Function Of Step Size Research Articles

A strongly monotonic polygonal Euler scheme

In recent years tamed schemes have become an important technique for simulating SDEs and SPDEs whose continuous coefficients display superlinear growth. The taming method involves curbing the growth of the coefficients as a function of stepsize, but so far has not been adapted to preserve the monotonicity of the coefficients. This has arisen as an issue in [4], where the lack of a strongly monotonic tamed scheme forces strong conditions on the setting. In this article we give a novel and explicit method for truncating monotonic functions in separable real Hilbert spaces, and show how this can be used to define a polygonal (tamed) Euler scheme on finite dimensional space, preserving the monotonicity of the drift coefficient, and converging to the true solution at the same rate as the classical Euler scheme for Lipschitz coefficients. Our construction is the first explicit method for truncating monotone functions we are aware of, and the first in infinite dimensions.

Some qualitative properties of the discrete models for malaria propagation

This paper addresses a reliable mathematical modeling of malaria propagation in infected societies for humans and mosquitoes with an extension of the basic Ross–Macdonald model. We analyze the extended Ross model numerically which is an initial value problem of a seven-dimensional system of the first-order ODEs. For this aim, the discretized scheme of the extended model is split into two parts. First, we apply the step-size functions to approximate the time derivatives with the first-order consistency. Then we use a nonlocal discretization of the standard θ-method to the right side of the system to obtain a linear system. We find the conditions for the step-size functions under which specific intervals are positively invariant for the total populations and each component of the solution of the extended Ross model. We suggest a step-size function for the extended Ross model to preserve the dynamical consistency of the model for any step size Δt. The numerical simulations confirm the theoretical results for the examples and we compare the efficiency of the nonstandard Runge–Kutta methods with the different step-size functions for sufficiently large step sizes.

Study of electrical circuits using Runge Kutta method of order 4

In this paper, Runge Kutta method of order 4 is used to study the electrical circuits designs through past, intermediate and present voltages. When integrating differential equations with Runge Kutta method of order 4, a constant step size (ℎ) is used until a testing procedure confirms that the discontinuity occurs in the present integration interval. This step size function calculations would take place at the end of the functional calculations, but before the dependent variables were updated. Runge Kutta methods along with convolution are given by array interpretation (Butcher matrix) representation, this leads to identify the equilibrium state. The input parameters indicate the voltage coefficient controlled by current sources and measures it a random periodic time. The output parameters provide stable independent values and calculated from past voltage and current values. Finally solutions are compared with exact values and RK method of order 4 along with Heun, Midpoint and Taylors’s method with various ℎ values.

Dynamic Systems Approach in Sensorimotor Synchronization: Adaptation to Tempo Step-Change.

This paper presents a dynamic systems model of a sensorimotor synchronization (SMS) task. An SMS task typically gives temporally discrete human responses to some temporally discrete stimuli. Here, a dynamic systems modeling approach is applied after converting the discrete events to regularly sampled time signals. To collect data for model parameter fitting, a previously published pilot study was expanded. Three human participants took part in an experiment: to tap a finger on a keyboard, following a metronome which changed tempo in steps. System identification was used to estimate the transfer function that represented the relationship between the stimulus and the step response signals, assuming a separate linear, time-invariant system for each tempo step. Different versions of model complexity were investigated. As a minimum, a second-order linear system with delay, two poles, and one zero was needed to model the most important features of the tempo step response by humans, while an additional third pole could give a somewhat better fit to the response data. The modeling results revealed the behavior of the system in two distinct regimes: tempo steps below and above the conscious awareness of tempo change, i.e., around 12% of the base tempo. For the tempo steps above this value, model parameters were derived as linear functions of step size for the group of three participants. The results were interpreted in the light of known facts from other fields like SMS, psychoacoustics and behavioral neuroscience.

