Accurate Solutions Research Articles

PSA-FL-CDM: A Novel Federated Learning-Based Consensus Model for Post-Stroke Assessment.

The rapid development of Internet of Things (IoT) technologies and the potential benefits of employing the vast datasets generated by IoT devices, including wearable sensors and camera systems, has ushered in a new era of opportunities for enhancing smart rehabilitation in various healthcare systems. Maintaining patient privacy is paramount in healthcare while providing smart insights and recommendations. This study proposed the adoption of federated learning to develop a scalable AI model for post-stroke assessment while protecting patients' privacy. This research compares the centralized (PSA-MNMF) model performance with the proposed scalable federated PSA-FL-CDM model for sensor- and camera-based datasets. The computational time indicates that the federated PSA-FL-CDM model significantly reduces the execution time and attains comparable performance while preserving the patient's privacy. Impact Statement-This research introduces groundbreaking contributions to stroke assessment by successfully implementing federated learning for the first time in this domain and applying consensus models in each node. It enables collaborative model training among multiple nodes or clients while ensuring the privacy of raw data. The study explores eight different clustering methods independently on each node, revolutionizing data organization based on similarities in stroke assessment. Additionally, the research applies the centralized PSA-MNMF consensus clustering technique to each client, resulting in more accurate and robust clustering solutions. By utilizing the FedAvg federated learning algorithm strategy, locally trained models are combined to create a global model that captures the collective knowledge of all participants. Comparative performance measurements and computational time analyses are conducted, facilitating a fair evaluation between centralized and federated learning models in stroke assessment. Moreover, the research extends beyond a single type of database by conducting experiments on two distinct datasets, wearable and camera-based, broadening the understanding of the proposed methods across different data modalities. These contributions develop stroke assessment methodologies, enabling efficient collaboration and accurate consensus clustering models and maintaining data privacy.

A highly accurate and efficient Genocchi‐based spectral technique applied to singular fractional order boundary value problems

This article focuses on an efficient and highly accurate approximate solver for a class of generalized singular boundary value problems (SBVPs) having nonlinearity and with two‐term fractional derivatives. The involved fractional derivative operators are given in the form of Liouville–Caputo. The developed algorithm for solving the generalized SBVPs consists of two main stages. The first stage is devoted to an iterative quasilinearization method (QLM) to conquer the (strong) nonlinearity of the governing SBVPs. Secondly, we employ the generalized Genocchi polynomials (GGPs) to treat the resulting sequence of linearized SBVPs numerically. An upper error estimate for the Genocchi series solution in the norm is obtained via a rigorous error analysis. The main benefit of the presented QLM‐GGPs procedure is that the required number of iteration in the first stage is within a few steps, and an accurate polynomial solution is obtained through computer implementations in the second stage. Three widely applicable test cases are investigated to observe the efficacy as well as the high‐order accuracy of the QLM‐GGPs algorithm. The comparable accuracy and robustness of the presented algorithm are validated by doing comparisons with the results of some well‐established available computational methods. It is apparently shown that the QLM‐GGPs algorithm provides a promising tool to solve strongly nonlinear SBVPs with two‐term fractional derivatives accurately and efficiently.

An efficient modelling and hosting capacity analysis of a distribution system integrating PVs supported by the V2G technology

Over the past decade, the production of photovoltaic (PV) systems has increased owing to the rising demand for electricity generation. Recently, the vehicle-to-grid (V2G) technology of electric vehicles (EVs) has also gained interest as a clean and green energy source to support PVs providing sustainable energy. However, this necessitates the efficient modelling of PV output generation and V2G scheme for integration in the distribution system. Despite the advantages of PV and V2G technology, excessive integration potential affects the distribution system. To circumvent these problems, an accurate evaluation of hosting capacity (HC) is essential. This study proposes efficient modelling and a novel, improved analytical-optimal power flow method for HC analysis of distribution systems with PV and V2G integration considering uncertainties. Furthermore, the effects of increasing integration and optimal allocation of PVs and V2G technology on the voltage profile and power losses, respectively, were analysed. The IEEE 33-bus and 69-bus distribution systems were employed to perform the simulation test to obtain results of HC that validated the effectiveness and robustness of the proposed method compared with those of conventional methods. The proposed method provides an accurate, robust, and global-optimum solution. The integration of V2G technology enhances the overall HC of distribution system.

