Bayesian prediction of crack growth based on a hierarchical diffusion model

A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide predictions for crack propagation in an early stage of the growth process. To improve the prediction, the information of other crack growth processes is used in a hierarchical (mixed‐effects) model. Two stochastic versions of a deterministic growth model are compared. One is a nonlinear regression setup where the trajectory is assumed to be the solution of an ordinary differential equation with additive errors. The other is a diffusion model defined by a stochastic differential equation where increments have additive errors. While Bayesian prediction is known for hierarchical models based on nonlinear regression, we propose a new Bayesian prediction method for hierarchical diffusion models. Six growth models for each of the two approaches are compared with respect to their ability to predict the crack propagation in a large data example. Surprisingly, the stochastic differential equation approach has no advantage concerning the prediction compared with the nonlinear regression setup, although the diffusion model seems more appropriate for crack growth. Copyright © 2016 John Wiley & Sons, Ltd.     

Short-term prediction method of wind speed series based on fractal interpolation

In order to improve the prediction performance of the wind speed series, the rescaled range analysis is used to analyze the fractal characteristics of the wind speed series. An improved fractal interpolation prediction method is proposed to predict the wind speed series whose Hurst exponents are close to 1. An optimization function which is composed of the interpolation error and the constraint items of the vertical scaling factors in the fractal interpolation iterated function system is designed. The chaos optimization algorithm is used to optimize the function to resolve the optimal vertical scaling factors. According to the self-similarity characteristic and the scale invariance, the fractal extrapolate interpolation prediction can be performed by extending the fractal characteristic from internal interval to external interval. Simulation results show that the fractal interpolation prediction method can get better prediction result than others for the wind speed series with the fractal characteristic, and the prediction performance of the proposed method can be improved further because the fractal characteristic of its iterated function system is similar to that of the predicted wind speed series.     

Multiple attribute decision-making method based on projection model for dual hesitant fuzzy set

Fuzzy Optimization and Decision Making - In the decision-making process, retaining the original data information has become a most crucial step. Dual hesitant fuzzy sets (DHFS), which can reflect...     

Estimation based on one step ahead prediction versus estimation based on multi-step ahead prediction

In this paper we consider a strictly stationary time series generated by a nonlinear autoregression. We are concerned with the estimation of the parameter θ₀ which specifies the autoregression Two estimators are considered, namely. θ _n obtained by minimising the sum of squarcs of the sample prediction emets of a one step ahead predictor and θ _n obtained by minimising the sum of squares of the sample prediction errors of a multi-step ahead predictor. It is shown that θ_n is a better estimator of θ₀ than θ _n .     

基于ROC方法对门脉高压脾切后PVT早期预测的诊断研究

以因肝硬化行门脉高压脾切除术的患者为研究对象,观察并记录患者术后并发门脉血栓（PVT）的情况,收集所有患者的P-选择素、血栓前体蛋白（TPP）和D2聚体（D2）含量（术后第1,3,5,7,14天）的临床观察指标数据,分析各临床观察指标与并发PVT的关系.建立相应的统计模型,并利用受试者工作特征曲线（ROC曲线）方法,比较各指标在单独和联合预测PVT时的价值和意义,确定最佳的术后预测时间和阈值,进而对PVT的形成进行较准确、早期的预测,为临床防治相关患者并发PVT打下基础.     

Overlapping for preconditioners based on incomplete factorizations and nested arrow form

In this paper, we discuss the usage of overlapping techniques for improving the convergence of preconditioners based on incomplete factorizations. To enable parallelism, these preconditioners are usually applied after the input matrix is permuted into a nested arrow form using k‐way nested dissection. This graph partitioning technique uses k‐way partitionning by vertex separator to recursively partition the graph of the input matrix into k subgraphs using a subset of its vertices called a separator. The overlapping technique is then based on algebraically extending the associated subdomains of these subgraphs and their corresponding separators obtained from k‐way nested dissection by their direct neighbours. A similar approach is known to accelerate the convergence of domain decomposition methods, where the input matrix is partitioned into a number of independent subdomains using k‐way vertex partitioning of a graph by edge separators, a different graph decomposition technique. We discuss the effect of the overlapping technique on the convergence of two classes of preconditioners, on the basis of nested factorization and block incomplete LDU factorization. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple crack fatigue growth modeling by displacement discontinuity method with crack-tip elements

