Surface tensor estimation from linear sections

From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n‐dimensional Euclidean space. The estimators are based on one‐dimensional linear sections. In a design based setting we suggest three types of estimators. These are based on isotropic uniform random lines, vertical sections, and non‐isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting.     

Particle methods for PDEs arising in financial modeling

We numerically study convection–diffusion equations arising in financial modeling. We focus on the convection-dominated cases, in which the diffusion coefficients are relatively small. Both finite-difference and Monte-Carlo methods which are widely used in the problems of this kind might be inefficient due to severe restrictions on the meshsize and the number of realizations needed to achieve high resolution.We propose an alternative approach based on particle methods which have extremely low numerical diffusion and thus do not have the aforementioned restrictions. Our approach is based on the operator splitting: The hyperbolic steps are made using the method of characteristics, while the parabolic steps are performed using either a special discretization of the integral representation of the solution (which leads to a deterministic particle method) or a stochastic random walk approach.We apply the designed particle methods to a variety of test problems and the numerical results indicate high accuracy, efficiency and robustness of both the deterministic and stochastic methods. In addition, our numerical experiments clearly demonstrate that the deterministic particle method outperforms its stochastic counterpart.     

On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.     

纯电动汽车磷酸铁锂电池组的建模及优化

鉴于传统神经网络和支持向量机机理复杂、计算量大的缺陷,很难实时跟踪磷酸铁锂电池组复杂快速的内部反应,影响电池荷电状态的估算精度,提出应用一种简单、有效的极限学习机对一额定容量为100Ah、额定电压为72V的纯电动汽车磷酸铁锂电池组建模,并分别与BP神经网络、RBF神经网络、支持向量机进行对比。随后,以学习时间和泛化性能为优化目标,应用粒子群方法寻找最佳隐层节点个数。结果表明,基于极限学习机的磷酸铁锂电池组模型的学习时间、泛化性能优于BP神经网络、RBF神经网络、支持向量机;隐层节点优化后,模型的学习时间和泛化性能达到最优。     

基于PSO-SVR算法的氧乐果合成过程建模研究

针对氧乐果合成过程中温度控制具有参数时变、时滞后、非线性的特点,提出了一种基于改进粒子群算法的支持向量回归的建模方法。对于支持向量回归模型,3个参数(ε,C,γ)的选取很大程度上决定了其拟合的精度和泛化能力的好坏,采用改进的粒子群算法对参数(ε,C,γ)进行同时寻优,建立了改进的氧乐果合成过程PSO-SVR回归模型,该模型具有很好的学习能力和推广能力。实验结果表明,模型较好地体现了系统的动态特性,可用于氧乐果合成过程的模型预估控制,提高系统的控制品质。     

基于GA-BP的移动通信设备故障诊断

针对通信设备故障发生随机性强,影响因素多,对应的故障诊断有高度非线性和不确定性的特点,采用BP神经网络算法,优化的GA-BP神经网络算法和POS-BP神经网络算法分别搭建基站设备故障诊断模型,提取设备故障历史数据进行MATLAB仿真,准确预测设备故障类型,帮助提高代维公司调度管理的智能化水平,提高基站设备运维的执行效率。仿真结果表明：本文的BP,GA-BP和POS-BP神经网络算法都能够实现设备故障类别的预测,且GA-BP神经网络算法相比BP和POS-BP神经网络算法对通信设备故障诊断有更好的适应性。     

基于改进DPSO算法的并行测试任务优化调度研究

并行测试以减少测试时间和降低测试成本的强大优势,已成为当前自动测试系统发展的方向。针对并行自动测试过程中,测试任务调度复杂,难以优化的问题,以PSO算法为基础,通过对问题空间编码的重新定义,并运用交叉、变异算子给出了新的粒子位置的更新公式,提出了一种改进后的DPSO算法。依据并行测试完成时间极限定理,给出了并行测试任务调度的目标函数与约束条件。以某雷达电子装备并行测试系统中三块电路板并行测试为例,对改进的DPSO算法进行了仿真验证,得到了最优调度测试序列。结果表明：与遗传算法相比,改进后的DPSO算法迭代次数更少,寻优性能更好,适用于工程应用。     

微粗糙结构表面液滴浸润特性的多体耗散粒子动力学研究

超疏水表面因其优异的自洁作用一直是表面科学领域关注的重点.本文使用多体耗散粒子动力学(many-body dissipative particle dynamics, MDPD)方法模拟研究了不同粗糙结构下液滴的浸润特性, 并与Cassie-Baxter理论进行了对比. 研究使用了一种具有长吸短斥作用的流固作用函数来获得不同的液滴浸润性, 并利用一种简洁的数值方法来测量接触角. 模拟结果表明本研究方法能够稳定地捕捉到液滴在粗糙表面的静态和动态特性. 模拟了粗糙结构对三相接触线运动的黏滞作用, 与物理实验结果相符合, 表明Cassie-Baxter理论在实际应用中尚存在一定局限性. 研究分析了在动态铺展过程中的能量转化关系, 并指出在低值表面容易引起液滴反弹.     

基于单粒子模型与偏微分方程的锂离子电池建模与故障监测

锂离子电池内部结构是一种复杂的分布参数系统, 如果为了降低计算难度而使用常微分方程描述锂离子电池, 可能会引入系统误差, 降低系统模型的可信度, 需要使用偏微分方程建立分布参数系统的精确模型. 本文提出了一种基于单粒子模型和抛物型偏微分方程的锂离子电池系统建模与故障监测系统设计方法, 当锂离子浓度实测值与理想值的残差大于预设门槛时判定分布参数系统处于故障状态. 通过一个仿真实例进行了锂离子电池系统建模和故障诊断实验, 实验证明基于单粒子模型和偏微分方程的锂离子电池故障监测系统具有更高的精确度和可信度.     

取向比对椭球气溶胶粒子散射特性的影响

利用T矩阵和离散坐标法研究了取向比对椭球粒子散射特性的影响, 计算了小尺度范围内椭球粒子的散射特征参量, 包括消光效率因子、不对称因子、单次散射反照率、散射相矩阵及双向反射函数(BRDF). 结果表明, 椭球粒子的散射特性与取向比密切相关, 粒子取向比会影响散射参量的振荡频率和振幅, 与球形粒子散射参量的相对差异也呈周期振荡趋势. 研究还发现, 某些特殊粒子尺寸的散射参量与粒子取向比基本无关. 在多次散射条件下, 分析不同取向比粒子群的BRDF随反射角和光学厚度的变化特性. 结果显示: 不同取向比粒子群的BRDF随反射角的变化趋势基本一致, 球形粒子群比非球形粒子群的BRDF曲线波动振幅更大; 球形-非球形粒子的BRDF相对差异随光学厚度和取向比的增大而减小, 随入射角的增大而增大.