Hilbert-Huang Transform Research Articles

Application of the Hilbert-Huang transform to evaluate signals in chromatic confocal spectral interferometry

Chromatic confocal spectral interferometry (CCSI) is a hybrid measurement technique that integrates the principles of spectral interferometry and chromatic confocal microscopy. This innovative approach enables scanning-free acquisition of axial dimensions while leveraging interferometric methods to enhance depth accuracy. This feature allows the CCSI signal to be processed using both peak extraction and evaluation of the interferometric optical path length difference. The phase information offers a decreased measurement uncertainty, making it a commonly used approach in existing studies. Methods such as Fourier transform (FT) and wavelet transform (WT) are frequently employed for this purpose. In this paper, we present a signal processing approach based on the Hilbert-Huang transform (HHT). Through simulations and experiments, we compare HHT with Fourier transform (FT) and wavelet transform (WT), demonstrating its stability, noise resistance, and effectiveness in phase extraction for CCSI measurement signals. Additionally, we leverage the characteristics of CCSI signals and the time-frequency analysis capabilities of HHT to address the direction ambiguity problem in white light interferometry.

ABAQUS-based research on the parameters of highway subgrade vibratory compaction and vibration wave propagation laws

Vibratory rollers are generally used in the process of highway subgrade compaction. In the paper, the vibratory roller—subgrade finite element model was established to simulate the field construction by using ABAQUS. We used Hilbert–Huang Transform to analyze the compaction in the field test from the time–frequency domain. By changing the parameters of the vibratory roller and the filler, the comprehensive influence of the parameters such as the elastic modulus of the filler, rolling speed, excitation force, vibration frequency and thickness of the filler on the compaction quality of the subgrade was investigated. We studied the propagation pattern of vibration waves in three-dimensional space. The study shows that the signals of different frequency bands in the Hilbert spectrum represent the compaction degrees of fillers in different zones. The peak acceleration generally decreases with the increase of horizontal and vertical distance, but there is an increase at the boundary of the vibration field. There is an optimal combination of the excitation force, vibration frequency and thickness of the filler. The vibration waves propagate in the form of an ellipsoid in three dimensions, and the amplitude decreases with distance.

A straightforward method for estimating evolutionary power spectral density of non-stationary typhoon wind speed

PurposeA precise estimation of the evolutionary power spectral density (EPSD) of typhoon wind speed is a difficult and significant undertaking in the analysis of turbulence effects on large-expansive structures. A majority of the prevailing EPSD estimation techniques rely on complex signal processing methodologies, such as wavelet decomposition, Hilbert–Huang transformation and time-varying autoregressive moving average (ARMA) model. However, these approaches often pose challenges in terms of comprehensibility and practical implementation for engineers. In light of this issue, the present study introduces a straightforward and effective EPSD estimation method tailored specifically for typhoon wind speed, aiming to facilitate its understanding and application in engineering contexts.Design/methodology/approachFirstly, the mathematical model of a uniformly modulated non-stationary process is employed to represent the typhoon wind speed. Secondly, the reverse arrangement test serves as an auxiliary tool in conjunction with wavelet transform or empirical mode decomposition, aiding in the determination of the optimal slowly varying mean wind speed. Thirdly, Kernel regression technique is utilized to discern the time-dependent standard deviation of wind speed fluctuations. Finally, the power spectral density (PSD) of wind speed residuals is computed to facilitate the estimation of the EPSD.FindingsFirstly, the reverse arrangement test-assisted approach enables the determination of an optimal time-dependent mean from the candidate results obtained through discrete wavelet transform (DWT) and empirical mode decomposition (EMD). Secondly, the application of the Kernel regression technique facilitates accurate identification of the time-dependent variance from the fluctuating wind speed data. Thirdly, due to the influence of the extreme weather, the Gaussianity of the reduced turbulent fluctuations in typhoon wind is easily disturbed, resulting in the obvious non-Gaussian features.Originality/valueThis paper employs the mathematical model of uniformly modulated non-stationary process to characterize typhoon wind speeds and then proposes a straightforward and efficient method for estimating the EPSD of typhoon wind. The accuracy and efficacy of the presented estimation method are verified using the field-measured wind speed data from Typhoon Rammasun. The proposed EPSD estimation method for typhoon wind exhibits suitability for engineering applications owing to its simplicity and computational efficiency.

