Reconstruction of Velocity Curve in Long Stroke and High Dynamic Range Laser Interferometry

To study the law that governs the complex movements of the mechanism in the process of automatic weapon operation, the velocity tracking test technology of photon Doppler velocimetry is introduced to accurately measure velocity, displacement and acceleration, on the condition that there are long displacement and rapid velocity change. In the traditional way, out of interference signal time-frequency (TF) transformation draws TF distribution, and then by modulus maxima frequency extraction, comes to the law of velocity change. Due to the influence resulting from the change of fundamental signal as well as that of light intensity signal in the test, based on the TF distribution obtained by TF transformation, the traditional modulus maxima frequency extraction can extract frequency signals, but they show abnormal sudden changes at some moments, making the velocity discontinuous, unsmooth and unreal, which brings obvious errors to the subsequent calculation of acceleration and accurate displacement. Addressing the above-mentioned problems, this paper proposes a ridge extracting correction algorithm based on modulus maxima frequency extraction; this method, based on a large number of experiments where rodless cylinders are used to simulate the motion of a gun automatic mechanism, conducts a detailed calculation and analysis of the experimental results. A comparison of the two algorithms’ processing results, in terms of the speed, displacement and acceleration, suggests that the ridge extracting correction algorithm successfully corrects the frequency selection error, which draws a more continuous and, therefore, effective curve of the velocity change, and by so doing, the error of the displacement test (within 1.36 m displacement) is reduced from more than 3.6% to less than 0.58%, and the uncertainty dropped 97.07%. All these show that the accurate measurement of velocity, displacement and acceleration, with sudden and rapid velocity changes considered, is realized successfully.

Wavelet-based multifractal analysis and fractal Signature of SARS-Cov-2 Coronavirus Variants genomes.

In this paper, the SARS-CoV-2 coronavirus variants of concern and of interest genomes are analyzed using the wavelet transform modulus maxima lines (WTMM) method. The goal is to track the monofractal behavior of the virus genomes and to investigate the Long-Range-Correlation (LRC) character through the estimation of the Hurst exponent. The obtained results demonstrate the multifractal and the anti-correlated characters in the variants of concern for the Knucleotidic and GC DNA coding. The fractal signatures of SARS-CoV-2 coronavirus variants are investigated through the indicator matrix maps of the genomes, they exhibit the same patterns for the variants (Alpha, Delta) and (Eta, Lota, Kappa) with moving positions, while the variants Beta, Gamma and Epsilon have different indicator matrixes. The fractal dimensions of SARS-CoV-2 variants are oscillating aroundI, except the Epsilon variant from USA, where the fractal dimension is 1.70.

Edge-Preserving Image Denoising Based on Lipschitz Estimation

The information transmitted in the form of signals or images is often corrupted with noise. These noise elements can occur due to the relative motion, noisy channels, error in measurements, and environmental conditions (rain, fog, change in illumination, etc.) and result in the degradation of images acquired by a camera. In this paper, we address these issues, focusing mainly on the edges that correspond to the abrupt changes in the signal or images. Preserving these important structures, such as edges or transitions and textures, has significant theoretical importance. These image structures are important , more specifically, for visual perception. The most significant information about the structure of the image or type of the signal is often hidden inside these transitions. Therefore it is necessary to preserve them. This paper introduces a method to reduce noise and to preserve edges while performing Non-Destructive Testing (NDT). The method computes Lipschitz exponents of transitions to identify the level of discontinuity. Continuous wavelet transform-based multi-scale analysis highlights the modulus maxima of the respective transitions. Lipschitz values estimated from these maxima are used as a measure to preserve edges in the presence of noise. Experimental results show that the noisy data sample and smoothness-based heuristic approach in the spatial domain restored noise-free images while preserving edges.

