Variable Step Size Research Articles

Monolithic and local time-stepping decoupled algorithms for transport problems in fractured porous media

Abstract The objective of this paper is to develop efficient numerical algorithms for the linear advection-diffusion equation in fractured porous media. A reduced fracture model is considered where the fractures are treated as interfaces between subdomains and the interactions between the fractures and the surrounding porous medium are taken into account. The model is discretized by a backward Euler upwind-mixed hybrid finite element method in which the flux variable represents both the advective and diffusive fluxes. The existence, uniqueness, as well as optimal error estimates in both space and time for the fully discrete coupled problem are established. Moreover, to facilitate different time steps in the fracture-interface and the subdomains, global-in-time, nonoverlapping domain decomposition is utilized to derive two implicit iterative solvers for the discrete problem. The first method is based on the time-dependent Steklov–Poincaré operator, while the second one employs the optimized Schwarz waveform relaxation (OSWR) approach with Ventcel-Robin transmission conditions. A discrete space-time interface system is formulated for each method and is solved iteratively with possibly variable time step sizes. The convergence of the OSWR-based method with conforming time grids is also proved. Finally, numerical results in two dimensions are presented to verify the optimal order of convergence of the monolithic solver and to illustrate the performance of the two decoupled schemes with local time-stepping on problems of high Péclet numbers.

A novel method for multiple targets localization based on normalized cross-correlation adaptive variable step-size dynamic template matching

The template matching method has been widely utilized in the defect detection of wafer surfaces. However, the traditional matching approaches are limited by illumination, noise, and deformation, which cannot meet the requirements of accuracy and robustness. In this paper, a novel multiple targets localization method, named Normalized Cross-correlation Adaptive Variable Step-Size Dynamic Template (NCC-AVSSDT) matching, is proposed to improve the accuracy and efficiency of image localization, which combines the advantages of NCC and AVSSDT. The AVSSDT method is utilized to dynamically adjust the scanning step size based on the NCC matching coefficients. This approach optimizes the scanning process, accelerating convergence toward the optimal matching position. Experimental results verify the accuracy and robustness of the proposed method under different conditions, especially when dealing with rotational variations and variations in noise textures. Therefore, NCC-AVSSDT can be used to perform multiple targets localization of chip image in nearly real-time. Three experiment types were used for comprehensive evaluations, including multiple targets, noise, and rotation angles. Experimental results show that NCC-AVSSDT is much better than the sequential similarity detection algorithm and mean absolute deviation methods in terms of multiple targets (0.667 vs 0.811 s, 0.832 s) and success rate (100% vs 35%, 20%).

Automatic lift path planning of prefabricated building components using semantic BIM, improved A* and GA

PurposePrefabricated building has been widely applied in the construction industry all over the world, which can significantly reduce labor consumption and improve construction efficiency compared with conventional approaches. During the construction of prefabricated buildings, the overall efficiency largely depends on the lifting sequence and path of each prefabricated component. To improve the efficiency and safety of the lifting process, this study proposes a framework for automatically optimizing the lifting path of prefabricated building components using building information modeling (BIM), improved 3D-A* and a physic-informed genetic algorithm (GA).Design/methodology/approachFirstly, the industry foundation class (IFC) schema for prefabricated buildings is established to enrich the semantic information of BIM. After extracting corresponding component attributes from BIM, the models of typical prefabricated components and their slings are simplified. Further, the slings and elements’ rotations are considered to build a safety bounding box. Secondly, an efficient 3D-A* is proposed for element path planning by integrating both safety factors and variable step size. Finally, an efficient GA is designed to obtain the optimal lifting sequence that satisfies physical constraints.FindingsThe proposed optimization framework is validated in a physics engine with a pilot project, which enables better understanding. The results show that the framework can intuitively and automatically generate the optimal lifting path for each type of prefabricated building component. Compared with traditional algorithms, the improved path planning algorithm significantly reduces the number of nodes computed by 91.48%, resulting in a notable decrease in search time by 75.68%.Originality/valueIn this study, a prefabricated component path planning framework based on the improved A* algorithm and GA is proposed for the first time. In addition, this study proposes a safety-bounding box that considers the effects of torsion and slinging of components during lifting. The semantic information of IFC for component lifting is enriched by taking into account lifting data such as binding positions, lifting methods, lifting angles and lifting offsets.

