Gradient Steepest Descent Method Research Articles

Model Predictive Control for a Voltage Sensorless Grid-Connected Inverter With LCL Filter Using Lumped Disturbance Observer

This paper introduces a disturbance observer-based model predictive control for a voltage sensorless grid-connected inverter (GCI), which minimizes the number of sensor measurements and eliminates the steady-state error by estimating the lumped disturbance in the presence of grid impedance variations. A full-state estimation and lumped disturbance observer are obtained based on the Luenberger observer and gradient steepest descent method, respectively. A cost function, which consists of state error, is used for controller gain design. An optimal full-state observer and controller gains are obtained by solving an optimization problem based on linear matrix inequality. The discrete-time frequency responses analysis of open-loop and closed-loop systems is presented to demonstrate the filter resonance suppression. The robustness of the proposed control against grid impedance variation is analyzed through the pole-zero map approach. Simulations and experiments are conducted for a GCI under the grid impedance variation to demonstrate the theoretical analysis and the efficacy of the proposed control schemes.

Point Orthogonal Projection onto a Spatial Algebraic Curve

Point orthogonal projection onto a spatial algebraic curve plays an important role in computer graphics, computer-aided geometric design, etc. We propose an algorithm for point orthogonal projection onto a spatial algebraic curve based on Newton’s steepest gradient descent method and geometric correction method. The purpose of Algorithm 1 in the first step of Algorithm 4 is to let the initial iteration point fall on the spatial algebraic curve completely and successfully. On the basis of ensuring that the iteration point fallen on the spatial algebraic curve, the purpose of the intermediate for loop body including Step 2 and Step 3 is to let the iteration point gradually approach the orthogonal projection point (the closest point) such that the distance between them is very small. Algorithm 3 in the fourth step plays an important double acceleration and orthogonalization role. Numerical example shows that our algorithm is very robust and efficient which it achieves the expected and ideal result.

Frequency Adaptive Current Control Scheme for Grid-connected Inverter without Grid Voltage Sensors Based on Gradient Steepest Descent Method

This paper presents a frequency adaptive grid voltage sensorless control scheme of a grid-connected inductive–capacitive–inductive (LCL)-filtered inverter, which is based on an adaptive current controller and a grid voltage observer. The frequency adaptive current controller is constructed by a full-state feedback regulator with the augmentation of multiple control terms to restrain not only the inherent resonance phenomenon that is caused by LCL filter, but also current harmonic distortions from an adverse grid environment. The number of required sensing devices is minimized in the proposed scheme by means of a discrete-time current-type observer, which estimates the system state variables, and gradient-method-based observers, which estimate the grid voltages and frequency simultaneously at different grid conditions. The estimated grid frequency is utilized in the current control loop to provide high-quality grid-injected currents, even under harmonic distortions and the frequency variation of grid voltages. As a result, the grid frequency adaptive control performance as well as the robustness against distorted grid voltages can be realized. Finally, an inverter synchronization task without using grid voltage sensors is accomplished by a fundamental grid voltage filter and a phase-locked loop to detect the actual grid phase angle. The stability and convergence performance of the proposed observers have been studied by means of the Lyapunov theory to ensure a high accuracy tracking performance of estimated variables. Simulation and experimental results are presented to validate the feasibility and the effectiveness of the proposed control approach.

An Improved Curvature Circle Algorithm for Orthogonal Projection onto a Planar Algebraic Curve

Point orthogonal projection onto planar algebraic curve plays an important role in computer graphics, computer aided design, computer aided geometric design and other fields. For the case where the test point p is very far from the planar algebraic curve, we propose an improved curvature circle algorithm to find the footpoint. Concretely, the first step is to repeatedly iterate algorithm (the Newton’s steepest gradient descent method) until the iterated point could fall on the planar algebraic curve. Then seek footpoint by using the algorithm (computing footpoint q ) where the core technology is the curvature circle method. And the next step is to orthogonally project the footpoint q onto the planar algebraic curve by using the algorithm (the hybrid tangent vertical foot algorithm). Repeatedly run the algorithm (computing footpoint q ) and the algorithm (the hybrid tangent vertical foot algorithm) until the distance between the current footpoint and the previous footpoint is near 0. Furthermore, we propose Second Remedial Algorithm based on Comprehensive Algorithm B. In particular, its robustness is greatly improved than that of Comprehensive Algorithm B and it achieves our expected result. Numerical examples demonstrate that Second Remedial Algorithm could converge accurately and efficiently no matter how far the test point is from the plane algebraic curve and where the initial iteration point is.

