Variable Step Size Research Articles

High-order methods for the simulation of unsteady counterflow flames subject to stochastic forcing of large amplitude

Unsteady counterflows are employed to understand and model the effect of turbulence on flames. We present a novel numerical approach for the simulation of one-dimensional unsteady counterflow flames with fourth order spatial discretization and up to fourth order time discretization. The approach couples a three-stage Lobatto IIIa formula for boundary value problems and variable-order, variable time step size Backward Differentiation Formulas for time integration. The framework is explained in detail, its computational performance is analysed, and its use is demonstrated for the case of stochastic forcing of premixed counterflow flames, whereby the imposed rate of strain is a multi-scale lognormal discrete random process with exponential autocorrelation. High-order spatial and temporal discretization make the approach well-suited for the accurate and computationally efficient simulation of the effect of turbulence on flames, which are characterised by large amplitude stochastic fluctuations of the local rate of strain.

Intelligent RBF-Fuzzy Controller Based Non-Isolated DC-DC Multi-Port Converter for Renewable Energy Applications

In this article, a multi-port non-isolated converter is implemented for renewable energy applications. High voltage gain is accomplished with a switched capacitor and coupled inductor, and power transfer between the inputs, battery, and load can be realized using three power switches. The power collected in the leakage inductance is reused to decrease the voltage stress on the power switch. Various functioning periods are also examined, and design requirements are offered. The proposed converter uses fewer parts to realize power flows and obtain high voltage gain compared to comparable converters. Additionally, under partial shading conditions, the traditional maximum power point tracking (MPPT) approaches are not able to collect the global maximum power point (MPP) from the numerous local MPPs. This work proposes an artificial neural-network-based MPPT technique with variable step size for tracing speed, MPP oscillations, and operating efficiency. The proposed converter experiment is also constructed and successfully tested in a laboratory environment.

Combined boosted variable step-size affine projection sign algorithm for environments with impulsive noise

The affine projection sign algorithm (APSA) is widely used to alleviate the impact of impulsive noise on weight updates for adaptive filters. When using the conventional APSA, the sign-based approach tends to degrade the rate of convergence; however, this can be remedied by adopting a variable step-size (VSS). Nonetheless, the tracking performance of the APSA tends to be poor in situations that involve identifying rapid changes in the system model. Inspired by the boosted adaptive filtering framework, we propose using multiple component filters (weak learners) to calculate the local boosted VSS. Specifically, this involves combining the boosted VSSs of the first and last stages of the component filters. In simulations, the proposed combined boosted VSS (CBVSS) method was shown to outperform comparable works in terms of convergence rate, even in situations where the unknown system model changes abruptly.

A versatile dynamic noise control framework based on computer simulation and modeling

Abstract This article attempts to effectively reduce the impact of active noise pollution on human life, and to make up for the traditional passive noise control technique. In low-frequency noise control, there are some shortcomings. The making of active noise control (ANC) technique, in low-frequency noise reduction, can achieve very good results. This article proposes a versatile dynamic noise control framework based on computer simulation and modeling. The research is mainly focused on the principle and application of versatile dynamic noise control framework. To accomplish this, a research method combining theoretical analysis, software simulation, and hardware realization is adopted. The derivation process of the adaptive algorithm (LMS algorithm, filter-XLMS algorithm, etc.) is introduced in detail, and the influencing factors of algorithm performance, a variable step size normalization algorithm based on relative error is proposed. Perform simulation calculations on various algorithms in MATLAB, analyze parameters such as step factor, filter order, etc., and the degree of influence on the algorithm’s convergence speed and steady-state performance. Common command set software is used, the path adaptive identification is realized, and the program design of the versatile dynamic noise control framework is used. After completion of software and hardware debugging on the experimental platform of generalized comfort, the experimental equipment layout is completed. Using the additive random noise method, the adaptive offline modeling of the first path of the versatile dynamic noise control framework is realized. Finally, utilizing the experimental platform of generalized comfort, the adaptive ANC experiment of the single-channel filtered least mean square algorithm is conducted, then the experimental data are analyzed, and at last, the actual application effect of the versatile dynamic noise control framework is verified.

