Variable Step Research Articles

Dynamic thermal simulation of a tree-shaped district heating network based on discrete event simulation

The computational complexity involved in modelling district heating (DH) networks impedes the integration of network operations into comprehensive DH system studies. We developed a flexible, accurate, and fast dynamic thermal simulation model utilising discrete event simulation (DES). This model is versatile, suitable for any tree-shaped DH network with a central heating plant and can estimate node temperatures and calculate pipe heat losses. The speed of the model is improved via using variable time steps and by incorporating two advanced techniques: lazy evaluation and a customised priority queue. To further improve the computational speed, we developed a technique to eliminate redundant sampling points. This model was tested and demonstrated excellent consistency with actual measurements. Remarkably, reducing sampling points can speed up the simulation by a factor of three without compromising the temperature accuracy. A 72-day simulation of a network with 102 pipes was completed within 0.219 s. Our findings highlight the significant potential of the DES model for large-scale dynamic network simulations and offer a promising solution for DH network simulations and system optimisation.

Photovoltaic Maximum Power Point Tracking Technology Based on Power Prediction Algorithm Combined with Variable Step Length Disturbance Observation Method

Under partial shading conditions, the system operating sequence of photovoltaic cells does not fall on a single characteristic curve, and the traditional maximum power point tracking (MPPT) control algorithm is prone to causing the system output power to oscillate around the maximum power point. In the case of multiple peaks, the traditional MPPT algorithm is prone to being trapped in a local optimum solution. This paper proposes an MPPT control algorithm based on the WOA-RF prediction algorithm combined with a variable step disturbance observation method. By establishing a photovoltaic system simulation model, the improved algorithm is verified through simulation. The improved MPPT control algorithm can adaptively adjust the step size under different conditions to ensure that the system can quickly and accurately track the maximum power point. At the same time, by optimizing the algorithm logic and parameter settings, it can effectively avoid problems such as local optimum solutions and instability in the system, and improve the system convergence speed and tracking accuracy.

A Maximum Power Point Tracking (MPPT) Strategy Based on Harris Hawk Optimization (HHO) Algorithm

To address the multi-peak characteristics of the P-U output characteristic curve when the photovoltaic array is partially shaded, a Maximum Power Point Tracking (MPPT) method combining Harris Hawk optimization, and a variable step conductance increment method is proposed in this article. Although the Harris Hawk Optimization algorithm has advantages in optimizing multi-modal P-U curves, when the lighting conditions suddenly change, the output characteristic curve will undergo drastic changes, causing the algorithm to oscillate repeatedly at the maximum power point. Moreover, due to its inherent limitations, the Harris Hawk algorithm has a low convergence accuracy, slow tracking speed, and is prone to getting trapped in a local optimum. In order to compensate for the shortcomings of the Harris Hawk Optimization algorithm, the variable step conductance increment method is switched for local exploration to improve the algorithm’s ability to escape from the local optimal solution and reduce power oscillation. Finally, the MPPT control of the proposed strategy was simulated and verified on the MATLAB/Simulink simulation (2021) platform. In the MPPT test experiment, the proposed composite algorithm was applied to simulate and verify uneven irradiance conditions.

Development and safety evaluation of an adaptive personalized speed guidance system for on-ramp merging in highway service areas

As autonomous driving and Vehicle-to-Everything (V2X) technologies evolve, the efficiency and safety of ramp merging in the highway service areas have become increasing critical. This study introduces a closed-loop feedback speed guidance system that accommodates individual driving styles, aiming to optimize merging behaviour, reduce traffic accidents, and enhance total traffic efficiency. The system dynamically adjusts the merging vehicle speeds by continuously monitoring their speed and location with variable steps to promote smoother merging. Moreover, this research also involves collecting naturalistic driving data from ramp merging scenarios, using the K-means clustering and point estimation method to recognize and analyse driving style characteristics, and integrating these styles into the developed closed-loop feedback speed guidance system. This approach results in personalized speed guidance curves tailored to different driving styles, facilitating more efficient mering. Additionally, the study conducts a Safety of the Intended Functionality (SOTIF) evaluation of this system using the System-Theoretic Process Analysis (STPA) method, which helps identify potential security risks and develop appropriate mitigation strategies to ensure the system’s safe and stable operation. The simulation results confirm that this innovative dynamic speed guidance system substantially improves traffic safety and efficiency in ramp merging areas.