A species-based flower pollination algorithm with increased selection pressure in abiotic local pollination and enhanced intensification

Flower Pollination Algorithm (FPA) is a bio-inspired metaheuristic that simulates pollination behavior of flowers. FPA is introduced to solve global optimization problems. Subsequently, it has been applied to a variety of problems. The present study introduces some new extensions and modifications for FPA. In this respect, first, abiotic pollination mechanism of FPA is modified. Secondarily, in order to control convergence speed, a step size function that is used in both global and local pollination along with the randomness factor is adopted. Finally, FPA is extended as a species-based algorithm by partitioning whole population into smaller-sized groups that independently search for promising regions. Performances of the proposed extensions are analyzed by using the well-known unconstrained function optimization problems and Morrison and De Jong’s field of cones function. Finally, non-parametric statistical tests are conducted to demonstrate possible significant improvements over standard FPA. As shown by these statistically verified results, the first FPA modification with the proposed selection mechanism and step size function achieves the best results in global optimization problems while the species-based FPA modification is found as a promising algorithm to solve multi-modal problems of De Jong’s field of cones function.

The optimized GRNN based on the FDS-FOA under the hesitant fuzzy environment and its application in air quality index prediction

The generalized regression neural network (GRNN) is one of the most effective neural models in the field of information prediction. In this paper, we take advantage of the hesitant fuzzy set (HFS) and develop the GRNN under the hesitant fuzzy environment. However, the performance of the GRNN only depends on the smooth factor after determining the input and output variables. To determine the most appropriate smooth factor of network, we propose an improved fruit fly optimization algorithm with fast decreasing step (FDS-FOA) based on a dynamic step size function. A specific implementation process of the optimized GRNN based on FDS-FOA is also presented. Moreover, we apply the proposed model to the prediction of air quality index (AQI) in Beijing. Comparative analysis and sensitivity analysis are further conducted to illustrate the advantages of the optimized GRNN based on FDS-FOA.

PV Model Parameter Estimation Using Modified FPA With Dynamic Switch Probability and Step Size Function

The development of highly efficient models of Photovoltaic (PV) cells and modules is essential for optimized performance, evaluation and control of solar PV systems. The accurate estimation of PV cells parameters is a challenging task because of their non-linear characteristics. In this paper, an improved variant of Flower Pollination Algorithm (FPA) is proposed for accurate estimation of PV cells and modules parameters. The proposed algorithm involves double exponential based dynamic switch probability and a dynamic step size function that mitigate the limitations of conventional FPA. The dynamic switch probability improves the overall performance of algorithm by maintaining a balance between local and global search, while dynamic step function controls the search speed which avoids premature convergence and local optima stagnation. Moreover, Newton Raphson Method is utilized for accurate computation of estimated current for optimum set of estimated parameters. The proposed methodology is evaluated using seven benchmark functions and three case studies; 1- RTC France silicon PV cell, 2- Photo-watt PWP-201 PV module and 3- a practical solar PV system (EAGLE PERC 60M 310W monocrystalline PV module) under different environmental conditions by estimating parameters for single and double diode models. The analysis of results indicates that, the proposed approach improves the convergence speed, precision, avoids premature convergence and stagnation in local optima of conventional FPA. Furthermore, comparative analysis of results illustrates that, the proposed approach is more reliable and efficient than many other techniques in literature.

A Variable Step Size for Maximum Correntropy Criterion Algorithm with Improved Variable Kernel Width

The maximum correntropy criterion (MCC) algorithm has popularly been used in suppressing impulsive noise. It mainly relies on the choice of step size and kernel width. With the study of step size, this paper proposes a novel algorithm that updates the step size based on constructing a variable step size function that uses the moving weighted average algorithm to keep performance stable and sigmoid function to speed the convergence rate. The proposed algorithm is robust against impulsive noises and generates a large step size to accelerate the convergence in iteration beginning, and system mutation makes the system identification performance more stable when the error is small. Based on the improved variable kernel width maximum entropy criterion (IVKW‐MCC) algorithm, which overcomes the shortcoming of how to choose a reliable kernel width in the MCC algorithm, simulation results are compared with other MCC algorithms under impulsive noise interference. Simulations in the system identification scenarios show that the proposed algorithm has better performance in improving the convergence speed over other algorithms. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A Novel CMA+DD_LMS Blind Equalization Algorithm for Underwater Acoustic Communication

