Symmetry-based optimal portfolio for a DC pension plan under a CEV model with power utility

In this article, explicit representation of solution for the Hamilton–Jacobi–Bellman (HJB) equation associated with the portfolio optimization problem for an investor who seeks to maximize the expected power (CRRA) utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model is derived based on the application of the Lie symmetry method to the partial differential equation and its associated terminal condition. Compared with the ingenious ansatz techniques used before, here we present a group theoretical analysis of the terminal value problem for the solution following the algorithmic procedure of the Lie symmetry analysis. It shows that the interesting properties of the group structures of the original HJB equation and its successive similarity reduced equations lead to an elegant resolution of the problem. Moreover, we identify the meaningful range of risk aversion coefficient which is ignored in the previous work. At last, the properties and sensitivity analysis of the derived optimal strategy are demonstrated by numerical simulations and several figures. The method used here is quite general and can be applied to other equations obtained in financial mathematics.

     

离心机上辨识加速度计模型参数的优化试验设计

本文针对离心机上测试加速度计时可以在多个球面上布测试点的特点,研究了双球面组合试验计划的优化设计问题,得出了Ｄ 最优准则下一个优化的组合试验计划测度比,并进行了工程简化,得到了一个实用的准Ｄ 最优组合试验计划。     

离心机上辨识陀螺加速度计二次项系数的优化试验设计

提出了一种在带有反转平台的精密离心机上标定陀螺加速度计误差模型二次项系数K 2的D-最优试验方案。应用该D-最优试验方案,通过重复试验,能够在测试点最少的情况下获得高测试精度,实现陀螺加速度计误差模型系数的最优(D-最优的)辨识。推导了测量随机误差、试验方案的测试点、测试点的重复测试次数以及误差模型系数方差之间的关系式。精度分析的结果表明,应用D-最优试验方案,采取重复试验的方法,能够有效地减小二次项系数K的估计量的方差,从而提高K的辨识精度。     

基于遗传算法的铅球投掷过程分析

运用有关力学知识建立了铅球投掷过程的数学模型，采用遗传算法对投掷过程进行优化，获得了投掷过程的各项最佳参数，并给出了最大的投掷距离．还对铅球投掷过程中的影响因素进行了灵敏度分析，确定出各影响因素的主次关系，为制定科学的运动训练计划提供了参考依据。     

基于不同目标使用期的既有结构构件可靠指标研究

在进行既有结构的安全性分析和可靠性评定时,对于不同的目标使用期仍直接采用现行规范中的目标可靠指标数值,显然缺乏合理性。基于此,本文选取了14种具有代表性的结构构件,基于恒载+办公楼楼面活荷载、恒载+住宅楼面活荷载、恒载+风荷载3种简单荷载组合,考虑不同可变荷载与永久荷载的比值,根据不同目标使用期内荷载与抗力的统计特性,对可靠指标的数值进行了校准并给出相应的建议值。结果为:目标使用期小于30年时,目标可靠指标?取2.7;目标使用期为30年时,?取3.0;目标使用期大于30年时,?取3.2,这更符合工程实际鉴定时的判断结果。     

覆盖层地基上面板堆石坝区间优化设计

用区间分析方法研究覆盖层地基上面板堆石坝的断面优化设计，根据该坝型的结构特点和工作条件，提出了合适的优化设计数学模型，探讨了区间优化的求解方法。实例计算表明，方法的收敛性好，计算量小；所得到的设计方案经济合理，安合可靠。     

The Relaxation of Two-well Energies with Possibly Unequal Moduli

The elastic energy of a multiphase solid is a function of its microstructure. Determining the infimum of the energy of such a solid and characterizing the associated optimal microstructures is an important problem that arises in the modeling of the shape memory effect, microstructure evolution, and optimal design. Mathematically, the problem is to determine the relaxation under fixed phase fraction of a multiwell energy. This paper addresses two such problems in the geometrically linear setting. First, in two dimensions, we compute the relaxation under fixed phase fraction for a two-well elastic energy with arbitrary elastic moduli and transformation strains, and provide a characterization of the optimal microstructures and the associated strain. Second, in three dimensions, we compute the relaxation under fixed phase fraction for a two-well elastic energy when either (1) both elastic moduli are isotropic, or (2) the elastic moduli are well ordered and the smaller elastic modulus is isotropic. In both cases we impose no restrictions on the transformation strains. We provide a characterization of the optimal microstructures and the associated strain. We also compute a lower bound that is optimal except possibly in one regime when either (1) both elastic moduli are cubic, or (2) the elastic moduli are well ordered and the smaller elastic modulus is cubic; for moduli with arbitrary symmetry we obtain a lower bound that is sometimes optimal. In all these cases we impose no restrictions on the transformation strains and whenever the bound is optimal we provide a characterization of the optimal microstructures and the associated strain. In both two and three dimensions the quasiconvex envelope of the energy can be obtained by minimizing over the phase fraction. We also characterize optimal microstructures under applied stress.     

