Frequency Wavelet Research Articles

Seismic tuning of dispersive thin layers

ABSTRACTThe wedge model is commonly used to study the limits of seismic resolution where conventionally the thickness of sub‐resolution seismic layers can be determined from thin layer tuning curves. Tuning curves relate the layer temporal thickness to the wavelet frequency, but, to our knowledge, no systematic study has been done to date of the effects of velocity dispersion and attenuation on tuning. In this work, we study the tuning properties of a thin layer dispersing according to the standard linear solid model. We show that the first tuning curve is sensitive to the attenuation, relative polarity and magnitude of the two reflection coefficients at the top and base of the layer. We provide an analytic formula for the upper bound in the mismatch between the elastic and dispersive tuning curves. We conclude that highly attenuative thin layers can appear thicker or thinner than they actually are depending on polarity and relative magnitude of reflection coefficients at the layer interfaces. Our results are particularly relevant in the quantification of CO2 where knowledge of the temporal thickness of CO2 layers is reliant on their tuning curves.

Damage to the rat cerebrum under in vitro sinusoidal translational shear deformation

Blast waves, which induce sinusoidal shear waves within brain tissue, may cause mild traumatic brain injury (mTBI). To identify damage from a shear deformation wave, sagittal slices of rat cerebra are subjected to 50 cycles of translational shear deformation at six fixed frequencies between 25 Hz and 125 Hz and displacement amplitudes of 10% or 25% of the original length of the specimen. Each deformation frequency produces transient and apparent steady shear stress states that frequency analysis describes by their harmonic wavelet and Fourier frequency components. The dominant frequency components are integer multiples of the applied deformation frequency. The morphology of the shear stress versus time curve, and probably the type of damage, changes with deformation frequency. Damage at the lower frequencies appears to be diffuse bond breaking. Imaging and histology do not clearly detect mild damage due to bond breaking that underlies mTBI, which the analysis of the shear stress response captures. Major transitions in the morphology of the stress response in the two regions occur at about 75 Hz deformation frequency, possibly due to minor damage to cerebral substructures. An increase in deformation frequency increases the drag force between the extracellular fluid and solid matter. The deformation frequency dependence of the shear stress response makes protection against blast mTBI more difficult because the frequency content of a blast wave is not known a priori.

Classification of heart sounds based on the combination of the modified frequency wavelet transform and convolutional neural network.

We purpose a novel method that combines modified frequency slice wavelet transform (MFSWT) and convolutional neural network (CNN) for classifying normal and abnormal heart sounds. A hidden Markov model is used to find the position of each cardiac cycle in the heart sound signal and determine the exact position of the four periods of S1, S2, systole, and diastole. Then the one-dimensional cardiac cycle signal was converted into a two-dimensional time-frequency picture using the MFSWT. Finally, two CNN models are trained using the aforementioned pictures. We combine two CNN models using sample entropy (SampEn) to determine which model is used to classify the heart sound signal. We evaluated our model on the heart sound public dataset provided by the PhysioNet Computing in Cardiology Challenge 2016. Experimental classification performance from a 10-fold cross-validation indicated that sensitivity (Se), specificity (Sp) and mean accuracy (MAcc) were 0.95, 0.93, and 0.94, respectively. The results showed the proposed method can classify normal and abnormal heart sounds with efficiency and high accuracy. Graphical abstract Block diagram of heart sound classification.

Integrated time-frequency wavelet analysis and impulse response filtering on SASW test for rigid pavement stiffness prediction

This paper employs an improved continuous wavelet transform (CWT) technique of Gaussian derivative function and impulse response filtering (IRF) in seismic surface wave analysis to improve data analysis in the Spectral Analysis of Surface Wave (SASW) method. Two procedures were used: first, the response spectrum of interest was chosen using a time–frequency wavelet spectrogram. Then, noisy distortions were eliminated by utilizing a time–frequency wavelet and impulse response filtering. The outcomes show that the SASW method is able to identify the surface wave velocity which coincides with the dynamic stiffness parameters of Portland Cement Concrete (PCC) slabs. The values of surface wave velocity increased during the curing stage, and in situ measurement of wave velocity could be helpful in determining the degree of curing. A good congruence has been demonstrated between the stiffness of PCC obtained from SASW measurements vis a vis that obtained using the American Concrete Institute (ACI) formulation.

