Fast Convergent Method Research Articles

Fast and Unconditional Convergent MRMHSS Iteration Method for Solving Complex Symmetric Linear Systems

Fast and Unconditional Convergent MRMHSS Iteration Method for Solving Complex Symmetric Linear Systems

Optimizing robotic arm control using deep Q-learning and artificial neural networks through demonstration-based methodologies: A case study of dynamic and static conditions

This paper uses robot programming techniques, such as Deep Q Network, Artificial Neural Network, and Artificial Deep Q Network, to address challenges related to controlling robotic arms through demonstration learning. Static and dynamic states of the subjects were the subjects of experiments. Each method's classification accuracy process success values and experimental condition combination were evaluated. The DQN method demonstrated favourable classification accuracy outcomes, achieving an Accuracy value of 0.64 for the fixed dice and 0.52 for the moving dice. The Response value was 0.51 for the fixed dice and 0.41 for the moving dice, indicating a moderate level. The ANN method demonstrated lower accuracy, with Accuracy values of 0.59 and 0.56 and Response values of 0.61 and 0.58, respectively. The ADQN method demonstrated superior outcomes, with Accuracy values of 0.66 and 0.59 and Response values of 0.67 and 0.61. During the initial learning iterations, ADQN demonstrated the highest success rate at 33.67 %, whereas DQN and ANN achieved 28.39 % and 20.13 % success rates, respectively. As the number of iterations increased, all methods demonstrated improvement in their results. ADQN maintained a high success rate of 97.59 %, while DQN and ANN attained 82.16 % and 88.66 %, respectively. As the number of iterations increases, the results of all methods improve, but the success rate of the Artificial Deep Q Network remains high. As the number of iterations increases, both Deep Q Network and Artificial Neural Network demonstrate the potential to achieve good results. Overall, the findings support the efficacy of robot programming techniques that incorporate demonstration learning. The Artificial Deep Q Network is the most successful and fast-converging method suitable for various robot control tasks. These findings provide a foundation for future research and large-scale, comprehensive learning applications for complex rot control.

Efficient 2D Tikhonov smoothness regularization with recursive filtering

In this work, we describe an implementation of the 2D Tikhonov regularization filter which scales linearly with the input signal’s size. In the homogeneous case, we propose a novel algorithm to decompose the filter’s 2D kernel as a sum of axis-aligned Gaussians. Our algorithm uses symmetries of the kernel to provide a fast computation of the Gaussian decomposition in the frequency domain, where the 2D Tikhonov kernel has a closed-form expression. The convolution with each Gaussian is then computed using linear-time separable recursive filtering. In the non-homogeneous case, we also decompose the 2D problem as a series of iterated linear-time separable recursive filters, which can be combined with the Biconjugate Gradient Stabilized method for fast convergence. In this way, a fast solution to the 2D Tikhonov regularization problem is obtained.

Development of a Fast Convergence Gray-Level Co-Occurrence Matrix for Sea Surface Wind Direction Extraction from Marine Radar Images

The new sea surface wind direction from the X-band marine radar image is proposed in this study using a fast convergent gray-level co-occurrence matrix (FC-GLCM) algorithm. First, the radar image is sampled directly without the need for interpolation due to the algorithm’s application of the GLCM to the polar co-ordinate system, which reduces the inaccuracy caused by image transformation. An additional process is then to merge the fast convergence method with the optimized GLCM so that the circular transition between rough and fine estimates is acquired, resulting in the fast convergence and accuracy improvement of the GLCM. Furthermore, the algorithm will affect the GLCM spatial distribution while calculating it, and it can automatically resolve the 180° ambiguity problem of sea surface wind direction retrieved from radar images. Finally, the proposed method is applied to 1436 X-band marine radar sequences collected from the coast of the East China Sea. Compared with in situ anemometer data, the correlation coefficient is as high as 0.9268, and the RMSE is 4.9867°. The new method was also tested under diverse sea conditions. The FC-GLCM wind direction results against the adaptive reduced method (ARM), energy spectrum method (ESM), and the traditional GLCM (T-GLCM) method produced the best stability and accuracy, in which the RMSE decreased by 91.6%, 67.7%, and 18.1%, respectively.

Regularization Solver Guided FISTA for Electrical Impedance Tomography.

