S-transformation based integrated approach for spectrum estimation, storage, and sensing in cognitive radio

Cognitive Radio (CR) uses the principle of dynamic spectrum allocation to improve the utilization of spectrum bands. The estimation of missing data is essential for maintaining an uninterrupted quality of service in the CR. However, the existing methods are not suitable for interpolating missing data in high frequency signals. The storage of spectrum occupancy information is crucial for learning the spectrum usage and prediction. The existing techniques for wideband spectrum sensing suffer from poor edge detection capabilities. This paper proposes an STransformation (ST) based approach to solve these problems. For missing samples, the proposed method improves the accuracy of estimation. The ST can also be used to store the spectrum occupancy information. The simulation results show that the proposed scheme outperforms others by improving the accuracy of edge detection. Further, the simple implementation of the ST in the frequency domain is an advantage for the real time application.

Characteristic Analysis of White Gaussian Noise in S-Transformation Domain

The characteristic property of white Gaussian noise (WGN) is derived in S-transformation domain. The results show that the distribution of normalized S-spectrum of WGN follows X2?distribution with two degrees of freedom. The conclusion has been confirmed through both theoretical derivations and numerical simulations. Combined with different criteria, an effective signal detection in S-transformation can be realized.

High impedance fault detection in distribution network based on S-transform and average singular entropy

When a high impedance fault(HIF)occurs in a distribution network,the detection efficiency of traditional protection devices is strongly limited by the weak fault information.In this study,a method based on S-transform(ST)and average singular entropy(ASE)is proposed to identify HIFs.First,a wavelet packet transform(WPT)was applied to extract the feature frequency band.Thereafter,the ST was investigated in each half cycle.Afterwards,the obtained time-frequency matrix was denoised by singular value decomposition(SVD),followed by the calculation of the ASE index.Finally,an appropriate threshold was selected to detect the HIFs.The advantages of this method are the ability of fine band division,adaptive time-frequency transformation,and quantitative expression of signal complexity.The performance of the proposed method was verified by simulated and field data,and further analysis revealed that it could still achieve good results under different conditions.

Recognition of Hybrid PQ Disturbances Based on Multi-Resolution S-Transform and Decision Tree

Aiming at the problems of multiple types of power quality composite disturbances,strong feature correlation and high recognition error rate,a method of power quality composite disturbances identification based on multiresolution S-transform and decision tree was proposed.Firstly,according to IEEE standard,the signal models of seven single power quality disturbances and 17 combined power quality disturbances are given,and the disturbance waveform samples are generated in batches.Then,in order to improve the recognition accuracy,the adjustment factor is introduced to obtain the controllable time-frequency resolution through multi-resolution S-transform time-frequency domain analysis.On this basis,five disturbance time-frequency domain features are extracted,which quantitatively reflect the characteristics of the analyzed power quality disturbance signal,which is less than the traditional method based on S-transform.Finally,three classifiers such as K-nearest neighbor,support vector machine and decision tree algorithm are used to effectively complete the identification of power quality composite disturbances.Simulation results showthat the classification accuracy of decision tree algorithmis higher than that of K-nearest neighbor and support vector machine.Finally,the proposed method is compared with other commonly used recognition algorithms.Experimental results show that the proposedmethod is effective in terms of detection accuracy,especially for combined PQ interference.

Fractional S-transform-part 2:Application to reservoir prediction and fluid identification

The fractional S-transform （FRST） has good time-frequency focusing ability. The FRST can identify geological features by rotating the fractional Fourier transform frequency （FRFTfr） axis. Different seismic signals have different optimal fractional parameters which is not conducive to multichannel seismic data processing. Thus, we first decompose the common-frequency sections by the FRST and then we analyze the low-frequency shadow. Second, the combination of the FRST and blind-source separation is used to obtain the independent spectra of the various geological features. The seismic data interpretation improves without requiring to estimating the optimal fractional parameters. The top and bottom of a limestone reservoir can be clearly recognized on the common-frequency section, thus enhancing the vertical resolution of the analysis of the low-frequency shadows compared with traditional ST. Simulations suggest that the proposed method separates the independent frequency information in the time-fractional-frequency domain. We used field seismic and well data to verify the proposed method.