A new approach to MPPT hybrid incremental conductance-sliding mode control for PV grid-connected

As photovoltaic energy is clean, renewable, and less noisy, it is increasingly integrated into the grid. This integration aims to overcome energy deficits and get rid of pollution from conventional sources. In this paper, a two-stage configuration of PV energy conversion to a three-phase grid has been studied. The control of this configuration can be divided into two parts, such as DC bus control and AC bus control. The DC bus is controlled by MPPT control. The AC bus is controlled by DC link voltage control, phase-looked loop control, and voltage source inverter control. The contribution in this study aims to improve the quality of energy injected via a new hybrid approach to MPPT control. The proposed control is a combination of robust sliding-mode control and incremental inductance. Unlike conventional hybridization, the proposed control estimates correct the error upon entry of the conductance incremental control. This correction provides an adaptive incremental step for increment conductance control. The proposed control is compared with three other controls under MATLAB/Simulink. Such as incremental conductance, variable step size incremental conductance, and conventional hybrid MPPT incremental inductance-sliding mode control. The simulation results show a remarkable minimization of the ripple phenomenon and the chatter phenomenon. Thus, the quality of the energy injected into the network is improved, such as by reducing the total harmonic distortion of the current and increasing efficiency.

Experimental Study of Micro-hole Pecking Drilling in High Volume Fraction SiCp/Al7075 Composites with Variable Step Size

Experimental Study of Micro-hole Pecking Drilling in High Volume Fraction SiCp/Al7075 Composites with Variable Step Size

Robust Variable Step Size Widely Linear Complex-Valued Least Mean M-estimate Adaptive Algorithm: Derivation and Performance Analysis

Robust Variable Step Size Widely Linear Complex-Valued Least Mean M-estimate Adaptive Algorithm: Derivation and Performance Analysis

A nonmonotone accelerated proximal gradient method with variable stepsize strategy for nonsmooth and nonconvex minimization problems

A nonmonotone accelerated proximal gradient method with variable stepsize strategy for nonsmooth and nonconvex minimization problems

A “step” in the right direction: Quantifying error in twinning analysis due to EBSD scan resolution

Accurate evaluation of deformation twinning statistics is key when performing research on the twinning behavior of magnesium alloys or other HCP materials, and typically utilizes electron backscatter diffraction (EBSD). However, many modern studies that perform EBSD for twinning analysis do not have a consistent step size used during EBSD data collection between studies, or do not report their step size at all. In this work, the effect of step size on the resultant twinning statistics calculated from the EBSD data was determined by comparing multiple scans of the same region with varying step size. Increasing the step size during data collection was found to increase the error of all considered twinning statistics, indicating a potential source of unquantified error in other studies. Additionally, a method for improving the accuracy from scans with coarse step sizes was considered and found to reduce error in most cases.

An efficient two-grid high-order compact difference scheme with variable-step BDF2 method for the semilinear parabolic equation

Due to the lack of corresponding analysis on appropriate mapping operator between two grids, high-order two-grid difference algorithms are rarely studied. In this paper, we firstly discuss the boundedness of a local bi-cubic Lagrange interpolation operator. And then, taking the semilinear parabolic equation as an example, we first construct a variable-step high-order nonlinear difference algorithm using compact difference technique in space and the second-order backward differentiation formula with variable temporal stepsize in time. With the help of discrete orthogonal convolution kernels, temporal-spatial error splitting idea and a cut-off numerical technique, the unique solvability, maximum-norm stability and corresponding error estimate of the high-order nonlinear difference scheme are established under assumption that the temporal stepsize ratio satisfies rk := τk/τk−1 < 4.8645. Then, an efficient two-grid high-order difference algorithm is developed by combining a small-scale variable-step high-order nonlinear difference algorithm on the coarse grid and a large-scale variable-step high-order linearized difference algorithm on the fine grid, in which the constructed piecewise bi-cubic Lagrange interpolation mapping operator is adopted to project the coarse-grid solution to the fine grid. Under the same temporal stepsize ratio restriction rk < 4.8645 on the variable temporal stepsize, unconditional and optimal fourth-order in space and second-order in time maximum-norm error estimates of the two-grid difference scheme is established. Finally, several numerical experiments are carried out to demonstrate the effectiveness and efficiency of the proposed scheme.

