High-accuracy Solution Research Articles

Crack analysis using a hybrid numerical manifold method with node-based strain smoothing and double-interpolation

In this paper, a hybrid numerical manifold method with node-based strain smoothing and double-interpolation is proposed for crack analysis and propagation. By introducing an allocation scheme, the empty strain smoothing domain issue encountered in the numerical manifold method framework is avoided, while the flexibility in smooth domain formulation is preserved. Our method’s hybrid approach stems from the double-interpolation locally implemented on the tip domain, where strain smoothing becomes cumbersome and costly. High accuracy and continuous nodal stress solutions were achieved in whole domains. The proposed model is validated through several comparisons of analytical and experimental results, and the results obtained for crack analysis and growths are shown to be accurate and efficient.

Use of mathematical modeling for solving tasks of optimal control of an electric drive

The object of study in this article is the control processes of electromechanical systems with an electric drive. The subject matter is a mathematical model in the problem of optimal control of the following electric drive. This article is devoted to the mathematical modeling of the control processes of electromechanical systems with an electric drive. In this paper, we use the approximation of vector-valued functions of one variable by splines of the first degree to solve the problem of rotation of the motor shaft in electromechanical system. As you know, it is not always possible to find exact solutions in optimal control problems. In this regard, there is a need to obtain approximate solutions for optimal control problems. Therefore, an urgent task is the development of new methods for the approximate solution to the problems of optimal control of the electric drive, which provide higher approximation accuracy. The following results are presented: Graphs of phase coordinates and optimal control of approximation by splines of the first order are obtained. The results obtained were compared with the exact solution. The given examples illustrate the high accuracy of approximate solutions to the control problem obtained using the proposed method. Conclusions. The scientific novelty of the results obtained lies in the fact that a method is proposed for an approximate solution to the problem of optimal control of a servo drive using spline functions, in which unknown control parameters are found simultaneously with unknown parameters of phase coordinates, which gives the best approximation to the exact solution.

An accurate and parallel method with post-processing boundedness control for solving the anisotropic phase-field dendritic crystal growth model

A fast, accurate, and stable numerical algorithm is proposed to solve the anisotropic phase-field dendritic crystal growth model. The algorithm combines the first-order direction splitting method and the linear stabilization technique, which preserve the energy stability while ensuring fast computing. The related stability analysis is shown. To obtain high accurate solution, the solution of first-order direction splitting method is extrapolated to be fourth-order, and the fourth-order difference method is applied to spatial discretization. To further improve the stability and prevent the blow-up of numerical solution, two post-processing methods, the bound preserving least-distance modification and the cut-off approach, are developed to control the boundedness of numerical solution, and their theoretical proofs are given. The proposed novel algorithm can be performed in parallel in each time step, significantly improving computing efficiency. Several numerical examples demonstrate the effectiveness of the proposed algorithm, including convergence and stability tests, the effectiveness of two post-processing techniques, and a series of 2D and 3D dendritic crystal growth simulations.

Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method

Abstract The paper calculates the nonlinear dynamic differential equation model based on the stiffness of the gear teeth and gives the calculation method of the spring stiffness of the transmission system. Choose the Lyapunov energy function and derive the adaptive law that can make the system asymptotically stable globally. At the same time, we discussed the influence of the phase combination of the coupling shaft’s torsional stiffness and the gears’ meshing stiffness in the multi-stage gear transmission system on the system dynamics. The example calculation shows that the asymptotic method has higher solution accuracy and higher calculation efficiency. This algorithm is a highly versatile analytical solution method.