Predicting electricity consumption in a building using an optimized back-propagation and Levenberg–Marquardt back-propagation neural network: Case study of a shopping mall in China

This study considered combinational control approaches for predicting electricity consumption in a building based on an optimized back-propagation (BP) neural network. Forecasting the electricity consumption of buildings is an important part of power management systems because it directly affects power dispatching and safe production. The BP neural network prediction method is used widely for this purpose because of its high plasticity and simple structure, but it has disadvantages such as slow convergence, fluctuations, and oscillation during training. We propose the use of the Levenberg–Marquardt back-propagation (LM-BP) neural network to enhance the accuracy of predictions by combining the gradient descent and Quasi-Newton method, thereby ensuring the fast convergence speed and maintaining better overall performance. Additionally, the network weights can be optimized by adaptive adjustment between the steepest gradient descent method and the Gauss–Newton method so the network can converge effectively. Hence, the accuracy and stability of the LM algorithm are improved, and a building electricity consumption prediction model can be established based on the improved BP neural network. Our results demonstrate that the forecasting model based on LM-BP neural network improves the accuracy and stability of predictions, and it is suitable for the short-term prediction of building electricity consumption.

Research of an algorithm for crystal lattice parameter identification based on the gradient steepest descent method

In the analysis of a crystalline substance, the problem of crystal lattice parameter identification is of a great interest. However, the existing methods for solving this problem, such as the Bravais cell parameters estimation method and Wigner-Seitz cell volume estimation method, do not provide the required level of accuracy. Aiming to address the problem of low identification accuracy, the paper proposes an algorithm for crystal lattice parameter identification based on the gradient steepest descent method. The study of the feasibility of the structure parameter identification is carried out using a large set of distorted lattices. The results obtained show a significant increase in the identification accuracy in comparison with the above-mentioned parameter identification methods.

ACTIVE HEAT DISSIPATION SYSTEM USING ADAPTIVE RECURRENT WAVELET NEURAL NETWORK CONTROL

This paper proposes a novel cooling control system with the intelligent active technique, which is based on the NI-PXI systems structure combined with the heat pipe cooling chips. In order to further solve the controlling problems of nonlinear heat transfer system, the proposed intelligent system involves the PID control, traditional control, and the adaptive recurrent wavelet neural network controller (ARWNNC) control techniques. The traditional control there exists the undesirable control chattering, The PID control the Response of Control cannot be processed immediately and the input voltage saturation phenomenon, the adaptive recurrent wavelet neural network controller, is employed to approximate the ideal controller, while the corresponding parameters are derived by the gradient steepest descent method, thus being provided with the adaptive real-time control ability.

A novel adaptive structure for SOA system effort estimation

AbstractThis paper addresses a novel adaptive structure to solve the problem of service‐oriented architecture (SOA) system effort estimation. The objective of our work is to combine the insights of signals theory with empirical research to find a recommendation scheme for the problem of SOA system effort estimation. The main motivation for using this structure is to enhance the principle of self‐adaptability to the situation at hand. The proposed structure consists of an adaptive filter composed of linear combiner of filter weights, input and desired values. Additionally, a gradient steepest descent method is used to adjust the filter parameters (training process) using the least mean square algorithm. Furthermore, an experimental analysis is conducted with the proposed structure using the data of 10 past SOA system industrial applications, and in the empirical analysis, two performance measurement metrics and an evaluation function are used to assess the performance in terms of predictive accuracy. The experimental analysis and comparison study are helpful to demonstrate the effectiveness of an estimation technique. The obtained results indicate that an improved predictive accuracy for the problem of SOA system effort estimation has been achieved using the proposed structure when compared with support vector machines, linear, stepwise and ordinary least square regression techniques. Copyright © 2016 John Wiley & Sons, Ltd.