This paper presents a numerical approach for modeling multiple crack fatigue growth in a plane elastic infinite plate. It involves a generation of Bueckner’s principle, a displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author and an extension of Paris’ law to a multiple crack problem under mixed-mode loading. Because of an intrinsic feature of the boundary element method, a general multiple crack growth problem can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. Fatigue growth modeling of an inclined crack in an infinite plate under biaxial cyclic loads is taken into account to illustrate the effectiveness of the present numerical approach. As an example, the present numerical approach is used to study the fatigue growth of three parallel cracks with same length under uniaxial cyclic load. Many numerical results are given.     

Mid-frequency dynamic characteristics prediction of thin plate based on B-spline wavelet on interval finite element method

Due to low computing efficiency and dispersion errors, Traditional Finite Element Methods (TFEMs) based on general polynomials cannot provide efficient dynamic solutions within mid-frequency domain which is the gap between low and high frequency domain. It is also defined as mid-frequency problem in the field of sound and vibration analysis. To solve this problem, it is essential to overcome these two disadvantages simultaneously based on much better computing efficiency and numerical stability. Fortunately, due to the multi-scale/multi-resolution features, the c₁ type Wavelet Finite Element Methods (WFEMs) own much better computing efficiency and numerical stability. Therefore, WFEMs will be introduced for dealing with the low computing efficiency and dispersion errors and solving the mid-frequency problem based on multi-element analysis. But, due to the complex nodes numbering and Degree of Freedoms (DOFs) numbering, the c₁ type WFEMs combined with existing assembling formulas cannot provide efficient solutions by multi-element analysis any more. Therefore, this paper mainly consists of two parts of research work. On the one hand, the proper assembling formulas are derived detailedly based on c₁ type WFEMs. On the other hand, the method combining c₁ type B-spline wavelet thin plate element with the newly derived assembling formulas is proposed for predicting dynamic characteristics and solving mid-frequency problem related to thin plate structures. The numerical study shows that both computing efficiency and numerical stability of the proposed method are much better than TFEMs’. Furthermore, the proposed method's prediction ability can break through the limitation of TFEMs’ highest computing accuracy. In addition, the proposed method is verified by experimental study for predicting acceleration Frequency Response Functions (FRFs) of thin plate within 5 Hz–1000 Hz, and the experimental results indicate that the proposed method provides the potential to solve mid-frequency problem related to thin plate structures.     

多目标决策问题的广义折衷解研究

引进决策偏好参数，提出了多目标决策问题的广义折衷解概念，然后探讨了广义折衷解的性质，最后也给出其数学规划的求解方法。     

A hybrid prediction for wind buffeting noises of vehicle rear window based on LES-LAA method

Based on the theories of computational fluid dynamics (CFD) and aeroacoustics, a hybrid simulation technique, the so-called LES-LAA method is proposed in this paper, for predicting the wind buffeting noises generated by opening rear windows of a running vehicle. The LES-LAA is developed by combining the large eddy simulation (LES) and the Lighthill acoustic analogy (LAA) methods. Based on the established vehicle and wind tunnel models, the wind buffeting noises from rear windows are predicted by using the proposed LES-LAA method and the obtained results are compared with experimental data. The results show that the calculation error of sound pressure level (SPL) from the LES-LAA method is less than 2%, which suggests that the proposed method has good accuracy in predicting the wind noise of the rear window of a vehicle. The wind noise when both sides of the rear window are opened at the same time is much lower than the case when just one window is opened. In conclusion, the hybrid LES-LAA technique presented in this paper is effective and feasible for predicting the wind buffeting noise, which can be applied to other types of vehicle and is a promising approach for solving other aero-acoustical engineering problems.     

一类重积分解法的探讨

从一道考研试题入手,给出了当二重积分的被积函数或积分区域边界含x2-y2时的"双曲坐标变换"法.通过实例,对比说明该方法能够解决一类用直角坐标不易计算或不能计算的二重积分问题,并且可以运用到三重积分的计算上.     

