Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition

In this paper, the adaptive chirplet decomposition combined with the Wigner-Ville transform and the empirical mode decomposition combined with the Hilbert transform are employed to process various non-stationary signals (strong ground motions and structural responses). The efficacy of these two adaptive techniques for capturing the temporal evolution of the frequency content of specific seismic signals is assessed. In this respect, two near-field and two far-field seismic accelerograms are analyzed. Further, a similar analysis is performed for records pertaining to the response of a 20-story steel frame benchmark building excited by one of the four accelerograms scaled by appropriate factors to simulate undamaged and severely damaged conditions for the structure. It is shown that the derived joint time–frequency representations of the response time histories capture quite effectively the influence of non-linearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event; in this context, tracing the mean instantaneous frequency of records of critical structural responses is adopted. The study suggests, overall, that the aforementioned techniques are quite viable tools for detecting and monitoring damage to constructed facilities exposed to seismic excitations

The estimation of geoacoustic properties from broadband acoustic data, focusing on instantaneous frequency techniques

The compressional wave velocity and attenuation of marine sediments are fundamental to marine science. In order to obtain reliable estimates of these parameters it is necessary to examine in situ acoustic data, which is generally broadband. A variety of techniques for estimating the compressional wave velocity and attenuation from broadband acoustic data are reviewed. The application of Instantaneous Frequency (IF) techniques to data collected from a normal-incidence chirp profiler is examined. For the datasets examined the best estimates of IF are obtained by dividing the chirp profile into a series of sections, estimating the IF of each trace in the section using the first moments of the Wigner Ville distribution, and stacking the resulting IF to obtain a composite IF for the section. As the datasets examined cover both gassy and saturated sediments, this is likely to be the optimum technique for chirp datasets collected from all sediment environments

Seismic characterisation based on time-frequency spectral analysis

We present high-resolution time-frequency spectral analysis schemes to better resolve seismic images for the purpose of seismic and petroleum reservoir characterisation. Seismic characterisation is based on the physical properties of the Earth's subsurface media, and these properties are represented implicitly by seismic attributes. Because seismic traces originally presented in the time domain are non-stationary signals, for which the properties vary with time, we characterise those signals by obtaining seismic attributes which are also varying with time. Among the widely used attributes are spectral attributes calculated through time-frequency decomposition. Time-frequency spectral decomposition methods are employed to capture variations of a signal within the time-frequency domain. These decomposition methods generate a frequency vector at each time sample, referred to as the spectral component. The computed spectral component enables us to explore the additional frequency dimension which exists jointly with the original time dimension enabling localisation and characterisation of patterns within the seismic section. Conventional time-frequency decomposition methods include the continuous wavelet transform and the Wigner-Ville distribution. These methods suffer from challenges that hinder accurate interpretation when used for seismic interpretation. Continuous wavelet transform aims to decompose signals on a basis of elementary signals which have to be localised in time and frequency, but this method suffers from resolution and localisation limitations in the time-frequency spectrum. In addition to smearing, it often emerges from ill-localisation. The Wigner-Ville distribution distributes the energy of the signal over the two variables time and frequency and results in highly localised signal components. Yet, the method suffers from spurious cross-term interference due to its quadratic nature. This interference is misleading when the spectrum is used for interpretation purposes. For the specific application on seismic data the interference obscures geological features and distorts geophysical details. This thesis focuses on developing high fidelity and high-resolution time-frequency spectral decomposition methods as an extension to the existing conventional methods. These methods are then adopted as means to resolve seismic images for petroleum reservoirs. These methods are validated in terms of physics, robustness, and accurate energy localisation, using an extensive set of synthetic and real data sets including both carbonate and clastic reservoir settings. The novel contributions achieved in this thesis include developing time-frequency analysis algorithms for seismic data, allowing improved interpretation and accurate characterisation of petroleum reservoirs. The first algorithm established in this thesis is the Wigner-Ville distribution (WVD) with an additional masking filter. The standard WVD spectrum has high resolution but suffers the cross-term interference caused by multiple components in the signal. To suppress the cross-term interference, I designed a masking filter based on the spectrum of the smoothed-pseudo WVD (SP-WVD). The original SP-WVD incorporates smoothing filters in both time and frequency directions to suppress the cross-term interference, which reduces the resolution of the time-frequency spectrum. In order to overcome this side-effect, I used the SP-WVD spectrum as a reference to design a masking filter, and apply it to the standard WVD spectrum. Therefore, the mask-filtered WVD (MF-WVD) can preserve the high-resolution feature of the standard WVD while suppressing the cross-term interference as effectively as the SP-WVD. The second developed algorithm in this thesis is the synchrosqueezing wavelet transform (SWT) equipped with a directional filter. A transformation algorithm such as the continuous wavelet transform (CWT) might cause smearing in the time-frequency spectrum, i.e. the lack of localisation. The SWT attempts to improve the localisation of the time-frequency spectrum generated by the CWT. The real part of the complex SWT spectrum, after directional filtering, is capable to resolve the stratigraphic boundaries of thin layers within target reservoirs. In terms of seismic characterisation, I tested the high-resolution spectral results on a complex clastic reservoir interbedded with coal seams from the Ordos basin, northern China. I used the spectral results generated using the MF-WVD method to facilitate the interpretation of the sand distribution within the dataset. In another implementation I used the SWT spectral data results and the original seismic data together as the input to a deep convolutional neural network (dCNN), to track the horizons within a 3D volume. Using these application-based procedures, I have effectively extracted the spatial variation and the thickness of thinly layered sandstone in a coal-bearing reservoir. I also test the algorithm on a carbonate reservoir from the Tarim basin, western China. I used the spectrum generated by the synchrosqueezing wavelet transform equipped with directional filtering to characterise faults, karsts, and direct hydrocarbon indicators within the reservoir. Finally, I investigated pore-pressure prediction in carbonate layers. Pore-pressure variation generates subtle changes in the P-wave velocity of carbonate rocks. This suggests that existing empirical relations capable of predicting pore-pressure in clastic rocks are unsuitable for the prediction in carbonate rocks. I implemented the prediction based on the P-wave velocity and the wavelet transform multi-resolution analysis (WT-MRA). The WT-MRA method can unfold information within the frequency domain via decomposing the P-wave velocity. This enables us to extract and amplify hidden information embedded in the signal. Using Biot's theory, WT-MRA decomposition results can be divided into contributions from the pore-fluid and the rock framework. Therefore, I proposed a pore-pressure prediction model which is based on the pore-fluid contribution, calculated through WT-MRA, to the P-wave velocity.Open Acces