PSO-FDM (Particle Swarm Optimization-Finite Difference Method)-Based Simulation Model of Temperature and Velocity of Full-Scale Continuous Annealing Furnace

Improving the accuracy of the temperature field prediction model for continuous annealing line strips and enhancing the model’s adaptability to full-size strips are key technical challenges in continuous annealing lines. This paper developed a continuous annealing temperature prediction model based on a variable step-size strategy for the heating section, even-heat section, slow-cooling section, and fast-cooling section of the continuous annealing line. To improve the prediction accuracy for different strip sizes, the PSO optimization algorithm was employed to determine the optimal heat transfer coefficient for each strip size. Additionally, due to the limited production of certain strip gauges, providing insufficient data for optimization, this study introduces a combined file approach to address gauge vacancies. The experimental results indicate that the optimized model with variable step size can control the absolute prediction error to less than 4 °C, improving prediction accuracy by 61.9% and prediction speed by 26.8% compared to the traditional equal-step prediction model. This study verified that the merger method is effective for addressing side gauge vacancies, while the proposed method is suitable for resolving middle gauge vacancies. The main technical contribution of this study is the establishment of a high-precision prediction model for continuous annealing temperature of variable step length strips, ensuring high temperature control accuracy for full-gauge strips when passing through the continuous annealing production line.

Improved active vibration control of a cantilever beam using MFC actuators with Hammerstein model-based hysteresis modeling and VSS-FxLMS control algorithm

This study aims to enhance active vibration control in a cantilever beam using macro fiber composite (MFC) actuators. To address the challenge of accurately modeling the complex hysteresis behavior of MFC actuators, an advanced hysteresis modeling technique is employed, integrating a non-symmetric Bouc–Wen model with an Auto-Regressive model with eXogenous inputs (ARX). The parameter estimation of this model is optimized using an adaptive mutation factor, and multiple mutation strategy differential evolution (AmFMMDE) algorithm. Additionally, a Variable Step Size Filtered-x Least Mean Square (VSS-FxLMS) algorithm with step size adaptation based on normalized error change is utilized for effective vibration control. This approach shows promising potential for practical engineering applications requiring precise and efficient active vibration control.

Robust variable step size least mean fourth with quotient form-based control scheme for DVR operation

ABSTRACT A robust variable step size least mean fourth with a quotient form control scheme (RVSSLMFQ) is implemented for addressing power quality concerns and delivering clean voltage to sensitive loads through a dynamic voltage restorer (DVR). This method estimates the fundamental components from distorted grid voltages, featuring an automated process with adaptive time-varying step sizes and utilizing a quotient structure to reduce mean squared error (MSE) effectively. The suggested control scheme overcomes the stability and performance issues of the least mean fourth (LMF) algorithm by improving convergence and adapting well to varying step sizes. Furthermore, RVSSLMFQ achieves remarkable results with reduced settling time and fewer peak overshoots compared to the least mean square (LMS) and LMF control algorithms. For tuning the load voltage and DC-link voltage proportional-integral (PI) controllers, the improved grey wolf optimization technique (I-GWO) is applied. The results are evaluated through MATLAB simulations.

Enhancing Accuracy and Efficiency in Stiff ODE Integration Using Variable Step Diagonal BBDF Approaches

Recent advancements in mathematical modelling have uncovered a growing number of systems exhibiting stiffness, a phenomenon that challenges the effectiveness of traditional numerical methods. Motivated by the need for more robust numerical techniques to address this issue, this paper presents an enhanced version of the Diagonally Block Backward Differentiation Formula (BBDF) that incorporates intermediate points, known as off-step points, to improve the accuracy and efficiency of solutions for stiff ordinary differential equations (ODEs). The new scheme leverages an adaptive step-size strategy to refine accuracy and efficiency between regular and off-grid integration steps. Theoretical analysis confirms that the proposed scheme is an A-stable and convergent method, as it satisfies the fundamental criteria of consistency, zero-stability, and A-stability. Numerical experiments on single and multivariable systems across varying time scales demonstrate significant improvements in solving stiff ODEs compared to existing techniques. Therefore, the new proposed method is an effective solver for stiff ODEs.