Multifractal correlation using wavelet transform modulus maxima

The wavelet transform modulus maxima method (WTMM) for a single time series is generalized to multiple time series. The new method, which is called the joint WTMM analysis in this work, allows analyses of multifractal correlation between simultaneously measured data. Dependent, partly dependent and independent binomial cascades are used to test the joint WTMM formulism and the degree of correlation assessed qualitatively is found to agree well with the theoretical predictions. Finally, the technique is applied to simultaneously measured surface scalp potential and heart rate data taken from two healthy human subjects. Via this new method, it is shown that there is multifractal correlation between the fractal dynamics in the cortex and the autonomic regulation of the heart rate.

Multifractal correlation using wavelet transform modulus maxima

The wavelet transform modulus maxima method (WTMM) for a single time series is generalized to multiple time series. The new method, which is called the joint WTMM analysis in this work, allows analyses of multifractal correlation between simultaneously measured data. Dependent, partly dependent and independent binomial cascades are used to test the joint WTMM formulism and the degree of correlation assessed qualitatively is found to agree well with the theoretical predictions. Finally, the technique is applied to simultaneously measured surface scalp potential and heart rate data taken from two healthy human subjects. Via this new method, it is shown that there is multifractal correlation between the fractal dynamics in the cortex and the autonomic regulation of the heart rate.

Multifractal analysis for seismic wave in Kathmandu valley after Gorkha Earthquake-2015, Nepal

We applied the multiscale signal processing technique, the Wavelet Transform Modulus Maxima (WTMM) to characterize high frequency properties of strong motion waveforms, in particular the temporal distribution and strength of singularities in Gorkha earthquake, 25th April 2015. We first explored their relation to earthquake data source. Then we applied the WTMM analysis to strong motion recordings. These showed that the timing and exponent of singularities measured by the WTMM method on the ground motion wave field are directly related to the position and exponent of assumed initial stress singularities on the fault plane. We found strong motion recordings at near the epicenter site have very high multifractality than far sites. Some differences and similarities among sites were successfully detected.

Dyadic wavelet analysis of bender element signals in determining shear wave velocity

Determining shear wave velocity is a critical technique in bender element tests, as it can be readily affected by near-field effects, wave reflection, and other factors. This study proposes a new method based on the dyadic wavelet transform modulus maxima. Combining the local modulus maxima of dyadic wavelet transform approximate coefficients at fine decomposition levels and an appropriate threshold value, the proposed method can automatically detect the target point. For validation, a comparative study among the dyadic wavelet transform modulus maxima, peak-to-peak, first arrival, and cross-correlation methods was carried out using 140 sets of bender element signals. The comparison results show that the proposed method not only mitigates the adverse effects of near-field, later major peaks, and noise contamination, but is also more robust in estimating shear wave velocity.

Multifractal behavior of SARS-CoV-2 COVID-19 pandemic spread, case of: Algeria, Russia, USA and Italy.

Here, the multifractal behavior of the SARS-CoV-2 COVID-19 pandemic daily and death cases is investigated through the so-called Wavelet Transform Modulus Maxima lines (WTMM) method, data available via the World Health Organization (WHO) dashboard of Algeria, Russia, USA and Italy are analyzed. The obtained results show the multifractal behavior of the COVID-19 pandemic data with different spectra of singularities. Keywords: Multifractal behavior, daily and death cases, WTMM, COVID-19 pandemic data

Multifractal Analysis of SARS-CoV-2 Coronavirus genomes using the wavelet transform

In this paper, the 1D Wavelet Transform Modulus Maxima lines (WTMM) method is used to investigate the Long-Range Correlation (LRC) and to estimate the so-called Hurst exponent of 21 isolate RNA sequence downloaded from the NCBI database of patients infected by SARS-CoV-2, Coronavirus, the Knucleotidic, Purine, Pyramidine, Ameno, Keto and GC DNA coding are used. Obtained results show the LRC character in the most sequences; except some sequences where the anti-correlated or the Classical Brownian motion character is observed, demonstrating that the SARS-Cov2 coronavirus undergoes mutation from a country to another or in the same country, they reveals also the complexity and the heterogeneous genome structure organization far from the equilibrium and the self-organization.