Customer choice prediction based on transfer learning

Choice behaviour prediction is valuable for developing suitable customer segmentation and finding target customers in marketing management. Constructing good choice models for choice behaviour prediction usually requires a sufficient amount of customer data. However, there is only a small amount of data in many marketing applications due to resource constraints. In this paper, we focus on choice behaviour prediction with a small sample size by introducing the idea of transfer learning and present a method that is applicable to choice prediction. The new model called transfer bagging extracts information from similar customers from different areas to improve the performance of the choice model for customers of interest. We illustrate an application of the new model for customer mode choice analysis in the long-distance communication market and compare it with other benchmark methods without information transfer. The results show that the new model can provide significant improvements in choice prediction.     

Multiple criteria decision making method based on normal interval‐valued intuitionistic fuzzy generalized aggregation operator

On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval‐valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval‐valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval‐valued intuitionistic fuzzy generalized weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. © 2015 Wiley Periodicals, Inc. Complexity 21: 277–290, 2016     

线性规划多重最优解判别准则刍议

本构造了一些线性规划问题来探讨多重最优解的判别准则，补充了现行献中关于多重最优解判别准则描述的不足，并指出多重最优解判别准则在出现退化解时可能失效的例外情况。     

基于协整理论的中国人口死亡率预测

近年来,人类寿命明显延长.长寿风险对于国家养老金制度,保险公司寿险业务的影响日益凸现.长寿风险源于人口死亡率的非预期变动,精准预测人口死亡率是长寿风险研究的一项重要内容.文中提出了一种死亡率预测的新方法,将计量经济学中的协整理论引入死亡率预测,以弥补中国死亡率历史数据缺乏,并结合极值理论方法给出中国死亡率的预测.     

基于errors-in-variables的预测模型及其应用

预测是统计学实际应用的一个主要方面,多元线性回归预测是一种很好的方法,广泛地应用在各种实际领域,但其局限性及不足也是明显的。本文以一种新的观点认识数据,即认为变量的观测里均含有误差,同时认为不应删除经慎重选择进来的解释变量。为此,本文提出了一种新的多元预测方法———多元线性EIV预测。本文还考虑了新预测模型的一个实例应用,并从相对偏差上与多元回归预测进行了比较,从而揭示了多元线性EIV预测的先进性及较好的预测精度。     

An asset residual life prediction model based on expert judgments

An appropriate and accurate residual life prediction for an asset is essential for cost effective and timely maintenance planning and scheduling. The paper reports the use of expert judgments as the additional information to predict a regularly monitored asset’s residual life. The expert judgment is made on the basis of measured condition monitoring parameters, and is treated as a random variable, which may be described by a probability distribution due to the uncertainty involved. Since most expert judgments are in the form of a set of integer numbers, we can either directly use a discrete distribution or use a continuous distribution after some transformation. A key concept used in this paper is condition residual life where the residual life at the point of checking is conditional on, among others, the past expert judgments made on the same asset to date. Stochastic filtering theory is used to predict the residual life given available expert judgments. Artificial, simulated and real data are used for validating and testing the model developed.     

A prognosis model for wear prediction based on oil-based monitoring

This paper reports on the development of a wear prediction model based on stochastic filtering and hidden Markov theory. It is assumed that observations at discrete time points are available such as metal concentrations from oil-based monitoring, which are related to the true underlying state of the system which is unobservable. The system state is represented by a generic term of wear which is modelled by a continuous hidden Markov Chain using a Beta distribution. We formulated a recursive model to predict the current and future system state given past observed monitoring information to date. The model is useful to wear-based monitoring such as oil analysis. Numerical examples are presented in the paper based on simulated and real data.     

基于提升小波的基因芯片数据的分类预测

针对肿瘤的早期诊断,提出了一种基于提升小波变换的特征提取的方法,对肿瘤数据样本进行分析鉴别.该方法利用提升小波变换对190例肝癌（包括对照）和107例肺癌（包括对照）基因表达谱芯片数据进行处理后,提取信号的低频信息,经支持向量机训练学习,构造分类器模型,用于癌和非癌样本的区分甄别.实验结果表明,经提升小波变换提取的特征基因,送入分类器中能得到较高的分类率,且在支持向量机中选取线性核函数或径向基函数都能达到较好的分类效果.通过随机选取的20例基因表达谱芯片样本,对所建立的模型进行了测试,获得了很好的效果,因此,本文提出的方法对肿瘤的诊断有一定的应用意义.