Optimization of an N2O Emission Flux Model Based on a Variable-Step Drosophila Algorithm

The application of intelligent process-based crop model parameter optimization algorithms can effectively improve both the model simulation accuracy and applicability. Based on measured values of soil N2O emission flux in wheat fields from 2020 to 2022, and meteorological data from 1971 to 2022, five parameters of the N2O emission flux module in the APSIM model were optimized using the variable step Fruit Fly algorithm (VSS-FOA). The optimized parameters were the soil nitrification potential, the range of concentrated KNH4 of ammonia and nitrogen at semi-maximum utilization efficiency, the proportion of nitrogen loss to N2O during the nitrification process, the denitrification coefficient, and the Power term P for calculating the denitrification water coefficient. Contrasting the optimized parameters using the VSS-FOA algorithm versus the default values supplied with the model substantially improved the goodness-of-fit to field measurements with the overall R2 increasing from 0.41 to 0.74, and a decrease in NRMSE from 17.1% to 11.4%. This work demonstrates that the VSS-FOA algorithm affords a straightforward mechanism for the optimization of parameters in models such as APSIM to enhance the accuracy of model N2O emission flux estimates.

Specific Characteristics of Numerical Simulation of Mechatronic Systems with PWM-Controlled Drives

This paper explores the features of numerical simulation used to analyze the dynamic behaviour of drives controlled by pulse-width modulators. Modern motor control systems commonly employ pulse-width modulation. Effective numerical modelling of such systems presents unique challenges because the models employed are continuous-event and have hybrid behaviour due to the presence of nonlinear links with discontinuities of the first kind. Therefore, it is essential to have special integration methods with variable steps, which should be factored in when developing the model. This paper shows how these problems are solved when modelling an electric drive with a DC motor using the SimInTech software.

An analysis of second-order sav-filtered time-stepping finite element method for unsteady natural convection problems

This paper presents an unconditionally stable time-filtering algorithm for natural convection equations. The algorithm is based on the scalar auxiliary variables in the exponential function and adopts a completely discrete Back-Euler combining time filter scheme. The proposed scheme requires minimal invasive modification of the existing program to improve the time accuracy from first-order to second-order without increasing the computational complexity, and we demonstrate the unconditional stability of the proposed algorithm and analyze its second-order convergence. In addition, due to the increasing demand for low-memory solvers, the application of a time-adaptive algorithm can improve the accuracy and efficiency of the proposed algorithm, so we extend the method to variable step sizes and construct an adaptive algorithm. Finally, the effectiveness of the proposed method and the accuracy of the theoretical results are verified by numerical experiments.

An improved takagi - sugeno variable step size perturb and observe MPPT algorithm based lead acid battery charge controller for photovoltaic system

The main objective of photovoltaic system controller is to reduce the price of the kWh compared to traditional fuel-based electricity. Thus, the improvement of simple and low – cost controllers is a major challenge. Perturb and Observe (P&O) is the commonly used algorithm in order to ensure the power maximization of the photovoltaic system, due to its simplicity and effectiveness. However, on the main drawbacks of that algorithm is the fixed step size of perturbation, due to working environmental changes, which require dynamic tuning of the controller parameter. In order to overcome the cited disadvantage, a new Takagi - Sugeno variable step P&O is proposed. Based on the real-time measurements of the solar radiation and temperature, the proposed fuzzy system schedules the appropriate step size based on human expertise. A zero order Takagi – Sugeno with singleton output is proposed. The fuzzification were carried out using triangular and trapezoidal membership functions. The centroid defuzzification method based 25 If -Then rules are adopted. In order to verify the effectiveness of the improved P&O, three scenarios were used. The obtained results show the effectiveness of the proposed controller under shaded conditions and various temperatures.

A novel advanced hybrid fuzzy MPPT controllers for renewable energy systems

At present, the availability of nonrenewable sources and their usage for electric vehicle technology is reducing gradually because of their disadvantages are more environmental pollution, direct effect on human health, less reliability, and taking more time to start functioning. So, in this article, the proton exchange membrane fuel cell (PEMFC) is considered for the automotive application because of its advantages quick startup, more power density, more safety to handle, high efficiency, and capability of operating at very low operational temperature conditions. However, the drawback of PEMFC is very difficult to identify the accurate MPP position of the fuel system. Here, the improved variable step genetic algorithm is added with the adaptive neuro-fuzzy inference system for tracking the operational point of the proposed system with high efficiency. These hybrid MPPT controller features are easy to understand, more accurate, have a better dynamic response, and have low design complexity. The evaluated proposed MPPT controller operational efficiency, and settling time of the converter voltage at different fuel stack temperature conditions are 98.7402%, and 0.01607 s respectively. Finally, the boost converter is used in this work to enhance the voltage supply capability of the entire system. The proposed system is investigated by applying the MATLAB tool.

