Decomposition Coefficients Research Articles

Complex shearlets and rotary phase congruence tensor for corner detection

Corner detection algorithms based on multi-scale analysis attract more attention due to their promising performance. However, they only consider amplitude information, neglect phase information and partially utilize multi-scale decomposition coefficients to detect corners. This limits their detection accuracy, repeatability and localization ability. This paper describes a new multi-scale analysis based corner detector. To overcome the problems of bilateral margin responses, edge extension and lack of phase information in traditional shearlets, a novel complex shearlet transform is proposed to better localize distributed discontinuities and especially to extract phase information from geometrical features. Moreover, a new rotary phase congruence tensor is proposed to utilize all amplitude and phase information for corner detection. Its tolerances to noise and ability for corner localization are improved further by screening and normalizing the amplitude information. Experimental results demonstrate that the localization ability and detection accuracy of the proposed method are superior to current detectors, and its repeatability is generally higher than current detectors and recent machine learning based interest point detectors.

Fault Detection of the Harmonic Reducer Based on CNN-LSTM With a Novel Denoising Algorithm

The harmonic reducer is a key component of the industrial robot. Its reliability has significant influence on the consecutive operation of the industrial robot. However, its failure rate is high due to the complicated internal structure and long-term working conditions of large load and high torque. To identify the fault type of the harmonic reducer under different working conditions, this article proposes the joint wavelet regional correlation threshold denoising (WRCTD) algorithm and convolutional neural network-long short term memory (CNN-LSTM) fault detection method. Firstly, the WRCTD algorithm utilizes the regional correlation of the wavelet decomposition coefficients and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\sigma $ </tex-math></inline-formula> criterion to suppress noise in the raw sensor data. Then, the CNN-LSTM model could mine hidden features of the processed sensor data to identify fault correctly. To evaluate the proposed method, the vibration signals of the harmonic reducer under different working conditions are collected by establishing a test rig. Comparative experimental results show that the proposed WRCTD algorithm can significantly improve the accuracy of the fault detection method. The specific values for the CNN-LSTM method and the LSTM method are 9.5% and 12.2%, respectively. In addition, the proposed CNN-LSTM method has better performance than traditional methods. It achieves the fault detection over 94.0%, which is 1.5%, 2.0%, 2.0%, 1.9%, and, 1.9% higher than the highest accuracy values of CNN, LSTM, and SVM methods in five experiments.

Cover Caption

January Online Cover: Hyperspectral imaging system, region of interest extraction, and hyperspectral data acquisition; spectra; feature wavelengths selected by variational mode decomposition and regression coefficients; and optimization γ and σ2 of least squares support vector machine model based on feature wavelengths selected by variational mode decomposition and regression coefficients algorithm using grid search method, from “Nondestructive detection of total soluble solids in grapes using VMD‐RC and hyperspectral imaging” by Min Xu, Jun Sun, Kunshan Yao, Xiaohong Wu, Jifeng Shen, Yan Cao, and Xin Zhou. p. 326–338.

Bayesian Energy Disaggregation At Substations With Uncertainty Modeling

This article considers energy disaggregation at substations (EDS) where the objective is to estimate the consumption of each load from aggregate measurements, in which whether or not some loads are consuming power is unknown to the operator. The existing EDS method cannot provide any reliability measure of the disaggregation results, while the disaggregation accuracy can vary significantly for different data due to the volatility of loads such as the solar generation. This article proposes a Bayesian-dictionary-learning-based approach to disaggregate the loads and provides an uncertainty measure of the returned estimation. Our approach learns the probability distributions of the load patterns and the decomposition coefficients from recorded data with partial labels at the offline stage. In real-time disaggregation of the obtained aggregate data, our approach computes the mean and covariance of the probability distribution of each load consumption, estimates the load using the mean, and computes the uncertainty index based on the covariance. Numerical experiments indicate that our method achieves improved disaggregation accuracy over the existing EDS method, and the uncertainty index measures the reliability of the returned estimation accurately.