Enhancing the resolution of seismic data based on the generalized S-transform

In this paper, we analyze the seismic signal in the time-frequency domain using the generalized S-transform combined with spectrum modeling. Without assuming that the reflection coefficients are random white noise as in the conventional resolution-enhanced techniques, the wavelet which changes with time and frequency was simulated and eliminated. After using the inverse S-transform for the processed instantaneous spectrum, the signal in the time domain was obtained again with a more balanced spectrum and broader frequency band. The quality of seismic data was improved without additional noise.

A Protection Method of VSC-HVDC Cables Based on Generalized S-Transform

Generalized S-transform is a time-frequency analysis method which has higher resolution than S-transform. It can precisely extract the time-amplitude characteristics of different frequency components in the signal. In this paper, a novel protection method for VSC-HVDC (Voltage source converter based high voltage DC) based on Generalized S-transform is proposed. Firstly, extracting frequency component of fault current by Generalized S-transform and using mutation point of high frequency to determine the fault time. Secondly, using the zero-frequency component of fault current to eliminate disturbances. Finally, the polarity of sudden change currents in the two terminals is employed to discriminate the internal and external faults. Simulations in PSCAD/EMTDC and MATLAB show that the proposed method can distinguish faults accurately and effectively.

Detection and correction of level echo based on generalized S-transform and singular value decomposition

The echo of the material level is non-stationary and contains many singularities.The echo contains false echoes and noise,which affects the detection of the material level signals,resulting in low accuracy of material level measurement.A new method for detecting and correcting the material level signal is proposed,which is based on the generalized S-transform and singular value decomposition(GST-SVD).In this project,the change of material level is regarded as the low speed moving target.First,the generalized S-transform is performed on the echo signals.During the transformation process,the variation trend of window of the generalized S-transform is adjusted according to the frequency distribution characteristics of the material level echo signal,achieving the purpose of detecting the signal.Secondly,the SVD is used to reconstruct the time-frequency coefficient matrix.At last,the reconstructed time-frequency matrix performs an inverse transform.The experimental results show that the method can accurately detect the material level echo signal,and it can reserve the detailed characteristics of the signal while suppressing the noise,and reduce the false echo interference.Compared with other methods,the material level measurement error does not exceed 4.01%,and the material level measurement accuracy can reach 0.40%F.S.

Comparison of ICA and WT with S-transform based method for removal of ocular artifact from EEG signals

Ocular artifacts are most unwanted disturbance in electroencephalograph (EEG) signals. These are characterized by high amplitude but have overlap-ping frequency band with the useful signal. Hence, it is difficult to remove the ocular artifacts by traditional filtering methods. This paper proposes a new approach of artifact removal using S-transform (ST). It provides an instantaneous time-frequency repre-sentation of a time-varying signal and generates high magnitude S-coefficients at the instances of abrupt changes in the signal. A threshold function has been defined in S-domain to detect the artifact zone in the signal. The artifact has been attenuated by a suitable multiplying factor. The major advantage of ST-fil- tering is that the artifacts may be removed within a narrow time-window, while preserving the frequency information at all other time points. It also preserves the absolutely referenced phase information of the signal after the removal of artifacts. Finally, a com-parative study with wavelet transform (WT) and in-dependent component analysis (ICA) demonstrates the effectiveness of the proposed approach.

Power Supply Quality Analysis Using S-Transform and SVM Classifier

In this paper, a SVM classifier based on S-Transform is presented for power quality disturbances classification. Firstly, seven types of PQ events are created using Matlab simulation. These signals are analyzed to detect and localize PQ events via S-Transform by visual inspection. Then five significant features of the PQ disturbances are extracted from the S-Transform output. Afterwards, PQ disturbance samples with the five features are fed to SVM for training and automatic classification. Besides, particle swarm optimization is implemented to improve the performance of SVM. The results of the classification indicate that SVM classifier is an effective mechanism to detect and classify power quality disturbances.