Electrical impedance tomography (EIT) is non-destructive monitoring technology that can visualize the conductivity distribution in the observed area. The inverse problem for imaging is characterized by a serious nonlinear and ill-posed nature, which leads to the low spatial resolution of the reconstructions. The iterative algorithm is an effective method to deal with the imaging inverse problem. However, the existing iterative imaging methods have some drawbacks, such as random and subjective initial parameter setting, very time consuming in vast iterations and shape blurring with less high-order information, etc. To solve these problems, this paper proposes a novel fast convergent iteration method for solving the inverse problem and designs an initial guess method based on an adaptive regularization parameter adjustment. This method is named the Regularization Solver Guided Fast Iterative Shrinkage Threshold Algorithm (RS-FISTA). The iterative solution process under the L1-norm regular constraint is derived in the LASSO problem. Meanwhile, the Nesterov accelerator is introduced to accelerate the gradient optimization race in the ISTA method. In order to make the initial guess contain more prior information and be independent of subjective factors such as human experience, a new adaptive regularization weight coefficient selection method is introduced into the initial conjecture of the FISTA iteration as it contains more accurate prior information of the conductivity distribution. The RS-FISTA method is compared with the methods of Landweber, CG, NOSER, Newton-Raphson, ISTA and FISTA, six different distributions with their optimal parameters. The SSIM, RMSE and PSNR of RS-FISTA methods are 0.7253, 3.44 and 37.55, respectively. In the performance test of convergence, the evaluation metrics of this method are relatively stable at 30 iterations. This shows that the proposed method not only has better visualization, but also has fast convergence. It is verified that the RS-FISTA algorithm is the better algorithm for EIT reconstruction from both simulation and physical experiments.

FAST CONVERGENCE METHOD FOR GLOBAL OPTIMAL 4DOF REGISTRATION

Abstract. Four degrees of freedom (4DoF) registration is a class of point cloud registration problems for finding a rigid transformation to align two point clouds under the constraint that the rigid transformation is composed of a three-dimensional (3D) translation and 1D rotation. This constraint is suitable to align scan pairs acquired using modern terrestrial Light Detection and Ranging (LiDAR) scanners, the scans of which can share the direction of gravity as the Z-axis due to such scanners using tripods or internal inclinometers. We propose a fast convergence method for global optimal 4DoF registration. The proposed method consists of (i) our newly developed 4DoF registration model formulated as an optimization problem involving the cylindrical norm to measure the distance between two points, and (ii) a fast convergence algorithm to find a global optimal solution of the model. We experimentally demonstrated that the proposed method reduced the number of iterations to convergence and computation time compared with a current 4DoF registration method, especially when the given scan pairs are similar but cannot be aligned, which often appears in registration of multiple point clouds.

Entropy Generation Minimization for Radiative Casson Fluid Flow through Permeable Walls and Convective Heating: A Comprehensive Numerical Investigation

Entropy generation minimization is a method that helps to improve the efficiency of real processes and devices. This study investigates the heat transfer in an electrically conducting Casson fluid flow between parallel plates under the influence of thermal radiation and convective boundary conditions. The thermodynamics first and second laws were employed to examine the problem. The present study provides a fast convergent method on the finite parallel plates, namely the Optimal Homotopy Analysis method (OHAM) and Collocation Method (CM) are used to analyzes the fluid flow, heat, transport. The impacts of governing parameters on Casson flow velocity, temperature profile, local skin friction, and Nusselt number were analysed. The obtained solutions were used to determine the heat transfer irreversibility and bejan number of the model. The method employed in this paper offers excellently convergence solutions with good accuracy. The results of the computation show that the effect of thermophysical properties such as thermal radiation parameter, suction/injection parameter, magnetic field parameter, radiation parameter, and Eckert number has a significant influence on Skin friction coefficient (Cf) and local Nusselt number (Nu) when compared to the Newtonian fluid. The application of this work can be found in polymer synthesis, metallic processing, and electromagnetic crucible systems.