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介绍了运动机器人针对动态变化环境的运动控制与决策(如运动障碍物规避,运动 目标跟踪等)问题. 分别从速度空间控制决策的角度分析阐述了运动 决策的基本方法,以及各自的特点. 提出了关于随机运动障碍物与目标的避障问题以及解 决思路,从而建立起基于概率分析的全局优化的速度避障决策方案. 通过仿真试验说明了方 法的有效性,并与传统非概率分析的实时局部决策的方法进了比较与评价.     

格子玻尔兹曼法多块网格的交界结构优化研究

基于格子玻尔兹曼方法LBM(Lattice Boltzmann Method)对多块网格方法(Multi-Block)的粗细网格交界结构进行了研究,提出了一种新的优化处理方案。解决了原有网格交界结构存在的三个问题,即两套插值运算造成的程序结构复杂的问题,存储前几个时间步的节点流场数据以备插值运算造成内存浪费的问题和基于时间插值结果进行空间插值计算造成插值误差积累的问题。用一次多点二维空间插值的方式,将原方法的空间和时间双插值,简并成一次空间插值。通过对经典的非定常的圆柱绕流算例和定常的标准顶盖方腔驱动流算例的仿真模拟,验证了交界面处质量、动量及应力的连续性以及网格交界面数据过渡的流畅度,最终验证了改进方法的正确性。数值模拟结果表明,改进后多块算法可实现局部网格细化,进一步推动LBM方法在实际工程问题中的应用。     

On the propagation of elastic waves in a multiperiodically reinforced medium

By a multiperiodically reinforced medium (multiperiodic composite) we mean a composite in which the matrix material is reinforced by two or more families of periodically spaced fibres. Moreover, at least along one direction the periods corresponding to different families are different. An example of this composite is shown in Fig. 1, where along the x ¹-axis we deal with two different periods . The aim of the contribution is twofold. First, we propose a macroscopic (averaged) model of a multiperiodic composite, describing the effect of period lengths on the overall dynamic behaviour of the medium, in contrast to the known homogenized models. Second, we apply this model to the analysis of elastic waves propagating across a composite reinforced by two pairs of families of parallel periodically spaced fibres with different periods along certain direction.     

Numerical solution of the St. Venant equations with the MacCormack finite-difference scheme

This paper describes the use of the MacCormack explicit time-spilitting scheme in the development of a two-dimensional (in plan) hydraulic simulation model that solves the St. Venant equations. Various tests devised to assess the performance of the method have been performed and the results are reported. Finally, two industrial applications of the model are presented. The method has been found to be computationally efficient and warrants further development.     

A novel aseismic foundation system for multipurpose asymmetric buildings

The vulnerability of civil engineering structures with fundamental frequency, say roughly above 1?Hz, (or buildings having less than ten stories), when exposed to the strong motion phase of an earthquake is considerably reduced by means of base isolation. The low-pass filter for isolating horizontal vibrations is redesigned where the classical elastomeric bearings are substituted by a number of prestressed helical steel springs with pivoted columns along their vertical axes carrying a fraction of the dead weight and guiding the remaining horizontal motion. The base-isolated building in its fundamental mode is considered to be rigid and low-cost tuned liquid column gas dampers (TLCGDs), in optimal arrangement within the plan of the basement of the building, supply the effective damping of the remaining horizontal vibrations. TLCGD-tuning in a first step is performed by a simple transformation of the well-documented optimal parameters of the tuned mass damper (TMD) followed by fine-tuning in state space. The action of the passive damping device is commonly considered to be sufficient. Since the gas-spring effect somewhat counter acts changes in fluid mass, the absorber can be used as a water reservoir. Compatible sliding elements are innovatively designed to resist the motion of the building relative to the ground for sufficiently small disturbances by static friction, thus complete the isolation system. However, during seismic excitation, the frictional contact is released over much of the time to avoid excessive wear.     

关于两种二阶应变梯度理论

对常见的两种应变梯度理论进行了深入的理论分析,比较了它们在公式推导、能量表达、物理解释和应用领域方面的差异. 选择钢筋拉拔弹性阶段和超薄悬臂梁受压弯曲两个典型的算例,采用可以通过C^{0\hbox{-}1}分片检验的18自由度应变梯度平面三角形单元和轴对称三角形单元,通过数值计算比较了两种理论在描述细观力学性能方面的差异.      

频率约束的三维连续体结构动力拓扑优化设计

针对频率约束和结构重量最小的动力拓扑优化问题, 基于(independent continuous mapping, ICM)独立、连续、映射方法,建立了频率约束下的三维连续体拓扑优化模型. 利用瑞利商和一阶泰勒展式对频率约束进行了显式化处理,并采用幂函数与复合指数函数作为过滤函数,将优化模型进行了标准化转换, 利用对偶理论及数学规划法进行了求解. 另外,利用质量矩阵和刚度矩阵过滤函数比值与动态约束处理了局部模态和模态交换等数值问题. 最后,通过应用两类不同过滤函数的数值算例表明了文中模型及方法在处理动力拓扑优化问题上的合理性与有效性.      