АСИМПТОТИЧЕСКОЕ РАЗЛОЖЕНИЕ И АСИМПТОТИЧЕСКАЯ ФОРМУЛА ДЛЯ КОРНЯ ТРАНСЦЕНДЕНТНОГО УРАВНЕНИЯ С ПАРАМЕТРОМ

We consider the classic finite equation containing a parameter. Under a certain condition on the left side of this equation after replacing the variable it is reduced to the kind that it is not difficult to classify the interrelations between its constituent parts. Every case entails a certain situation with the existence of the solution of the equation under study, and it is shown that it can have, in essence, the same standard form. For the latter one fundamental result of the construction of the asymptotic decomposition is given. Next, the proof of formula for coefficients of the desired decomposition is presented using inductive technique. Another approach to finding a solution of the specified equation is associated with the possibility of obtaining an asymptotic formula in appearance resembling an infinite continued fraction. At first, approximations are naturally constructed recursively as consistently refined inequalities for the solution, and then, the convergence of these approximations is strictly proved. The pointwise convergence of separately even and odd approximations is related to their monotony and limitations, and the additional condition of continuous differentiability of the equation’s incoming data also guarantees uniform convergence of approximations to the solution. In conclusion, a simple example of such continued fraction is given.

Design and Characterization of Phase Holograms for Standoff Localization at Millimeter and Submillimeter Waves

We present design, simulation, and experimental characterization of dual-band frequency-diverse holograms for distributed beamforming. The holograms operate in the 50–75 GHz (WR-15) and 220–330 GHz (WR-3.4) bands for millimeter- and submillimeter-wave imaging. The holograms are designed to create a dispersive field in the region of interest (RoI) located 600 mm from the aperture. The holograms lie in the front end of an imaging setup and modulate the phase of the incident collimated beam from a parabolic mirror. The distributed beamforming enables interrogation of the RoI so that the measured reflection through the dispersive propagation path conveys the spatial information of the target. Different phase modulation schemes are evaluated, and two prototype holograms are manufactured. The dispersive operation and efficiency of the hologram are characterized with both simulations and measurements. The frequency diversity of the holograms is quantified using singular-value decomposition and spatial-spectral correlation coefficient methods. The results identified a design frequency of 120 GHz, a phase quantization step of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> /2 radians, and an added phase of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.9\pi $ </tex-math></inline-formula> radians as a good dispersion-efficiency compromise. A fully connected neural network is trained to localize a corner-cube reflector in the RoI illuminated by the hologram. The localization accuracy follows the diffraction-limited resolution and confirms the best performance for the hologram considered optimal in the design metrics.

Thermal Conductivity Decomposition and Accommodation Coefficient Extraction for Thermal Insulation Materials

Thermal Conductivity Decomposition and Accommodation Coefficient Extraction for Thermal Insulation Materials

Image encryption algorithm based on rear-mountedphase mask and random decomposition

To escalate the image encryption a new method has been devised which includes double random phase encoding (DRPE) using rear phase masking and random decomposition (RD) technique stranded on fractional Fourier transform. Here, asymmetric cryptographic system is developed in fractional Fourier transform (FrFT) mode using two random phase masks (RPM) and a rear mounted phase mask. In the projected scheme a colored image is decomposed into R, G and B channels. The amplitude of each channel is normalized, phase encoded and modulated using RPM. The modulated R, G and B channels of the colored image are individually transformed using FrFT to produce corresponding encrypted image. The proposed scheme is authorized on grayscale image also. The norm behind the development of the suggested scheme has been elaborated by carrying out cryptanalysis on system based on the RD. The method helps in escalations of the protection of double random phase encoding by cumulating the key length and the parameter amount, so that it vigorously can be used against various attacks. The forte of the suggested cryptographic system was verified using simulations with MATLAB 7.9.0 (R2008a). The efficiency of the suggested scheme includes the analysis using singular value decomposition (SVD), histogram and correlation coefficient.

Research on Feature Extraction and Separation of Mechanical Multiple Faults Based on Adaptive Variational Mode Decomposition and Comprehensive Impact Coefficient

Research on Feature Extraction and Separation of Mechanical Multiple Faults Based on Adaptive Variational Mode Decomposition and Comprehensive Impact Coefficient

МАРКИРОВКА НЕПОДВИЖНЫХ ИЗОБРАЖЕНИЙ С ИСПОЛЬЗОВАНИЕМ ФРАКТАЛЬНОГО ГАУССОВСКОГО ШУМА И ДВУМЕРНОГО ДИСКРЕТНОГО ВЕЙВЛЕТ ПРЕОБРАЗОВАНИЯ ДЛЯ ЗАЩИТЫ АВТОРСКИХ ПРАВ