Joint time-frequency representation of simulated earthquake accelerograms via the adaptive chirplet transform

Seismic accelerograms are inherently nonstationary signals since both the intensity and frequency content of seismic events evolve in time. The adaptive chirplet transform is a signal processing technique for joint time-frequency representation of nonstationary data. Analysis of a signal via the adaptive chirplet decomposition in conjunction with the Wigner-Ville distribution yields the so-called adaptive spectrogram which constitutes a valid representation of the signal in the time-frequency plane. In this paper the potential of this technique for capturing the temporal evolution of the frequency content of strong ground motions is assessed. In this regard, simulated nonstationary earthquake accelerograms compatible with an exponentially modulated and appropriately filtered Kanai-Tajimi spectrum are processed using the adaptive chirplet transform. These are samples of a random process whose evolutionary power spectrum can be represented by an analytical expression. It is suggested that the average of the ensemble of the adaptive chirplet spectrograms can be construed as an estimate of the underlying evolutionary power spectrum. The obtained numerical results show, indeed, that the estimated evolutionary power spectrum is in a good agreement with the one defined analytically. This fact points out the potential of the adaptive chirplet analysis for as a tool for capturing localized frequency content of arbitrary data- banks of real seismic accelerograms

Wavelet: a new tool for business cycle analysis

One basic problem in business-cycle studies is how to deal with nonstationary time series. The market economy is an evolutionary system. Economic time series therefore contain stochastic components that are necessarily time dependent. Traditional methods of business cycle analysis, such as the correlation analysis and the spectral analysis, cannot capture such historical information because they do not take the time-varying characteristics of the business cycles into consideration. In this paper, we introduce and apply a new technique to the studies of the business cycle: the wavelet-based time-frequency analysis that has recently been developed in the field of signal processing. This new method allows us to characterize and understand not only the timing of shocks that trigger the business cycle, but also situations where the frequency of the business cycle shifts in time. Our empirical analyses show that 1973 marks a new era for the evolution of the business cycle.Business cycles