Multiple slip nonlinear radiative bioconvective flow of nanofluid with variable thermal conductivity

Owing to the improved thermal applications of nanomaterials, various applications have been suggested in various era of engineering including heat transfer devices, chemical processes, thermal management devices, electronic cooling etc. The aim of current investigation is to presents the bioconvective flow of nanofluid with applications of multiple slip effects. The motivations for considering the slip effects for heat and mass transfer analysis are associated to its significance in the petroleum sciences, extrusion processes, oil recovery and plasma physics. The nonlinear thermal radiation effects and chemical reaction consequences have been attributed. In contrast to traditional investigations, the thermal conductivity of nanofluid have been assumed to be temperature dependent. Following the assumptions of dimensionless variables, a system of nonlinear differential equations is obtained. The shooting technique is employed for computing the numerical simulations. The accuracy of solution is ensured. The physical assessment of problem is incorporated in view of involved parameter. It has been claimed that interaction of slip effects enhances the heat and mass transfer effects. Change in microbes density slip parameter leads to improvement in the microorganisms profile. Moreover, local Nusselt number and Sherwood number reduces for slip parameters. Current results present significance in heat transfer systems, thermal engineering, chemical engineering, fertilizers, biofuels etc.

Postbuckling behaviour of anisotropic shear deformable laminated cylindrical shells with general imperfection distribution subjected to torsion

Composite cylindrical shells belong to typical basic structure in engineering, whose buckling and postbuckling behaviours determine the stability and safety of overall structures under complex service loadings. In this paper, a nonlinear mechanical model for anisotropic laminated composite cylindrical shells with general distributed initial imperfection is derived to analyse the buckling and postbuckling behaviours under torsional loads, in which the general distributed imperfections are represented by a generic two-dimensional imperfection function reconstructed by using measured data. Based on a higher order shear deformation shell theory, the governing equations are established with consideration of von Kármán–Donnell-type of kinematic nonlinearity and the coupling effects of extension/twist, extension/flexural and flexural/twist. By using a two-step perturbation technique, a new set of explicit solutions is obtained to determine the buckling loads and postbuckling equilibrium paths of the torsional composite cylindrical shells. Furthermore, the internal quantitative relationship between the shear stress with torsional characteristics along with an associate compressive stress of anisotropic laminated shell is for the first time obtained. Numerical analyses are performed to validate the accuracy and effectiveness of the present explicit solutions, and obtain the postbuckling response of different types of imperfections, anisotropic laminated cylindrical shells with different values of shell parameters.

Bridging Large Eddy Simulation and Reduced-Order Modeling of Convection-Dominated Flows through Spatial Filtering: Review and Perspectives