An Online Generalized Multiscale finite element method for heat and mass transfer problem with artificial ground freezing

The Online Generalized Multiscale Finite Element Method (Online GMsFEM) is presented in this study for heat and mass transfer problem in heterogeneous media with artificial ground freezing process. The mathematical model is based on the classical Stefan model, which depicts heat transfer with a phase change and includes filtration in a porous media. The model is described by a set of temperature and pressure equations. We employ a finite element method with the fictitious domain method to solve the problem on a fine grid. We apply a model reduction approach based on Online GMsFEM to derive a solution on the coarse grid. We can use the online version of GMsFEM to take less offline multiscale basis functions. We use decoupled offline basis functions built with snapshot space and based on spectral problems in our method. This is the standard approach of basis construction. We calculate additional basis functions in the offline stage to account for artificial ground freezing pipes. We use online multiscale basis functions to get a more precise approximation of phase change. We create an online basis that reduces error using local residual values. The accuracy of standard GMsFEM is greatly improved by using an online approach. Numerical results in a two-dimensional domain with layered heterogeneity are presented. To test the method’s accuracy, we show results from a variety of offline and online basis functions. The results suggest that Online GMsFEM can deliver high-accuracy solutions with minimal processing resources.

Blockchain-Based Optimization Model for Evaluating Psychological Mental Disease and Mental Fitness.

The current work describes a blockchain-based optimization approach that mimics the psychological mental illness evaluation procedure and evaluates mental fitness. Combining lightweight models with blockchains can give a variety of benefits in the healthcare business. This study aims to offer an improved review and learning optimization technique (SPLBO) based on the social psychology theory to overcome the biogeography-based optimization (BBO) algorithm's shortcomings of low optimization accuracy and instability. It also creates high-accuracy solutions in recognized domains quickly. To retain student individuality, students can be divided into two groups: Human psychological variables are incorporated in the algorithm's improvement: in the “teaching” step of the original BBO algorithm; the “expectation effect” theory of social psychology is combined: “field-independent” and “field-dependent” cognitive styles. As a consequence, low-weight deep neural networks have been designed in such a manner that they require fewer resources for optimal design while also improving quality. A responsive student update component is also introduced to duplicate the effect of the environment on students' learning efficiency, increase the method's global search capabilities, and avoid the problem of falling into a local optimum in the first repetition.

Research on Maximum Power Tracking of Grey Wolf Optimization Algorithm Introducing Levy Flight

In the case of partial shadow, the power-voltage characteristic curve of photovoltaic array output will show multi-peak phenomenon, the traditional maximum power point tracking method is easy to fall into the local maximum power point, resulting in the loss of output power. Aiming at the common problems of traditional swarm intelligence optimization algorithms, such as slow convergence speed, large oscillation amplitude, and easy to fall into local optimum, a control method of gray wolf optimization algorithm with Levy flight was proposed. The algorithm uses GWO’s excellent ability of fast convergence speed and high solution accuracy to quickly converge to the vicinity of the maximum power point, and then uses CSA to achieve a stable state near the maximum power point. The power fluctuation is smaller. The simulation statistics show that compared with the traditional The improved gray wolf optimization algorithm has higher solution accuracy, shorter tracking time, and improves the output efficiency of the photovoltaic array.

A Dynamic Adaptive Weighted Differential Evolutionary Algorithm.

This study proposed a dynamic adaptive weighted differential evolution (DAWDE) algorithm to solve the problems of differential evolution (DE) algorithm such as long search time, easy stagnation, and local optimal solution. First, adaptive adjustment strategies of scaling factor and crossover factor are proposed, which are utilized to dynamically balance the global and local search, and avoid premature convergence. Second, an adaptive mutation operator based on population aggregation degree is proposed, which takes population aggregation degree as the amplitude coefficient of the basis vector to determine the influence degree of the optimal individual on the mutation direction. Finally, the Gauss perturbation operator is introduced to generate random disturbance and accelerate premature individuals to jump out of the local optimum. The simulation results show that the DAWDE algorithm can obtain better optimization results and has the characteristics of stronger global optimization ability, faster convergence, higher solution accuracy, and stronger stability compared with other optimization algorithms.