Abstract The performance of underwater acoustic communication system is affected seriously by inter-symbol interference caused by multipath effects. Therefore, a novel blind equalization algorithm based on constant modulus algorithm (CMA) and decision-directed least mean square (DD_LMS) is adopted to improve the equalization ability of the system. Firstly, the LMS algorithm is improved by introducing inverse hyperbolic sine function and three adjustment factors to control step-size and the appropriate parameter values are set through the simulation of three adjustment factors. Secondly, the error values of the step-size function are replaced with error expectations to improve the anti-noise performance. Finally, the improved step-size function is introduced into the CMA and DD_LMS algorithm and the difference of the iteration error of adjacent k times is used as the switching condition of the dual mode algorithm. The results show that the algorithm has good equalization and anti-noise performance at both high and low signal-to-noise ratio (SNR), especially at low SNR, its steady-state error is ~10 dB lower than the traditional CMA and its convergence speed is ~15% higher than the traditional CMA. This algorithm can be used to effectively improve the communication efficiency of the communication system of underwater robots, which has good application value.

Derivative-Free Feasible Backtracking Search Methods for Nonlinear Multiobjective Optimization with Simple Boundary Constraint

In this paper, a derivative-free linear feasible direction models with backtracking search technique is considered for solving nonlinear multiobjective optimization problems subject to simple boundary constraint. The algorithm is designed to build linear interpolation models for each function of problem [Formula: see text]. We build the linear programming subproblem using linear interpolation function without the second-order derivative information. The new backtracking search step size function is given in our algorithm which guarantees both the monotone descent property of each function and the feasibility of the iterative point. Under reasonable assumptions, we prove that the algorithm converges to a weakly Pareto critical point of problem. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

Analysing the effects of various switching probability characteristics in flower pollination algorithm for solving unconstrained function minimization problems

Due to their unique offerings, bio-inspired algorithms have become popular in problem solving. Flower pollination algorithm (FPA), which is relatively a new member of this family, is shown to be one promising algorithm and this optimizer is still open to possible enhancements. One of the reasons that adds to the popularity of FPA is indeed the simplicity in implementation. It has two basic procedures, namely global and local pollination, which correspond to global and local search, respectively. Moreover, a single parameter, referred to as switching probability, puts control on these search procedures. Thus, the mentioned switching probability actually defines the search characteristics throughout generations, which directly affects the success of FPA. Accordingly, the present work analyses the effects of various switching probability characteristics, including exponentially, linearly and sawtooth changing patterns. This is the main motivation of the present study. Secondarily, a systematically intensifying step size procedure, which is commonly ignored by most of the stochastic search algorithms, is adopted along with these strategies. The aim of the proposed step size function is to encourage a more intensified search towards the end, while providing a more diversified search at the initialization stage to avoid local optima and premature convergence. Thus, more promising results might be obtained. All developed modifications are tested by using well-known unconstrained function minimization problems. As demonstrated by several nonparametric statistical tests, results point out significant improvements over the standard FPA.

A Simple Brain Storm Optimization Algorithm With a Periodic Quantum Learning Strategy