Damage detection on framed structures: modal curvature evaluation using Stockwell Transform under seismic excitation

The key parameters for damage detection and localization are eigenfrequencies, related equivalent viscous damping factors and mode shapes. The classical approach is based on the evaluation of these structural parameters before and after a seismic event, but by using a modern approach based on time-frequency transformations it is possible to quantify these parameters throughout the ground shaking phase. In particular with the use of the S-Transform, it is possible to follow the temporal evolution of the structural dynamics parameters before, during and after an earthquake. In this paper, a methodology for damage localization on framed structures subjected to strong motion earthquakes is proposed based on monitoring the modal curvature variation in the natural frequency of a structure. Two examples of application are described to illustrate the technique: Computer simulation of the nonlinear response of a model, and several laboratory(shaking table) tests performed at the University of Basilicata(Italy). Damage detected using the proposed approach and damage revealed via visual inspections in the tests are compared.

An Improved Chirplet Transform and Its Application for Harmonics Detection

The chirplet transform is the generalization form of fast Fourier transform , short-time Fourier transform, and wavelet transform. It has the most flexible time frequency window and successfully used in practices. However, the chirplet transform has not inherent inverse transform, and can not overcome the signal reconstructing problem. In this paper, we proposed the improved chirplet transform (ICT) and constructed the inverse ICT. Finally, by simulating the harmonic voltages, The power of the improved chirplet transform are illustrated for harmonic detection. The contours clearly showed the harmonic occurrence time and harmonic duration.

Reliability Evaluation on Weak Signal Extraction for Airgun Source Surveys

Based on the data synthesis simulation and the actual processing of the airgun seismic source signal,three quantitative indicators of signal-to-noise ratio,waveform correlation coefficient and phase offset,are superimposed. We systematically evaluate the functions of the following three stack methods including linearity,phase weighting and S-transform in the extraction of weak signals under strong background noise and quantitatively estimate the reliability of the stack results. Through the comprehensive discussion of the above three methods of stack results,the preliminary comparative analysis believes that the linear stack signal-to-noise ratio is low,but the waveform distortion is minimal; the phase-weighted superimposed signal-to-noise ratio is high and the phase offset is small,but the results of the waveform quality and linear stack are larger than the deviation; the S-transform stack has a relatively higher signal-to-noise ratio and a small loss of waveform amplitude,but there is a certain phase shift phenomenon. It is therefore suggested that linear stack technology should be used when the requirements of both waveform quality and time precision are high. However,the selection of the stack method when the airgun source excitation is limited should be emphasized. If high fidelity is required, the S-transform stack method should be selected; if the required time is high,accuracy can be selected by phase-weighted stack method to achieve reasonable extraction of weak signals.

A New Principle of Fault Identification of on the Same Tower Based on Traveling Wave Reactive Powers

In order to improve the reliability of fault identification of the double-circuit transmission lines on the same tower, a new algorithm for fast protection of double-circuit transmission lines on the same tower based on the reactive powers of traveling wave is proposed. With the implementation of S-transform, the initial traveling wave reactive powers are calculated and the change characteristics of reactive power under different fault conditions are studied. The protection criterion is constructed by analyzing the ratio of the reactive powers of the same end on double-circuit transmission lines and the ratio of the reactive powers at both ends on the same line. According to the ratio of reactive power on the same side of the line and both ends of the same line, it is possible to identify whether the faults of the double-circuit line of the same tower occurred in or out of the protection zone. A large number of simulation results show that the protection performance is sensitive and reliable, and quick to respond. The criterion is simple and is basically not affected by fault initial angles, fault types, and transitional resistances.

Study on Azimuth Variation of Airgun Signal Propagation

Based on the data recorded by the observation network during the intensive excitation period from November to December 2015 at Binchuan Earthquake Signal Transmitting Seismic Station(BESTSS)in Yunnan Province,the noise in waveform recording is removed by S-transform template filtering method,and the azimuth of airgun signal propagation is calculated and analyzed from the horizontal waveform recordings.The results show that:①the azimuth angle of airgun signal after propagation is sensitive to stress change,and can clearly reflect the diurnal variation of tidal stress,which can be used to monitor the change of stress state in crustal medium;②the azimuth angle of airgun signal in some stations has changed abruptly after propagation on December 4,which may be related to the change of airgun source;③five-shot superposition or fivepoint smoothing of azimuth angle of single shot are carried out for airgun signals in stations far away from epicenter,and results show that azimuth angle from superposition or smoothing is more stable and has clear diurnal variation characteristics after propagation.