A modified inertial proximal alternating direction method of multipliers with dual-relaxed term for structured nonconvex and nonsmooth problem

In this research, we introduce a novel optimization algorithm termed the dual-relaxed inertial alternating direction method of multipliers (DR-IADM), tailored for handling nonconvex and nonsmooth problems. These problems are characterized by an objective function that is a composite of three elements: a smooth composite function combined with a linear operator, a nonsmooth function, and a mixed function of two variables. To facilitate the iterative process, we adopt a straightforward parameter selection approach, integrate inertial components within each subproblem, and introduce two relaxed terms to refine the dual variable update step. Within a set of reasonable assumptions, we establish the boundedness of the sequence generated by our DR-IADM algorithm. Furthermore, leveraging the Kurdyka–Łojasiewicz (KŁ) property, we demonstrate the global convergence of the proposed method. To validate the practicality and efficacy of our algorithm, we present numerical experiments that corroborate its performance. In summary, our contribution lies in proposing DR-IADM for a specific class of optimization problems, proving its convergence properties, and supporting the theoretical claims with numerical evidence.

Reduction Accelerated Adaptive Step‐Size FISTA Based Smooth‐Lasso Regularization for Fluorescence Molecular Tomography Reconstruction

ABSTRACTIn this paper, a reduced accelerated adaptive fast iterative shrinkage threshold algorithm based on Smooth‐Lasso regularization (SL‐RAFISTA‐BB) is proposed for fluorescence molecular tomography (FMT) 3D reconstruction. This method uses the Smooth‐Lasso regularization to fuse the group sparse prior information which can balance the relationship between the sparsity and smoothness of the solution, simplifying the process of calculation. In particular, the convergence speed of the FISTA is improved by introducing a reduction strategy and Barzilai‐Borwein variable step size factor, and constructing a continuation strategy to reduce computing costs and the number of iterations. The experimental results show that the proposed algorithm not only accelerates the convergence speed of the iterative algorithm, but also improves the positioning accuracy of the tumor target, alleviates the over‐sparse or over‐smooth phenomenon of the reconstructed target, and clearly outlines the boundary information of the tumor target. We hope that this method can promote the development of optical molecular tomography.

Adaptive current decoupling control scheme based on online multi-parameter identification for high-speed permanent magnet synchronous motor in fuel cell

The precise control of centrifugal hydrogen compressor (CHC) driven by high-speed permanent magnet synchronous motor (PMSM) is the key to the stable and efficient operation of hydrogen fuel cell (HFC). In this paper, an adaptive current deviation decoupling control (CDDC) strategy based on variable step size affine projection algorithm (VSS-APAs) is proposed to solve the high-speed PMSM control problem caused by current cross-coupling and parameter perturbation under complex operating conditions. Firstly, the step size is dynamically adjusted by VSS-APA through a normalized gradient descent to respond to system fluctuations, achieving rapid parameter identification during dynamic changes and accurate tracking in steady states. Secondly, stator inductance, magnetic flux linkage, stator resistance, and disturbance torque are identified in two-time-scale based on the characteristics of parameter changes, overcoming the rank deficiency in motor mathematical equations. Finally, utilizing online-identified motor parameters, the gains of the CDDC are adjusted, and compensation is applied for back electromotive force (BEMF) and disturbance torque, thereby ensuring the control accuracy of the motor under parameter perturbations and system disturbances. Experimental results demonstrate that the proposed method enhances the responsiveness and accuracy of the control strategy through efficient parameters identification. Consequently, it guarantees high-efficiency and stable performance of the CHC across different working conditions, markedly advancing the overall functionality and dependability of hydrogen energy system.