Fault Detection of an Internal Combustion Engine through Vibration Analysis by Wavelets Transform

This paper presents a vibration analysis of an internal alternative combustion engine through frequency analysis and wavelet transform, where a form study of the temporary signal and the energy of that signal is carried out to extract certain characteristic values that allow to differentiate and identify to which pre-established operating conditions, a specific vibration signal belongs. Software is used to make the data decomposition, analysis and value extraction. Different analysis results are presented on this investigation like frequency analysis, spectrogram analysis, wavelet analysis, cross wavelet analysis, and results validation by extracting values of the signals of two tests generating a variation chart showing runs variability if it is big o tiny variability. This analysis is performed to characterize the engine vibration signals so that it is possible to identify an incipient failure in a non-intrusive manner and optimize its maintenance. Also, it can be determined the repetitive form that describes a temporary signal of mechanical vibrations of a motor, if its work cycle it is considered to separate the temporary signal into sections, as long as there are no lower frequency components than the result of dividing the sampling frequency for the number of points that are in a work cycle (the limit frequency).

A robust Q estimation scheme for adaptively handling asymmetric wavelet spectrum variations in strongly attenuating media

The central frequency shift technique for estimating wave attenuation in seismic exploration assumes a quasi-symmetric amplitude spectrum and has its limitations in low quality factor ([Formula: see text]) regions. The asymmetry of the wavelet amplitude spectrum becomes more pronounced during wave propagation, so using a constant parameter [Formula: see text] (the asymmetry index estimated) in the modified frequency-weighted exponential formula method to estimate [Formula: see text] still leads to errors and can degrade the results of inverse [Formula: see text]-filtering. We have derived a new [Formula: see text]-estimation scheme that does not require constant parameter fitting that also works for strongly asymmetric receiver spectra. It is based on forming a synthetic wavelet as the geometric mean of the source spectrum (approximated by the near-source receiver spectrum) and the subsequent attenuated (receiver) wavelet spectrum. The changing centroid frequency and variance of this new wavelet as a function of traveltime can automatically adapt to a changing asymmetric spectrum caused by attenuation. It yields more stable and accurate results, especially in low-[Formula: see text] regions. This adopted approach is successfully applied to synthetic data and vertical seismic profile field survey data and proves to be superior to previous frequency-shift methods.

Heart Sound Segmentation Using Bidirectional LSTMs With Attention.

This paper proposes a novel framework for the segmentation of phonocardiogram (PCG) signals into heart states, exploiting the temporal evolution of the PCG as well as considering the salient information that it provides for the detection of the heart state. We propose the use of recurrent neural networks and exploit recent advancements in attention based learning to segment the PCG signal. This allows the network to identify the most salient aspects of the signal and disregard uninformative information. The proposed method attains state-of-the-art performance on multiple benchmarks including both human and animal heart recordings. Furthermore, we empirically analyse different feature combinations including envelop features, wavelet and Mel Frequency Cepstral Coefficients (MFCC), and provide quantitative measurements that explore the importance of different features in the proposed approach. We demonstrate that a recurrent neural network coupled with attention mechanisms can effectively learn from irregular and noisy PCG recordings. Our analysis of different feature combinations shows that MFCC features and their derivatives offer the best performance compared to classical wavelet and envelop features. Heart sound segmentation is a crucial pre-processing step for many diagnostic applications. The proposed method provides a cost effective alternative to labour extensive manual segmentation, and provides a more accurate segmentation than existing methods. As such, it can improve the performance of further analysis including the detection of murmurs and ejection clicks. The proposed method is also applicable for detection and segmentation of other one dimensional biomedical signals.