Unveiling the rebrightening mechanism of GRS 1915+105: Insights from a change in the quasi-periodic oscillations and from a wind analysis

We report a significant rebrightening event in the microquasar GRS 1915+105 that was observed in July 2021 with NICER and NuSTAR. This event was characterized by quasi-periodic oscillations (QPOs) in the soft state, but is typically free of these oscillations. It was also marked by an increase in the disk wind ionization degree. By employing the Hilbert-Huang transform (HHT), we decomposed the stable low-frequency QPO from the light curves using data from NICER and NuSTAR. Our spectral analysis shows a weak change in the Fe XXV absorption lines and a strong change in the Fe XXV absorption edge with QPO phase. Other spectral parameters, including the photon index and the seed photon temperature, correlate positively with the QPO phase, but the electron temperature is inversely correlated. Based on our findings we propose that the observed QPOs were caused by magnetic activity and not by precession. The magnetic field drove a failed disk wind of high-ionization low-velocity material. These results support the accretion ejection instability model and provide deeper insights into the dynamics of accretion-ejection processes that are magnetized by a black hole.

Detecting damage on engine mounts using hilbert-huang transform vibration analysis

Engine mounts, which are usually composed of elastomeric materials like rubber that can absorb excessive vibrations, are built to withstand vibration sources from engines. Engine mounts may eventually degrade from extended use. When rubber products age or sustain damage, they may grow harder and crack. Engine mounts need to be maintained regularly to ensure optimal performance. Visual examinations and the detection of excessive vibrations can be used to accomplish this. Vibration sensors are mounted on the engine mount in axial, vertical, and horizontal orientations using a vibration detection technique utilizing the Hilbert-Huang Transform (HHT) methodology. Matlab is used to examine the data that is gathered at three distinct rotational speeds: 750 rpm, 2000 rpm, and 3000 rpm. The HHT approach combines two key components: the Hilbert Transform, which analyzes the time-frequency signal of the first decomposition until only residuals remain, and Empirical Mode Decomposition (EMD), which breaks down the signal into Intrinsic Mode Functions (IMFs). According to test data, a damaged mount had an amplitude of 0.00005212 m/s² and a frequency of 8 Hz. On the other hand, in typical circumstances, the highest frequency was 7 Hz with the same amplitude. Five frequency increases were made in the damaged mount throughout this operation. In the damaged mount, the Hilbert Transform showed a frequency of 2124 Hz with an amplitude of 0.007594 m/s², indicating a significant resonance. This illustrates how the Hilbert-Huang Transform's capacity to handle non-stationary and nonlinear signal forms allows it to detect damage in components efficiently

Multi-scale analysis of nutrient and environmental dynamics in Hongfeng Lake Southwest China

Traditional linear correlation analysis may not fully capture the true relationship between these variables. Therefore, multi-scale running correlation analysis, such as time-dependent intrinsic correlation (TDIC) and continuous wavelet transform based on Hilbert–Huang transform (HHT), provides valuable insights into local correlations and the evolving relationship between nutrients and environmental factors over time. In this study, we investigated seven environmental factors and four water quality nutrient indicators in deep lakes on the Yungui Plateau in southwestern China. The results revealed that there may be strong correlations between environmental factors and nutrient levels during certain periods, while opposite trends may emerge at other times. These variations in correlation could be attributed to uncertain physical processes, spatial heterogeneity, or the impact of different climatic factors on local hydrological processes. Wavelet analysis indicated that changes in environmental factors lag behind those in nutrient levels, particularly on a cycle of about 12 months. This suggests that changes in environmental factors align with natural patterns after the water body has been polluted. These conclusions underscore the complexity and dynamic nature of the relationship between environmental factors and nutrient levels in water bodies, highlighting the importance of employing advanced analysis techniques to capture this complexity.

Robot terrain classification based on improved Hilbert-Huang transform and long short-term memory network

Nowadays, with the rapid development of science and technology, the innovation and application of robot technology has become an important force to promote industrial development, which requires robots to have a high degree of autonomy and adaptability. Among them, terrain classification technology is one of the key technologies to achieve this goal. In order to improve the ground adaptability of robots in complex environments, this paper proposes a terrain classification algorithm based on improved Hilbert-Huang transform(HHT) combined with ensemble empirical mode decomposition(EEMD) and long short-term memory network(LSTM). Firstly, the signal data is processed by EEMD, and then the frequency domain features of the signal are extracted by Hilbert transform to expand the feature dimension. Finally, the features are learned and classified by the LSTM model, which effectively improves the classification accuracy. In this paper, we conducted sufficient experiments to compare the effects of EMD and EEMD and the effects of different neural network models, and verified the contribution of the Hilbert-Huang transform to improve the classification performance through ablation experiments, which proves the effectiveness and reliability of our proposed algorithm, and provided powerful technical support for the robot to adapt to the ground information in the complex environment.