A New Chaos-Based Image Encryption Algorithm Based on Discrete Fourier Transform and Improved Joseph Traversal

To further enhance the security of image encryption, a new chaos-based image encryption algorithm (IEA) based on discrete Fourier transform and Joseph traversal is proposed to encrypt the plain image in both the frequency domain and space domain simultaneously. In the proposed IEA, the logistic map is used to generate the appropriate chaotic sequence, and the improved Joseph traversal is used to scramble the image in different starting positions and variable step sizes. Then, block diffusion is performed at the end. The main finding concerning the proposed IEA is that the combination of discrete Fourier transform and Joseph traversal can enhance the security of the image information, which has been validated by measuring the performance in resisting the common types of attacks.

Improved artificial potential field method for mobile robot path planning

Path planning has already been used in areas like robots and unmanned vehicles to prevent collisions in certain environments. A Path planning algorithm is needed to achieve such tasks and Artificial Potential Field (APF) method is one of the methods. However, APF has limitations facing various situations like being stuck in a local minimum such as a dead-end or a narrow path. To solve the problem, First, a side force is added to the algorithm along with two types of definitions of the force direction. Then a variable is proposed to prevent the dead-end situation. Finally, the variable step size is used to improve the efficiency of the algorithm. The simulation results demonstrate the effectiveness of the method. In comparison to APF, the improved APF could prevent the local minimum and reach the target position with fewer processing steps and better performance.

Estimating the potential maximum power point based on the calculation of short‐circuit current and open‐circuit voltage

AbstractThis paper presents a technique to quickly determine the potential maximum power point (MPP) of a photovoltaic system using the duty cycle (D) of the DC/DC converter. The proposed method depends on estimating the open‐circuit voltage (Voc) and short‐circuit current (Isc) values under different operating conditions. It is an adapted version derived from the conventional Perturb and Observe (P&O) algorithm, designed to restrict the search area for the MPP. The working conditions, including temperature variations, irradiance, or both, are simulated in the PSIM environment and experimented with a simulator with parameters satisfied according to the proposed operating conditions. The research objective of this study also involves operating under partially shaded conditions. When comparing the results of this research with those obtained from the traditional P&O method and the Variable Step Size Perturb and Observe (VSSP&O) approach, it becomes evident that the proposed solution excels in terms of both convergence speed and performance, particularly when operating under partial shade conditions. In addition, this study's methods of determining Isc, Voc, and Dmp can be widely applied in low‐voltage and power systems.

On the correlation between the noise and a priori error vectors for standard and augmented affine projection algorithms

This paper analyzes the correlation matrix between the a priori error and measurement noise vectors for standard and augmented affine projection algorithms using a unified approach. This correlation stems from the dependence between the filter tap estimates and the noise samples, and has a strong influence on the mean square behavior of the algorithm. We show that the correlation matrix is upper triangular, and compute the diagonal elements in closed form, showing that they are independent of the input process statistics. Also, for white inputs we show that the matrix is fully diagonal. These results are valid in the transient and steady states, considering a possibly variable step-size. Our only assumption is that the filter order is large compared to its projection order and that the input signal is stationary. Using these results, we perform a steady-state analysis for small step size and provide a new simple closed-form expression for the mean-square error, which has comparable or better accuracy to many preexisting expressions, and is much simpler to compute. Finally, we also obtain expressions for the steady-state energy of the other components of the error vector.

Variable step size VLF/ELF nonlinear channel adaptive filtering algorithm based on Sigmoid function

The signals received by very low-frequency/extremely low-frequency nonlinear receivers are frequently affected by intense atmospheric pulse noise stemming from thunderstorms and global lightning activity. Current noise processing algorithms designed for nonlinear channels within these frequency ranges, which are predicated on fractional p-order moment alpha stable distribution criteria (where 0 < p < α < 2, and p and α denote distinct characteristic indices of alpha stable distribution noise), are constrained by their reliance on limited p-order moment statistics. As a result, the performance of low-frequency nonlinear channel receivers experiences significant degradation when confronted with robust pulse noise interference (0 < p < α < 2). To tackle this challenge, the present study introduces a novel variable step robust mixed norm (RMN) adaptive filtering algorithm, designated as SVS-RMN, which is based on the Sigmoid function. Leveraging the nonlinearity of the Sigmoid function and building upon the power function Hammerstein nonlinear channel model, the algorithm aims to enhance the RMN algorithm by deriving new cost functions and adaptive iteration formulas. The performance of the proposed algorithm is evaluated in comparison to conventional RMN algorithms based on fractional low-order moment (FLOM) criteria (0 < p < 2), as well as other algorithms employing variable step sizes and either FLOM or radial basis function (RBF) criteria, across various intensities of pulse noise and mixed signal-to-noise ratios. The experimental results reveal the following: (1) The proposed algorithm effectively mitigates strong pulse noise interference and significantly enhances the tracking performance of the RMN algorithm compared to conventional RMN algorithms based on FLOM criteria. (2) In terms of computational efficiency, simplicity of structure, convergence speed, and stability, the proposed algorithm surpasses other algorithms based on FLOM or RBF criteria.