A novel nonuniformity correction algorithm based on speeded up robust features extraction

The traditional image-registration based non-uniformity correction algorithm assumes that the displacements of inter-frame images are horizontal or vertical which ignores rotation, affine transformation, etc. This restriction results in low registration accuracy and then depresses the quality of nonuniformity correction. In this paper, we bring forward a novel nonuniformity correction algorithm based on speeded up robust features extraction (SURF). The feature points are extracted by hessian operator in the algorithm and are described in use of the 64-dimensional descriptor. Then the algorithm gets all the matching pairs by matching threshold, and all matching pairs can be used to estimate transform converting relations between the two consecutive images. The converting relations combined with the steepest gradient descent method can adaptively correct the gain and offset calibration parameters, which can get the accurate registration including rotation and affine transformation, and then reduce excessive noise and ghost artifacts in the process of correction. The experiments also show that our algorithm can solve the registration accuracy problem in complex conditions, and improve the correction results effectively.

Learning dynamics of a single polar variable complex-valued neuron.

This letter investigates the characteristics of the complex-valued neuron model with parameters represented by polar coordinates (called polar variable complex-valued neuron). The parameters of the polar variable complex-valued neuron are unidentifiable. The plateau phenomenon can occur during learning of the polar variable complex-valued neuron. Furthermore, computer simulations suggest that a single polar variable complex-valued neuron has the following characteristics in the case of using the steepest gradient-descent method with square error: (1) unidentifiable parameters (singular points) degrade the learning speed and (2) a plateau can occur during learning. When the weight is attracted to the singular point, the learning tends to become stuck. However, computer simulations also show that the steepest gradient-descent method with amplitude-phase error and the complex-valued natural gradient method could reduce the effects of the singular points. The learning dynamics near singular points depends on the error functions and the training algorithms used.

Application of SDGM to Digital PID and Performance Comparison with Analog PID Controller

Now -a-days PID (proportional-integral-derivative) controller is used in every type of small or large industries. For this the digital PID controller is so popular. But it is necessary to design and tune the PID controller in a proper method for applying the plant. The paper represents a method of tuning a digital proportional-integral-derivative (PID) controller. The name of the method is Steepest Gradient Descent Method (SDGM). It is an iterative method. The SDGM method is very simple, easy to use and each iteration is very fast. It is also a guaranteed method to find the minima through numerous times of iterations as long as it exists. By applying this optimization method PID controller is tuned both of digital and analog process. In the paper by applying the method of some plant the comparison result of analog and digital are shown. From the comparison it is found that the digital scheme is preferable than analog scheme. Index Terms—PID controller, SDGM. I. INTRODUCTION The fi rst controllers with proportional, integral, and derivative (PID) feedback control action became commercially available during the 1930s. The 1940s saw widespread acceptance in industry of pneumatic PID controllers, and their electronic counterparts entered the market in the 1950s. Digital hardware has been routinely used since the 1980s with significant impact on process control. Even several decades after three-mode controllers were introduced; the vast majority of controllers used in the chemical process industry are based on PI/PID models (1). The popularity of these controllers has led to research on tuning methods, resulting in hundreds of publications on this topic. Ziegler-Nichols tuning relations and Cohen-Coon tuning rules are among the earliest published methods. Tuning relations based on error criteria are more recent model-based tuning rules, which offer improvements over earlier tuning methods. Tuning rules also exist for unstable processes as well as for tuning in the presence of plant model mismatch (2). Despite the numerous approaches available for controller tuning, surveys indicate that poorly tuned control loops are abundant in industry. In general, the gain scheduling of the PID controllers is an optimization problem. The method of steepest descent (SDGM) is also known as The Gradient Descent, which is basically an optimization algorithm to find the local minimum of a function. By applying the SDGM to the PID controller, the controller is tuned and applied to some conventional plant then the digital and analog results are compared to the paper.