Brain storm optimization (BSO) is a young and promising population-based swarm intelligence algorithm inspired by the human process of brainstorming. The BSO algorithm has been successfully applied to both science and engineering issues. However, thus far, most BSO algorithms are prone to fall into local optima when solving complicated optimization problems. In addition, these algorithms adopt complicated clustering strategies, such as K-means clustering, resulting in large computational burdens. This paper proposes a simple BSO algorithm with a periodic quantum learning strategy (SBSO-PQLS), which includes three new strategies developed to improve the defects described above. First, we develop a simple individual clustering strategy that sorts individuals according to their fitness values and then allocates all individuals into different clusters. This reduces computational burdens and resists premature convergence. Second, we present a simple individual updating strategy by simplifying the individual combinations and improving the step size function to enrich the diversity of newly generated individuals and reduce redundancy in the pattern for generating individuals. Third, a quantum-behaved individual updating with periodic learning (QBIU-PL) strategy is developed by introducing a quantum-behaved mechanism into SBSO-PQLS. QBIU-PL provides new momentum, enabling individuals to escape local optima. With the support of these three strategies, SBSO-PQLS effectively improves its global search capability and computational burdens. SBSO-PQLS is compared with seven other BSO variants, particle swarm optimization, and differential evolution on CEC2013 benchmark functions. The results show that SBSO-PQLS achieves a better global search performance than do the other nine algorithms.

The effect of length scale on the determination of geometrically necessary dislocations via EBSD continuum dislocation microscopy

Electron backscatter diffraction (EBSD) dislocation microscopy is an important, emerging field in metals characterization. Currently, calculation of geometrically necessary dislocation (GND) density is problematic because it has been shown to depend on the step size of the EBSD scan used to investigate the sample. This paper models the change in calculated GND density as a function of step size statistically. The model provides selection criteria for EBSD step size as well as an estimate of the total dislocation content. Evaluation of a heterogeneously deformed tantalum specimen is used to asses the method.

Fast variable step-size maximum power point tracking method for photovoltaic systems

Maximum power point tracking (MPPT) is a key technology in high efficient Photovoltaic (PV) systems. Against the contradiction between the tracking speed and tracking accuracy of the MPPT in the PV systems, this paper presents a self-adaptive step-size MPPT method. First, PV modeling is built under different sunlight intensity and temperatures. Then, by discussing the due features of a self-adaptive step-size function, a new variable step-size function is built based on the logarithm form. Through modeling in Matlab/Simulink and experiment, both results show that the proposed method can improve the MPPT response in both tracking speed and accuracy steadily compared with other published results.

Variance and Covariance of Accumulated Displacement Estimates

Tracking large deformations in tissue using ultrasound can enable the reconstruction of nonlinear elastic parameters, but poses a challenge to displacement estimation algorithms. Such large deformations have to be broken up into steps, each of which contributes an estimation error to the final accumulated displacement map. The work reported here measured the error variance for single-step and accumulated displacement estimates using one-dimensional numerical simulations of ultrasound echo signals, subjected to tissue strain and electronic noise. The covariance between accumulation steps was also computed. These simulations show that errors due to electronic noise are negatively correlated between steps, and therefore accumulate slowly, whereas errors due to tissue deformation are positively correlated and accumulate quickly. For reasonably low electronic noise levels, the error variance in the accumulated displacement estimates is remarkably constant as a function of step size, but increases with the length of the tracking kernel.

Modified NLMF adaptation of Volterra filters used for nonlinear acoustic echo cancellation

When dealing with adaptive nonlinear filters used in acoustic echo cancellation, the tradeoff between convergence rate and steady-state error is an important issue. This tradeoff is favorably addressed here using a modified version of the normalized least-mean-fourth (NLMF) algorithm applied to an adaptive second-order Volterra structure. A convergence rate improvement is obtained at the same steady-state error by amending the step size of the conventional NLMF algorithm using a new step-size function that depends on the norm of an error vector of a certain length. The efficiency of the proposed method is compared with that of the conventional adapted second-order Volterra filter for nonlinear acoustic echo cancellation in terms of echo return loss enhancement (ERLE). From simulations conducted for input signals with different probability density functions, the new approach is shown to outperform the normalized least-mean-square (NLMS) second-order Volterra filter in terms of the convergence rate of the same steady-state error. The proposed technique was also tested in acoustic scenarios with impulse noise and separately with distinct local signal powers. The performance of the method was also compared to that of the traditional NLMF algorithm and of the variable NLMF (XE-NLMF) algorithm.

