脆性断裂的微观机理和非平衡统计特性

Ⅰ.引言如何才能将断裂的微观机理与宏观特性结合起来,把断裂理论建立于微裂纹演化的微观动力学基础上,从而统一导出所有重要的宏观力学量并以某些更基本的物理量表示之?这是人们为实现材料的强度和韧性设计必需解决的一个重要理论课题。就脆性断裂来说,尽管现有几个主要代表性的理论如断裂力学理论、位错理论和统计理论都各取得一定成就,但就其理论框架来说,由于明显的局限性,却难以发展成可供指导设计的理论。因此,人们在探索微观与宏观相结合的断裂理论。最近的工作表明:从微裂纹演      

基于贝叶斯参数优化的无模型自适应硅单晶直径控制

直拉硅单晶的生长过程涉及多场多相耦合与复杂的物理化学变化,其中工艺参数的波动是导致晶体直径不均匀的重要原因,如何实现工艺参数的控制以获得理想的、均匀的晶体直径具有重要的研究意义。本文分析现有控制方法存在不稳定以及控制效果不佳的问题后,提出基于贝叶斯参数优化的无模型自适应控制模型来控制硅单晶生长过程中的晶体直径。首先以坩埚上升速度与加热器的功率作为控制输入参数,晶体直径作为输出,搭建无模型自适应控制模型,并分析算法的稳定性。其次将控制模型进行仿真实验,发现硅单晶直径控制模型中不同的超参数设定会影响控制过程的迭代次数以及控制效果。最后,利用贝叶斯优化超参数的取值范围,并进行最终的仿真实验,结果表明,经贝叶斯参数优化后的控制模型计算快、迭代次数少,输出的晶体直径稳定,同时将生长工艺参数控制在实际生产要求范围内。因此,基于贝叶斯参数优化的无模型自适应控制实现了硅单晶直径均匀稳定的有效控制,具有结合工程背景的实际应用前景。     

玻璃态高聚物细观损伤断裂统计力学

对玻璃态高聚物内部细观损伤断裂判据、机理、动力学及统计模型的最新进展，进行了较为全面、系统的介绍和总结，并简要概述了细观损伤统计描述在金属材料及玻璃态高聚物领域里的应用。     

广义变系数模型的Bayesian B样条估计

提出了广义变系数模型函数系数的一种新的估计方法．我们用B样条函数逼近函数系数,不具体选择节点的个数,而是节点个数取均匀的无信息先验,样条函数系数取正态先验,用Bayesian模型平均的方法估计各个函数系数．这种估计方法一个主要特点是允许各个函数系数所需节点个数的后验分布不同,因此允许不同函数系数使用不同的光滑参数．另外,本文还给出了Bayesian B样条估计的计算方法,并通过模拟例子,说明广义变系数模型的函数系数可以由Bayesian B样条估计方法得到很好的估计．     

一个捕捉与再捕捉模型的贝叶斯分析

本文在无信息先验和Jeffreys先验下 ,就捕捉与再捕捉试验和多次重复的捕捉与再捕捉试验两种情况 ,推导了封闭总体中个体总数N的贝叶斯点估计与区间估计 ,并计算了一个实例     

样本区间的概率分布

设(X1，X2，…Xn)为服从I=[0,1]上均匀分布的容量为n的简单随机样本，它们将I=[0，1]分隔成(n 1)个样本区间(sample spacing)．记Y0,Y1，…Yn分别为这些样本区间的长度，又设Zx(x,ω)为包含点X∈I的唯一的左闭右开区间的长度．由于随机选取的点集被广泛运用于许多概率模型中．例如流行病学、遗传学、时间序列分析以及交通流理论等．因此，对Zn(x)及其相关统计量分布的研究也就引起了人们的广泛关注．本文利用顺序统计量的性质讨论了Yi(O≤i≤n)以及Zn(x，ω)的概率分布，有利于今后对上述理论的研究。     

Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects

Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.     

Analysis of large experimental datasets in electrochemical impedance spectroscopy

An approach for the analysis of large experimental datasets in electrochemical impedance spectroscopy (EIS) has been developed. The approach uses the idea of successive Bayesian estimation and splits the multidimensional EIS datasets into parts with reduced dimensionality. Afterwards, estimation of the parameters of the EIS-models is performed successively, from one part to another, using complex nonlinear least squares (CNLS) method. The results obtained on the previous step are used as a priori values (in the Bayesian form) for the analysis of the next part. To provide high stability of the sequential CNLS minimisation procedure, a new hybrid algorithm has been developed. This algorithm fits the datasets of reduced dimensionality to the selected EIS models, provides high stability of the fitting and allows semi-automatic data analysis on a reasonable timescale. The hybrid algorithm consists of two stages in which different zero-order optimisation strategies are used, reducing both the computational time and the probability to overlook the global optimum. The performance of the developed approach has been evaluated using (i) simulated large EIS dataset which represents a possible output of a scanning electrochemical impedance microscopy experiments, and (ii) experimental dataset, where EIS spectra were acquired as a function of the electrode potential and time. The developed data analysis strategy showed promise and can be further extended to other electroanalytical EIS applications which require multidimensional data analysis.     

Modelling Operational Risk Losses with Graphical Models and Copula Functions

The management of Operational Risk has been a difficult task due to the lack of data and the high number of variables. In this project, we treat operational risks as multivariate variables. In order to model them, copula functions are employed, which are a widely used tool in finance and engineering for building flexible joint distributions. The purpose of this research is to propose a new methodology for modelling Operational Risks and estimating the required capital. It combines the use of graphical models and the use of copula functions along with hyper-Markov law. Historical loss data of an Italian bank is used, in order to explore the methodology’s behaviour and its potential benefits.