Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

A Deep Learning Approach to Shape Optimization Problems for Flexoelectric Materials Using the Isogeometric Finite Element Method

A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.

Seismic effectiveness evaluation and optimized design of tie up method for securing museum collections

To quantify the seismic effectiveness of the most commonly used fishing line tie up method for securing museum collections and optimize fixed strategies for exhibitions,shaking table tests of the seismic systems used for typical museum collection replicas have been carried out.The influence of body shape and fixed measure parameters on the seismic responses of replicas and the interaction behavior between replicas and fixed measures have been explored.Based on the results,seismic effectiveness evaluation indexes of the tie up method are proposed.Reasonable suggestions for fixed strategies are given,which provide a basis for the exhibition of delicate museum collections considering the principle of minimizing seismic responses and intervention.The analysis results show that a larger ratio of height of mass center to bottom diameter led to more intense rocking responses.Increasing the initial pretension of fishing lines was conducive to reducing the seismic responses and stress variation of the lines.Through comprehensive consideration of the interaction forces and effective securement,it is recommended to apply 20%of breaking stress as the initial pretension.For specific museum collections that cannot be effectively protected by the independent tie up method,an optimized strategy of a combination of fishing lines and fasteners is recommended.

Optimal operation of Internet Data Center with PV and energy storage type of UPS clusters

With the development of green data centers,a large number of Uninterruptible Power Supply(UPS)resources in Internet Data Center(IDC)are becoming idle assets owing to their low utilization rate.The revitalization of these idle UPS resources is an urgent problem that must be addressed.Based on the energy storage type of the UPS(EUPS)and using renewable sources,a solution for IDCs is proposed in this study.Subsequently,an EUPS cluster classification method based on the concept of shared mechanism niche(CSMN)was proposed to effectively solve the EUPS control problem.Accordingly,the classified EUPS aggregation unit was used to determine the optimal operation of the IDC.An IDC cost minimization optimization model was established,and the Quantum Particle Swarm Optimization(QPSO)algorithm was adopted.Finally,the economy and effectiveness of the three-tier optimization framework and model were verified through three case studies.

A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Research on Regulation Method of Energy Storage System Based on Multi-Stage Robust Optimization

To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method,which helps overcome the limitations of traditional methods in terms of time scale.The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day.To achieve this,a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power.The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem.By decomposing the problem into a series of sub-objectives,the system scale is effectively reduced,and the algorithm’s convergence ability is improved.Compared with other algorithms,the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.

Optimized air-ground data fusion method for mine slope modeling

Refined 3D modeling of mine slopes is pivotal for precise prediction of geological hazards.Aiming at the inadequacy of existing single modeling methods in comprehensively representing the overall and localized characteristics of mining slopes,this study introduces a new method that fuses model data from Unmanned aerial vehicles(UAV)tilt photogrammetry and 3D laser scanning through a data alignment algorithm based on control points.First,the mini batch K-Medoids algorithm is utilized to cluster the point cloud data from ground 3D laser scanning.Then,the elbow rule is applied to determine the optimal cluster number(K0),and the feature points are extracted.Next,the nearest neighbor point algorithm is employed to match the feature points obtained from UAV tilt photogrammetry,and the internal point coordinates are adjusted through the distanceweighted average to construct a 3D model.Finally,by integrating an engineering case study,the K0 value is determined to be 8,with a matching accuracy between the two model datasets ranging from 0.0669 to 1.0373 mm.Therefore,compared with the modeling method utilizing K-medoids clustering algorithm,the new modeling method significantly enhances the computational efficiency,the accuracy of selecting the optimal number of feature points in 3D laser scanning,and the precision of the 3D model derived from UAV tilt photogrammetry.This method provides a research foundation for constructing mine slope model.

A new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning

In this paper,a new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning is presented in this paper.The existence of nonlinear terms in the studied system makes it very difficult to design the optimal controller using traditional methods.To achieve optimal control,RL algorithm based on critic–actor architecture is considered for the nonlinear system.Due to the significant security risks of network transmission,the system is vulnerable to deception attacks,which can make all the system state unavailable.By using the attacked states to design coordinate transformation,the harm brought by unknown deception attacks has been overcome.The presented control strategy can ensure that all signals in the closed-loop system are semi-globally ultimately bounded.Finally,the simulation experiment is shown to prove the effectiveness of the strategy.

Optimization of Open-cast Mining Procedure Based on RSR Method

To explore the optimal evaluation mechanism of open-cast mining procedure,this paper takes the actual operation status of Huolinhe No.1 Open-cast Mine as the research basis,and makes a deep analysis of the four representative mining procedures proposed by this mine.A detailed and comprehensive evaluation system is constructed using rank-sum ratio(RSR)method.The system covers 17 key indicators and aims to evaluate the advantages and disadvantages of each scheme in an all-round and multi-angle manner.Through the calculation and analysis by RSR method,the comprehensive evaluation of the four types of mining procedure schemes is carried out,and finally the secondary river improvement project is determined as the optimal mining implementation scheme,and the joint mining scheme of the south and north areas is the alternative strategy.The research results of this paper are objective,clear and definite,can not only reveal the effectiveness and feasibility of RSR method in solving the problem of open-cast mining procedure optimization,but also provide a strong technical support and decision-making basis for the future production development of Huolinhe No.1 Open-cast Mine.Thus,this study is expected to further promote the scientific and refined process of mining operations.