Introduction. The relevance of copyright protection for multimedia content is determined by the using digital objects in all areas of life. The number and qualification of malefactors aimed at using someone else's intellectual work is constantly growing. The problem of copyright protection can be solved by using steganography methods. Despite the wide development of the topic, there are a number of problems that limit the use of classical steganography methods. The resistance of many well-known methods to unauthorized access is based on knowledge of the algorithm without the use of additional keys. This leaves the methods vulnerable to modification and removal of the embedded label by an intruder. The aim of the study is to increase the stability of copyright protection algorithms from unauthorized access. It is proposed to embed watermarks in two stages: at the first stage, the digital watermark values are replaced by sequences of fractal Gaussian noise, then the resulting fractal key is embedded in the protected image by replacing the wavelet decomposition coefficients. Methods: The fast Fourier transform algorithm was used to generate fractal Gaussian noise. The Hurst exponent of noise sequences was estimated using R/S analysis. Results: A new algorithm for embedding digital watermarks into images based on fractal Gaussian noise and discrete wavelet transform is proposed. The values of rational parameters of the algorithm, such as the decomposition level, the scaling factor, the length of the noise sequence, the values of the Hurst exponent for a single sequence, and the threshold value, are determined to achieve the best balance between the quality of embedding and extraction.

Smoothing Filter-Based Panchromatic Spectral Decomposition for Multispectral and Hyperspectral Image Pansharpening

This paper proposes an efficient and high-fidelity panchromatic (PAN) spectral decomposition method based on smoothing filtering for multispectral (MS) and hyperspectral (HS) image pansharpening. The proposed method assumes that the high-frequency spatial details at the same scale are the same for different spectral images captured by the satellite at the same time. When the PAN image is pre-filtered and down-sampled to the MS scale, it will have the same high-frequency spatial detail as the MS image, with only low-frequency spectral differences. Pre-filtering for anti-aliasing when downsampling. Then the spectral decomposition coefficients from down-sampled PAN image to MS image can be calculated on MS scale. The low-frequency spectral information of an image at different scales is the same, the spectral decomposition coefficients on the MS scale can be up-sampled to the PAN scale, and the original PAN image can be spectrally decomposed to obtain the sharpened image. The proposed method only decomposes the low-frequency spectrum, and the high-frequency spatial details are the same as the original PAN image, the spatial detail is well preserved. This paper verifies the effect of the proposed method on MS and HS image sharpening through experiments, and the results show that the proposed method is better than the comparison method. This paper also controls other variables to compare with the HPM method. The results show that the hybrid quality with no reference (HQNR) and spatial distortion index (D_s) of the proposed method are better than the HPM method.

SPHEROIDAL BASIS OF THE GENERALIZED MIK-KEPLER PROBLEM

Super integrated systems have an extremely important property: they allow the separation of variables in the Hamilton-Jacobi and Schrödinger equations in several orthogonal coordinate systems. The choice of a specific coordinate system is dictated by considerations of convenience, for example, the spectroscopic problem of hydrogen-like systems uses a spherical coordinate system, when considering the Stark effect - a parabolic coordinate system, and in the two-center problem - elongated spheroid coordinates. This abundance of separation of variables in the Schrödinger equation for super integrated systems leads to the problem of interphasic decompositions, i.e. there is a need to move from one wave function to another. The generalized MIC-Kepler problem in spherical coordinates is considered as an explicit form of the additional motion integral and the generalized MIC-Kepler problem in spheroid coordinates is given Λ ̂=M ̂+(R√(μ_0 ))/ℏ Ω ̂^((s) ) main function of which is the spheroid basis and three-membered recurrent relations are derived to which the decomposition coefficients of the spheroid basis according to spherical and parabolic bases as well.

Minimization of errors in discrete wavelet filtering of signals during ultrasonic measurements and testing

Error minimizing methods for discrete wavelet filtering of ultrasonic meter signals are considered. For this purpose, special model signals containing various measuring pulses are generated. The psi function of the Daubechies 28 wavelet is used to generate the pulses. Noise is added to the generated pulses. A comparative analysis of the two filtering algorithms is performed. The first algorithm is to limit the amount of detail of the wavelet decomposition coefficients in relation to signal interference. The minimum value of the root mean square error of wavelet decomposition signal deviation which is restored at each level from the initial signal without noise is determined. The second algorithm uses a separate threshold for each level of wavelet decomposition to limit the magnitude of the detail coefficients that are proportional to the standard deviation. Like in the first algorithm, the task is to determine the level of wavelet decomposition at which the minimum standard error is achieved. A feature of both algorithms is an expanded base of discrete wavelets ‒ families of Biorthogonal, Coiflet, Daubechies, Discrete Meyer, Haar, Reverse Biorthogonal, Symlets (106 in total) and threshold functions garotte, garrote, greater, hard, less, soft (6 in total). The model function uses random variables in both algorithms, so the averaging base is used to obtain stable results. Given features of algorithm construction allowed to reveal efficiency of ultrasonic signal filtering on the first algorithm presented in the form of oscilloscopic images. The use of a separate threshold for limiting the number of detail coefficients for each level of discrete wavelet decomposition using the given wavelet base and threshold functions has reduced the filtering error.