Early prediction of sudden cardiac death using multimodal fusion of ECG Features extracted from Hilbert–Huang and wavelet transforms with explainable vision transformer and CNN models

Background and Objective:Sudden cardiac death (SCD) is a critical health issue characterized by the sudden failure of heart function, often caused by ventricular fibrillation (VF). Early prediction of SCD is crucial to enable timely interventions. However, current methods predict SCD only a few minutes before its onset, limiting intervention time. This study aims to develop a deep learning-based model for the early prediction of SCD using electrocardiography (ECG) signals. Methods:A multimodal explainable deep learning-based model is developed to analyze ECG signals at discrete intervals ranging from 5 to 30 min before SCD onset. The raw ECG signals, 2D scalograms generated through wavelet transform and 2D Hilbert spectrum generated through Hilbert–Huang transform (HHT) of ECG signals were applied to multiple deep learning algorithms. For raw ECG, a combination of 1D-convolutional neural networks (1D-CNN) and long short-term memory networks were employed for feature extraction and temporal pattern recognition. Besides, to extract and analyze features from scalograms and Hilbert spectra, Vision Transformer (ViT) and 2D-CNN have been used. Results:The developed model achieved high performance, with accuracy, precision, recall and F1-score of 98.81%, 98.83%, 98.81%, and 98.81% respectively to predict SCD onset 30 min in advance. Further, the proposed model can accurately classify SCD patients and normal controls with 100% accuracy. Thus, the proposed method outperforms the existing state-of-the-art methods. Conclusions:The developed model is capable of capturing diverse patterns on ECG signals recorded at multiple discrete time intervals (at 5-minute increments from 5 min to 30 min) prior to SCD onset that could discriminate for SCD. The proposed model significantly improves early SCD prediction, providing a valuable tool for continuous ECG monitoring in high-risk patients.

Study on seismic response characteristics of living stumps slope based on large-scale shaking table test

A large-scale shaking table test of a living stump slope with a geometric similarity ratio of 1:7 was designed and completed. The peak acceleration, acceleration amplification factor, and displacement response patterns of living stumps slopes under different types of seismic waves and excitation intensities were obtained. The time-frequency and energy variation characteristics were analyzed using the Hilbert-Huang Transform (HHT). The results showed that: (1) Regardless of the type of seismic wave, the peak acceleration and acceleration amplification factor of the living stumps slope surface are positively correlated with relative height and seismic excitation intensity. When the excitation intensity is ≤ 0.4 g, the acceleration amplification effect is more pronounced; when the excitation intensity is > 0.4 g, the acceleration amplification effect weakens. (2) Under the action of different seismic waves, the peak displacement of slope surface shows amplification effect along the elevation, and increases with the increase of excitation intensity. In addition, the incremental displacement gradually decreases from the toe to the top of the slope, which is expressed as D2 > D3 > D1 > D4 > D5. The peak displacement at the top of the slope is the greatest, but the incremental displacement is the smallest; the peak displacement at the toe of the slope is the smallest, but the incremental displacement is relatively large. (3) Regardless of the type of seismic wave, living stumps slope shows the characteristics of filtering the low-frequency components of the seismic waves and amplifying their high-frequency components. At the same time, the seismic Hilbert energy gradually accumulates along the elevation. PSHEA and PMSA significantly increase with elevation and excitation intensity, and they reach the maximum at the top of the slope. (4) The seismic Hilbert energy is positively correlated with the relative height and excitation intensity, and reaches the maximum at the top of the slope. With the accumulation of seismic Hilbert energy increases, the dynamic response parameters such as peak acceleration, acceleration amplification coefficient and displacement also increase synchronously, reaching the maximum at the top of the slope. The research conclusions can provide an experimental basis for the seismic design of living stumps slopes.

