模糊数据中异常点的一种识别方法

针对输入为确定数、输出为LR型模糊数的模糊数据集,利用最小二乘法建立了该模糊数据集的模糊线性回归分析模型及参数估计,用数据删除的方法研究了数据删除模糊线性回归模型,构造了统计诊断量—模糊Cook距离来识别模糊数据集中的异常点,通过数值模拟和对实例的研究,识别出其异常点,证实了本文构造的统计诊断量的有效性.     

An efficient metamodeling approach for uncertainty quantification of complex systems with arbitrary parameter probability distributions

This paper proposes an efficient metamodeling approach for uncertainty quantification of complex system based on Gaussian process model (GPM). The proposed GPM‐based method is able to efficiently and accurately calculate the mean and variance of model outputs with uncertain parameters specified by arbitrary probability distributions. Because of the use of GPM, the closed form expressions of mean and variance can be derived by decomposing high‐dimensional integrals into one‐dimensional integrals. This paper details on how to efficiently compute the one‐dimensional integrals. When the parameters are either uniformly or normally distributed, the one‐dimensional integrals can be analytically evaluated, while when parameters do not follow normal or uniform distributions, this paper adopts the effective Gaussian quadrature technique for the fast computation of the one‐dimensional integrals. As a result, the developed GPM method is able to calculate mean and variance of model outputs in an efficient manner independent of parameter distributions. The proposed GPM method is applied to a collection of examples. And its accuracy and efficiency is compared with Monte Carlo simulation, which is used as benchmark solution. Results show that the proposed GPM method is feasible and reliable for efficient uncertainty quantification of complex systems in terms of the computational accuracy and efficiency. Copyright © 2016 John Wiley & Sons, Ltd.     

Regularization in statistics

This paper is a selective review of the regularization methods scattered in statistics literature. We introduce a general conceptual approach to regularization and fit most existing methods into it. We have tried to focus on the importance of regularization when dealing with today's high-dimensional objects: data and models. A wide range of examples are discussed, including nonparametric regression, boosting, covariance matrix estimation, principal component estimation, subsampling.     

ADMM for High-Dimensional Sparse Penalized Quantile Regression

Sparse penalized quantile regression is a useful tool for variable selection, robust estimation, and heteroscedasticity detection in high-dimensional data analysis. The computational issue of the sparse penalized quantile regression has not yet been fully resolved in the literature, due to nonsmoothness of the quantile regression loss function. We introduce fast alternating direction method of multipliers (ADMM) algorithms for computing the sparse penalized quantile regression. The convergence properties of the proposed algorithms are established. Numerical examples demonstrate the competitive performance of our algorithm: it significantly outperforms several other fast solvers for high-dimensional penalized quantile regression. Supplementary materials for this article are available online.     

An integrated simulation-based fuzzy regression-time series algorithm for electricity consumption estimation with non-stationary data

This study presents an integrated fuzzy regression, computer simulation, and time series algorithm to estimate and predict electricity demand for seasonal and monthly changes in electricity consumption especially in developing countries such as China and Iran with non-stationary data. Since, it is difficult to model the uncertain behavior of energy consumption with only conventional fuzzy regression or time series, the integrated algorithm could be an ideal method for such cases. Computer simulation is developed to generate random variables for monthly electricity consumption. The fuzzy regression is run with computer simulation output too. A Granger–Newbold test is used to select the optimum model, which could be a time series, a fuzzy regression (with or without pre-processed data, PD) or a simulation-based fuzzy regression (with or without PD). The preferred time series model is selected from linear or nonlinear models. At last, the preferred model from fuzzy regression and time series models is selected by Granger–Newbold. Monthly electricity consumption in Iran from 1995 to 2005 is considered as the basis of this study. The mean absolute percentage error estimates of a genetic algorithm, an artificial neural network, and a fuzzy inference system versus the proposed algorithm show the appropriateness of the proposed algorithm. This is the first study that introduces an integrated simulation-based fuzzy regression-time series for electricity consumption estimation with an imprecise set of data.     

Model-based process optimization in the presence of parameter uncertainty

In model-based process optimization one uses a mathematical model to optimize a certain criterion, for example the product yield of a chemical process. Models often contain parameters that have to be estimated from data. Typically, a point estimate (e.g. the least squares estimate) is used to fix the model for the optimization stage. However, parameter estimates are uncertain due to incomplete and noisy data. In this article, it is shown how parameter uncertainty can be taken into account in process optimization. To quantify the uncertainty, Markov Chain Monte Carlo (MCMC) sampling, an emerging standard approach in Bayesian estimation, is used. In the Bayesian approach, the solution to the parameter estimation problem is given as a distribution, and the optimization criteria are functions of that distribution. The formulation and implementation of the optimization is studied, and numerical examples are used to show that parameter uncertainty can have a large effect in optimization results.     