Nondestructive detection of total soluble solids in grapes using VMD-RC and hyperspectral imaging.

Total soluble solids (TSS) are one of the most essential attributes determining the quality and price of fruit. This study aimed to use hyperspectral imaging (HSI) and wavelength selection for nondestructive detection of TSS in grape. A novel method involving variational mode decomposition and regression coefficients (VMD-RC) was proposed to select feature wavelengths. VMD was introduced to decompose the hyperspectral images data of samples with bands of (400.68-1001.61nm) to get a series of feature components. Afterward, these components were processed separately using regression analysis to obtain the stability values of RC of each component. Finally, a filter-based selection strategy was used to screen key wavelengths. The least squares support vector machine (LSSVM) and partial least squares (PLS) were constructed under full and feature wavelengths for predicting TSS. The VMD-RC-LSSVM model obtained the best prediction accuracy for TSS, with of 0.93, with of 0.6 %, with of 18.14 and of 3.69. The overall results indicated that the VMD-RC algorithm can be used as an alternative to handle high-dimensional hyperspectral images data, and HSI has great potential for nondestructive and rapid evaluation of quality attributes in fruit. PRACTICAL APPLICATION: Traditional methods of evaluating grape quality attributes are destructive, time-consuming and laborious. Therefore, HSI was used to achieve rapid and nondestructive determination of TSS in grape. The results indicated that it was feasible to use HSI and variable selection for predicting TSS. It is of great significance to improve grape quality, guide postharvest handling and provide a valuable reference for noninvasively evaluating other internal attributes of fruit.

A new method of vibration signal denoising based on improved wavelet

Noise cancellation is one of the most successful applications of the wavelet transform. Its basic idea is to compare wavelet decomposition coefficients with the given thresholds and only keep those bigger ones and set those smaller ones to zero and then do wavelet reconstruction with those new coefficients. It is most likely for this method to treat some useful weak components as noise and eliminate them. Based on the cyclostationary property of vibration signals of rotating machines, a novel wavelet noise cancellation method is proposed. A numerical signal and an experimental signal of rubbing fault are used to test and compare the performances of the new method and the conventional wavelet based denoising method provided by MATLAB. The results show that the new noise cancellation method can efficaciously suppress the noise component at all frequency bands and has better denoising performance than the conventional one.

Characteristics of flow past elongated bluff bodies with underbody gaps due to varying inflow turbulence

An experimental study was performed on two elongated bluff bodies with underbody gaps, a square-back Ahmed body and a cuboid, to investigate the effects of geometry and the approach flow conditions on the time-averaged and temporal characteristics. The flow fields produced from two approach turbulent boundary layers with moderate (∼4%) and high (∼7%) turbulence levels were studied using time-resolved and double-frame particle image velocimetry systems. With the moderate turbulence, the wake topology and the loci of the centroid of vortices exhibit the well-known toroidal structure behind the Ahmed body, though it is skewed away from the wall. Also, the regions of elevated Reynolds stresses are considerably larger in the upper shear layer compared to the lower shear layer due to the reduced underbody velocity. The dominant frequencies obtained from the velocity fluctuations, reverse flow area, and the coefficient of the first proper orthogonal decomposition (POD) mode are identical. The flow structures are more complex behind the cuboid and the Ahmed body mounted in the high turbulent flow due to the enhanced interaction between the lower and upper shear layers, which is also evident from the shape of the turbulent structures in these shear layers. Consequently, the dominant vortex shedding frequencies varied as the streamwise distance from the bodies increased. The probability density function of the reverse flow area and the POD analysis performed in the spanwise plane revealed that the bi-stability phenomenon is absent in the present study due to the significant modification of the wake topology.

