thickness of contaminated soil. The experimental results show that the limited bandwidth IMF with specific sparsity obtained by VMD method is more conducive to the processing and interpretation of GPR data.