Periodic boundary value problems for nonlinear impulsive fractional differential equation

In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle

An Accelerated Stochastic ADMM for Nonconvex and Nonsmooth Finite-Sum Optimization

The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the lack of efficient algorithms with convincing convergence theories. A popular approach to solve it is the stochastic Alternating Direction Method of Multipliers (ADMM), but most stochastic ADMM-type methods focus on convex models. In addition, the variance reduction (VR) and acceleration techniques are useful tools in the development of stochastic methods due to their simplicity and practicability in providing acceleration characteristics of various machine learning models. However, it remains unclear whether accelerated SVRG-ADMM algorithm (ASVRG-ADMM), which extends SVRG-ADMM by incorporating momentum techniques, exhibits a comparable acceleration characteristic or convergence rate in the nonconvex setting. To fill this gap, we consider a general nonconvex nonsmooth optimization problem and study the convergence of ASVRG-ADMM. By utilizing a well-defined potential energy function, we establish its sublinear convergence rate $O(1/T)$, where $T$ denotes the iteration number. Furthermore, under the additional Kurdyka-Lojasiewicz (KL) property which is less stringent than the frequently used conditions for showcasing linear convergence rates, such as strong convexity, we show that the ASVRG-ADMM sequence has a finite length and converges to a stationary solution with a linear convergence rate. Several experiments on solving the graph-guided fused lasso problem and regularized logistic regression problem validate that the proposed ASVRG-ADMM performs better than the state-of-the-art methods.Comment: 40 Pages, 8 figure

Experimental Study: Investigating The Anions And Cations\u27 Effects On The Elasticity Of The Anionic And Cationic High Viscosity Friction Reducers

High viscosity friction reducers (HVFRs) are widely used as friction-reducing agents and proppant carriers during hydraulic fracturing. The reuse of produced water has gained popularity due to environmental and economic benefits. Currently, the field\u27s most commonly used friction reducers are anionic and cationic HVFRs. Anionic HVFRs are typically pumped with freshwater, while cationic HVFRs are used with high Total Dissolved Solids (TDS) produced water. Cationic friction reducers are believed to have better TDS tolerance, friction reduction performance, and proppant transport capabilities compared to anionic friction reducers under high TDS conditions due to their superior viscoelastic properties. In addition, the impact of different anions and cations on the viscosity of HVFRs has been thoroughly studied, and viscosity reduction mechanisms include charge shielding, increasing the degree of hydrolysis, and forming coordination complexes. However, anions and cations\u27 effects on the elasticity of HVFRs still remain to be investigated. Besides, most previous experimental studies either do not specify experimental procedures or control the experimental variables well. Therefore, the ultimate objective of this experimental study is to analyze various cations and anions\u27 effects on the elasticity of anionic and cationic HVFRs comparably and precisely with experimental variables well controlled. Two hypotheses based on anions and cations\u27 effects on the viscosity of HVFRs are proposed and will be tested in this study. First, the elasticity reduction of anionic HVFRs is mainly due to cations, whereas the elasticity reduction of cationic HVFRs is mainly due to anions. Second, the salts\u27 effects on the elasticity reduction of HVFRs should follow the same trend as the salts\u27 effects on the viscosity reduction of HVFRs. For anionic HVFRs, monovalent Alkali metals should have a similar effect; divalent Alkaline earth metals should have a similar effect; transition metals should have the most severe effect. For cationic HVFRs, SO42- should have more pronounced effects than Cl-. To demonstrate both hypotheses, an anionic and a cationic HVFR at 4 gallons per thousand gallons (GPT) were selected and analyzed. The elasticity measurements of both anionic and cationic HVFRs were conducted with deionized (DI) water and various salts respectively. Fe3+ and H+ (or pH) effects were specifically investigated. The results showed both hypotheses were accepted

Prediction Of Single Proppant Terminal Settling Velocity In High Viscosity Friction Reducers By Using Artificial Neural Networks And XGBoost