The velocity-stress finite-difference method with a rotated staggered grid applied to seismic wave propagation in a fractured medium

To enable a mathematical description, geologic fractures are considered as infinitely thin planes embedded in a homogeneous medium. These fracture structures satisfy linear slip boundary conditions, namely, a discontinuous displacement and continuous stress. The general finite-difference (FD) method described by the elastic wave equations has challenges when attempting to simulate the propagation of waves at the fracture interface. The FD method expressed by velocity-stress variables with the explicit application of boundary conditions at the fracture interface facilitates the simulation of wave propagation in fractured discontinuous media that are described by elastic wave equations and linear slip interface conditions. We have developed a new FD scheme for horizontal and vertical fracture media. In this scheme, a fictitious grid is introduced to describe the discontinuous velocity at the fracture interface and a rotated staggered grid is used to accurately indicate the location of the fracture. The new FD scheme satisfies nonwelded contact boundary conditions, unlike traditional approaches. Numerical simulations in different fracture media indicate that our scheme is accurate. The results demonstrate that the reflection coefficient of the fractured interface varies with the incident angle, wavelet frequency, and normal and tangential fracture compliances. Our scheme and conclusions from this study will be useful in assessing the properties of fractures, enabling the proper delineation of fractured reservoirs.

A Class of Warped Filter Bank Frames Tailored to Non-linear Frequency Scales

A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function. The warping function is a $${\mathcal {C}}^1$$-diffeomorphism that determines the frequency progression and can be chosen freely, apart from minor technical restrictions. The resulting functions are interpreted as filter frequency responses. Combined with appropriately chosen decimation factors, a non-uniform analysis filter bank is obtained. Classical Gabor and wavelet filter banks are special cases of the proposed construction. Beyond the state-of-the-art, we construct a filter bank adapted to a frequency scale derived from human auditory perception and families of filter banks that can be interpreted as an interpolation between linear (Gabor) and logarithmic (wavelet) frequency scales. We derive straightforward conditions on the prototype filter decay and the decimation factors, such that the resulting warped filter bank forms a frame. In particular, a simple and constructive method for obtaining tight frames with bandlimited filters is derived by invoking previous results on generalized shift-invariant systems.

Accurate Fault Location Method of the Mechanical Transmission System of Shearer Ranging Arm

In the process of coal mine production, the fault of the mechanical transmission system of the shearer ranging arm directly affects safety production. Therefore, it is very important to achieve the accurate fault location of the shearer ranging arm. The combination method of optimized continuous complex Morlet wavelet envelope demodulation spectrum analysis and spectrum analysis is proposed. Firstly, the spectrum contrast analysis of vibration signals between the normal state and fault state is performed, which can obtain the fault characteristics frequency and preliminary fault location. Then, the optimized continuous complex Morlet wavelet envelope demodulation algorithm is proposed to extract the side-bands characteristics of vibration signals, which can obtain the rotation frequency of fault location by the contrast analysis of side-bands characteristics in normal and fault state. In the algorithm, the center frequency and bandwidth of Morlet wavelet are optimized by wavelet Shannon entropy, and the optimal scale factor can be accurately determined by spectrum contrast analysis of vibration signals in normal and fault state. Finally, the accurate gear fault location is achieved by comprehensive analysis results of optimized continuous complex Morlet wavelet envelope demodulation spectrum and spectrum contrast. The simulation signals and practical vibration signals are applied to verify the proposed accurate gear fault location method. The experiment results indicate that the center frequency and bandwidth determined by wavelet Shannon entropy make the wavelet waveform best match the fault impact signal, and the optimal scale factor can be accurately determined by spectrum contrast analysis of vibration signals in normal and fault state, and the proposed method can achieve the precise fault location of the mechanical transmission system of shearer ranging arm. It provides the method for the on-site rapid accurate fault location of the mechanical transmission system. It is of great significance to the safe and efficient production of the coal mine.