Chemical entropy generation and second-order slip condition on hydrodynamic Casson nanofluid flow embedded in a porous medium: a fast convergent method

The chemical entropy generation analysis is an approach to optimize the performance of different thermal systems by investigating the related irreversibility of the system. The influences of second-order slip with the chemical reaction on the boundary layer flow and heat transfer of a non-Newtonian nanofluid in a non-Darcian porous medium have been investigated numerically. Simultaneous solutions are presented for first and second-order velocity slips. The second-order boundary conditions serve as a closure of a system of the continuity, transport, and energy differential equations. The current work differs from the previous studies in the application of a new second-order slip velocity model. The Casson fluid model is applied to characterize the non-Newtonian fluid behavior. The effect of the second slip parameter on the present physical parameters was discussed through graphs and it was found that this type of slip is a very important one to predict the investigated physical model. The present study provides two fast convergent methods on the semi-infinite interval, namely Chebyshev collocation method and optimal homotopy analysis method are used to analyze the fluid flow, heat, and mass transport. Compared with available analytical and numerical solutions, current methods are effective, quickly converging, and with great accuracy. It was shown that the account for the second-order terms in the boundary conditions noticeably affects the fluid flow characteristics and does not influence on the heat transfer characteristics.

Sparse Zernike Fitting for Dynamic LAS Tomographic Images of Temperature and Water Vapor Concentration

Laser absorption spectroscopy (LAS) tomography yields cross-sectional images of flame temperature and gas molar concentration in combustions. The total laser absorbance of a specific gas, such as water vapor at each point in the region of interest, was obtained from local normalized second harmonics on limited detectors. These detectors restrict the spatial resolution during image reconstructions through typical iterative methods. A sparse Zernike fitting method was introduced for LAS tomography, as the temperature in real physical reality is smoothly distributed. The distributions of total absorbance were sparsely fit as finite Zernike polynomials, and the coefficients were mostly zero or about zero. The number of coefficients was much smaller than that of pixels, i.e., unknowns in iterative methods. The underdetermined inverse problem was effectively alleviated, and a higher spatial resolution was achieved. A fast convergence and effective method for optimal step selection was also introduced for the iterative solution of the sparse model. The effectiveness of the proposed method was validated by both simulated and experimental data for temperature and concentration imaging. Performance comparisons were made with the typical iterative methods, such as SART and Landweber methods; temporal variations of reconstructed distributions for dynamical flames were captured with higher signal-to-noise ratios. Both the fundamental frequencies of 8.797 Hz without acoustic excitation and 12.7 Hz in the case of 150-Hz excitation were successfully captured, and tomographic images agreed well with the dynamical flame evolutions.

Heat and mass transfer in an unsteady squeezed Casson fluid flow with novel thermophysical properties: Analytical and numerical solution

AbstractThis study investigates the heat and mass transfer in an unsteady squeezing flow between parallel plates under the influence of novel variable diffusivity. In most of the literature, it is believed that the thermophysical properties of the fluid are unchanged. However, this present study bridges this gap by assuming that viscosity, conductivity, and diffusivity are all temperature‐dependent. Physically, an appropriate analysis of thermophysical variables in such a system is required to achieve the best performance for effective heat and mass transfer processes. The equations controlled were first nondimensional and then simplified by a similarity transformation to ordinary nonlinear differential equations. The present study provides a fast convergent method on finite parallel plates, namely, the optimal homotopy analysis method (OHAM) and spectral collocation method (SCM) are used to analyze the fluid flow, heat, and mass transport. The graphical and table understanding is given via an error table and flow behavior of physical parameters. The result reveals that the SCM is more accurate than OHAM. However, the method employed in this paper offers excellent convergence solutions with good accuracy. The solution convergence is also discussed. In this type of problem, squeeze numbers play an important role and the rise in the squeezing parameter increases the fluid temperature.

The use of homotopy analysis method for solving generalized Sylvester matrix equation with applications

In this research, we introduce and analyze homotopy analysis method (HAM) for solving approximately linear matrix equation $$ \sum \limits \limits _{i=1}^{s}A_iXB_i+C=\mathbf{0} $$ , where $$ A_i,\;B_i \;(i=1,\ldots ,s), \; C \in \mathbb {C}^{n \times n} $$ and $$X\in \mathbb {C}^{n \times n} $$ must be determined. In this method we consider a convergence control parameter $$ \delta $$ , and then we determine the optimum value of $$ \delta $$ for obtaining fast convergence method. Moreover, we obtain the corresponding spectral radius of convergence factor of HAM method. Finally, we will apply this method to solve some test problems to support the theoretical results.