Improved method in calculating the surface charge distribution of DC‐GIL insulators with 3D geometry models

Surface charge accumulation is an important issue when dealing with the insulation property of direct-current gas-insulated transmission lines with insulators. An improved method is introduced to calculate the surface charge distribution of insulators based on three-dimensional (3D) geometry models with high solution accuracy and computing efficiency. More than 90% of the computing memory and time are reduced by applying weak form partial differential equation (PDE) to the ion transport equation compared to adding artificial diffusion term. The computing memory and time are further reduced by 70% when removing the diffusion term from the ion transport equation, whereas the accuracy remains unchanged. Thus, the method of combining the modification of ion transport equation and the application of weak form PDE is suggested in calculating the surface charge of 3D geometry models. Finally, this method is applied in calculating the surface charge distribution of a ±200-kV basin-type insulator under thermal-electric coupled fields and a ±500-kV tri-post insulator. Results show satisfying accuracy and efficiency. It is concluded that the proposed method can be applied in analysing the charge accumulation and ion transport behaviour based on 3D models under various operating conditions.

A collocation algorithm based on septic B-splines and bifurcation of traveling waves for Sawada–Kotera equation

In present work, a mathematical model standing for the numerical solutions of the nonlinear Sawada–Kotera (S–K) equation has been examined. For this purpose, we have used collocation finite element method for the model problem. The solution for each unknown is written as a linear combination of time parameters and combination of the septic B-splines. Next, applying Von-Neumann theory, we demonstrate that the scheme is marginally stable. Error norms L2 and L∞ are computed for single soliton solutions to display the practicality and robustness the suggested scheme. The obtained numerical results have been illustrated with tables. Furthermore, to show the numerical behavior of the single soliton, some of the simulations are depicted in 2D and 3D. Present results show that the method procures high accurate solutions so present scheme will be useful for the other nonlinear scientific problems. After that, bifurcation behavior of traveling waves for the S-K equation has been examined depending on the velocity (v) of the traveling wave. It has been seen that velocity (v) of the traveling wave plays a key role for the existence of different kind of quasiperiodic motions of the nonlinear S-K equation. Coexisting quasiperiodic motions for traveling wave solutions of the equation have been presented.

A novel computational analysis of fractional differential equation based on elliptic discrete equation

This paper proposes a novel computational analysis to solve fractional differential equations based on elliptic discrete equations. The traditional solution method of the fractional differential equation was complex, and the solution efficiency and accuracy were low. In the process of solving, the definition, properties, and integral transformation of fractional calculus were analyzed, and then solving the fractional differential equation on the basis of the elliptic discrete equation. From the evaluation of the results, it can be concluded that the proposed method has high solution accuracy.

Intelligent Data-Driven Decision-Making Method for Dynamic Multisequence: An E-Seq2Seq-Based SCUC Expert System

Under the background of the rapid change of energy technology and the deep integration of artificial intelligence into the power system, it is of great significance to study the intelligent decision-making method of security-constrained unit commitment (SCUC) with high adaptability and high accuracy. Thus, in this article, an expanded sequence-to-sequence (E-Seq2Seq)-based data-driven SCUC expert system for dynamic multiple-sequence mapping samples is proposed. First, dynamic multiple-sequence mapping samples of SCUC are reconstructed by analyzing the input–output sequence characteristics. Then, an E-Seq2Seq approach with a multiple-encoder–decoder architecture and a fully connected extension layer is proposed. On this basis, the simple recurrent unit is introduced as a neuron of the E-Seq2Seq approach to construct deep learning models, and an intelligent data-driven expert system for SCUC is further developed. The proposed approach has been simulated on a typical IEEE 118-bus system and a practical system in Hunan province in China. The results indicate that the proposed approach could possess strong generality, high solution accuracy, and efficiency over traditional methods.

Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks.

The Schrödinger equation describes the quantum-mechanical behaviour of particles, making it the most fundamental equation in chemistry. A solution for a given molecule allows computation of any of its properties. Finding accurate solutions for many different molecules and geometries is thus crucial to the discovery of new materials such as drugs or catalysts. Despite its importance, the Schrödinger equation is notoriously difficult to solve even for single molecules, as established methods scale exponentially with the number of particles. Combining Monte Carlo techniques with unsupervised optimization of neural networks was recently discovered as a promising approach to overcome this curse of dimensionality, but the corresponding methods do not exploit synergies that arise when considering multiple geometries. Here we show that sharing the vast majority of weights across neural network models for different geometries substantially accelerates optimization. Furthermore, weight-sharing yields pretrained models that require only a small number of additional optimization steps to obtain high-accuracy solutions for new geometries.