The multilingual digits-in-noise (DIN) test: development and evaluation

Objective To develop a methodologically uniform digits-in-noise (DIN) test in 17 different languages. Design The DIN test was developed for Android devices as an extension to the open-access Hearing Test™ app, available on the Google Play store. It utilised professionally recorded female speech, speech-shaped noise, a digit scoring method and a variable step size. The test was adaptively optimised and evaluated as the results of tests taken online by users of the app became available. Study sample Optimisation using 35,534 ears, evaluation using 6012 ears. Results Optimisation improved the slopes of the psychometric functions for all languages by an average of 6.8%/dB. Evaluation included calculation of normative speech reception thresholds (SRTs) and estimation of test-retest standard deviations. Normative values for SRTs ranged from −14.2 dB SNR (95% CI −14.3 to −14.0) for Chinese to −11.2 dB SNR (95% CI −11.3 to −11.1) for Japanese, with reliability estimates ranging from 0.48 dB (95% CI 0.36–0.64) for Portuguese to 0.91 dB (95% CI 0.73–1.21) for Romanian. Conclusions The optimisation of each language version was confirmed by the improvement in the slopes of the psychometric functions. The normative values obtained from the test evaluation were in agreement with literature data. Trial Registration Science Support Centre of Wroclaw Medical University BW-59/2020

Solving hyperchaotic initial value problems using second derivative extended trapezoidal rule of the second kind blended with generalized backward differentiation formulae with variable step size

This paper aims to evaluate the accuracy and performance of the second derivative block extended trapezoidal rule of the second kind, blended with generalized backward differentiation formulae using variable step sizes, in solving hyperchaotic initial value problems. Hyperchaotic systems, known for their rapidly changing solutions and extreme sensitivity to initial conditions, pose significant challenges for numerical methods. Traditional approaches often involve linearizing the systems or solving them in multiple sub-intervals, followed by combining the results. However, these methods can introduce errors due to the subdivision of intervals. The proposed method, which integrates the second derivative block extended trapezoidal rule with generalized backward differentiation formulae, offers a more precise solution by eliminating the need for interval subdivision and direct linearization. The continuous formulation of this method is derived using a multistep inversion technique that blends two linear multistep methods, while the discrete schemes are deduced from their continuous interpolants. Convergence analyses of these schemes are presented, demonstrating the efficiency and accuracy of the proposed block methods. As a result, these methods are well-suited for solving hyperchaotic and other nonlinear ordinary differential equations.

Dynamic contact and stiffness characteristic analysis of angular contact ball bearings under combined external loads

A nonlinear dynamic model of angular contact ball bearing under combined external loads is established based on the nonlinear elastic Hertz contact theory and raceless control theory. The established dynamic model is solved by employing variable step size Newton Raphson iteration method and the validation of model is verified by comparing the proposed results with the corresponding results come from the existing literatures. The solution of the presented model has high accuracy compared with the existing experimental results. In addition, the computational efficiency of the proposed model is improved significantly by introducing iteration step size adjustment factor. According to the proposed model, the dynamic contact and stiffness characteristics of angular contact ball are studied systematically by investigating the effects of combined external load working conditions on the contact parameters including contact angle and contact force and the stiffness parameters including diagonal stiffness and off-diagonal stiffness. This research can provide the theoretical basis and technique guidance for the designation and manufacture of angular contact ball bearing under combined external loads.

A modified feedforward-feedback time-frequency domain hybrid algorithm for multichannel active road noise control system

Multi-channel Active Road Noise Control (ARNC) systems require numerous adaptive filters to reduce noise at multiple positions inside the vehicle. However, road noise conditions are more complex, and the correlation between the reference signals and the target noise is often poor. When the driving conditions become slightly complex, the correlation between the reference signal and the target noise is often poor. As a result, traditional road noise control algorithms applied to multi-channel ARNC systems often suffer from high computational cost and poor noise reduction performance in non-steady-state and high-speed driving conditions. To address this issue,a reference signal selection method based on the genetic algorithm (GA) is proposed to obtain a reference signals combination with stronger coherence. On this basis, we introduce the time–frequency domain structure into the forward-feedback hybrid algorithm and a multi-channel time–frequency domain hybrid algorithm with a novel variable step size method (VSS-TF-HANC) is proposed in this paper.The feedforward part adopts a time–frequency domain structure and introduces a novel variable step-size strategy to reduce computational complexity and improve noise reduction performance. The feedback part adopts a control system based on the Internal Model Control (IMC) architecture to attenuate the interior noise components that have a strong response but poor correlation with the reference signals. Simulation results demonstrate that the proposed algorithm achieves excellent control results under complex driving conditions, with significantly better noise reduction performance compared to the control algorithms that solely employ the feedforward structure, while also exhibiting low computational cost.