Fault diagnosis of modular multilevel converter based on adaptive chirp mode decomposition and temporal convolutional network

The reliability of the insulated gate bipolar transistors (IGBTs) is essential to the stable operation of the modular multilevel converter (MMC) system. However, there are a large number of IGBTs in the MMC system and the open-circuit faults of IGBTs are usually so hidden that it is difficult to find. Therefore, this article proposes a fault diagnosis framework based on temporal convolutional network (TCN) integrating adaptive chirp mode decomposition (ACMD) and silhouette coefficient (SC). First, ACMD is used to extract and reconstruct signal components from the original signal. Then, in order to avoid artificial selection of signal components, silhouette coefficient is introduced to characterize the importance of each component. Finally, the TCN model automatically extracts the features of the signal components and outputs the classification results. The main contributions are as follows: (1) A complete fault diagnosis framework that can adaptively extract features and perform fault classification is proposed in the paper. (2) For the MMC using the carrier-phase-shifted pulsewidth modulation strategy, the fault can be located to the IGBT by the output current. (3) Under certain noise conditions, the fault diagnosis proposed in the paper method still has good robustness. (4) The signal visualization of different residual blocks and channels explains the working mechanism of the AMCD-SC-TCN framework.

Study of hydration of kaolinite and montmorillonite mixture by IR spectroscopy

KGa-1b kaolinite and STx-1b montmorillonite, as well as their mechanical mixture in 1:1 mass ratio, have been experimentally investigated by total reflection IR spectroscopy (IR-ATR) at different moisture modes. The aim of this research was to investigate the spectral features during the formation of water films on the surface of individual minerals, and in mixtures. The analysis of mineral composition of the wetted samples has been carried out by decomposing the experimental spectra into the linear combination of basic spectra of H2O and the minerals used. The obtained dependences of the decomposition coefficients on moisture allow studying the peculiarities of the formation of a water layer on mineral particles, studying the dynamics of moisture redistribution between mineral particles in mixtures, and evaluating the plastic characteristics of clays.

Cotton stubble detection based on wavelet decomposition and texture features

BackgroundAt present, the residual film pollution in cotton fields is crucial. The commonly used recycling method is the manual-driven recycling machine, which is heavy and time-consuming. The development of a visual navigation system for the recovery of residual film is conducive, in order to improve the work efficiency. The key technology in the visual navigation system is the cotton stubble detection. A successful cotton stubble detection can ensure the stability and reliability of the visual navigation system.MethodsFirstly, it extracts the three types of texture features of GLCM, GLRLM and LBP, from the three types of images of stubbles, residual films and broken leaves between rows. It then builds three classifiers: Random Forest, Back Propagation Neural Network and Support Vector Machine in order to classify the sample images. Finally, the possibility of improving the classification accuracy using the texture features extracted from the wavelet decomposition coefficients, is discussed.ResultsThe experiment proves that the GLCM texture feature of the original image has the best performance under the Back Propagation Neural Network classifier. As for the different wavelet bases, the vertical coefficient texture feature of coif3 wavelet decomposition, combined with the texture feature of the original image, is the feature having the best classification effect. Compared with the original image texture features, the classification accuracy is increased by 3.8%, the sensitivity is increased by 4.8%, and the specificity is increased by 1.2%.ConclusionsThe algorithm can complete the task of stubble detection in different locations, different periods and abnormal driving conditions, which shows that the wavelet coefficient texture feature combined with the original image texture feature is a useful fusion feature for detecting stubble and can provide a reference for different crop stubble detection.

On the seven-diagonals splitting for the cubic spline wavelets with six vanishing moments on an interval

This study uses a zeroing property of the first six moments for constructing a splitting algorithm for the cubic spline wavelets. First, we construct a system of cubic basic spline-wavelets, realizing orthogonal conditions to all polynomials up to any degree. Then, using the homogeneous Dirichlet boundary conditions, we adapt spaces to the orthogonality to all polynomials up to the fifth degree on the closed interval. The originality of the study consists of obtaining implicit finite relations connecting the coefficients of the spline decomposition at the initial scale with the spline coefficients and wavelet coefficients at the nested scale by a tape system of linear algebraic equations with a non-degenerate matrix. After excluding the even rows of the system, the resulting transformation matrix has seven diagonals, instead of five as in the previous case with four zero moments. A modification of the system is performed, which ensures a strict diagonal dominance, and, consequently, the stability of the calculations. The comparative results of numerical experiments on approximating and calculating the derivatives of a discrete function are presented.