Frequency Spectrum and Wavelet Packet Analyses of Blasting Vibration Signals for Different Charge Structures in Blasting Peripheral Holes

Based on the blasting principle of the cutting seam cartridge, smooth blasting with the charge structures of the usual cartridge and cutting seam cartridge has been designed and implemented, respectively, for different peripheral holes in the same face. Meanwhile, the blasting vibration has been monitored. Through the analysis of the frequency spectrum of blasting vibration signals, it is found that the maximum blasting vibration velocity of the cutting seam cartridge charge is lower than that of the usual cartridge charge, from 0.21 m/s to 0.12 m/s. Moreover, the blasting energy distribution is more balanced. Especially in the low‐frequency part, the blasting energy is less, and there is a transferring trend to the high‐frequency part, which shows that the cutting seam cartridge charge has a better optimization effect. Furthermore, using wavelet packet analysis, the cutting seam cartridge charge could effectively reduce the energy concentration in the low‐frequency part. The energy distribution is much more dispersed, and the disturbance to the structure could be less, which is conducive to the stability of the structure. According to the blasting effect, the overbreak and underexcavation quantity at the cutting seam cartridge charge is better than that at the usual cartridge charge.

Wavelet-Based Enhanced Medical Image Super Resolution

Low-resolution medical images can seriously interfere with the medical diagnosis, and poor image quality can lead to loss of detailed information. Therefore, improving the quality of medical images and accelerating the reconstruction is of particular importance for diagnosis. To solve this problem, we propose a wavelet-based mini-grid network medical image super-resolution (WMSR) method, which is similar to the three-layer hidden-layer-based super-resolution convolutional neural network (SRCNN) method. Due to the amplification characteristics of wavelets, a stationary wavelet transform (SWT) is used instead of a discrete wavelet transform (DWT). Also, due to the nature of redundant (scale-by-scale) wavelets, it is possible to retain additional information about the image and restore high-resolution images in detail. For a large amount of training data, wavelet sub-band images, including approximation and frequency subbands are combined into a predefined full-scale factor. The mapping between the wavelet sub-band image and its approximate image is then determined. In order to ensure the reproducibility of the image, a method of adding a sub-pixel layer is proposed to realize the hidden layer, and replacing the small mini-grid-network on the hidden layer is of considerable significance to speed up the image recovery speed. Experimental results on the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) show that the model has better performance.

РОЗРОБКА СИСТЕМИ ВБУДОВИ ЦИФРОВИХ ВОДЯНИХ ЗНАКІВ В ЗОБРАЖЕННЯ НА ОСНОВІ DCT-LWT-SVD

Copyright protection of digital content is a rather actual problem of humanity in the 21st century. Misuses of multimedia content is very common, and their number is growing with each passing day. One type of copyright protection is the embedding of digital watermark (DW) in the content. In this paper a new method of embedding digital watermark into image using discrete cosine transform, lifting wavelet transform (LWT) with maternal wavelet "Dobeshi-8" and singular coefficients decomposition is proposed. Embedding is performed into the first singular number of the low frequency wavelet transform region. As a digital watermark, we will use a grayscale image normalized to a range from zero to ten to provide a high peak signal-to-noise ratio (PSNR). The research analyzed the developed method: the method of embedding and detecting information was tested for its resistance to various types of attacks, namely: application of noise overlay (Gauss and pulse noise, "salt and pepper"), "unsharp" filter and median filter, and compression attack (with quality coefficients for a complete container from 60 to 100). As a result of the conducted testing, it was established that the method is quite resistant to all the attacks, except for the "unsharp" filtering (the resulting performance is not satisfactory). The method showed good results in peak signal-to-noise ratio - the average PSNR value is 50.5 dB, as well as high rates of similarity between the embedded DW and the extracted one - from 77% to 97.6% while saving the full container in a lossless format, and up to 53, 05 dB and 91.96% while saving the image in a lossless format (JPEG).