Application of EBSD technique to ultrafine grained and nanostructured materials processed by severe plastic deformation: Sample preparation, parameters optimization and analysis

With the help of FESEM, high resolution electron backscatter diffraction can investigate the grains/subgrains as small as a few tens of nanometers with a good angular resolution (∼0.5°). Fast development of EBSD speed (up to 1100 patterns per second) contributes that the number of published articles related to EBSD has been increasing sharply year by year. This paper reviews the sample preparation, parameters optimization and analysis of EBSD technique, emphasizing on the investigation of ultrafine grained and nanostructured materials processed by severe plastic deformation (SPD). Detailed and practical parameters of the electropolishing, silica polishing and ion milling have been summarized. It is shown that ion milling is a real universal and promising polishing method for EBSD preparation of almost all materials. There exists a maximum value of indexed points as a function of step size. The optimum step size depends on the magnification and the board resolution/electronic step size. Grains/subgrains and texture, and grain boundary structure are readily obtained by EBSD. Strain and stored energy may be analyzed by EBSD.

Error growth in the numerical integration of periodic orbits

This paper is concerned with the long term behaviour of the error generated by one step methods in the numerical integration of periodic flows. Assuming numerical methods where the global error possesses an asymptotic expansion and a periodic flow with the period depending smoothly on the starting point, some conditions that ensure an asymptotically linear growth of the error with the number of periods are given. A study of the error growth of first integrals is also carried out. The error behaviour of Runge–Kutta methods implemented with fixed or variable step size with a smooth step size function, with a projection technique on the invariants of the problem is considered.

Adaptive Stochastic Gradient Descent Optimisation for Image Registration

We present a stochastic gradient descent optimisation method for image registration with adaptive step size prediction. The method is based on the theoretical work by Plakhov and Cruz (J. Math. Sci. 120(1):964---973, 2004). Our main methodological contribution is the derivation of an image-driven mechanism to select proper values for the most important free parameters of the method. The selection mechanism employs general characteristics of the cost functions that commonly occur in intensity-based image registration. Also, the theoretical convergence conditions of the optimisation method are taken into account. The proposed adaptive stochastic gradient descent (ASGD) method is compared to a standard, non-adaptive Robbins-Monro (RM) algorithm. Both ASGD and RM employ a stochastic subsampling technique to accelerate the optimisation process. Registration experiments were performed on 3D CT and MR data of the head, lungs, and prostate, using various similarity measures and transformation models. The results indicate that ASGD is robust to these variations in the registration framework and is less sensitive to the settings of the user-defined parameters than RM. The main disadvantage of RM is the need for a predetermined step size function. The ASGD method provides a solution for that issue.

Toward a Unified Theory of Muscle Contraction. II: Predictions with the Mean-Field Approximation

The contractile behavior of a single half-sarcomere has been calculated from the lattice model with dimeric myosin and extensible filaments, using the model cycle with two working strokes, explicit Pi-release transitions and faster binding for the second head of the dimer. The mean-field approximation is used to generate independent state probabilities for myosin heads, assuming that the positional symmetry of actin filaments in the half-sarcomere is preserved. This model predicts absolute values of the active tension, stiffness and ATPase of fast fibers and their variation with shortening velocity, the phase-2 tension response to a length-release step and the transient tension rise during ramp stretching, in reasonable agreement with experimental data for frog muscle. It accounts for three observations beyond the reach of traditional models: (i) with elastically stiff myosin, a two-stroke model explains the rate of rapid tension recovery as a function of step size, (ii) slow Pi release from A.M.ADP.Pi after the first stroke generates the flat tension response observed after rapid recovery from a small release step, (iii) a discrete lattice model generates undamped oscillations in the isotonic length response to a force step, as observed when the sarcomeres are highly ordered. The discrete lattice also generates length-dependent oscillations in the tension-length curve and the tension response to ramp shortening, which may be smoothed out if lattice symmetry is broken.