Reduced-order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. In fluid dynamics, ROMs have been successful in providing efficient and relatively accurate solutions for the numerical simulation of laminar flows. For convection-dominated (e.g., turbulent) flows, however, standard ROMs generally yield inaccurate results, usually affected by spurious oscillations. Thus, ROMs are usually equipped with numerical stabilization or closure models in order to account for the effect of the discarded modes. The literature on ROM closures and stabilizations is large and growing fast. In this paper, instead of reviewing all the ROM closures and stabilizations, we took a more modest step and focused on one particular type of ROM closure and stabilization that is inspired by large eddy simulation (LES), a classical strategy in computational fluid dynamics (CFD). These ROMs, which we call LES-ROMs, are extremely easy to implement, very efficient, and accurate. Indeed, LES-ROMs are modular and generally require minimal modifications to standard (“legacy”) ROM formulations. Furthermore, the computational overhead of these modifications is minimal. Finally, carefully tuned LES-ROMs can accurately capture the average physical quantities of interest in challenging convection-dominated flows in science and engineering applications. LES-ROMs are constructed by leveraging spatial filtering, which is the same principle used to build classical LES models. This ensures a modeling consistency between LES-ROMs and the approaches that generated the data used to train them. It also “bridges” two distinct research fields (LES and ROMs) that have been disconnected until now. This paper is a review of LES-ROMs, with a particular focus on the LES concepts and models that enable the construction of LES-inspired ROMs and the bridging of LES and reduced-order modeling. This paper starts with a description of a versatile LES strategy called evolve–filter–relax (EFR) that has been successfully used as a full-order method for both incompressible and compressible convection-dominated flows. We present evidence of this success. We then show how the EFR strategy, and spatial filtering in general, can be leveraged to construct LES-ROMs (e.g., EFR-ROM). Several applications of LES-ROMs to the numerical simulation of incompressible and compressible convection-dominated flows are presented. Finally, we draw conclusions and outline several research directions and open questions in LES-ROM development. While we do not claim this review to be comprehensive, we certainly hope it serves as a brief and friendly introduction to this exciting research area, which we believe has a lot of potential in the practical numerical simulation of convection-dominated flows in science, engineering, and medicine.

Laser-Tracing Multi-Station Measurements in a Non-Uniform-Temperature Field

Due to the increasing requirements for the improvement of the accuracy of large coordinate-measuring machines (CMMs), the laser-tracing multi-station measurement technology, as one of the advanced precision measurement technologies, is worth studying in depth in terms of its practical application for the compensation of errors in large CMMs. Since it is difficult to maintain a constant temperature of about 20 °C in the actual workshop under the influence of solar radiation and convective heat transfer, there is a gradient in the spatial temperature distribution, and the overall temperature changes with the influence of external factors with synchronous hysteresis, it is difficult for the actual calibration environment to meet the standard environmental requirements. Therefore, the influence of temperature and other environmental factors on the accuracy of laser ranging and large-scale CMM calibration should not be ignored. In this paper, on the basis of analyzing the temperature distribution and change rule of large CMM measurement space under different working conditions, the radial basis function (RBF) neural network algorithm was used to build a non-uniform-temperature field model, and based on this model and the measurement principle of the laser-tracking instrument, the method of laser tracking and interferometric ranging accuracy enhancement was put forward under a non-uniform-temperature field. Finally, based on the multi-station technique of laser tracing, an accurate solution for the volumetric error of large CMMs under the condition of non −20 °C ambient temperature was realized. Simulation results proved that compared with the traditional temperature-compensation method, the proposed method improved the measurement accuracy of the volumetric error of a large-scale CMM using laser-tracing multi-station technology in a non-uniform-temperature field by 33.5%. This study provides a new approach for improving the accuracy of laser-tracer multi-station measurement systems.

The numerical solution of Fredholm integral equation of the first kind using the Sinc-Galerkin method

Sinc-Galerkin scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. In this article, a numerical solution of Fredholm integral equation of the first kind which arise in a large number of problems in applied mathematics will be discussed, for this result, we choose Sinc functions as basis functions and Galerkin method to estimate a solution for an unknown function in this equation. So, in this paper, some properties of the Sinc-Galerkin method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some linear algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to confirm applicability and justify rapid convergence of our method.

Advanced neural network approaches for coupled equations with fractional derivatives

We investigate numerical solutions and compare them with Fractional Physics-Informed Neural Network (FPINN) solutions for a coupled wave equation involving fractional partial derivatives. The problem explores the evolution of functions u and v over time t and space x. We employ two numerical approximation schemes based on the finite element method to discretize the system of equations. The effectiveness of these schemes is validated by comparing numerical results with exact solutions. Additionally, we introduce the FPINN method to tackle the coupled equation with fractional derivative orders and compare its performance against traditional numerical methods.Key findings reveal that both numerical approaches provide accurate solutions, with the FPINN method demonstrating competitive performance in terms of accuracy and computational efficiency. Our study highlights the significance of employing FPINNs in solving fractional differential equations and underscores their potential as alternatives to conventional numerical methods. The novelty of this work lies in its comparative analysis of traditional numerical techniques and FPINNs for solving coupled wave equations with fractional derivatives, offering insights into advancing computational methods for complex physical systems.

