S-transform Research Articles

Deconvolutive Frequency Corrected Three-Parameter S-Transform and Its Application in Tight Sandstone Reservoir

As an effective time-frequency (TF) analysis method, S transform (ST) has an extensive application in signal processing. However, for broad-band seismic signals, the peaks of the frequency distribution in the TF spectrum of ST biases the actual Fourier spectrum. Besides, the TF resolution of ST is affected by the relatively fixed window function and the Heisenberg uncertainty principle. In order to correct the frequency bias and improve the TF resolution of ST, and at the same time, to increase the flexibility of the window function, we propose a new TF analysis method, called the deconvolutive frequency corrected three-parameter S transform (DFC-TPST). The DFC-TPST includes two steps: modifying the window function to achieve the frequency corrected three-parameter S transform (FC-TPST) and deconvoluting FC-TPST to achieve DFC-TPST. The synthetic example proves the superiority of the method in characterizing seismic signals. Through comparison of field data testing, we find that the proposed method can be well applied to the hydrocarbon detection in tight sandstone reservoir.

Sand Bodies Delineation by Fusing Multifrequency Attributes via t-SNE

Multi-frequency attribute analysis is an effective tool to delineate sand bodies with different thicknesses. Conventionally, red-green-blue (RGB) blending technique is often used to fuse three frequency components for depicting reservoir thicknesses, i.e. the low-, medium-, and high–frequency components. However, seismic signal is a typically broadband signal, while RGB blending can only fuse three frequency components. Moreover, how to select these three specific frequency components is also a difficult and unsolved task. In this study, we suggest a multi-frequency attribute analysis workflow for delineating sand bodies. First, we introduce the S-transform (ST) to extract multi-frequency components of the analyzed seismic data. Then, the t-distributed Stochastic Neighbor Embedding (t-SNE) based workflow for fusing multi-frequency components is proposed, which is used to capture the local structural features of the analyzed high-dimensional data and reveal the global structures simultaneously. Afterward, we adopt a synthetic trace and a 3D field data volume to test the effectiveness of the proposed workflow. Compared with the contrastive methods, our workflow performs better on delineating the spatial distribution and thicknesses of sand bodies, which benefits for further well deployment.

An Anomaly Detector Using Filtering Stockwell Transform and Siamese Convolutional Neural Network in Radio Monitoring (AnoFSTSCNN)

An Anomaly Detector Using Filtering Stockwell Transform and Siamese Convolutional Neural Network in Radio Monitoring (AnoFSTSCNN)

Stockwell Transform of Quadrature Stator Current-Based Fault Assessment in Induction Machine at Different Load Condition

Stockwell Transform of Quadrature Stator Current-Based Fault Assessment in Induction Machine at Different Load Condition

ECG Analysis-Based Cardiac Disease Prediction Using Signal Feature Selection with Extraction Based on AI Techniques

ECG (Electrocardiogram) performs classification using a machine learning model for processing different features in the ECG signal. The electrical activity of the heart is computed with the ECG signal with machine learning library. The key issue in the handling of ECG signals is an estimation of irregularities to evaluate the health status of patients. The ECG signal evaluate the impulse waveform for the specialized tissues in the cardiac heart diseases. However, the ECG signal comprises of the different difficulties associated with waveform estimation to derive certain features. Through machine learning (ML) model the input features are computed with input ECG signals. In this paper, proposed a Noise QRS Feature to evaluate the features in the ECG signals for the effective classification. The Noise QRS Feature model computes the ECG signal features of the waveform sequences. Initially, the signal is pre-processed with the Finite Impulse response (FIR) filter for the analysis of ECG signal. The features in the ECG signal are processed and computed with the QRS signal responses in the ECG signal. The Noise QRS Feature evaluate the ECG signal with the kNN for the estimation and classification of features in the ECG signals. The performance of the proposed Noise QRS Feature features are comparatively examined with the Discrete Wavelet Transform (DWT), Dual-Tree Complex Wavelet Transforms (DTCWT) and Discrete Orthonormal Stockwell Transform (DOST) and the machine learning model Cascade Feed Forward Neural Network (CFNN), Feed Forward Neural Network (FFNN). Simulation analysis expressed that the proposed Noise QRS Feature exhibits a higher classification accuracy of 99% which is ~6 – 7% higher than the conventional classifier model.