Maximum Power Point Tracker Optimization for Photovoltaic Systems based on III-V Elements

A photovoltaic system consists of several components that are interconnected into a grid network or standalone system. The overall efficiency of a photovoltaic system is the result of component selection, accurate implementation, and stable operation. Therefore, if these factors are not in harmony during the design and execution of the system, optimal efficiency will not be achieved. This paper summarizes the technological trend of photovoltaic cells which lead to the development of multijunction photovoltaic cells based on III-V elements. Additionally, the challenges within the implementation of multijunction cells based on III-V elements into terrestrial applications will also be discussed, followed by a potential solution to counter the efficiency loss of these cells caused by the atmospheric gases filtering the solar irradiance across the optical band length of absorption. The implementation of Adaptive-Perturbation-Frequency (APF) in a Perturb and Observe (P&amp;O) algorithm, instead of a linear step size variation, combined with several hardware optimizations on the Maximum Power Point Tracker (MPPT), maybe an ideal approach to reduce the impacts of having a multijunction photovoltaic cell based on elements III-V operating at terrestrial conditions.

Oblique impact dynamic analysis of wedge friction damper with Dankowicz dynamic friction

&lt;abstract&gt; &lt;p&gt;Aiming at the wedge friction damper for freight train bogie, considering Dankowicz dynamic friction, the mechanical model of a three-degree-of-freedom inclined impact vibration system with gap and dynamic friction, is simplified. The mechanical model of the system is established, the motion equation of the system is obtained, and the motion state and conditions of the system are analyzed. The Poincare map is constructed by selecting a fixed collision section, and the response of the system is solved by the fourth-order Runge-Kutta numerical method with variable step size. The transition process of the system motion and the phenomenon of sticking and chatter are analyzed by numerical simulation when the external excitation frequency changes. The results show that: 1) Under certain parameters, with the change of excitation frequency, the system undergoes periodic doubling bifurcation, inverse periodic doubling bifurcation, Grazing bifurcation and Hopf bifurcation, and there is a "periodic bubble" phenomenon in the system motion. When the system excitation frequency is between 3.35–3.55, 4.425–6.12, and 7.34–7.758, the system motion has chatter and sticking phenomena; when the system excitation frequency is between 1.75–3.24 and 3.92–4.425, the sticking phenomenon disappears, and only the chatter phenomenon exists. 2) When other parameters remain unchanged, and the mass ratio decreases from 1.15 to 0.85, nonlinear dynamic phenomena such as the transition between periodic bubbles and chaotic bubbles will be found. In this paper, the bifurcation and chaos characteristics of the impact vibration system of the wedge friction damper are studied, and the rich friction-induced vibration forms such as chatter and sticking are revealed, which provides a reference for improving the stability of vehicle operation and the selection of parameters in vehicle vibration reduction design in engineering practice.&lt;/p&gt; &lt;/abstract&gt;

Analysis of Gradient Descent with Varying Step Sizes using Integral Quadratic Constraints

Analysis of Gradient Descent with Varying Step Sizes using Integral Quadratic Constraints

A Novel Adaptive ANC Algorithm for Removal of Background Noise in Speech Applications