High viscosity friction reducers (HVFRs) have been recently gaining more attention and increasing in use, not only as friction-reducing agents but also as proppant carriers. The settling velocity of the proppant is one of the key outputs to describe their proppant transport capability. However, it is influenced by many factors such as fluid properties, proppant properties, and fracture properties. Many empirical/physics-based models and correlations to predict particle settling velocity have been developed. However, they are usually based on certain assumptions and have applicable limits. In contrast, machine learning models can be considered as a black box. The objective of this study is to use machine learning models to find the relationship between the multiple factors mentioned above and particle settling velocity in order to correctly predict it. Two of the most popular and powerful machine learning algorithms, Artificial neural networks (ANN) and XGBoost, were comparatively investigated with standard data processing and training procedures. Mean Absolute Errors (MAEs) for ANNs and XGBoost were 0.010379 and 0.004253 respectively. The XGBoost learning algorithm had overall better prediction performance than the ANN model in terms of the data sets used for this study and had the potential to properly handle missing values by itself

Flame image segmentation using multiscale color and wavelet-based texture features

Accurate and reliable segmentation of flame images are crucial in vision based monitoring and characterization of flames. It is, however, difficult to maintain the segmentation accuracy while achieving fast processing time due to the impact of the background noise in the images and the variation of operation conditions. To improve the quality of the image segmentation, a flame image segmentation method is proposed based on Multiscale Color and Wavelet-based Textures?MCWT? of the images. By combining the color and texture features, a characteristic matrix is built and then compressed using a local mean method. The outer contour of the flame image under the compressed scale is detected by a cluster technique. Subsequently, the flame edge region under the original scale is determined, following that, the characteristic matrix of the edge region is constructed and classified, and finally, the flame image segmentation is achieved. Flame images captured from an industrial-scale coal-firedtest rig under different operation conditions are segmented to evaluate the proposed method. The test results demonstrate that the performance of segmenting flame images of the proposed method is superior to other traditional methods. It also has been found that the proposed method performs more effectively in segmenting the flame images with Gaussian and pepper and salt noise

Fractal Characteristics of Thin Thermal Mixing Layers in Coal-Fired Flame

The images of turbulent flame were acquired by using a digital imaging system on an industry-scale pulverized coal-fired test rig?The fractal dimensions of thin thermal mixing layers in flame were computed through morphology-based flame image processing techniques?The effects of the ratios of primary air and secondary/tertiary air on fractal dimensions were characterized?The results presented in this work show that the variations of fractal dimension are closely related to the ratio changes of primary air and secondary/tertiary air. Therefore?the fractal dimensions of flame thin thermal mixing layers can be used as an important indicator for the control and optimization of a combustion process

Measurement of Coal Particle Combustion Behaviors in A Drop Tube Furnace Through High-speed Imaging and Image Processing

This paper presents the measurement and characterization of single coal particles in a drop tube furnace through high speed imaging and image processing. A high speed camera coupling with a long distance microscope is employed to acquire the images of the particle during its residence time in the furnace. A set of physical quantities of the particle, including size, shape and boundary roughness, are defined and computed based on the images obtained, which are then used describe the combustion behaviors of the particle. Experimental results show that the combined high speed imaging and image processing technique has provided an effective means for measuring and quantifying the characteristics of single coal particles during combustion

A Self-diagnostic Flame Monitoring System Incorporating Acoustic, Optical, and Electrostatic Sensors

Reliable flame monitoring is essential to enhance the safety of industrial boilers. This paper presents a new self-diagnostic system to measure the oscillation frequency of a burner flame. The system incorporates three sensors including a microphone, a photodiode and an electrostatic electrode and simultaneously acquires three signals. The oscillation frequencies from the three sensors are determined through power spectral analysis, and a fused result of the three frequencies is obtained as the oscillation frequency of the burner flame. Moreover, detection and location of the system faults are realized using a self-diagnostic algorithm through the cross-correlation signal processing. Experimental tests were performed on a laboratory-scale combustion test rig with methane as the test fuel. The results demonstrate that the method is capable of measuring the oscillation frequency of a burner flame. In addition, the results are helpful for the comprehensive analysis of the oscillatory behaviors of burner flames. The self-diagnostic algorithm is able to detect the fault of the monitoring system and no additional self-diagnostic hardware is required