Dynamic analysis of planetary gear transmission based on Lagrange interpolation polynomials

Abstract This paper proposes a novel dynamic model considering manufacturing errors and eccentricity errors to analyze the dynamics of planetary gear transmission (PGT). The dynamic model is established based on the fractional-order calculus (FOC) and solved by an enhanced fourth-order Lagrange interpolation polynomials (LIP) method. Three numerical examples and the vibration experiments of planetary gear transmission are employed for verification. The comparison results indicate that the proposed solution method has higher solution accuracy and efficient than the existing algorithms in solving fractional equations, and the relative errors of the proposed solution method in three examples are 0.32%, 0.78% and 0.16%, respectively. The proposed dynamic model of PGT has better agreement with the experimentally measured signal compared with the integer-order dynamic model, and the maximum error and average error of the characteristic frequency amplitude between the proposed dynamic model and the measured signal are 4.76% and 3.57%, respectively. The proposed method contributes to the theoretical foundation for the signal monitoring of PGT.

Temperature Effect on the Properties and Response of Composite Materials and Plates

The paper illustrates the effect of temperature on composite material properties and its influence on the response of composite plates. Two composites considered include laminae with uniaxially oriented and with in-plane randomly oriented fibers. Analytical solutions are presented for a uniformly heated large-aspect-ratio plate deforming into a cylindrical surface. The solutions are demonstrated for thermal buckling and natural frequencies for the cases of controlled loading and controlled displacements. Micromechanical residual and lifetime thermally induced stresses at the interface of fibers and matrix are assessed to predict a possible onset of local damage after the curing and during lifetime. The material considered in numerical examples consists of silicon carbide fibers and a titanium alloy matrix. The moduli of elasticity and shear as well as the coefficients of thermal expansion of this composite are significantly affected by temperature. The thermally induced microscopic radial stress at the fiber–matrix interface is high, so it should be monitored in silicon fiber titanium matrix composites to avoid the onset of local damage. In conclusion, accounting for the effect of temperature on material properties is highly desirable since it produces more accurate solution than those utilizing the properties at the room temperature.

Fuzzy logic-based particle swarm optimization for integrated energy management system considering battery storage degradation

Considering the rapidly evolving microgrid technology and the increasing complexity associated with integrating renewable energy sources, innovative approaches to energy management are crucial for ensuring sustainability and efficiency. This paper presents a novel Fuzzy Logic-Based Particle Swarm Optimization (FLB-PSO) technique to enhance the performance of hybrid energy management systems. The proposed FLB-PSO algorithm effectively addresses the challenge of balancing exploration and exploitation in optimization problems, thereby enhancing convergence speed and solution accuracy with robustness across diverse and complex scenarios. By leveraging the adaptability of fuzzy logic to adjust PSO parameters dynamically, the method optimizes the allocation and utilization of diverse energy resources within a grid-connected microgrid. Under fixed grid tariffs, the investigation demonstrates that FLB-PSO achieves grid power purchase and battery degradation costs of $1935.07 and $49.93, respectively, compared to $2159.67 and $61.43 for the traditional PSO. This results in an optimal cost of $1985.00 for FLB-PSO, leading to a cost saving of $236.09 compared to the $2221.10 of PSO. Furthermore, under dynamic grid tariffs, FLB-PSO incurs grid power purchase and battery degradation costs of $2359.20 and $64.66, respectively, in contrast to $2606.47 and $54.61 for PSO. The optimal cost for FLB-PSO is $2423.86, representing a cost reduction of $237.23 compared to the $2661.08 of PSO. The FLB-PSO algorithm proficiently manages energy sources while addressing complexities associated with battery storage degradation. Overall, the FLB-PSO algorithm outperforms traditional PSO in terms of robustness to system dynamics, convergence rate, operational cost reduction, and improved energy efficiency.