Research on ultrasound image of interventional catheterization processing method based on wavelet transform and fuzzy theory

Interventional catheterization can help patients to accurately assess the condition, early diagnosis and intervention. Confirming the location of catheter by ultrasound has the advantages of real-time imaging, non-invasive, radiative, fast and convenient. Due to speckle noise and similar acoustic impedance, ultrasound images are not clear. In this paper an ultrasonic image processing algorithm based on wavelet transform and fuzzy theory is proposed. First, logarithmic transformation of ultrasound images is used to convert multiplicative noise into additive noise. Then the wavelet coefficients of the image are obtained by multiscale wavelet transform. The high frequency wavelet coefficients of the image are denoised by thresholding, and the low-frequency wavelet coefficients of the image are processed by fuzzy enhancement. Finally, the processed image is obtained through wavelet reconstruction and exponential transformation. Experiments show that this proposed method can effectively improve the visual effect of images.

Strain rate effect on the acoustic emission characteristics of concrete under uniaxial tension

Abstract Concrete is an important engineering material whose tensile property plays an important role in structural safety. Thus, the effect of strain rate on crack evolution in concrete during tension cracking cannot be neglected. Within a strain rate range of 10−6 to 10−4 s−1, an acoustic emission monitoring test for the whole process of concrete under uniaxial tension including the post-peak softening stage was conducted. Moreover, damage evolution, along with the cracking mechanism of concrete at various strain rates was discussed with respect to the effect of strain rate on acoustic emission. The results show that the acoustic emission activity of concrete is delayed due to an increase in strain rate. This indicates that the hysteresis of deformation and cracking can be observed in a uniaxial tension test of concrete. During the whole loading process, as the strain rate increased, the average level of the acoustic emission hit rate increased significantly, indicating that an increase in strain rate accelerates crack initiation and propagation in concrete. Average acoustic emission values, duration and energy also show an increasing trend, and the scatter distribution range between them and the acoustic emission amplitude changes significantly, a fact that can be used to identify the damage degree of concrete under different strain rates. A peak frequency and cd4 band wavelet energy spectrum coefficient tends to decrease, while the ca8 band wavelet energy spectrum coefficient increases. In other words, the proportion of low frequency acoustic emission signals increases, indicating that an increase in strain rate increases the proportion of macroscopic cracks in concrete. At various strain rates, the average level of acoustic emission characteristic parameters and the proportion of high frequency signals at the post-peak stage in concrete are higher than those at the pre-peak stage, indicating that the development of microcracks in concrete mainly concentrates during the post-peak softening stage.

Application of non-stationary iterative time-domain deconvolution

In this study, non-stationary iterative time-domain deconvolution (CNS-ITD) is investigated. The propagating wavelets are first estimated in several overlapping Gabor windows of the data. Matrix-vector operations in the time-domain are then performed by estimating a small number of columns of the wavelet matrix by interpolation within a sparse iterative estimation for the largest reflectivities. The iteration process is stopped when a minimum root mean square (RMS) residual or a maximum number of iterations is reached. Although initially formulated on the basis of work in earthquake seismology, CNS-ITD is a matching pursuit type of approach performed continuously in the time-domain for the non-stationary case. The results can then be convolved with a higher frequency wavelet in order to make the results stationary in time and to increase the resolution of the data. We first apply CNS-ITD to synthetic data with a time-varying attenuation, where the method successfully identifies the largest reflectors in the data. We then apply CNS-ITD to two observed shallow seismic datasets where improved resolution is obtained.

Direct prediction of petrophysical and petroelastic reservoir properties from seismic and well-log data using nonlinear machine learning algorithms

An analytical comparison of seismic inversion with several multivariate predictive techniques is made. Statistical data reduction techniques are examined that incorporate various machine learning algorithms, such as linear regression, alternating conditional expectation regression, random forest, and neural network. Seismic and well-log data are combined to estimate petrophysical or petroelastic properties, like bulk density. Currently, spatial distribution and estimation of reservoir properties is leveraged by inverting 3D seismic data calibrated to elastic properties (VP, VS, and bulk density) obtained from well-log data. Most commercial seismic inversions are based on linear convolution, i.e., one-dimensional models that involve a simplified plane-parallel medium. However, in cases that are geophysically more complex, such as fractured and/or fluid-rich layers, the conventional straightforward prediction relationship breaks down. This is because linear convolution operators no longer adequately describe seismic wavefield propagation due to nonlinear energy absorption. Such nonlinearity is also suggested by the seismic nonstationarity phenomenon, expressed by vertical and horizontal changes in the shape of the seismic wavelet (amplitude and frequency variations). The nonlinear predictive operator, extracted by machine learning algorithms, makes it possible in certain cases to estimate petrophysical reservoir properties more accurately and with less influence of interpretational bias.

