Use of Discrete Orthonormal S-Transform to Simulate Earthquake Ground Motions

2020 ◽  
Vol 110 (2) ◽  
pp. 565-575 ◽  
Author(s):  
Xi Zhong Cui ◽  
Han Ping Hong
Keyword(s):  
Power Distribution ◽  
Fourier Spectrum ◽  
Response Spectrum ◽  
Ground Motions ◽  
Frequency Resolution ◽  
Average Amplitude ◽  
Time Frequency ◽  
S Transform ◽  
Practical Tool ◽  
The Fourier Transform

ABSTRACT The S-transform and discrete orthonormal S-transform (DOST) produce time–frequency representations, which is in contrast to the wavelet transformations. Similar in the Fourier transform, the use of the S-transform and DOST provides frequency-dependent resolution with absolutely referenced phase information. Although the decomposed signal using DOST is expressed as a sum of orthonormal basis function, this is not the case if the S-transform is used. In the present study, a procedure to simulate nonstationary ground motions based on DOST is proposed based on a seed record or given a target amplitude of DOST coefficients. It is shown that the model has zero mean, and its variance equals the assigned target. Using five real records, each from a larger earthquake, the application of the DOST and S-transform to the records is carried out. Although the time–frequency resolution obtained from DOST is coarse as compared to that obtained using the S-transform, its use identifies clearly time–frequency characteristics. Samples of ground motions are simulated using the proposed method based on the amplitude of the DOST coefficients of a seed record or on the average amplitude of the DOST coefficients of a set of actual records. The comparison of the time–frequency resolution, Fourier spectrum, time-varying power distribution, and response spectrum of the simulated and seed records indicates that the proposed simulation model is a useful and practical tool to simulate nonstationary ground motions.

A Time–Frequency Representation Model for Seismic Ground Motions

2020 ◽  
Author(s):  
Xi Zhong Cui ◽  
Han Ping Hong
Keyword(s):  
Ground Motions ◽  
Seismic Source ◽  
Model Parameters ◽  
Time Frequency ◽  
Motion Models ◽  
Power Spectral ◽  
Frequency Representation ◽  
Site Characteristics ◽  
S Transform ◽  
Proposed Model

ABSTRACT A probabilistic model of the time–frequency power spectral density (TFPSD) is presented. The model is developed, based on the time–frequency representation of records from strike-slip earthquakes, in which the time–frequency representation is obtained by applying the S-transform (ST). The model for the TFPSD implicitly considers the amplitude modulation and frequency modulation for the nonstationary ground motions; this differs from the commonly used evolutionary PSD model. Predicting models for the model parameters, based on seismic source and site characteristics, are developed. The use of the model to simulate ground motions for scenario seismic events is illustrated, in which the simulation is carried out using a recently developed model that is based on the discrete orthonormal ST and ST. The illustrative example highlights the simplicity of using the proposed model and the physical meaning of some of the model parameters. A model validation analysis is carried out by comparing the statistics of the pseudospectral acceleration obtained from the simulated records to those obtained using a few ground-motion models available in the literature and considered actual records. The comparison indicates the adequacy of the proposed model.

A Study on Maximum Responses and Their Variances of Elasto-Plastic Structures Subjected to Synthesized Ground Motions

2014 ◽  
Author(s):  
Akira Sone ◽  
Ichiro Ichihashi ◽  
Arata Masuda
Keyword(s):  
Wavelet Transform ◽  
Coefficient Of Variation ◽  
Response Spectrum ◽  
Ground Motions ◽  
Frequency Characteristics ◽  
Target Response ◽  
Maximum Displacement ◽  
Time Frequency ◽  
Earthquake Ground Motions ◽  
The Given

A number of artificial earthquake ground motions compatible with time-frequency characteristics of recorded actual earthquake ground motions as well as the given target response spectrum are generated using wavelet transform. The coefficient of variation (C.O.V..) of maximum displacement on elasto-plastic SDOF systems excited by these artificial ground motions are numerically evaluated.