Noise is an unsafe mechanical toxin that causes serious hearing misfortune in the working environment of every nation. The working people in the military, mining, development, printing, and saw factories tend to lose their hearing performance due to the adverse effects of noise generated by the machines. They undergo elevated levels of noise, with various machinery producing greater levels of noise measured in decibels. These sounds may cause major health problems that may not allow the person to work in such conditions. Algorithms like Least Mean Square (LMS), Normalized Least Mean Squared (NLMS), Filtered-x Least Mean Squared (FxLMS) and Filtered-x Normalized Least Mean Squared (FxNLMS) are frequently being used for noise cancellation. Moreover, these filters have instability and poor noise reduction; slow convergence also requires a greater number of filter taps and less performance to identify the unknown system in the Active Noise Canceller (ANC). In this paper, a Précised FxNLMS (P-FxNLMS) algorithm is introduced for an ANC. This algorithm consists of dual adaptive filters, an updated Variable Step Size (VSS), a delay in the primary path, a slight improvement in the on-line secondary path, and a modified filter step size when compared to an existing ANC system, with the purpose of minimizing the demerits of existing algorithms. Initially, the P-FxNLMS algorithm was tested with Additive White Gaussian Noise (AWGN) and later tested with real noises from the NOISEUS dataset to check the noise reduction performance. The increase in Signal to Noise Ratio (SNR) segmentation for P-FxNLMS is around 1.45 dB to 4.07 dB and 38.46 % to 73.68 % of the Mean Square Error (MSE) as compared to the algorithms available for different sounds with different SNR input levels. From the performance results of MSE and SNR improvement (SNRi), we found improvements compared with existing algorithms

Weak pulse signal detection method based on improved strongly coupled oscillators

A strongly coupled oscillator can be used to detect weak pulse signals and recover waveforms, but its detection frequency of weak pulse signal is limited by the system’s built-in frequency. With a fixed built-in frequency, the system can only effectively detect and recover pulse signals in a certain frequency range, and waveform distortion occurs when pulse signals of higher frequencies are detected. In this work, the relationship between the built-in frequency of the coupled oscillator and the frequency detection range of weak pulse signal is analyzed, and two kinds of improved strongly coupled oscillator structures are proposed to extend the frequency detection range of weak pulse signals. By introducing the nonlinear restoring force coupling term, the nonlinear restoring force strongly coupled oscillator can effectively retain the high-frequency component of the signal, and can also better retain the signal characteristics when the pulse signal is input at a higher frequency. By introducing the Van der Pol-Duffing oscillator, the two-oscillator strong coupling system strengthens the stability of the internal structure of the system, and also achieves the effect of expanding the frequency detection range of the pulse signal. In addition, based on the variable iteration step size and frequency correlation of chaos detection, a method of detecting unknown frequency pulse signals is proposed. Instead of changing the built-in frequency of the system for frequency scanning, the method of changing the iteration step size is used. And using the frequency correlation of chaos detection, the correlation coefficient of the received signal and the recovered signal is compared with the correlation coefficient of the pure noise input case, then the pulse signals can be effectively detected based on the apparent difference between the two correlation coefficients. It is verified by simulation experiments that the proposed method can effectively detect the pulse signal of unknown frequency, and the proposed improved strong coupling oscillator has a greater performance improvement than that of the strong coupling oscillator.

GAO-RRT*: A path planning algorithm for mobile robot with low path cost and fast convergence

&lt;abstract&gt;&lt;p&gt;Path planning is an essential research topic in the navigation of mobile robots. Currently, rapidly-exploring random tree star (RRT*) and its variants are known for their probabilistic completeness and asymptotic optimality, making them effective in finding solutions for many path planning problems. However, slow convergence rate of the RRT* limits its practical efficiency. To address this problem, this paper proposed an enhanced RRT* algorithm by refining the extension process of the exploring tree. This enhancement aims to guide the tree approaching to obstacles (GAO) while exploring toward the target point. First, GAO-RRT* employed a dual-weighted sample strategy instead of random sample to guide search direction of the exploring tree. Second, a variable step size extension strategy was adopted to increase the efficiency of node generation, balancing searching time and path safety in regions with different obstacles densities. Third, growth status of new nodes was monitored in real-time, and a reverse growth strategy was proposed to guide the exploring tree to escape local optima. In addition, parent node creation procedure for new nodes was used to produce a better initial path. Finally, the proposed GAO-RRT* was compared with three state of the art algorithms on 16 different instances of four representative environments. Compared to RRT*, Quick-RRT* (Q-RRT*), and Fast-RRT* (F-RRT*), the results showed that (1) the average path cost of initial solutions obtained by GAO-RRT* decreased by 38.32%, 29.69%, and 20.44%, respectively; and (2) the average convergence time of solution obtained by GAO-RRT* to suboptimal (1.05*$ C_{best} $) was reduced by 71.22%, 69.69%, and 58.37%, respectively. Simulation results indicated that GAO-RRT* outperforms the compared algorithms in terms of path cost and convergence speed.&lt;/p&gt;&lt;/abstract&gt;