Hilbert-Huang Transform and machine learning based electromechanical analysis of induction machine under power quality disturbances

Monitoring and predicting Power Quality (PQ) is crucial for quickly minimizing risk, protecting induction machines (IMs), and increasing productivity. This paper proposes an electromechanical analytical framework for IM working with various PQ disturbances based on machine learning (ML). This work collects the motor characteristics and PQ data, motor vibration signals, and other sensor data to identify the failures. The complicated electromechanical data is broken down into intrinsic mode functions (IMFs) using the Hilbert-Huang Transform (HHT), which reveals the modes present in the signals. This frequency-domain data is retrieved, paired with time-domain characteristics, and used as input features for ML algorithms. Support Vector Machines (SVMs) trained on labeled datasets in which features extracted from PQ disturbances are used to categorize the disturbances into several groups. The PQ disturbances caused by voltage sags, swells, harmonics, and transients can all be efficiently classified using SVM classifiers, allowing for real-time determination of the kind of disturbance influencing the IM. The accuracy for the SVM in the proposed scheme is 97.2 %. The SVM method is trained with PQ data and classification results using MATLAB classifier and Python software.

Status Monitoring System of Reciprocating Hydrogen Compressor Based on Hilbert−Huang Transform

ABSTRACTA reciprocating hydrogen compressor status monitoring system for predictive maintenance is developed based on HHT (Hilbert−Huang Transform) with multiple functions, strong applicability, and high accuracy to address the problem of difficulty in identifying fault signals and failure to provide advance warning before faults occur in the reciprocating hydrogen compressor state monitoring system. Design framework of monitoring system is confirmed, and function modules are designed based on LabView platform. HHT is applied to monitor the status of reciprocating hydrogen compressor based on LabView platform. A reciprocating hydrogen compressor is selected as research object, status monitoring analysis is carried out. Five working states of reciprocating hydrogen compressor are collected, which conclude normal state, filler malfunction, cross‐head malfunction, air valve malfunction, and piston rod malfunction. HHT is carried out for five signals, and results show that HHT marginal spectrum of five signals has different characteristics. Based on comparison results, precision of HHT ranges from 0.757 to 0.784, recall of HHT ranges from 0.738 to 0.766, F1‐score of HHT ranges from to 0.788 to 0.804, HHT has better performance than other two methods. Proposed monitoring system designed in this study provides a comprehensive and efficient online monitoring and data analysis solution for reciprocating hydrogen compressors, which can achieve fault prediction of reciprocating hydrogen compressor, reduce failure rate, and effectively improve the reliability of the compressor oil injection system.

Bridge modal identification method based on adaptive VMD-HT algorithm

ABSTRACT Bridge engineering structures play a crucial role in transportation. Traditional methods of road and bridge closures for inspection and evaluation, while effective, increase bridge inspection costs and disrupt normal traffic flow. Therefore, a rapid detection and evaluation method for bridge structural modal parameters in the operational state is more suitable for practical engineering applications. However, under real operating conditions, bridge vibration signals typically contain a large amount of noise and interference, and modal identification must overcome issues of non-stationarity and non-linearity in the vibration signals caused by vehicle loads and environmental changes to ensure the accuracy of the identification. This study replaces the traditional Empirical Mode Decomposition algorithm in the Hilbert-Huang Transform with the Variational Mode Decomposition algorithm. It proposes a new method that combines the VMD algorithm with the Hilbert Transform, referred to as the Variational Mode Decomposition-Hilbert Transform method. Compared to the EMD algorithm, it offers significant improvements in suppressing mode mixing and endpoint effects. A vehicle-bridge coupling model was constructed, and the bridge’s natural modal information was successfully extracted from the vibration response signals. The research results indicate that the improved algorithm offers higher accuracy and faster computational speed compared to traditional identification algorithms.

Underwater Acoustic Target Recognition Based on Hilbert–Huang Transform and Data Augmentation

Underwater Acoustic Target Recognition Based on Hilbert–Huang Transform and Data Augmentation

Ensemble Fusion Models Using Various Strategies and Machine Learning for EEG Classification.

Electroencephalography (EEG) helps to assess the electrical activities of the brain so that the neuronal activities of the brain are captured effectively. EEG is used to analyze many neurological disorders, as it serves as a low-cost equipment. To diagnose and treat every neurological disorder, lengthy EEG signals are needed, and different machine learning and deep learning techniques have been developed so that the EEG signals could be classified automatically. In this work, five ensemble models are proposed for EEG signal classification, and the main neurological disorder analyzed in this paper is epilepsy. The first proposed ensemble technique utilizes an equidistant assessment and ranking determination mode with the proposed Enhance the Sum of Connection and Distance (ESCD)-based feature selection technique for the classification of EEG signals; the second proposed ensemble technique utilizes the concept of Infinite Independent Component Analysis (I-ICA) and multiple classifiers with majority voting concept; the third proposed ensemble technique utilizes the concept of Genetic Algorithm (GA)-based feature selection technique and bagging Support Vector Machine (SVM)-based classification model. The fourth proposed ensemble technique utilizes the concept of Hilbert Huang Transform (HHT) and multiple classifiers with GA-based multiparameter optimization, and the fifth proposed ensemble technique utilizes the concept of Factor analysis with Ensemble layer K nearest neighbor (KNN) classifier. The best results are obtained when the Ensemble hybrid model using the equidistant assessment and ranking determination method with the proposed ESCD-based feature selection technique and Support Vector Machine (SVM) classifier is utilized, achieving a classification accuracy of 89.98%.