Robust DOA Estimation Using VSS-LMS With Low-Rank Matrix Approximation

Direction-of-arrival (DOA) estimation performance of adaptive filtering-based methods, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> , least mean square (LMS), degrades significantly in adverse conditions ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.,</i> at low signal-to-noise ratio (SNR), small number of antenna array elements and snapshots, and in presence of two closely spaced signal sources). Moreover, these estimation methods require many regulating parameters to efficiently update the step size, which are very difficult to tune manually in practical scenarios. Although the subspace decomposition-based methods, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g</i> ., multiple signal classification (MUSIC), provide somewhat better performance in adverse conditions, they are based on the statistical properties of the signal such as spatial covariance matrix (SCM) and its eigenvalue decomposition (EVD), resulting in high computational complexity. In this paper, a robust DOA estimation method is proposed based on a variable step size LMS algorithm with low rank matrix approximation (LRMA), where the received signal de-noising problem is formulated first as a LRMA problem directly using the received signal observations instead of the SCM, and then the variable step size is calculated from the predicted instantaneous error and the estimated powers of reference and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de-noised</i> signals. The output spatial spectrum is determined by the reciprocal of the antenna array pattern, and the high peaks in the output spatial spectrum give the received signals estimated directions. The proposed method updates the step size efficiently without choosing any regulating parameter, and achieves improved performance even in adverse conditions due to the de-noising feature of LRMA with low computational complexity. Further, we also conduct the convergence and stability analyses of the proposed iterative estimation method with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de-noised</i> signal. Numerical results demonstrate that the proposed method outperforms state-of-the-art methods especially those, which yielded based on adaptive filtering.

Photovoltaic MPPT Control Strategy Based on Improved Conductance Increment Method

In this research, a new incremental conductance approach with variable step size is suggested in order to address the inadequacies of the conventional incremental conductance method in tracking accuracy and dynamic reaction speed. In this paper, an absolute value of dP / (dV – dI) is used as the change in step size, and the step size of the tracking process is dynamically adjusted using the exponential function as the adjustment coefficient to reduce the maximum power point’s tracking duration. Finally, on the Matlab platform, a simulation system was created. According to the simulation findings, the suggested approach has less steady-state oscillations and can track the maximum power point more quickly than the conventional conductance increment method, which increases the efficiency of solar power generation.

A P&amp;O Based Variable Step Size MPPT Algorithm for Photovoltaic Applications

Maximum power point tracking (MPPT) is an indispensable component of the Photovoltaic (PV) systems to maximize efficiency. Perturb and observe (P&amp;amp;O) is one of the prevalent MPPT methods owing to its easier structure for implementation but it suffers from problems of slow tracking and oscillations around the MPP. In this paper, a modified variable step size MPPT algorithm based on P&amp;amp;O method is proposed to obtain maximum power output from the PV system coupled with a boost DC-DC converter. The proposed method employs the scaled power difference as a control variable to enable variation of step size for each cycle. Results obtained by simulation and experimental work verified that the proposed algorithm is potent mitigating the problems related with classical P&amp;amp;O method.

A Path Planning Method with a Bidirectional Potential Field Probabilistic Step Size RRT for a Dual Manipulator

The search efficiency of a rapidly exploring random tree (RRT) can be improved by introducing a high-probability goal bias strategy. In the case of multiple complex obstacles, the high-probability goal bias strategy with a fixed step size will fall into a local optimum, which reduces search efficiency. Herein, a bidirectional potential field probabilistic step size rapidly exploring random tree (BPFPS-RRT) was proposed for the path planning of a dual manipulator by introducing a search strategy of a step size with a target angle and random value. The artificial potential field method was introduced, combining the search features with the bidirectional goal bias and the concept of greedy path optimization. According to simulations, taking the main manipulator as an example, compared with goal bias RRT, variable step size RRT, and goal bias bidirectional RRT, the proposed algorithm reduces the search time by 23.53%, 15.45%, and 43.78% and decreases the path length by 19.35%, 18.83%, and 21.38%, respectively. Moreover, taking the slave manipulator as another example, the proposed algorithm reduces the search time by 6.71%, 1.49%, and 46.88% and decreases the path length by 19.88%, 19.39%, and 20.83%, respectively. The proposed algorithm can be adopted to effectively achieve path planning for the dual manipulator.