Characterization Theorem of Generalized Operators

In this paper, by using the W-transform of an operator on white noise functionals, we establish a general characterization theorem for operators on white noise functionals in term of growth condition. We also discuss convergence of operator sequences.

A New Method for Visual Real-Time Monitoring of Low Frequency Oscillation

Visual real-time monitoring is the premise of low frequency oscillation control in power grids. This paper showed a visual method for the control center of power grids to monitor low frequency oscillation. It processed the PMU real-time data with incomplete S-transform, and converted the waveforms to two-dimensional time-frequency figures which showed the initial time, frequency and amplitude of each low frequency oscillation mode directly. GPU was used to show figures and calculate FFT with the purpose of improving calculation efficiency. The results of practical cases show that the real-time characters of low frequency oscillation can be identified availably by this visualization real-time monitoring method which is helpful and suitable for practical application.

An Effective Detection of Inrush and Internal Faults in Power Transformers Using Bacterial Foraging Optimization Technique

Power transformers in transmission network are utilized for increasing or decreasing the voltage level. Power Transformers fail to connect directly to the consumers that result in the less load fluctuations. Power transformer operation under any abnormal condition decreases the lifetime of the transformer. Power Transformer protection from inrush and internal fault is critical issue in power system because the obstacle lies in the precise and swift distinction between them. Due to the limitation of heterogeneous resources, occurrence of fault poses severe problem. Providing an efficient mechanism to differentiate between faults (i.e. inrush and internal) is the key for efficient information flow. In this paper, the task of detecting inrush and internal fault in power transformers is formulated as an optimization problem which is solved by using Hyperbolic S-Transform Bacterial Foraging Optimization (HS-TBFO) technique. The Gaussian Frequency- based Hyperbolic S-Transform detects the faults at much earlier stage and therefore minimizes the computation cost by applying Cosine Hyperbolic S-Transform. Next, the Bacterial Foraging Optimization (BFO) technique has been proposed and has demonstrated the capability of identifying the maximum number of faults covered with minimum test cases and therefore improving the fault detection efficiency in a wise manner. The HS-TBFO technique is evaluated and validated in various simulation test cases to detect inrush and internal fault in a significant manner. This HS-TBFO technique is investigated based on three phase power transformer embedded in a power system fed from both ends. Results have confirmed that the HS-TBFO technique is capable of categorizing the inrush and internal faults by identifying maximum number of faults with minimum computation cost as compared to the state-of-the-art works.

Time-extracting S-transform algorithm and its application in rolling bearing fault diagnosis

Time-frequency(TF)analysis(TFA)is one of the effective methods to deal with non-stationary signals.Due to their advantages,many experts and scholars have recently developed post-processing algorithms based on traditional TFA.Among them,shorttime Fourier transform(STFT)based post-processing algorithms have developed the fastest.However,these methods rely heavily on the window length selected in STFT,which has great influence on the post-processing algorithm.In this paper,a postprocessing algorithm for effectively processing pulse signals was proposed and called time-extracting S-transform(TEST).The time-domain extraction method based on S-transform avoids the influence of uncertain parameters.After comparing the performance of various TFA methods when processing analog signals,the proposed TEST can clearly show the pulse occurrence time under the premise of ensuring high TF aggregation.The actual signal proves that the method can be used for fault diagnosis of rolling bearings.

Improved signal de-noising in underwater acoustic noise using S-transform: A performance evaluation and comparison with the wavelet transform

Sound waves propagate well underwater making it useful for target locating and communication.Underwater acoustic noise(UWAN)affects the reliability in applications where the noise comes from multiple sources.In this paper,a novel signal de-noising technique is proposed using S-transform.From the time-frequency representation,de-noising is performed using soft thresholding with universal threshold estimation which is then reconstructed.The UWAN used for the validation is sea truth data collected at Desaru beach on the eastern shore of Johor in Malaysia with the use of broadband hydrophones.The comparison is made with the more conventionally used wavelet transform de-noising method.Two types of signals are evaluated:fixed frequency signals and time-varying signals.The results demonstrate that the proposed method shows better signal to noise ratio(SNR)by 4 dB and lower root mean square error(RMSE)by 3 dB achieved at the Nyquist sampling frequency compared to the previously proposed de-noising method like wavelet transform.