Characterization of Seismic Signal Patterns and Dynamic Pore Pressure Fluctuations Due to Wave-Induced Erosion on Non-Cohesive Slopes

Wave erosion of slopes can easily trigger landslides into marine environments and pose severe threats to both the ecological environment and human activities. Therefore, near-shore slope monitoring becomes crucial for preventing and alerting people to these potential disasters. To achieve a comprehensive understanding, it is imperative to conduct a detailed investigation into the dynamics of wave erosion processes acting on slopes. This research is conducted through flume tests, using a wave maker to create waves of various heights and frequencies to erode the slope models. During the tests, seismic signals, acoustic signals, and pore pressure generated by wave erosion and slope failure are recorded. Seismic and acoustic signals are analyzed, and time-frequency spectra are calculated using the Hilbert–Huang Transform to identify the erosion events and signal frequency ranges. Arias Intensity is used to assess seismic energy and explore the relationship between the amount of erosion and energy. The results show that wave height has a more decisive influence on erosion behavior and retreat than wave frequency. Rapid drawdown may potentially cause the slope to slide during cyclic swash and backwash wave action. As wave erosion changes from swash to impact, there is a significant increase in the spectral magnitude and Power Spectral Density (PSD) of both seismic and acoustic signals. An increase in pore pressure is observed due to the rise in the run-up height of waves. The amplitude of pore pressure will increase as the slope undergoes further erosion. Understanding the results of this study can aid in predicting erosion and in planning effective management strategies for slopes subject to wave action.

Comparative analysis of empirical decomposition algorithms in predicting tire-pavement friction from asphalt surface textures: a Hilbert–Huang transform (HHT) analysis

The frictional properties of pavement are contingent on its surface texture, which consists of multiple scales that each contribute differently to friction generation at the tire-surface interface. Consequently, this study applied three adaptive decomposition algorithms of the Hilbert–Huang Transformation (HHT) to extract essential texture parameters from surface profiles, aiming to improve understanding of how pavement texture impacts friction properties. The decomposition algorithms used are Empirical Mode Decomposition (EMD), Ensemble EMD (EEMD) and Complete EEMD with Adaptive Noise (CEEMDAN). A Circular Track Meter (CTMeter) was used to measure the surface texture profiles of twelve asphalt mixture slabs with high macrotexture, while friction properties were assessed using a dynamic friction tester (DFT). Additionally, sixteen texture parameters related to height, spacing, and shape were computed to characterize the surface texture of both the original profile and the derived intrinsic mode functions (IMFs). The statistical analysis revealed that while the third IMF (IMF3) obtained by the EEMD exhibited the strongest correlation with the original profile, reaching up to 0.69, the IMFs obtained by EMD demonstrated the highest correlation with the DFT results. Under different polishing conditions and DFT speeds, the friction-texture correlation varied significantly, with the highest correlation observed at the peak values of DFT results and DFT values at 20 km/h (DFT20). Among the texture indicators, in addition to the mean profile depth (MPD), the root mean square (Rq), root mean square wavelength (λq), and two points slope variance (SV2) were recommended for characterizing both the original texture and IMFs profiles in the correlation analysis of the friction-texture relationship.

Investigations into the flow dynamics of mixed biomass particles in a fluidized bed through Hilbert-Huang transformation and data-driven modelling

Flow dynamics of binary particles are investigated to realize the monitoring and optimization of fluidized beds. It is a challenge to accurately classify the mass fraction of mixed biomass, considering the limitations of existing techniques. The data collected from an electrostatic sensor array is analyzed. Cross correlation, empirical mode decomposition (EMD), Hilbert-Huang transform (HHT) are applied to process the signals. Under a higher mass fraction of the wood sawdust, the segregation behavior occurs, and the high energy region of HHT spectrum increases. Furthermore, two data-driven models are trained based on a hybrid wavelet scattering transform and bidirectional long short-term memory (ST-BiLSTM) network and a EMD and BiLSTM (EMD-BiLSTM) network to identify the mass fractions of the mixed biomass, with accuracies of 92% and 99%. The electrostatic sensing combined with the EMD-BiLSTM model is effective to classify the mass fraction of the mixed biomass.