Variable Step Size Methods of the Hybrid Affine Projection Adaptive Filtering Algorithm under Symmetrical Non-Gaussian Noise

The idea of variable step-size was introduced into the Hybrid Affine Projection Algorithm (H-APA) and we propose two variable step size algorithms based on H-APA, which are called the Variable Step-Size Hybrid Affine Projection Algorithm (VSS-H-APA) and the Modified Variable Step-Size Hybrid Affine Projection Algorithm (MVSS-H-APA). These are two variable-step algorithms aim to further improve the robust performance and convergence speed of H-APA under non-Gaussian noise. This allows for faster convergence while maintaining stability. The MVSS-H-APA goes further than VSS-H-APA to estimate the noise in order to achieve better convergence performance. The proposed algorithm performs better than the existing algorithms in system identification under symmetric non-Gaussian noise.

Adaptive Image Enhancement Algorithm Based on Variable Step Fruit Fly Optimization Algorithm and Nonlinear Beta Transform.

Due to the traditional use of manual methods for the parameter adjustment of a nonlinear beta transform, which is inefficient and unstable, an adaptive image enhancement algorithm based on a variable step size fruit fly optimization algorithm and a nonlinear beta transform is proposed. Utilizing the intelligent optimization characteristics of the fruit fly algorithm, we automatically optimize the adjustment parameters of a nonlinear beta transform to achieve better image enhancement effects. Firstly, the dynamic step size mechanism is introduced into the fruit fly optimization algorithm (FOA) to obtain a variable step size fruit fly optimization algorithm (VFOA). Then, with the adjustment parameters of the nonlinear beta transform as the optimization object, and the gray variance of the image as the fitness function, an adaptive image enhancement algorithm (VFOA-Beta) is obtained by combining the improved fruit fly optimization algorithm with the nonlinear beta function. Finally, nine sets of photos were used to test the VFOA-Beta algorithm, while seven other algorithms were used for comparative experiments. The test results show that the VFOA-Beta algorithm can significantly enhance images and achieve better visual effects, which has a certain practical application value.

A Family of Nested General Linear Methods for Solving Ordinary Differential Equations

General linear methods (GLMs) was introduced as a generalization of Runge{Kutta methods (RKMs) and linear multistep methods (LMMs). The discovery of general linear method gave insight into the discovery of new methods that are neither RKMs or LMMs. Here, new classes of GLMs that are nested in their stages and mono-implicit in the output are presented, these methods are referred to as nested general linear methods (NGLMs). Procedures for deriving members that are algebraically stable are discussed herein and algebraically stable NGLMs have been derived up to order p = 5. Implementation procedure of these nested general linear methods which include the solution of non-linear systems of equations by simplified Newton iterations and step size changing strategy are discussed. The order p = 3 NGLM has been implemented on two test problems by variable step size, and the results compared with the results of MATLAB ode15s and RADAU IIA.

A variable step size robust normalized least mean absolute third‐based control scheme for a grid‐tied multifunctional photovoltaic system

SummaryThis paper develops a variable step size robust normalized least mean absolute third (VSSRNLMAT)‐based control scheme for a three‐phase grid‐tied multifunctional photovoltaic system (GTMPVS). The GTMPVS delivers PV power to grid‐connected loads and feeds excess power to the grid through a voltage source converter (VSC) when PV power is available. It enhances power quality (PQ) by mitigating current harmonics and compensating for an unbalanced load and reactive power simultaneously. The proposed control scheme accurately extracts the fundamental active and reactive weight components of nonlinear load current. The power exchange at the grid side occurs with balanced and sinusoidal grid currents. During the absence of PV power, the VSC continues its operation as a distribution static compensator (DSTATCOM), thus increasing the effective utilization of the power electronic switches employed in the VSC. The GTMPVS model is created in MATLAB/Simulink. The response of GTMPVS is observed under steady‐state and dynamic operating conditions while feeding power to a nonlinear load. The dynamic operating conditions are created by a change in solar irradiation and an unbalanced nonlinear load. Further, the proposed VSSRNLMAT control scheme is compared with some of the other adaptive filtering‐based control schemes, including least mean square (LMS), least mean fourth (LMF), least mean absolute third (LMAT), and normalized LMAT (NLMAT) in terms of convergence, oscillations, mean square deviation (MSD), computational complexity, and grid current total harmonic distortion (THD). It is found that the VSSRNLMAT control scheme offers THD of grid current as per IEEE‐519 standard. The proposed control scheme is implemented to operate the laboratory‐developed GTMPVS to verify the simulation results.