A Quantitative Measure of Mono-Componentness for Time-Frequency Analysis

Joint time-frequency (TF) analysis is an ideal method for analyzing non-stationary signals, but is challenging to use leading to it often being neglected. The exceptions being the short-time Fourier transform (STFT) and spectrogram. Even then, the inability to have simultaneously high time and frequency resolution is a frustrating issue with the STFT and spectrogram. However, there is a family of joint TF analysis techniques that do have simultaneously high time and frequency resolution – the quadratic TF distribution (QTFD) family. Unfortunately, QTFDs are often more troublesome than beneficial. The issue is interference/cross-terms that causes these methods to become so difficult to use. They require that the “proper” joint distribution be selected based on information that is typically unavailable for real-world signals. However, QTFDs do not produce cross-terms when applied to a mono-component signal. Clearly, determining the mono-componentness of a signal provides a key piece of information. However, until now, the means for determining if a signal is a monocomponent or a multi-component has been to choose a QTFD, generate the TF representation (TFR), and visually examine it. The work presented here provides a method for quantitatively determining if a signal is a mono-component. This new capability provides an important step towards finally allowing QTFDs to be used on multi-component signals, while producing few to no interference terms through enabling the use of the quadratic superposition property. The focus of this work is on establishing the legitimacy for “measuring” mono-componentness along with its algorithmic implementation. Several applications are presented, such as quantifying the quality of the decomposition results produced by the blind decomposition algorithm, Empirical Mode Decomposition (EMD). The mono-componentness measure not only provides an objective means to validate the outcome of a decomposition algorithm, it also provides a practical, quantitative metric for their comparison. More importantly, this quantitative measurement encapsulates mono-componentness in a form which can actually be incorporated in the design of decomposition algorithms as a viable condition/constraint so that true mono-components could be extracted. Incorporating the mono-component measure into a decomposition algorithm will eventually allow interference free TFRs to be calculated from multi-component signals without requiring prior knowledge

Induction Machine Diagnosis using Stator Current Advanced Signal Processing

International audienceInduction machines are widely used in industrial applications. Safety, reliability, efficiency and performance are major concerns that direct the research activities in the field of electrical machines. Even though the induction machines are very reliable, many failures can occur such as bearing faults, air-gap eccentricity and broken rotor bars. Therefore, the challenge is to detect them at an early stage in order to prevent breakdowns. In particular, stator current-based condition monitoring is an extensively investigated field for cost and maintenance savings. In fact, several signal processing techniques for stator current-based induction machine faults detection have been studied. These techniques can be classified into: spectral analysis approaches, demodulation techniques and time-frequency representations. In addition, for diagnostic purposes, more sophisticated techniques are required in order to determine the faulty components. This paper intends to review the spectral analysis techniques and time-frequency representations. These techniques are demonstrated on experimental data issued from a test bed equipped with a 0.75 kW induction machine. Nomenclature O&M = Operation and Maintenance; WTG = Wind Turbine Generator; MMF = Magneto-Motive Force; MCSA = Motor Current signal Analysis; PSD = Power Spectral Density; FFT = Fast Fourier Transform; DFT = Discrete Fourier Transform; MUSIC = MUltiple SIgnal Characterization; ESPRIT = Estimation of Signal Parameters via Rotational Invariance Techniques; SNR = Signal to Noise Ratio; MLE = Maximum Likelihood Estimation; STFT = Short-Time Fourier Transform; CWT = Continuous Wavelet Transform; WVD = Wigner-Ville distribution; HHT = Hilbert-Huang Transform; DWT = Discrete Wavelet Transform; EMD = Empirical Mode Decomposition; IMF = Intrinsic Mode Function; AM = Amplitude Modulation; FM = Frequency Modulation; IA = Instantaneous Amplitude; IF = Instantaneous Frequency; í µí± ! = Supply frequency; í µí± ! = Rotational frequency; í µí± ! = Fault frequency introduced by the modified rotor MMF; í µí± ! = Characteristic vibration frequencies; í µí± !"# = Bearing defects characteristic frequency; í µí± !" = Bearing outer raceway defect characteristic frequency; í µí± !" = Bearing inner raceway defect characteristic frequency; í µí± !" = Bearing balls defect characteristic frequency; í µí± !"" = Eccentricity characteristic frequency; í µí± ! = Number of rotor bars or rotor slots; í µí± = Slip; í µí°¹ ! = Sampling frequency; í µí± = Number of samples; í µí±¤[. ] = Time-window (Hanning, Hamming, etc.); í µí¼ = Time-delay; í µí¼ ! = Variance; ℎ[. ] = Time-window