A Method for the Pattern Recognition of Acoustic Emission Signals Using Blind Source Separation and a CNN for Online Corrosion Monitoring in Pipelines with Interference from Flow-Induced Noise.

As a critical component in industrial production, pipelines face the risk of failure due to long-term corrosion. In recent years, acoustic emission (AE) technology has demonstrated significant potential in online pipeline monitoring. However, the interference of flow-induced noise seriously hinders the application of acoustic emission technology in pipeline corrosion monitoring. Therefore, a pattern-recognition model for online pipeline AE monitoring signals based on blind source separation (BSS) and a convolutional neural network (CNN) is proposed. First, the singular spectrum analysis (SSA) was employed to transform the original AE signal into multiple observed signals. An independent component analysis (ICA) was then utilized to separate the source signals from the mixed signals. Subsequently, the Hilbert-Huang transform (HHT) was applied to each source signal to obtain a joint time-frequency domain map and to construct and compress it. Finally, the mapping relationship between the pipeline sources and AE signals was established based on the CNN for the precise identification of corrosion signals. The experimental data indicate that when the average amplitude of flow-induced noise signals is within three times that of corrosion signals, the separation of mixed signals is effective, and the overall recognition accuracy of the model exceeds 90%.

Seismic response and damage evolution process of a bedded slope‒tunnel system via the continuum‒discontinuum element method

To investigate the failure evolution process and failure mechanism of the bedded slope‒tunnel system under earthquakes, this work examines a specific layered slope at a tunnel portal in southeast China and conducts a 2D dynamic analysis with the continuum‒discontinuum element method (CDEM). It investigates the slope's dynamic behavior and potential for instability by evaluating the wave patterns, acceleration, displacement, Hilbert‒Huang transform (HHT) spectral analysis, and equivalent crack ratio. The research results indicate that the analysis of acceleration and displacement over time provides insights into wave propagation within a slope. During minor earthquakes (< 0.3 g), the slope experiences dynamic amplification at the surface and elevation-dependent effects, which are less evident during stronger seismic events. This work also revealed a positive correlation between the tunnel's dynamic amplification and elevation. A method leveraging HHT energy analysis, in conjunction with the slope's equivalent fracture ratio, is introduced to trace the progression of seismic damage across temporal and spatial dimensions. The progression of seismic intensity is characterized by stages of local failure initiation, expansion, and eventual holistic failure. Similarly, the temporal dynamics of instability are categorized into phases of initial instability, acceleration, and eventual sliding. Furthermore, this work explores the impact of tunnels on slope stability by comparing the equivalent fracture ratios and dynamic displacement patterns of slopes both with and without tunnels, revealing the evolution process of seismic damage to slope‒tunnel systems. This work provides a reference for the seismic design of complex slope‒tunnel systems.

Application of the wavelet transform and Hilbert–Huang transform in stratigraphic sequence division of Jurassic Shaximiao Formation in Southwest Sichuan Basin

Abstract In the southwestern Sichuan Basin, the Jurassic Shaximiao Formation encompasses a multitude of working areas, displaying intricate sedimentary traits. Traditional methods of stratigraphic division based on sequence suffer from inherent subjectivity and limitations. This study employs a combined mathematical approach to use the wavelet transform (WT) and the Hilbert–Huang transform (HHT). It decomposes the natural gamma ray (GR) logging curve into energy spectrum plots and wavelet coefficients at different scales, high and low frequency signals at different frequencies, and a set of intrinsic mode function components and residual functions. The study conducted a detailed stratigraphic division of the Jurassic Shaximiao Formation in the southwestern Sichuan Basin using these methods. The WT offers greater resolution for the periodic changes in the base level, whereas the HHT demonstrates a superior correlation with the positions of stratigraphic interfaces. The combined utilization of the continuous wavelet transform, the discrete wavelet transform, and HHT methods has demonstrated encouraging outcomes in the stratigraphic division of the Jurassic Shaximiao Formation. These methods have been shown to enhance the accuracy of stratigraphic division and to reduce the influence of subjective factors. This study presents new insights and approaches for geological data processing, offering significant theoretical and practical implications and novel technical means for oil and gas exploration and development.