Harmonic Detection in Micro-Grid Based on Modified S-Transform

2014 ◽  
Vol 568-570 ◽  
pp. 270-273 ◽  
Author(s):  
Guan Qi Liu ◽  
Li Na Wu
Keyword(s):  
Harmonic Signal ◽  
Frequency Resolution ◽  
Harmonic Detection ◽  
New Approach ◽  
Time Frequency ◽  
Feature Vectors ◽  
S Transform ◽  
Attractive Candidate ◽  
Micro Grid ◽  
Grid Based

The excellent time–frequency resolution of the modified S-transform (MST) makes it an attractive candidate for analysis and detection of harmonic in micro-grid. This paper presents a new approach for micro-grid harmonic detection based on the MST. Firstly, the MST was performed for the harmonic signal, and then the feature vectors were extracted from the resulting time-frequency matrix. Finally, the frequency, amplitude and phase of the harmonic were obtained by analyzing and processing these feature vectors. Simulation results show that the proposed approach can detect the harmonic in micro-grid with high accuracy and strong noise immunity.

Investigation of generalized S-transform analysis windows for time-frequency analysis of seismic reflection data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. V235-V247 ◽  
Author(s):  
Duan Li ◽  
John Castagna ◽  
Gennady Goloshubin
Keyword(s):  
Temporal Resolution ◽  
Seismic Reflection ◽  
Frequency Resolution ◽  
Low Frequencies ◽  
Seismic Reflection Data ◽  
Time Frequency ◽  
Gaussian Window ◽  
Reflection Data ◽  
S Transform ◽  
Generalized S Transform

The frequency-dependent width of the Gaussian window function used in the S-transform may not be ideal for all applications. In particular, in seismic reflection prospecting, the temporal resolution of the resulting S-transform time-frequency spectrum at low frequencies may not be sufficient for certain seismic interpretation purposes. A simple parameterization of the generalized S-transform overcomes the drawback of poor temporal resolution at low frequencies inherent in the S-transform, at the necessary expense of reduced frequency resolution. This is accomplished by replacing the frequency variable in the Gaussian window with a linear function containing two coefficients that control resolution variation with frequency. The linear coefficients can be directly calculated by selecting desired temporal resolution at two frequencies. The resulting transform conserves energy and is readily invertible by an inverse Fourier transform. This modification of the S-transform, when applied to synthetic and real seismic data, exhibits improved temporal resolution relative to the S-transform and improved resolution control as compared with other generalized S-transform window functions.

A Study of Elasto-Plastic Response of Single Degree of Freedom System Using Artificial Ground Motions With Given Time-Frequency Characteristics

2010 ◽  
Author(s):  
Ichiro Ichihashi ◽  
Akira Sone ◽  
Arata Masuda ◽  
Daisuke Iba
Keyword(s):  
Ground Motion ◽  
Response Spectrum ◽  
Ground Motions ◽  
Frequency Characteristics ◽  
Earthquake Ground Motion ◽  
Time Frequency ◽  
Displacement Response ◽  
Earthquake Ground Motions ◽  
Design Response Spectrum ◽  
The Given

In this paper, a number of artificial earthquake ground motions compatible with time-frequency characteristics of recorded actual earthquake ground motion as well as the given target response spectrum are generated using wavelet transform. The maximum non-dimensional displacement of elasto-plastic structures excited these artificial earthquake ground motions are calculated numerically. Displacement response, velocity response and cumulative input energy are shown in the case of the ground motion which cause larger displacement response. Under the given design response spectrum, a selection manner of generated artificial earthquake ground motion which causes lager maximum displacement response of elasto-plastic structure are suggested.

scholarly journals S-Transform Based Analysis for Stock Market Volatility Estimation

2019 ◽  
Vol 8 (11) ◽  
pp. 3669-3675
Keyword(s):  
Financial Time Series ◽  
Theory And Practice ◽  
Frequency Resolution ◽  
Gaussian Kernel ◽  
Bench Mark ◽  
Data Sets ◽  
Stock Market Volatility ◽  
Asset Valuation ◽  
Time Frequency ◽  
S Transform

Financial Time series analysis (FTSA) is concerned with theory and practice of asset valuation over time. Generally, FTSA is useful for forecasting the asset volatility. This paper proposes the discrete S-Transform technique driven by Gaussian kernel for the estimation of volatility in FTSA. S-Transform is found to be a better tool in finding the time frequency resolution so as to predict and estimate the risk and returns of financial market. S-Transform prediction on two different bench mark data sets namely, Standard & Poor(S&P) 500 and Dow Jones Industrial Average(DJIA) index clearly indicates its superiority for the prediction of short and long-term trends in stock markets

scholarly journals Time-Frequency Domain Deconvolution based on Synchrosqueezing Generalized S Transform