Micro-plasticity constitutive model taking account of size effects for pure aluminum by microindentation

The macro-plasticity power function constitutive model (MPFCM), the modified macroplasticity power function constitutive model (MMPFCM) and the micro-plasticity constitutive model (MCM) taking the material intrinsic length were established to characterize the microindentation size effects of pure aluminum, respectively. The experimental results indicated MPFCM only determined precisely in the great indentation load. While a modified one named MMPFCM was subsequently established taking account of the parameters variation with the increase of indentation depth. The conventional dimensional analysis method was employed to determine the strength coefficient K and the strain hardening exponent n of this modified model. And then MCM taking account of size effects was proposed based on the Taylor dislocation model. The firstorder steepest gradient descent method was adopted to obtain the material intrinsic length for the geometrically necessary dislocations. The parameters of MCM were identified by using the UMAT subroutine of ABAQUS software. The average absolute relative error of MCM is relatively lower than that of the macro-one. Although the precision of the modified one is also high, the applied scope is limited, only for the microindentation material. In addition, the intrinsic length 5.09 μm of pure aluminum is also obtained based on the strain gradient theory.

Hybrid morphological methodology for software development cost estimation

In this paper we propose a hybrid methodology to design morphological-rank-linear (MRL) perceptrons in the problem of software development cost estimation (SDCE). In this methodology, we use a modified genetic algorithm (MGA) to optimize the parameters of the MRL perceptron, as well as to select an optimal input feature subset of the used databases, aiming at a higher accuracy level for SDCE problems. Besides, for each individual of MGA, a gradient steepest descent method is used to further improve the MRL perceptron parameters supplied by MGA. Finally, we conduct an experimental analysis with the proposed methodology using six well-known benchmark databases of software projects, where two relevant performance metrics and a fitness function are used to assess the performance of the proposed methodology, which is compared to classical machine learning models presented in the literature.

A class of hybrid morphological perceptrons with application in time series forecasting

In this work a class of hybrid morphological perceptrons, called dilation–erosion perceptron (DEP), is presented to overcome the random walk dilemma in the time series forecasting problem. It consists of a convex combination of fundamental operators from mathematical morphology (MM) on complete lattices theory (CLT). A gradient steepest descent method is presented to design the proposed DEP (learning process), using the back propagation (BP) algorithm and a systematic approach to overcome the problem of nondifferentiability of morphological operators. The learning process includes an automatic phase fix procedure that is geared at eliminating time phase distortions observed in some time series. Finally, an experimental analysis is conducted with the proposed DEP using five real world time series, where five well-known performance metrics and an evaluation function are used to assess the forecasting performance of the proposed model. The obtained results are compared with those generated by classical forecasting models presented in the literature.

Hybrid group search optimiser with quadratic interpolation method and its application

Group Search Optimiser (GSO) is a new swarm intelligence optimiser algorithm inspired by animal social behaviours. In this paper, we proposed two variants of GSO to improve its search capability, and applied them to solving non-linear equations. Producers in the GSO are like the eyes of animals, which determine the i¾˜food' position and the movement direction of scroungers. However, due to the random sample mechanism, the computational efficiency is poor. To improve its search efficiency, a new GSO based on quadratic interpolation method (QIGSO) is proposed, in which the estimated position with quadratic interpolation theory is used to replace the random point in each iteration to increase the speed of convergence. Furthermore, the steepest gradient descent method is also incorporated into QIGSO (QIGSO_SDO) to improve the local search capability. Numerical simulation and a special problem about radar detection are used to test the proposed two variants.

A linear ridgelet network approach for fault diagnosis of analog circuit

A linear ridgelet network combining ridgelet, linear term and the standard feed-forward neural network used for diagnosing the faults of analog circuit is constructed, and a training algorithm based on the steepest gradient descent method and momentum method for this network and the procedure for diagnosing these faults are proposed. The resulting linear ridgelet network can learn more rapidly from training samples and handle more effectively the complicated fault information of circuit under test than wavelet network and ridgelet network, classifying these faults efficiently and correctly and achieving a high classification accuracy. The simulation results demonstrate the effectiveness of this approach.