Flow-Induced Vibration Hybrid Modeling Method and Dynamic Characteristics of U-Section Rubber Outer Windshield System of High-Speed Trains

The flow-induced vibration characteristic of the U-section rubber outer windshield structure of high-speed train is the key factor to limit its high-speed movement. Accurate and effective flow-induced vibration analysis of windshield structures is an important topic. In this paper, a hybrid modeling method for the analysis of flow-induced vibration of windshield structure is innovatively proposed for the U-section rubber windshield system of high-speed train. The method uses the external aerodynamic load obtained by aerodynamic simulation as the input condition of the flow-induced vibration model, and maps the aerodynamic load to the structural dynamics model characterized by the modal test data of the windshield structure. The flow-induced vibration model is established by means of modal superposition method and the time-domain response is effectively integrated by Runge Kutta method with variable step size. The results show that this method can effectively simulate the flow induced vibration of the wind baffle structure, and the real-time relationship between the aerodynamic load and the modal characteristics of the structure and the response of displacement and velocity can be obtained. On this basis, the comprehensive dynamic performance of the windshield system of high-speed trains at 400 km/h under external aerodynamic load is studied, that is, the force, displacement and velocity variation rules of the flexible structure are examined. It is determined that the displacement and velocity response curve of the measuring point near the lower side of the U-section rubber outer windshield is significantly higher than that of other parts. Moreover, the contribution of the first mode to the dynamic response of the structure is very obvious. This method provides an efficient calculation method for analyzing the flow-induced vibration characteristics of complex flexible structures.

Design and experimental validation of an efficient control based on variable step size P&amp;O MPPT technique and predictive current controller for a single-phase grid-connected photovoltaic system

Design and experimental validation of an efficient control based on variable step size P&amp;O MPPT technique and predictive current controller for a single-phase grid-connected photovoltaic system

Design and Research of Thermoelectric Generator Simulation System for Boiler Flue Gas Waste Heat

One of the significant factors contributing to high energy consumption is the unutilized waste heat from flue gas in industrial boilers. Thermoelectric generator (TEG) technology can directly convert thermal energy into electrical energy, and has been gradually applied in the field of waste heat recovery due to its simple and reliable structure, environmental protection, and other advantages. In this paper, a thermoelectric generator simulation system of boiler flue gas waste heat is proposed. The experimental platform is designed by simulating the flue gas waste heat temperature condition of boiler, and the structure of cold end module and hot end module is optimized. During the experiment, the fixed temperature difference was set at 120 °C (hot end:150 °C~cold end: 30 °C). An analysis is conducted on the volt-ampere characteristics and output power of the TEG module. The output characteristics of the TEG system are analyzed under the conditions of variable load, constant load, different pump speed, different heat dissipation modes, and series and parallel connection method. The results show that the experimental platform can instantaneously and accurately test the output parameters of the TEG system, and ensure the intended design requirements. When the ratio of the load resistance to the internal resistance of the TEG module is approximately 1–1.15, the output power of the system reaches its maximum. In order to optimize the output power of the TEG system, a power prediction-based adaptive variable step size maximum power point tracking (MPPT) algorithm is introduced. Additionally, a corresponding mathematical model is formulated. Simulations demonstrate that the time of the improved algorithm to reach the stable maximum power point is 1.54 s faster than that of the traditional algorithm. The improved MPPT algorithm satisfies the criteria for speed and accuracy, diminishes superfluous energy waste, and enhances the overall system efficiency. The research results have certain guiding significance for the design and application of subsequent TEG system.

Improved climbing algorithm with variable step size in tidal energy Application of maximum power tracking control technique for power generation system

In the context of carbon neutral carbon peak, in order to cope with climate change caused by environmental pollution and energy shortage caused by excessive use of fossil energy, the vigorous development of clean, low-carbon, and efficient renewable energy has become a major strategic direction. The development and utilization of tidal energy in China is still a certain gap with the European powerhouse, the efficiency of tidal energy generation at a low flow rate is low and the scale of development and utilization is small. The feasibility of the proposed strategy is verified by simulation analysis, and the results show that the improved variable step climbing algorithm can quickly track the maximum power point and operate stably at this point.