Combined ST/MST and radial basis function neural networks for power quality disturbance signal classification

In this paper, the classification of power quality disturbances using combined ST/MST (S-Transform/Modified S-Transform) and Radial Basis Function Neural Network (RBFNN) is proposed. The extraction of significant features from the power quality disturbance signals is one of the challenging tasks in recognizing different disturbances. The Stockwell Transform/Modified Stockwell Transform (ST/MST) based features are distinct, understandable and more immune to noise. The important attributes present in the signals are retrieved from the ST/MST contours, MST 3D plots and MST based statistical curves. The relevant features are also extracted from the statistical curves. The extracted features are given as input to the RBFNN for further classification. This method is evaluated under both noisy and noiseless conditions. The performance of the proposed approach is compared with other conventional approaches in the literature. The simulation results demonstrate that the proposed MST based RFNN technique is more effective for the detection and classification of power quality disturbances.

Demodulated Multisynchrosqueezing S Transform for Fault Diagnosis of Rotating Machinery

Time–frequency analysis (TFA) plays an important role in fault diagnosis of rotating machinery. However, a time–frequency representation (TFR) with lower resolution is not conducive to extracting fault features of the equipment. In this article, a novel method, termed demodulated multisynchrosqueezing S transform (DMSSST), is proposed to achieve a highly energy-concentrated TFR, which combines demodulation and multireassignment (MT) techniques for S transform (ST). The proposed method integrates the adaptability of demodulated ST to the frequency with the iterative procedure of MT to optimize the instantaneous frequency (IF) estimation. Compared with the traditional approaches, the presented method has better robustness with respect to noise and can be well applied to the discrimination of several faults. Furthermore, the simulated signal shows that this method can effectively improve the resolution of a TFR and has excellent anti-noise ability. The real examples, including bearing fault and rotor rub-impact, further validate the effectiveness of the DMSSST method in fault diagnosis of rotating machinery.

An Efficient Method for Feature Extraction and Selection in Power Quality Recognition

—Since decade, many time-frequency analysis methods with combination of classifiers have been studied in literature for recognition of power quality (PQ) events. In these studies, feature extraction and selection have a vital role to enhance PQ classification accuracy and to reduce computational complexity for PQ recognition. This paper presents a new method to detect and classify PQ disturbances based on modified Stockwell Transform (ST) for extraction of features and Hybrid Grey Wolf Optimization (HGWO) for feature selection along with K Nearest Neighbor (KNN) classifier. Simulation of the proposed method using MATLAB is carried out through a wide range of eighteen synthetic PQ events to validate the effectiveness of the selected features. Further, an experiment is extended for six classes of real PQ events acquired from self excited induction generator (SEIG) system in a laboratory experimental setup. Proposed method is also employed on those real time data to study the classification accuracy performance. In these experiments, an impressive accuracy of 99.94% and 99.3% for synthetic and real time PQ event data, respectively are reported. Hence, it is observed from result analysis, this proposed method can be utilized for recognition of PQ events in real time power system.

A deep capsule neural network with data augmentation generative adversarial networks for single and simultaneous fault diagnosis of wind turbine gearbox