Enhanced slime mould algorithm with multiple mutation strategy and restart mechanism for global optimization

Slime mould algorithm (SMA) is a new metaheuristic algorithm proposed in 2020, which has attracted extensive attention from scholars. Similar to other optimization algorithms, SMA also has the drawbacks of slow convergence rate and being trapped in local optimum at times. Therefore, the enhanced SMA named as ESMA is presented in this paper for solving global optimization problems. Two effective methods composed of multiple mutation strategy (MMS) and restart mechanism (RM) are embedded into the original SMA. MMS is utilized to increase the population diversity, and the RM is used to avoid the local optimum. To verify the ESMA’s performance, twenty-three classical benchmark functions are employed, as well as three well-known engineering design problems, including welded beam design, pressure vessel design and speed reducer design. Several famous optimization algorithms are also chosen for comparison. Experimental results show that the ESMA outperforms other optimization algorithms in most of the test functions with faster convergence speed and higher solution accuracy, which indicates the merits of proposed ESMA. The results of Wilcoxon signed-rank test also reveal that ESMA is significant superior to other comparative optimization algorithms. Moreover, the results of three constrained engineering design problems demonstrate that ESMA is better than comparative algorithms.

Splitting extrapolation algorithms for solving linear delay Volterra integral equations with a spatial variable

This paper presents a numerical algorithm for solving linear delay Volterra integral equations with a spatial variable. The theory on compact operators is utilized to prove the existence and uniqueness of solution for the original equation, by combining the trapezoidal quadrature formula with interpolation to obtain an approximate equation. Then, we validate the existence of the approximate solution by analyzing the convergence of iterative sequence. The uniqueness of the approximate solution is proved by applying a two-dimensional discrete Gronwall inequality. Next, the convergence of the approximate solution and the asymptotic expansion of errors are obtained. Moreover, a higher accuracy solution is obtained by means of splitting extrapolation algorithms. Some numerical experiments are provided to demonstrate the efficiency of the proposed method.

Two Methods to Improve the Efficiency of Supersonic Flow Simulation on Unstructured Grids

The paper presents two methods to improve the efficiency of supersonic flow simulation using arbitrarily shaped unstructured grids. The first method promotes increasing the numerical solution convergence rate and is based on the geometric multigrid method for initialization of the flow field. The method is used to obtain the initial field of distributed physical quantity values, which maximally corresponds to the converged solution. For this purpose, the problem simulation is performed on a series of coarse grids beginning from the coarsest one in this series. Upon completion of simulations, the solution obtained is interpolated to a finer grid and used for initialization of simulations on this grid. The second method allows increasing the numerical solution accuracy and is based on statically adapting the computational grid to the flow specifics. The static adaptation algorithm provides automatic refinement of the computational grid in the region of specific features of flow, such as shock waves typical for supersonic flows. This algorithm provides a better description of the shock-wave front owing to the local grid refinement, with the local refinement region being automatically selected. Results of using these methods are demonstrated for the two supersonic aerodynamics problems: the simulation of the bow shock strength at a given distance under axially symmetric body Seeb-ALR and a mock-up aircraft Lockheed Martin 1021. It is shown that in both cases, the numerical solution convergence rate is increased owing to the use of the geometric multigrid method for initialization and a higher quality and a higher accuracy of solution is gained owing to the local grid refinement (using static adaptation means) near the shock-wave front.

Research on improved sparrow algorithm based on random walk

The optimization problem is a hot issue in today’s science and engineering research. The sparrow algorithm has the advantages of simple structure, few control parameters and high solution accuracy, and has been widely used in the research of optimization problems. Purposing at the problem that the sparrow search algorithm (SSA) can’t take into account the global and local optimization, an improved sparrow algorithm based on random walk strategy is proposed. After the sparrow search, the random walk is used to perturb the optimal sparrow to demonstrate its search-ability. At the original of the iteration, the random walk boundary is large, which is favourable to demonstrate the whole search-ability. After several iterations, the walk boundary becomes smaller, which improves the local search-ability of the best location of the algorithm. Taking the convergence speed, algorithm stability and convergence precision as evaluation indicators, the improved Sparrow Algorithm (RWSSA) is verified by 4 unimodal functions and 5 multimodal classical test functions, and compared with the traditional Sparrow algorithm. The experimental results show that the capacity of the improved sparrow algorithm based on random walk is significantly improved. At the same time, RWSSA is put into practice the power prediction problem, which checkouts the feasibility of RWSSA in actual engineering problems.

