Stochastic Programming for Hub Energy Management Considering Uncertainty Using Two-Point Estimate Method and Optimization Algorithm

To maximize energy profit with the participation of electricity,natural gas,and district heating networks in the day-ahead market,stochastic scheduling of energy hubs taking into account the uncertainty of photovoltaic and wind resources,has been carried out.This has been done using a new meta-heuristic algorithm,improved artificial rabbits optimization(IARO).In this study,the uncertainty of solar and wind energy sources is modeled using Hang’s two-point estimating method(TPEM).The IARO algorithm is applied to calculate the best capacity of hub energy equipment,such as solar and wind renewable energy sources,combined heat and power(CHP)systems,steamboilers,energy storage,and electric cars in the day-aheadmarket.The standard ARO algorithmis developed to mimic the foraging behavior of rabbits,and in this work,the algorithm’s effectiveness in avoiding premature convergence is improved by using the dystudynamic inertia weight technique.The proposed IARO-based scheduling framework’s performance is evaluated against that of traditional ARO,particle swarm optimization(PSO),and salp swarm algorithm(SSA).The findings show that,in comparison to previous approaches,the suggested meta-heuristic scheduling framework based on the IARO has increased energy profit in day-ahead electricity,gas,and heating markets by satisfying the operational and energy hub limitations.Additionally,the results show that TPEM approach dependability consideration decreased hub energy’s profit by 8.995%as compared to deterministic planning.

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

A Two-Point Boundary Value Problem by Using a Mixed Finite Element Method

This paper describes a numerical solution for a two-point boundary value problem. It includes an algorithm for discretization by mixed finite element method. The discrete scheme allows the utilization a finite element method based on piecewise linear approximating functions and we also use the barycentric quadrature rule to compute the stiffness matrix and the L2-norm.

A two-parameter multiple shooting method and its application to the natural vibrations of non-prismatic multi-segment beams

This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.

Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.

Precise integration method for solving singular perturbation problems

This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.

A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations

We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional derivatives.The main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral equations.Then,a Legendre-based spectral collocation method is developed for solving the transformed system.Therefore,we can make good use of the advantages of the Gauss quadrature rule.We present the construction and analysis of the collocation method.These results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange equations.Two numerical examples are given to confirm the convergence analysis and robustness of the scheme.

Mathematical analysis of EEP method for one-dimensional finite element postprocessing

For a class of two-point boundary value problems, by virtue of onedimensional projection interpolation, it is proved that the nodal recovery derivative obtained by Yuan＇s element energy projection （EEP） method has the accuracy O（h^min{2k,k＋4}） The theoretical analysis coincides the reported numerical results.

Coupling of high order multiplication perturbation method and reduction method for variable coefcient singular perturbation problems

Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.

High order multiplication perturbation method for singular perturbation problems

This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations （ODEs） are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.

Analytical Solutions of Some Two-Point Non-Linear Elliptic Boundary Value Problems

Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.

A new method for evaluating wedges of steel plates and strips

To overcome the inaccuracy problem of the traditional wedge evaluation of steel plates and strips caused by the ran-domness of the thicknesses of two local points and improve the reliability of the wedge index,the double-centroid method for the wedge evaluation was proposed,and a model based on the centroid theory was established.Meanwhile,an integral model for the discrete thickness values of the cross-section profiles was derived.The discussion focused on the distinct characteristics of the two-point method,asymmetric method,and double-centroid method in evaluating the asymmetric distribution of cross-sections.The three methods were employed to evaluate the wedge values of both the theoretical and measured cross-sections of steel plates and strips,and the accuracies of three wedge evaluation models were analyzed and discussed.The results showed that the double-centroid method objectively reflects the degree and variation characteristics of the wedge values of the cross-sections of steel plates and strips,and this method is feasible,reliable,and outstanding.

红外焦平面器件二点多段非均匀性校正算法研究

分析了红外焦平面探测器的非均匀性机理和各种非均匀性校正算法 ,提出两点多段非均匀性校正算法 ,该算法避免了二点校正算法的低精度和多点校正算法的大运算量 .在红外多谱段相机上的应用结果表明二点多段非均匀性校正算法具有运算量小、精度高、实用性强的优点 .

光谱成像仪CCD焦平面组件非均匀性校正技术研究

分析了光谱成像仪CCD焦平面的非均匀性机理和各种非均匀性校正算法,提出两点多段的非均匀性校正算法,该算法避免了两点校正算法的低准确度和多点校正算法的大运算量·在光谱成像仪上的应用结果表明,两点多段的非均匀性校正算法具有运算量小、准确度高、实用性强的优点·

基于DSP的红外焦平面阵列非均匀性校正技术

红外焦平面成像系统是红外成像技术发展的趋势,焦平面阵列的非均匀性校正技术是一项正在探索的关键技术。在分析了红外成像系统非均匀性的产生机理及表现特征的基础上,介绍了红外焦平面阵列非均匀性校正的基本方法;基于TMS320C62x DSP为核心的系统硬件平台,采用两点多段的方法,完成了红外图像非均匀性的实时校正;最后给出了实验结果,验证了本系统能够满足红外焦平面成像系统的要求,具有实时性好、实用性强的特点。

空基紫外成像仪关键器件ICCD非均匀性校正技术

从理论上分析了ICCD光电响应非均匀性的产生机理,并由此建立光电响应数学模型。基于两点多段非均匀性校正算法给出了ICCD非均匀性校正方程,并通过大量实验得到ICCD在特定条件下的校正系数。在实验过程中发现IC-CD的雪花点(主要由探测器的随机噪声引起)和盲点是影响非均匀性改善的主要因素,采取相应照度的响应进行了补偿。结果表明:通过补偿和校正输出图像,可以有效地减小紫外成像仪由探测器的非均匀性所带来的测量误差,使非均匀性降低了37.1%,在一定程度上减少了由于ICCD的物理特性和制造缺陷所带来的固有图像噪声。

多点定标非均匀性校正方法的综合应用

分析了某红外评估系统的点校正算法的优缺点,提出两点多段温度校正法,有效提高了校正效果。

一种基于两点线性校正的改进算法

针对传统的两点校正法准确度不高的缺点,提出一种二点多段线性校正的改进算法。这种算法对增益系数和偏移系数重新进行推导,弥补了两点多段校正法中由于校正因子推导带来结果值偏大的不足,并对算法进行了仿真。