The fault diagnosis (FD) of wind turbine gearbox (WTG) is of special importance for keeping the wind turbine drivetrain working normally and safely. However, owing to the limited training data and the mutual interference of various mechanical parts, it is of great difficulty to realize the simultaneous-fault monitoring task of WTG using existing intelligent FD methods or manual inspection-based approaches. To tackle the issue, a deep capsule neural network with data augmentation generative adversarial networks, named ST-DAGANs-CapNet, is developed for the single and simultaneous FD of WTG by integrating capsule neural network (CapsNet) with Stockwell transform (ST) and data augmentation generative adversarial networks (DAGANs). The proposed ST-DAGANs-CapNet method mainly consists of three steps. First of all, ST is adopted to extract two-dimension (2-d) image features of time–frequency domain from raw time-domain vibration signals of WTG. Then, DAGANs are employed for generating more fake image samples to address the problem of lacking training data. At last, the built CapsNet model is utilized to diagnose the single and compound faults of WTG by the primary 2-d feature images and the made fake 2-d feature images in training set. Two experimental studies are implemented to prove the effectiveness of the proposed method, and the result is compared with some existing intelligent FD of WTG. It indicates that DAGANs are effective in helping to tackle the issue of limited and unbalanced training samples in real FD of WTG, and the diagnosis result of the proposed approach in test sample set is better than that of several commonly used FD methods in literatures.

Use of S-transform and a new multi-taper S-transform for spectral and coherence estimates: With application to characterize and simulate multivariate non-Gaussian wind pressure coefficient

Obtaining a long duration time series of wind pressure coefficient from wind tunnel tests may not be economically feasible for some projects, and simulated synthetic time series of wind pressure coefficient can be used. In this study, we propose a new multi-taper S-transform (ST), where the discrete prolate spheroidal sequences are used for tapering, and ST is applied to each tapered time series. The proposed multi-taper ST is simple and efficient. The simulation results indicate that the proposed transform provides an unbiased estimate of the power spectral density (PSD) function with small variability. It is also shown that the use of the temporally-averaged results from ST or the proposed multi-taper ST leads to an unbiased estimate of the coherence function. As an application, we use the obtained PSD and coherence, and marginal probability distribution function (PDF) from the time series of the wind pressure coefficient as the targets to simulate univariate and multivariate processes. For the simulation of the non-Gaussian processes, we use the iterative power and amplitude correction but include a digital filter to consider sample-to-sample variability in the PSD function. We show that the PSD and coherence functions and the marginal PDF from the samples match their targets.

A novel distance protection scheme using single‐ended transient voltage based on generalized S transform

Concerning the distance protection steady-state over-reach or under-reach caused by the transition resistance, a novel distance protection scheme based on transient information is proposed. First, multiple fault features are extracted using the Generalized Stockwell Transform (GST), and a criterion for identifying low-resistance and high-resistance ground faults is constructed. Then, a GST coefficient matrix is established for the single-ended transient voltage of the line, the attenuation coefficient and delay coefficient are derived by the least-squares method and the beat phenomenon, and the transition resistance is calculated. On this basis, adjust the operation boundary in the +R axis direction of the operation zone according to the transition resistance value. Finally, test results on real-time digital simulation system (RTDS) demonstrate that the protection scheme operates reliably in different fault cases and is highly immune to fault resistance. Compared with the traditional distance protection scheme, this scheme performs better when the transition resistance is large.

S-Transform based time–frequency analysis tool with application to detection of bearing fault

Faults developed in bearings are one of the prime reasons leading to mechanical damage. Recently, the novel technology synchrosqueezing extracting transform was proposed to capture the transient impulses in the non-stationary signal for fault diagnosis. Compared with traditional technology, this method has better anti-interference ability and faster processing speed. However, the method is a method based on short-time Fourier transform (STFT), S-transform (ST) is superior due to its higher time resolution in T-F spectrogram, ability to realize lossless inverse transformation, and property of retaining the original signal phase. Considering the advantages of ST over STFT, we apply this method to the ST in the study, time-reassigned synchrosqueezing extracting S-transform (TSSEST) is proposed and applied to perform analog signal and experimental bearing defect data to verify the effectiveness of the technique developed in a step-by-step manner. The results show that the effectiveness of our method.