A Fast Convergent Homotopy Perturbation Method for Solving Selective Harmonics Elimination PWM Problem in Multi Level Inverter

Pulse width modulation (PWM) control for power converters have been vastly investigated and used in many industrial application. For medium voltage and high power applications, low switching frequency PWM techniques are preferred over high switching frequency-based PWM techniques. The preprogrammed low switching frequency-based PWM technique known as selective harmonics elimination (SHE) gives the better quality waveform at a lower switching frequency. The main difficulty in applying SHE PWM is in solving of non-linear transcendental equations for obtaining switching angles. Several methods have been proposed for computation of switching angles that include numerical techniques, optimization techniques, and algebraic techniques. However, the computation of switching angles is still a challenging task in the application of SHE PWM. In this paper, a novel fast convergent homotopy perturbation method (HPM) is proposed to compute switching angles for a multilevel inverter at a faster rate. The solutions obtained by the proposed technique is as accurate as obtained by the algebraic methods with no dependency on the initial guess. The proposed technique can compute the higher number of switching angles with multiple solutions in some modulation index range. A prototype is developed and the computed switching angles have been verified using field-programmable gate arrays (FPGA) controller to validate the results for practical applications.

Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation

In this paper, we develop in a general framework a non overlapping Domain Decomposition Method that is proven to be well-posed and converges exponentially fast, provided that specific transmission operators are used. These operators are necessarily non local and we provide a class of such operators in the form of integral operators. To reduce the numerical cost of these integral operators, we show that a truncation process can be applied that preserves all the properties leading to an exponentially fast convergent method. A modal analysis is performed on a separable geometry to illustrate the theoretical properties of the method and we exhibit an optimization process to further reduce the convergence rate of the algorithm.

Push-Pull Finite-Time Convergence Distributed Optimization Algorithm

With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution rate of the distributed convex optimization algorithm. Each agent in the network has its own convex cost function. We consider a gradient-based distributed method and use a push-pull gradient algorithm to minimize the total cost function. Inspired by the current multi-agent consensus cooperation protocol for distributed convex optimization algorithm, a distributed convex optimization algorithm with finite time convergence is proposed and studied. In the end, based on a fixed undirected distributed network topology, a fast convergent distributed cooperative learning method based on a linear parameterized neural network is proposed, which is different from the existing distributed convex optimization algorithms that can achieve exponential convergence. The algorithm can achieve finite-time convergence. The convergence of the algorithm can be guaranteed by the Lyapunov method. The corresponding simulation examples also show the effectiveness of the algorithm intuitively. Compared with other algorithms, this algorithm is competitive.

Upgrade and development of elastic surface inverse design method for axial compressor cascade with sharp-edged blades

The aim of an inverse design method is to calculate the geometry corresponding to a target pressure distribution along the walls. Elastic Surface Algorithm (ESA), as one of the newest residual-corrective inverse design method, was proposed for external flows in 2014. In this method, the airfoil walls were considered as a flexible elastic beam that deforms due to the difference between the target and current pressure distribution at each shape modification step. Nevertheless, the previous version of ESA is subjected to oscillation, instability, and divergence for a cascade of sharp-edged blades due to the steep pressure gradient at the leading edge. This study upgrades the ESA for the shape design of sharp-edged blades with steep gradients of pressure near the stagnation point. The basis of this upgrade was to use the deflection curve of Timoshenko beam which is continuous and differentiable at all the nodes. The upgraded ESA against the original ESA used only the physical characteristics of Timoshenko beam instead of applying a geometric filtration for the removal of fractures in the intermediate profiles at large deformations. To increase the beam deformation at each shape modification, the upgraded ESA removed the constraint of node displacement along the spine direction, which is normal to the chord line, so that the nodes of Timoshenko beam could freely move based on the large deformation equations. In addition, the optimal values of elastic modulus, thickness, and width of the beam were obtained to increase the convergence rate of the ESA. The upgraded ESA was finally verified for a DCA blade cascade in subsonic and transonic flow regimes under different angles of attack and different initially-guessed geometries. The results showed the upgraded ESA to be a robust, flexible, and fast-converging inverse design method for sharp-edged blades with steep pressure gradients.