Research on Optimal Design of Campus Space Based on POE Concept: A Case Study of Anhui Xinhua College

Through the analysis of the overall landscape,revetments and roads and plant landscape,10 evaluation factors were determined.The comprehensive evaluation model for the campus space of Anhui Xinhua University was constructed by analytic hierarchy process(AHP).The results showed that revetment safety,road convenience,plant disease resistance and campus activity space were important factors affecting the spatial form planning of campus.Through the comparative analysis of the collected data,optimization suggestions were put forward to provide a basis for the establishment of“people-oriented”campus open space system.

Horizontal-to-vertical spectral ratio inversion method based on multimodal forest optimization algorithm

The exploration of urban underground spaces is of great significance to urban planning,geological disaster prevention,resource exploration and environmental monitoring.However,due to the existing of severe interferences,conventional seismic methods cannot adapt to the complex urban environment well.Since adopting the single-node data acquisition method and taking the seismic ambient noise as the signal,the microtremor horizontal-to-vertical spectral ratio(HVSR)method can effectively avoid the strong interference problems caused by the complex urban environment,which could obtain information such as S-wave velocity and thickness of underground formations by fitting the microtremor HVSR curve.Nevertheless,HVSR curve inversion is a multi-parameter curve fitting process.And conventional inversion methods can easily converge to the local minimum,which will directly affect the reliability of the inversion results.Thus,the authors propose a HVSR inversion method based on the multimodal forest optimization algorithm,which uses the efficient clustering technique and locates the global optimum quickly.Tests on synthetic data show that the inversion results of the proposed method are consistent with the forward model.Both the adaption and stability to the abnormal layer velocity model are demonstrated.The results of the real field data are also verified by the drilling information.

A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

A Priori Error Analysis for NCVEM Discretization of Elliptic Optimal Control Problem

In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H1 and L2 norms. Finally, some numerical experiments are carried out to support the theoretical results.

Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method

How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

探讨无约束优化的一族最优条件数自调比变尺度（ＯＣＳＳＶＭ）算法的收敛性。证明了采用Ｗｏｌｆｅ线性搜索的此族算法对于一般的凸函数是整体收敛的。

Topology Optimization for Steady-State Navier-Stokes Flow Based on Parameterized Level Set Based Method

In this paper,we consider solving the topology optimization for steady-state incompressibleNavier-Stokes problems via a new topology optimization method called parameterized level set method,which can maintain a relatively smooth level set function with a local optimality condition.The objective of topology optimization is to􀀀nd an optimal con􀀀guration of theuid and solid materials that minimizes power dissipation under a prescribeduid volume fraction constraint.An arti􀀀cial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition.Although a great deal of work has been carried out for topology optimization ofuidow in recent years,there are few researches on the topology optimization ofuidow with physical body forces.To simulate theuidow in reality,the constant body force(e.g.,gravity)is considered in this paper.Several 2D numerical examples are presented to discuss the relationships between the proposed method with Reynolds number and initial design,and demonstrate the feasibility and superiority of the proposed method in dealing with unstructuredmesh problems.Three 3D numerical examples demonstrate the proposedmethod is feasible in three-dimensional.

The study of a neutron spectrum unfolding method based on particle swarm optimization combined with maximum likelihood expectation maximization

The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In order to solve the problem of the maximum likelihood expectation maximization(MLEM) algorithm which is easy to suffer the pitfalls of local optima and the particle swarm optimization(PSO) algorithm which is easy to get unreasonable flight direction and step length of particles, which leads to the invalid iteration and affect efficiency and accuracy, an improved PSO-MLEM algorithm, combined of PSO and MLEM algorithm, is proposed for neutron spectrum unfolding. The dynamic acceleration factor is used to balance the ability of global and local search, and improves the convergence speed and accuracy of the algorithm. Firstly, the Monte Carlo method was used to simulated the BSS to obtain the response function and count rates of BSS. In the simulation of count rate, four reference spectra from the IAEA Technical Report Series No. 403 were used as input parameters of the Monte Carlo method. The PSO-MLEM algorithm was used to unfold the neutron spectrum of the simulated data and was verified by the difference of the unfolded spectrum to the reference spectrum. Finally, the 252Cf neutron source was measured by BSS, and the PSO-MLEM algorithm was used to unfold the experimental neutron spectrum.Compared with maximum entropy deconvolution(MAXED), PSO and MLEM algorithm, the PSO-MLEM algorithm has fewer parameters and automatically adjusts the dynamic acceleration factor to solve the problem of local optima. The convergence speed of the PSO-MLEM algorithm is 1.4 times and 3.1 times that of the MLEM and PSO algorithms. Compared with PSO, MLEM and MAXED, the correlation coefficients of PSO-MLEM algorithm are increased by 33.1%, 33.5% and 1.9%, and the relative mean errors are decreased by 98.2%, 97.8% and 67.4%.

Topology Optimal Design of Material Microstructures Using Strain Energy-based Method

Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing efficiency and simplified programming. Both the dual convex programming method and perimeter constraint scheme are used to optimize the 2D and 3D microstructures. Numerical results indicate that the strain energy-based method has the same effectiveness as that of homogenization method for orthotropic materials.

An improved optimal elemental method for updating finite element models

The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results.This situation occurs when the test modal model is incomplete,as is often the case in practice.An improved optimal elemental method is presented that defines a new objective function,and as a byproduct,circumvents the need for mass normalized modal shapes,which are also not readily available in practice.To solve the group of nonlinear equations created by the improved optimal method,the Lagrange multiplier method and Matlab function fmincon are employed.To deal with actual complex structures, the float-encoding genetic algorithm(FGA)is introduced to enhance the capability of the improved method.Two examples,a 7- degree of freedom(DOF)mass-spring system and a 53-DOF planar frame,respectively,are updated using the improved method. The example results demonstrate the advantages of the improved method over existing optimal methods,and show that the genetic algorithm is an effective way to update the models used for actual complex structures.