Fast Calculation of Broadband Battery Impedance Spectra Based on S Transform of Step Disturbance and Response

Electrochemical impedance spectroscopy (EIS) is one of the most powerful tools for battery sorting, state estimation, and diagnosis. To obtain EIS, a conventional and time-consuming sweeping sine method is commonly used in a laboratory depending on professional equipment, which is limited for practical applications. For the first time, this article proposed a fast calculation method of broadband battery impedance based on the S transform (ST). It reduces the requirements for the broadband impedance acquisition greatly by processing the step disturbance and response, which can be generated with a common charging/discharging device. For a pouch lithium-ion battery cell, the method can obtain its impedance of 1 kHz–0.01 Hz with the real part errors smaller than 5%. Also, the imaginary part errors of 1.9953–501.19 Hz in the charging case and 1–316.23 Hz in the discharging case are within ±10%. Compared to the sweeping sine method, at least 19% of the acquisition time can be saved. Also, more than 84% of the calculation time is also shortened compared to the previously reported Morlet wavelet transform. For practical guidance, the effects of the algorithm parameters (integration interval, sampling frequency, signal length, and signal amplitude) are also comprehensively studied.

Estimation for rotational barriers of unsymmetrical tert-amide-containing pyridine ligands and their silver(I) complexes

Structures of silver(I) complexes with unsymmetrical tert-amide-containing pyridine ligand isomers (1a-1d) are reported. Because these ligands exist as s-cis and s-trans forms in solution, the ratios of s-cis and s-trans forms in solution and their rotational barriers were estimated by 1H NMR experiments. Despite the presence of s-cis and s-trans-form in solution, silver(I) complexes with these ligands were all s-trans form in the solid-state. Because of the semi-flexible properties of isomers (1a-1d), various ligand shapes showed the coordination networks depending on the direction of the pyridine nitrogen. For example, on the silver(I) triflate complexations, the tertiary amide incorporating two 4‑pyridyl units (1a) yields a wavy 2D coordination polymer. On the other hand, the complexation of 1b afforded double-stranded 1D coordination polymer. Furthermore, the complexations of 1c and 1d afforded 2D coordination polymer and cyclic dimer, respectively. The complexations of isomers (1a-1d) with AgBF4 instead of AgOTf were also investigated. As a result, the AgBF4 complexations of 1a, 1c, and 1d gave 1D, 2D, and 1D structures, respectively.

Genetic algorithm based image reconstruction applying the digital holography process with the Discrete Orthonormal Stockwell Transform technique for diagnosis of COVID-19

World Health Organization has described the real-time reverse transcription-polymerase chain reaction test method for the diagnosis of the novel coronavirus disease (COVID-19). However, the limited number of test kits, the long-term results of the tests, the high probability of the disease spreading during the test and imaging without focused images necessitate the use of alternative diagnostic methods such as chest X-ray (CXR) imaging. The storage of data obtained for the diagnosis of the disease also poses a major problem. This causes misdiagnosis and delays treatment. In this work, we propose a hybrid 3D reconstruction method of CXR images (CXRI) to detect coronavirus pneumonia and prevent misdiagnosis on CXRI. We used the digital holography technique (DHT) for obtaining a priori information of CXRI stored in created digital hologram (CDH). In this way, the elimination of the storage problem that requires high space was revealed. In addition, Discrete Orthonormal S-Transform (DOST) is applied to the reconstructed CDH image obtained by using DHT. This method is called CDH_DHT_DOST. A multiresolution spatial-frequency representation of the lung images that belong to healthy people and diseased people with the COVID-19 virus is obtained by using the CDH_DHT_DOST. Moreover, the genetic algorithm (GA) is adopted for the reconstruction process for optimization of the CDH image and then DOST is applied. This hybrid method is called CDH_GA_DOST. Finally, we compare the results obtained from CDH_DHT_DOST and CDH_GA_DOST. The results show the feasibility of reconstructing CXRI with CDH_GA_DOST. The proposed method holds promises to meet demands for the detection of the COVID-19 virus.