Hybrid backpropagation neural network-particle swarm optimization for seismic damage building prediction

The evaluation of the vulnerability of buildings to earthquakes is of prime importance to ensure a good plan can be generated for the disaster preparedness to civilians. Most of the attempts are directed in calculating the damage index of buildings to determine and predict the vulnerability to certain scales of earthquakes. Most of the solutions used are traditional methods which are time consuming and complex. Some of initiatives have proven that the artificial neural network methods have the potential in solving earthquakes prediction problems. However, these methods have limitations in terms of suffering from local optima, premature convergence and overfitting. To overcome this challenging issue, this paper introduces a new solution to the prediction on the seismic damage index of buildings with the application of hybrid back propagation neural network and particle swarm optimization (BPNN-PSO) method. The prediction was based on damage indices of 35 buildings around Malaysia. The BPNN-PSO demonstrated a better result of 89% accuracy compared to the traditional backpropagation neural network with only 84%. The capability of PSO supports fast convergence method has shown good effort to improve the processing time and accuracy of the results.

Optimization of Water-Supply and Hydropower Reservoir Operation Using the Charged System Search Algorithm

The Charged System Search (CSS) metaheuristic algorithm is introduced to the field of water resources management and applied to derive water-supply and hydro-power operating policies for a large-scale real-world reservoir system. The optimum algorithm parameters for each reservoir operation problems are also obtained via a tuning procedure. The CSS algorithm is a metaheuristic optimization method inspired by the governing laws of electrostatics in physics and motion from the Newtonian mechanics. In this study, the CSS algorithm’s performance has been tested with benchmark problems, consisting of highly non-linear constrained and/or unconstrained real-valued mathematical models, such as the Ackley’s function and Fletcher–Powell function. The CSS algorithm is then used to optimally solve the water-supply and hydropower operation of “Dez” reservoir in southern Iran over three different operation periods of 60, 240, and 480 months, and the results are presented and compared with those obtained by other available optimization approaches including Genetic Algorithm (GA), Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) and Constrained Big Bang–Big Crunch (CBB–BC) algorithm, as well as those obtained by gradient-based Non-Linear Programming (NLP) approach. The results demonstrate the robustness and superiority of the CSS algorithm in solving long term reservoir operation problems, compared to alternative methods. The CSS algorithm is used for the first time in the field of water resources management, and proves to be a robust, accurate, and fast convergent method in handling complex problems in this filed. The application of this approach in other water management problems such as multi-reservoir operation and conjunctive surface/ground water resources management remains to be studied.

Global maximum operating point tracking for PV system using fast convergence Firefly algorithm

Global maximum operating point (GMOP) tracking is an important requirement of solar photovoltaic (PV) systems under partial shading conditions (PSCs). Though the perturb and observe algorithm is simple and effective, it fails to recognize the GMOP. This paper explores the application of the firefly algorithm (FA) to the maximum power point tracking (MPPT) problem of PV systems. In order to determine the shortest path to reach the GMOP under various PSCs, a new fast convergence firefly algorithm (FA) is proposed. Additionally, the change in firefly position is limited to a maximum value identified based on the characteristics of the PSC. The fast convergence method is guaranteed to find the GMOP, avoiding the local operating point obstacle through a repeated space search technique. Using MATLAB, the algorithm is implemented on a model PV system. An experimental 300-W PV system is developed to validate the operating point of the PV system under various PSCs. The proposed method is tested on a 5-kW solar power plant. The results demonstrate that the proposed MPPT algorithm outperforms particle swarm optimization, FA-based MPPTs, and other methods available in the literature.

A Spectral Projected Gradient-Newton Two Phase Method for Constrained Nonlinear Equations

In this paper, we proposed a spectral gradient-Newton two phase method for constrained semismooth equations. In the first stage, we use the spectral projected gradient to obtain the global convergence of the algorithm, and then use the final point in the first stage as a new initial point to turn to a projected semismooth asymptotically newton method for fast convergence.

Accurate parametrization and methodology for selection of pertinent single diode photovoltaic model with improved simulation efficiency

An accurate model of photovoltaic (PV) panel is indispensable for simulations studies. In general, the PV circuit parameters for simulation studies are extracted from the manufacturer’s data sheet under different environmental conditions. The PV characterizing equations are nonlinear and requires a more involved computation. This paper presents a fast convergent third order Newton-type method to solve such nonlinear equations and thereby, to accurately parameterize any of the possible PV circuit models. The applicability and suitability of the proposed method are demonstrated through modeling of multi and mono-crystalline PV cells. Further an algorithm to evaluate the efficacy of the available methods and the proposed method is presented. PV characteristics of the suitable circuit model at various levels of temperature and irradiation are also examined. Finally, the effectiveness of the developed method is comprehensively assessed through comparison with the most recent and available effective techniques by considering various performance indices based on current-voltage, power-voltage curves and experimental data is carried out.