A three-dimensional optimal control problem in determining the boundary control heat fluxes

A three-dimensional optimal control algorithm in determining the strength of the unknown optimal boundary control heat fluxes utilizing the Conjugate Gradient Method (CGM) and a general purpose commercial code CFX4.2 is applied successfully in the present study based on the desired domain temperature distributions at the final time of heating. Results obtained by using the conjugate gradient method to solve this three-dimensional optimal control problems are justified based on the numerical experiments. Two different computational domains and two different desired temperature distributions are given and the corresponding optimal control heat fluxes are to be determined. Results show that the optimal control heat fluxes can always be obtained with any arbitrary initial guesses of the boundary fluxes.     

尼泊尔波迪·科西水利枢纽三维渗流分析

针对尼泊尔波迪·科西水电工程首部枢纽布置和软土坝基的岩性条件和渗透特征 ,通过对混凝土防渗墙深度、灌浆帷幕长度、混凝土渗透性、地基渗透性的敏感性分析 ,确定出防渗墙和防渗帷幕的优化方案 ,并对三种库水位工况下的三维渗流场进行了详细的计算分析 ,为工程优化设计提供依据.     

Thermal-economic multi-objective optimization of shell and tube heat exchanger using particle swarm optimization (PSO)

Many studies are performed by researchers about shell and tube heat exchanger (STHE) but the multi-objective particle swarm optimization (PSO) technique has never been used in such studies. This paper presents application of thermal-economic multi-objective optimization of STHE using PSO. For optimal design of a STHE, it was first thermally modeled using e-number of transfer units method while Bell–Delaware procedure was applied to estimate its shell side heat transfer coefficient and pressure drop. Multi objective PSO (MOPSO) method was applied to obtain the maximum effectiveness (heat recovery) and the minimum total cost as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. In order to show the accuracy of the algorithm, a comparison is made with the non-dominated sorting genetic algorithm (NSGA-II) and MOPSO which are developed for the same problem.     

Local detrended fluctuation analysis for spectral red-edge parameters extraction

Nowadays, spectrum technology makes it possible to nondestructively monitor crop and provide real-time diagnostic advice. Spectral red-edge parameters are important detection target for the growth of rapeseed. In this work, we propose a new method to acquire the rapeseed’s spectral red-edge parameters based on local detrended fluctuation analysis (L-DFA). In practice, by using the L-DFA, local Hurst exponent of the spectrum is calculated firstly. And then, six traditional red-edge parameter extraction methods, namely maximum first derivative method, adjusted linear extrapolation method, linear four-point interpolation method, inverted Gaussian method, Lagrangian interpolation method, and polynomial fitting interpolation, are employed to act on the estimated local Hurst exponent, and thus four red-edge parameters, i.e., red-edge position, red-edge amplitude, and left and right red-edge area, are obtained. In our experiments, by using the above four local Hurst exponent-based red-edge parameters as argument, a prediction model is developed to forecast the SPAD values (soil and plant analyzer development, often used as a parameter to indicate the chlorophyll content) for the five rapeseed’s growth periods based on random decision forest method. The results show that the local Hurst exponent-based red-edge feature can produce better model effect than the original spectrum-based one for the all phenological periods. Significance test for the four kinds of plant patterns shows that there is huge difference of the proposed four-dimensional red-edge features between the transplant and direct plant in the whole process of rapeseed’s growth. The differences between the other three groups of plant factors (two planting densities, two fertilizer types, and two weed controls) are not significant in certain specific growth periods of rapeseed. These findings provide a basis for studying difference of rapeseed yield and oil differences between different planting patterns.     

线性时滞系统的离散最优控制

介绍了对线性时滞系统进行最优控制的设计，将具有时滞控制的线性系统离散后引入增广状态向量。获得不显含时滞的差分方程，根据时滞量的两种分类情况采用连续和离散形式的性能指标函数导出了最优控制律。控制律包含当前状态和此前若干步状态向量的叠加，最优控制律直接从时滞方程中得到，可保证系统的稳定性，此方法亦适用于大时滞的情况。数值算例验证了控制策略的有效性。     

Doubly periodic patterns of modulated hydrodynamic waves: Exact solutions of the Davey-Stewartson system

Exact doubly periodic standing wave patterns of the Davey-Stewartson (DS) equations are derived in terms of rational expressions of elliptic functions.In fluid mechanics,DS equations govern the evolution of weakly nonlinear,free surface wave packets when long wavelength modulations in two mutually perpendicular,horizontal directions are incorporated.Elliptic functions with two different moduli (periods) are necessary in the two directions.The relation between the moduli and the wave numbers constitutes the dispersion relation of such waves.In the long wave limit,localized pulses are recovered.