SEMG time–frequency features for hand movements classification

Surface Electro-MyoGraphic (sEMG) signals recorded on the forearm can provide information about the hand movement, which can help control a prosthetic implant for disabled people. To do so, the sEMG signals must be accurately classified despite the signals’ non-stationarity, noise from sensors, involved muscles, and patient’s peculiarities. This study deals with the classification of hand movement using sEMG signals, and focus especially on the use of time–frequency domain for feature extraction and on several linear and non-linear methods for the dimension reduction. Methods as the Discrete Orthonormal Stockwell Transform (DOST) and Multidimensional Scaling (MDS) are applied for the first time on sEMG signals, and an extensive comparison study is performed on the combinations of the proposed methods. Classical classifiers are then used on a public dataset in order to evaluate the applied methods. Short-time Fourier transform, continuous wavelet transform and Stockwell transform performed well, with respectively 90.05%, 89.92 and 90.96% accuracy, but the average calculation times per window were 1.75ms, 2.30ms, and 1.60ms respectively. Promising results were obtained using DOST and MDS with classification rate 87.13% and significant improvement in feature extraction computation time as the average was 0.13ms per window.

Sampling Techniques and Error Estimation for Linear Canonical S Transform Using MRA Approach

A linear canonical S transform (LCST) is considered a generalization of the Stockwell transform (ST). It analyzes signals and has multi-angle, multi-scale, multiresolution, and temporal localization abilities. The LCST is mostly suitable to deal with chirp-like signals. It aims to possess the characteristics lacking in a classical transform. Our aim in this paper was to derive the sampling theorem for the LCST with the help of a multiresolution analysis (MRA) approach. Moreover, we discuss the truncation and aliasing errors for the proposed sampling theory. These types of sampling results, as well as methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.

An IoMT enabled deep learning framework for automatic detection of fetal QRS: A solution to remote prenatal care

The amalgamation of the Internet of medical things with artificial intelligence shows tremendous benefits in health care. Accurate detection of the fetal QRS complex is highly demanded in fetal heart rate monitoring. Detecting fetal heart rate using electrophysiological signals obtained from abdominal electrodes seems a promising alternative approach. The challenges in determining fetal heart rate from abdominal ECG (AECG) require eliminating maternal components and other noises from the signal at higher accuracy. We propose a novel approach using an IoT-based deep learning architecture to detect fetal QRS complex without eliminating the maternal components in the abdominal ECG. The novelty of the proposed algorithm is twofold: (1) The method uses the time–frequency image (TFI) of abdominal signals as input to the deep neural network and hence promotes the availability of rich features and improves the accurate detection of the fetal QRS complex. (2) The algorithm adapts pre-trained models based on transfer learning for the classification task and thus improves the fetal QRS detection. Two time–frequency approaches, namely Hilbert Huang Transform (HHT) and Stockwell transform (ST), are used to represent input AECG signals as two-dimensional images. The 2013 challenge database is used to evaluate the performance of the proposed approach. The TFI representations of training data using HHT and ST are independently used to train the pre-trained models MobileNet and ResNet18. A comparative analysis is provided in the results between the TFI and deep network architecture. The proposed solution can be suitable for an IoT environment enabling remote fetal monitoring.

Generation of spectrum-compatible ground motion records based on time-frequency decomposition

Spectrum-matched records are used in seismic engineering applications. The available approaches in the literature are based on the Fourier transform or wavelet transform. In the present study, we propose a novel and easy-to-implement approach to generate spectrum-matched records for a given seed record. The approach is based on the S-transform (ST). The use of the transform is advantageous since they provide refined time-frequency decomposition. The approach adjusts the amplitude of the ST coefficients in the S-transform domain. The approach is effective in matching a prescribed response spectrum at specified frequencies without complex parameter adjustment. The spectrum-matched records qualitatively retain the look of the seed records. The spectral acceleration of the spectrum-matched records is equal to the target spectrum at the specified frequencies, where the matching is required and specified.

Whittaker–Stockwell Transform and Tikhonov Regularization Problem

Whittaker–Stockwell Transform and Tikhonov Regularization Problem