Continuous wavelet transform and iterative decrement algorithm for the Lidar full-waveform echo decomposition.

In this paper, we propose a continuous wavelet transform and iterative decrement algorithm to decompose the light detection and ranging (LiDAR) full-waveform echoes into a series of components, each of which can be assumed as Gaussian essentially. We calculate the scale of continuous wavelet transform in real time according to the relationship between the center frequency of the mother wavelet and the approximate frequency of the transmitted laser pulse. The approximated frequency is calculated according to the half-width of the effective part of transmitted laser pulse. The positions of the Gaussian model components in the echoes can be precisely predicted according to the positions of the maxima of the continuous wavelet transform coefficient. And the boundary points which locate at the left and right sides of the position of the detected components can be detected. Then, the effective sections can be clipped according to the positions of the boundary points. In order to detect the hidden components which are obscured by the high responses from their adjacent components and estimate the initial parameters, the iterative decrement algorithm is carried out. The initial parameters are fitted by the Levenberg-Marquardt algorithm. In order to verify the proposed method, the simulations and experiments whose data is recorded by our coding LiDAR have been done. The simulations and experiments results indicate that the proposed method exhibits excellent performances, and it is valid for the complex full-waveform echo, which includes serious overlapping components.

Two level de-noising algorithm for early detection of bearing fault using wavelet transform and zero frequency filter

Abstract Rolling element bearings are used widely in rotating machinery such as, generators, motors, pumps, and turbines. Early detection of bearing fault is necessary for preventing machinery breakdown. Localised fault in a rolling element bearing gives rise to periodic impulses in vibration signal. At early stage vibration signal is weak. A zero frequency filter (ZFF) and wavelet transform based two level de-noising algorithm is proposed for the identification of these periodic impulses. First level de-noising is performed by ZFF. Envelope signal is passed through the zero frequency filter to enhance the impulse information and attenuate the noise and sinusoids. Second level de-noising is performed by wavelet transform. Wavelet transform helps in extracting the impulse information which is hidden in large amplitude of ZFF output. An expression is developed for optimum level of wavelet decomposition. Working of the algorithm is explained through simulated signal with periodic impulses. The algorithm is verified with experimental datasets of both seeded and naturally grown bearing faults.

Invisible Medical Image Watermarking using Edge Detection And Discrete Wavelet Transform Coefficients

Protection and authentication of medical images is essential for the patient’s disease identification and diagnosis. The watermark in medical imaging application needs to be invisible and it is also required to preserve the low and high frequency features of image data which makes watermarking a difficult assignment. Within this manuscript an unseen medical image watermarking approach is projected apply edge detection in the discrete wavelet transform domain. The wavelet transform is brought into play to decay the medical picture interested in multi-frequency secondary band coefficients. The edge detection applies to high frequency wavelet group in the direction of generating the boundary coefficients used as a key. The Gaussian noise pattern is utilized as watermark as well as embedded within the edge coefficients around the edges. To add the robustness scaled dilated edge coefficient is added with the edge coefficients to generate the watermarked image. Preserving the small frequency secondary band fulfills the information requirement of the medical imaging application. At the same time as adding together the watermark during high frequency sub-bands improve the watermark invisibility. To add additional robustness the dilation is applied on the edged coefficient before being embedded with sub band coefficients. presentation of the technique is experienced on the dissimilar set of medical imagery as well as evaluation of the proposed watermarking method founds it robust not in favor of the different attacks such at the same time as filtering, turning round plus resizing. Parametric study foundation going on Mean Square Error along with Signal to Noise Ratio shows that how good method performs for invisibility.