SU-GG-I-12: Low Dose and Edge-Preserving CBCT Reconstruction by Compressed Sensing with Anisotropic Diffusion Filter Utilizing Prior Images in IGRT

Purpose: Radiation dose incurred to patients during repeated CBCT scans has caused great concerns. Decreasing the number of projections reduces the radiation dose, but this leads to significantly degraded image quality. In this work, we propose a method to solve the sparse data CBCTreconstruction problem by compressed sensing (CS) technique with anisotropicdiffusion filter (ADF) utilizing prior images. Method and Materials: The reconstructed images from full projections taken in the first day of the patient’s treatment were used as prior knowledge. In a subsequent scan of the same patient on a different day, the prior images were utilized as an initial guess in the iterative reconstruction process with limited projections. Our CS method minimized ADF of image subject to the data fidelity by using a constrained optimization strategy. The data fidelity constraint is enforced by the simultaneous algebraic reconstruction technique and the image constraint is minimized by the standard steepest gradient descent method. A series of phantom and patient studies were carried out. Results and discussion: A CS‐based CBCTreconstruction technique with ADF has been established. The technique allows us to effectively take advantage previously obtained CBCTimages and provides high quality CBCTimages with undersampled projections. With the prior knowledge assisted CS‐ADT method, we were able to use as little as 36 projections to obtain high contrast‐to‐noise images with spatial resolution comparable to imagesreconstructed with fully sampled data. With such sparse projection data, the traditional FDK‐only reconstruction failed to yield meaningful images. View aliasing artifacts seen in FDK images were greatly suppressed in imagesreconstructed by the prior knowledge assisted CS‐ADT method. Conclusions: Use of prior knowledge and CS method provides an effective way for sparse data CBCTreconstruction. It reduces radiation dose in the repeated CBCT scans and greatly enhances image quality.

The Application of The Steepest Gradient Descent for Control Design of Dubins Car for Tracking a Desired Path

In this paper, we consider the control design of the Dubins car system to track a desired path. We design the control of the Dubins car system using optimal control approach. The control of the Dubins car system is designed for tracking the desired path. Instead of the usual quadratic cost function, a special type of cost functional which includes a tracking error term will be considered. By this special cost functional, the minimum tracking error of path of the Dubins car toward a desired path using Pontryagin Maximum Principle is obtained. The analytical solution of the Hamiltonian system is di±cult to obtain. So, a numerical solution with the steepest gradient descent method is proposed. The numerical results are given at the last section of this paper.

Closed-shell numbers and two-dimensional rare gas microclusters

The binding energy and the sublimation energy of two-dimensional rare gas microclusters have been calculated by the steepest gradient descent method, a kind of molecular dynamics simulation, up to 92 atoms. The stable structure of the microclusters is based on hexagonal forms. Unlike the three- dimensional case, most of the microclusters with closed-shell numbers 19, 37, 61, 91 in the hexagonal model do not show the property of magic numbers. The magic number 7 and the even–odd alternation in the range of 9–18 atoms have been reconfirmed. By a definition of the film, the minimal number of constituent atoms in a film has been estimated to be 6000. For Lennard–Jones microclusters, the contribution of remote atomic pairs other than the nearest neighbor ones to the total energy is significant, which results in the reduction of the interatomic distance from the equilibrium value for the Lennard–Jones potential.

FUZZY-GENETIC ALGORITHMS AND TIME-OPTIMAL OBSTACLE-FREE PATH GENERATION FOR MOBILE ROBOTS

This paper, describes a new yet efficient technique based on fuzzy logic and genetic algorithms (Gas) to solve the find-path problems of a mobile robot, which is formulated as a nonlinear programming problem. In the proposed algorithm, a fuzzy logic controller is used to find obstracle-free directions locally and GAs are used as optimizer to find optimal/near-optimal locations along the obstracle-free directions. This algorithm is found to be more efficient than a steepest gradient descent method. Although the fuzzy-GA method is shown to find slightly inferior or similar solutions to those found using the best-known tangent-graph and A* algorithms, it is computationally faster than them. Moreover, the fuzzy-GA approach is practically more viable than the tangent-graph method, because of former's lesser sensitivity to the number and type of obstacles. The efficiency of the proposed method demonstrated in this paper suggests that it can be extended to solve motion planning problems having moving obstacles.