Analysis of a Filtered Time-Stepping Finite Element Method for Natural Convection Problems

In this paper, we present, analyze, and test a novel low-complexity time-stepping finite element method for natural convection problems utilizing a time filter (TF). First, via a TF to postprocess the solutions of backward Euler (BE) schemes, we make a minimally intrusive modification to the existing codes to improve the time accuracy by one order. This also provides, at no extra complexity, an estimate of the temporal error,which is easy to construct a novel adaptive algorithm. Additionally, the TF can remove the overdamping of the BE scheme while remaining unconditionally energy stable. Hence, this paper addresses the question, how can one improve the time accuracy without increasing computational and cognitive complexity? Then long time stability and error estimates of BE plus time filter (BETF) with constant time stepsize are proved. Moreover, we construct adaptive algorithms by extending the approach to variable time stepsize, and we extend the methods to higher order algorithms. Finally, numerical tests confirm the convergence rates of our method and validate the theoretical results.

Optimizing Multi-Layer Perceptron using Variable Step Size Firefly Optimization Algorithm for Diabetes Data Classification

According to a survey conducted by the International Diabetes Federation, the proportion of people living with diabetes is gradually rising. Diabetes mellitus is a chronic disorder caused by elevated blood sugar levels. For the early diagnosis and treatment of diabetes patients, efficient machine-learning methods are needed. Data Classification is a significant subject in many areas of life, and it is also a very challenging job in data mining. Clinical data mining has recently gained attention in complicated healthcare challenges relying on healthcare datasets. The principal objective of classification is to classify all data in a given dataset to a certain class label. In the healthcare field, classification is commonly employed in much research articles. A hybrid method for diabetes data classification is suggested by integrating multilayer perceptron with a modified firefly optimization algorithm for diabetes data classification. The performance of the proposed hybrid multilayer perceptron variable step size firefly algorithm is compared with other hybrid models such as the hybrid multilayer perceptron particle swarm optimization algorithm, hybrid multilayer perceptron differential evolution algorithm, and hybrid multilayer perceptron firefly optimization algorithm. The performance of these models is calculated based on accuracy, precision, recall, F1 score, and mean square error. In comparison to other models, the proposed hybrid model produces superior outcomes for diabetes data classification.

Control Study for Compensating Rotor Vibration of Four-DOF Six-Pole Hybrid Magnetic Bearings Based on Variable Step Size LMS Algorithm

In order to solve the problem that the unbalance vibration caused by rotor mass eccentricity of the four-degree-of-freedom (four-DOF) six-pole hybrid magnetic bearings (HMBs), a feed-forward compensation control strategy based on variable step size least-mean-square (LMS) adaptive filter is proposed. First, the structure, operation principle and mathematical model of the four-DOF six-pole HMBs are introduced, the motion law of rotor vibration is analyzed, and the dynamic equation is derived. Second, the variable step size LMS adaptive filter is improved by using the Versoria function. The step size of LMS algorithm is adjusted adaptively by using Versoria function model and Takagi–Sugeno (TS) fuzzy inference machine. The LMS adaptive filter can generate a signal with the same frequency, amplitude, and phase as the rotating speed to offset the vibration signal, so as to realize the vibration compensation control of the four-DOF six-pole HMB rotor. Finally, the simulations and experiments not only prove the effectiveness of this method but also show that the method has good compensation accuracy. The result shows that the Versoria function used in variable step size LMS adaptive filter for vibration compensation is better than the traditional variable step size filtering algorithm based on Sigmoid function.

A Normalized Least Means Absolute Third-Based Adaptive Control Algorithm Design for Grid-Connected PV System

This article presents design and real-time control of a single-stage grid-connected photovoltaic (SSGCPV) system. A normalized least means absolute third (NLMAT) algorithm has been employed to design an adaptive controller to achieve effective grid synchronization. The objective is to mitigate harmonics generated by nonlinear load and inject active power to the utility grid with unity power factor (PF). A 20-kW PV system with the above controller has been simulated using MATLAB/Simulink and then verified with a 1.4-kW prototype. A comparison of the proposed controller with least means fourth, variable step size least means square (VSS-LMS), variable leaky least mean square(VLLMS), and NLMAT algorithms has been made. It is found out that although the total harmonic distortion (THD) of the grid current remains within the prescribed limit of the IEEE-519 standard for all the three algorithms, the proposed controller outperforms among all. It provides reduced THD even with unbalanced loading and change in irradiance conditions.