2021 ◽  
pp. 148-155
Author(s):  
Shulin Zheng ◽  
Zijun Shen
Keyword(s):  
Frequency Domain ◽  
Seismic Data ◽  
Oil And Gas ◽  
Amplitude Spectrum ◽  
Frequency Resolution ◽  
Good Effect ◽  
Time Frequency ◽  
S Transform ◽  
Convolution Model ◽  
Generalized S Transform

Complex geological characteristics and deepening of the mining depth are the difficulties of oil and gas exploration at this stage, so high-resolution processing of seismic data is needed to obtain more effective information. Starting from the time-frequency analysis method, we propose a time-frequency domain dynamic deconvolution based on the Synchrosqueezing generalized S transform (SSGST). Combined with spectrum simulation to estimate the wavelet amplitude spectrum, the dynamic convolution model is used to eliminate the influence of dynamic wavelet on seismic records, and the seismic signal with higher time-frequency resolution can be obtained. Through the verification of synthetic signals and actual signals, it is concluded that the time-frequency domain dynamic deconvolution based on the SSGST algorithm has a good effect in improving the resolution and vertical resolution of the thin layer of seismic data.

scholarly journals Study on the Thick-Walled Pipe Ultrasonic Signal Enhancement of Modified S-Transform and Singular Value Decomposition

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Haichao Cai ◽  
Chunguang Xu ◽  
Shiyuan Zhou ◽  
Hongjuan Yan ◽  
Liu Yang
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Frequency Resolution ◽  
Scanning System ◽  
Frequency Noise ◽  
Echo Signal ◽  
Time Frequency ◽  
S Transform ◽  
Ultrasonic Flaw ◽  
Value Decomposition

When detecting the ultrasonic flaw of thick-walled pipe, the flaw echo signals are often interrupted by scanning system frequency and background noise. In particular when the thick-walled pipe defect is small, echo signal amplitude is often drowned in noise signal and affects the extraction of defect signal and the position determination accuracy. This paper presents the modified S-transform domain singular value decomposition method for the analysis of ultrasonic flaw echo signals. By changing the scale rule of Gaussian window functions with S-transform to improve the time-frequency resolution. And the paper tries to decompose the singular value decomposition of time-frequency matrix after the S-transform to determine the singular entropy of effective echo signal and realize the adaptive filter. Experiments show that, using this method can not only remove high frequency noise but also remove the low frequency noise and improve the signal-to-noise ratio of echo signal.

scholarly journals STUDY OF TIME FREQUENCY TRANSFORMS APPLIED TO POWER QUALITY SIGNALS

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Richard Bini Almeida ◽  
Kenji Watanabe ◽  
Silvia Mara da Costa Campos Victer
Keyword(s):  
Power Quality ◽  
Fourier Transforms ◽  
Spectral Content ◽  
Time Frequency ◽  
Quality Signals ◽  
S Transform ◽  
C Programming ◽  
The Fourier Transform ◽  
Short Time ◽  
Over Time

This work presents a scientific study on Short-Time Frequency Transforms (STFT) with different windows, also called Windowed Fourier Transforms, applied to power quality signals.   Additionally, it deals with S transforms, with its frequency-dependent window.  The disturbances related to energy quality have non-stationary nature, in which the spectral content varies over time.   So, the Fourier Transform is not appropriate for such analysis, because it doesn’t show time locations, only information about existing frequencies in the signal.  Therefore, the spectral analysis by windowed transforms helps to identify and detect a series of defects associated to these power signals.  The motivation behind this document is to verify which window will provide a more precise identification of the characteristics of the disturbances in time-frequency domain.    For this work, synthetic signals were generated for some of these disturbances, and their spectra were compared considering Gaussian, Hann and Blackman windows, as well as the S transform. Based on the obtained results, it was verified that each transform presents different behaviours acording to the input signal,  except for the ones with Hann and Blackman windows, that showed similar spectra. For all of them, there is always a tradeoff between time and frequency resolutions. Therefore, the choice of the window must be done according to the desired outputs.  The Dev-C ++ ® IDE was used for C ++ programming, and the Gnuplot ® program for graphics generation.

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