Flexible-Center Hat Complete Electrode Model for EEG Forward Problem.

This study aims to develop a more realistic electrode model by incorporating the non-uniform distribution of electrode contact conductance (ECC) and the shunting effects, to accurately solve EEG forward problem (FP). Firstly, a hat function is introduced to construct a more realistic hat-shaped distribution (HD) for ECC. Secondly, this hat function is modified by applying two parameters - offset ratio and offset direction - to account for the variability in ECC's center and to develop the flexible-center HD (FCHD). Finally, by integrating this FCHD into the complete electrode model (CEM) with the shunting effects, a novel flexible-center hat complete electrode model (FCH-CEM) is proposed and used to solve FP. Simulation experiments using a realistic head model demonstrate the necessity of FCH-CEM and its potential to improve the accuracy of the FP solution compared to current models, i.e., the point electrode model (PEM) and CEM. And compared to PEM, it has better performance under coarse mesh conditions (2 mm). Further experiments indicate the significance of considering shunting effects, as ignoring them results in larger errors than coarse mesh when the average contact conductance is large (101S/m2). The proposed FCH-CEM has better accuracy and performance than PEM and complements CEM in finer meshes, making it necessary for coarse meshes. This study proposes a novel model that enhances electrode modeling and FP accuracy, and provides new ideas and methods for future research.

Load restoration of electricity distribution systems using a novel two‐stage method

AbstractThis paper proposes a new comprehensive load restoration (LR) method for electrical distribution networks. Since two main technologies of switching equipment are there in the modern distribution networks, namely manual switches (MSs) and remote‐controlled switches (RCSs), this article has benefited from this concept effectively. A two‐stage algorithm that provides the system operators with the ability to recover part of the loads in the shortest possible time by RCSs is proposed. After this step, the remaining loads will be restored by a combination of MSs and RCSs. The other strength of this algorithm is to provide accurate and practical solutions so that the sequence of switching actions is clearly defined. Also, using an innovative index called expected weighted energy not supplied as the objective function of the main problem will ensure the operators recover the maximum amount of load in the shortest time possible. This novel method was applied on a sample standard IEEE distribution test network. The simulation results proved the effectiveness of this proposed method.

Numerical treatment of the KP–MEW equation and the Konno–Oono equation using the first-integral method

Finding new, more widely applicable accurate traveling wave solutions to nonlinear partial differential equations is the aim of this work. The Konno–Oono equation and the Kadomtsev–Petviashvili modified equal width equation have various possible applications in mathematical physics and engineering disciplines, and their exact solutions are presented in this article. Using the first integral approach as an analytical method and the traveling wave transformation, we explore the precise traveling wave solutions. This approach is effective and yields unique exact solutions that fall into two categories: solutions in the form of trigonometric functions and solutions in the form of hyperbolic functions. Furthermore, graphical illustrations in two and three dimensions are showcased to offer a thorough explanation of their dynamic nature. In addition, it is critical to emphasize the significance of mastering the Konno–Oono equation and the KP–MEW equation, both of which have applications in a variety of fields Our findings are also crucial for understanding the many oceanographic applications that involve ocean gravity waves, offshore rigs in the water, energy from moving ocean waves, and several other related phenomena. This approach requires less computing work and is straightforward and succinct. That is its main advantage.