A novel computational approach for a nonlinear fractional model of plasma physics

In the current study, a well-known fractional nonlinear differential equation called Zakharov–Kuznetsov equation which has many applications in engineering and physics is investigated. An effective computational techniques namely Daftardar–Jafari Method (DJM) and He’s fractional derivative are employed to model the problem for obtaining a high accuracy of the analytical solution. The governing equations are solved and comparison of the results with exact solutions is presented to evaluate the precision of the presented method. The outcomes reveal that the DJM is efficient and easy to utilize. Further, three-dimensional contour plots are depicted according to the suitable parameters values.

Optimal detumbling strategy for a non-cooperative target with unknown inertial parameters using a space manipulator

Capturing tumbling target is considered as one of the greatest challenges in on-orbit service missions due to tumbling motion and parameter uncertainty of the space non-cooperative target. The tumbling motion of the target should be attenuated as quickly as possible before grasping to avoid the unexpected collisions and possible damages to the space manipulator or the target, which means the shortest-time detumbling trajectory is necessary. In many studies about the optimal detumbling trajectory planning the inertial parameters of the target have been assumed to be accurately known, which is usually difficult for a non-cooperative target so that parameter identification is needed before planning a optimal detumbling trajectory. In this paper, a novel strategy for parameter identification and detumbling of a tumbling target by a space manipulator is proposed. The strategy includes two phases. First, unknown inertial parameters of the target are identified in finite-time by a new estimation method with the assumption of interval excitation (IE), which relaxes the strict persistent excitation (PE) condition required in most prior studies. Second, the shortest-time detumbling trajectory of the tumbling target is generated by formulating a time-optimal control problem (OCP) in which the target attitude bounds and the limitations of the contact force as well as the relative velocity between the space manipulator and the target are represented as extended dynamical sub-systems and saturation functions. Then, the Calculus of Variations method is used to solve the OCP to obtain a high accuracy solution. During two phases, the contact force between the space manipulator and the target is utilized to generate external moment for identifying the inertia parameters of the target and detumbling the target. Meanwhile, a unified hybrid impedance control framework is applied to the space robot to track the desired contact force and motion trajectory. The whole strategy is verified by a space manipulator capturing a tumbling target, and numerical simulations demonstrate the effectiveness of the proposed methods.

Shape optimization of fluid cooling channel based on Darcy reduced-order isogeometric analysis

There exists the inconsistency among the design model, the analysis model, and the optimization model for the fluid cooling channel, as well as the numerical difficulty and the high computational cost caused by solving the problem of forced convection heat transfer. Our method overcomes these issues by three steps. Firstly, the seamless conversion among the three models is achieved through volume parametric reconstruction. The initial fluid cooling channel model is obtained based on some topological optimization methods, then a suitable model for isogeometric analysis (IGA) is reconstructed. Secondly, the IGA of the heat flux coupling problem is realized. To get a low-cost but sufficiently accurate analysis results, the Darcy reduced-order model is introduced when applying the IGA method, and the method is called DRIGA. After derivation of formulas for DRIGA, and applying the material properties and the boundary conditions, the problem of forced convection heat transfer is solved. With the same Darcy’s reduced-order model, the calculation is finished by the finite element method (FEM), and the method is called DRFEM. Solution accuracy is studied by comparing with the solution results from the COMSOL, DRFEM and DRIGA to verify the precision and effectiveness of DRIGA. Finally, the shape optimization is realized by taking the control points on the boundary of the solid and liquid as design variables and the average temperature as objective function. After optimization, not only the average temperature is reduced, but also the boundary is continuous and smooth. The given examples show that high solution accuracy and efficient convergence can be obtained with the condition of fewer computing elements in our method.