Treatment for the Singularity Problem in the Phase Segregation

In the Eulerian–Eulerian two-fluid model, comprising air and droplets, singularities often arise as the phase fraction of dispersed droplets approaches zero. The nonconservative momentum equations can address this issue, but it will lead to inaccurate solutions when encountering discontinuities. To tackle the singularity problem and ensure accurate solutions for the droplet field, a novel adaptive form of momentum equations is proposed. The adaptive form defaults to the conservative form and smoothly transitions to the phase-intensive form when the phase fraction falls below a critical value, specifically 1/1000 of the inlet. The LU-SGS algorithm, enhanced with the inner iteration step method, is employed for numerical solutions of the droplet field. Comparative analysis reveals that the discrepancy between the results obtained from the adaptive form and the conservative form is negligible, under 0.5‰. Notably, with larger Courant numbers, the conservative form diverges from waterless regions despite imposing the minimum phase fraction constraint. Conversely, the adaptive form consistently maintains a Courant number of five times or more, potentially exceeding a hundredfold in complex flows. Although the adaptive form moderately increases complexity and computational time for a single time step, the improvement of the maximum Courant number will bring significant computational efficiency advantages. Moreover, the adaptive form holds promise for application in various other multiphase flow scenarios.

Accurate Solution of Adjustment Models of 3D Control Network

Accurate Solution of Adjustment Models of 3D Control Network

An improved grey wolf optimization algorithm based on scale-free network topology

The grey wolf optimizer is a novel intelligent optimization algorithm that has become popular due to its low number of parameters, fast convergence speed, and simplicity. However, the classical algorithm, with its update strategy allowing wolves to learn only from the alpha wolves, often leads to premature convergence and lower convergence accuracy. Therefore, in this paper, an improved grey wolf optimization algorithm based on scale-free network topology (SFGWO) is proposed to address these issues. The improved algorithm first employs a strategy for formulating a population based on a scale-free network topology, where interaction between wolves is limited to topological neighbors, which helps enhance the exploration capabilities of the algorithm. Second, a neighbor learning strategy is introduced to capture individual diversity, facilitating the solution space exploration. Finally, an adaptive individual regeneration strategy is adopted to balance the exploration and exploitation processes and reduce the risk of falling into local optima. The proposed algorithm is evaluated through simulation experiments using 23 classical and the CEC2019 benchmark functions. The experimental results demonstrate that the SFGWO algorithm excels in terms of solution accuracy and exploration capabilities. The applicability and effectiveness of the SFGWO algorithm are further validated through testing on three practical engineering problems.

Optimal scheduling of integrated energy systems for eco-economic operation

Abstract In the context of rising environmental awareness and the pursuit of sustainable development, it is critical to advance low-carbon economies, especially within the field of energy system management. Our research is dedicated to enhancing the efficiency of Combined Cooling, Heating, and Power (CCHP) systems to meet both cost and environmental objectives. We have devised an optimized CCHP model that employs the particle swarm optimization algorithm to manage complex constraints and improve solution accuracy. Through case studies, we have verified that our model significantly increases the system’s eco-efficiency and operational excellence.

Fourier-Based Function Generation of Four-Bar Linkages With an Improved Sampling Points Adjustment and Sylvester's Dialytic Elimination Method

Abstract Four-bar linkages are critical fundamental elements of many mechanical systems, and their design synthesis is often mathematically complicated with iterative numerical solutions. Analytical methods based on Fourier coefficients can circumvent these difficulties but have difficulties with sampling points adjustment and solutions of the design equations in previous studies. In this paper, an improved Fourier-based analytical synthesis method is presented, which transforms the function generation synthesis of planar four-bar linkages into a problem of solving design equations. Calculation of the Fourier coefficients is discussed, including the discretization of the prescribed function and an improved sampling points adjustment method. It is shown that the Fourier coefficients can be computed efficiently and accurately by discretizing the prescribed function with a small number of sampling points. The proposed sampling adjustment method overcomes the difficulty of easily resulting in non-Grashof solutions by considering the complete period of the prescribed function. An improved Sylvester's dialytic elimination method is presented to solve design equations. The method reduces the computation time and avoids cumbersome procedures without generating additional invalid solutions. Several examples are presented to demonstrate the advantages of the proposed synthesis method, which is easy-understanding and efficient, and yields more accurate solutions than available synthesis methods.