稀疏偏最小二乘回归-多项式混沌展开代理模型方法

为解决传统多项式混沌展开方法在高维全局灵敏度和结构可靠度分析当中存在的维数灾难与多重共线性问题,该文提出一种稀疏偏最小二乘回归-多项式混沌展开代理模型方法。该方法首先采用偏最小二乘回归技术得到多项式混沌展开系数的初步估计,然后根据回归误差阈值允许下的最大稀疏度原则,采用带有惩罚的矩阵分解技术自适应地保留与结构响应相关性强的多项式,并采用偏最小二乘回归得到多项式混沌展开系数的更新估计。通过对展开系数进行简单后处理即可得到Sobol灵敏度指数。在此基础上保留重要输入变量并按新方法重新进行回归可实现对代理模型的精简,从而在不增加计算代价的情况下实现高精度结构可靠度分析。算例结果表明在保证精度的情况下,采用新方法进行全局灵敏度和结构可靠度分析比传统方法在计算效率方面有显著优势。     

计量中回归模型参数值及其不确定度评估

针对计量领域中广泛应用的数据回归处理方法,阐述了在基于正态分布噪声条件下,最小二乘法与贝叶斯推断法用于回归模型参数估计以及相应不确定度评估的过程。GUM系列不确定度评估准则中没有明确指出如何对回归参数进行不确定度评估,同时有些回归模型也无法唯一地转化为相应的测量方程。通过计量校准的实例说明了如何处理相应参数的确定等问题,以此说明2种方法的相同与不同之处。最小二乘方法计算简单直接且便于使用;而基于贝叶斯推断的方法则能充分利用计量校准中的经验和历史数据等信息,但由于其参数后验分布计算通常较为复杂,需采用马尔科夫链-蒙特卡罗(MCMC)法通过数值计算得到关注参数的结果。     

Capacity and material requirement planning modelling by comparing deterministic and fuzzy models

A model for the capacity and material requirement planning problem with uncertainty in a multi-product, multi-level and multi-period manufacturing environment is proposed. An optimization model is formulated which takes into account the uncertainty that exists in both the market demand and capacity data, and the uncertain costs for backlog. This work uses the concept of possibilistic programming by comparing trapezoidal fuzzy numbers. Such an approach makes it possible to model the ambiguity in market demand, capacity data, cost information, etc. that could be present in production planning systems. The main goal is to determine the master production schedule, stock levels, backlog, and capacity usage levels over a given planning horizon in such a way as to hedge against the uncertainty. Finally, the fuzzy model and the deterministic model adopted as the basis of this work are compared using real data from an automobile seat manufacturer. The paper concludes that fuzzy numbers could improve the solution of production planning problems.     

A Phase Estimation Algorithm for Quantum Speed-Up Multi-Party Computing

Security and privacy issues have attracted the attention of researchers in the field of IoT as the information processing scale grows in sensor networks. Quantum computing, theoretically known as an absolutely secure way to store and transmit information as well as a speed-up way to accelerate local or distributed classical algorithms that are hard to solve with polynomial complexity in computation or communication. In this paper, we focus on the phase estimation method that is crucial to the realization of a general multi-party computing model, which is able to be accelerated by quantum algorithms. A novel multi-party phase estimation algorithm and the related quantum circuit are proposed by using a distributed Oracle operator with iterations. The proved theoretical communication complexity of this algorithm shows it can give the phase estimation before applying multi-party computing efficiently without increasing any additional complexity. Moreover, a practical problem of multi-party dating investigated shows it can make a successful estimation of the number of solution in advance with zero communication complexity by utilizing its special statistic feature. Sufficient simulations present the correctness, validity and efficiency of the proposed estimation method.     

Robust Regression using Probability Plots for Estimating the Weibull Shape Parameter

The Weibull shape parameter is important in reliability estimation as it characterizes the ageing property of the system. Hence, this parameter has to be estimated accurately. This paper presents a study of the efficiency of using robust regression methods over the ordinary least‐squares regression method based on a Weibull probability plot. The emphasis is on the estimation of the shape parameter of the two‐parameter Weibull distribution. Both the case of small data sets with outliers and the case of data sets with multiple‐censoring are considered. Maximum‐likelihood estimation is also compared with linear regression methods. Simulation results show that robust regression is an effective method in reducing bias and it performs well in most cases. Copyright © 2006 John Wiley & Sons, Ltd.     

The Derivative of |X′X| and Its Uses

The determinant of matrices of the form X′X is used as the D-optimal design criterion for parameter estimation in nonlinear regression and as the estimation criterion for multiresponse parameter estimation. It is helpful to be able to calculate the gradient of this determinant so that sophisticated optimization methods can be used. A method is given to efficiently compute the determinant using modern computational linear algebra and, at the same time, to provide the necessary information to compute the gradient. The method is extended to cases in which a part of the X matrix is fixed. Examples from multiresponse parameter estimation and from experimental design are given.     

Asymptotic efficiency properties of least squares in an ultrastructural model

This paper considers the estimation of both the intercept term and the slope parameter in a linear ultrastructural model using direct regression and reverse regression methods. Without assuming the errors to be normally distributed, asymptotic expressions for the bias and the variance of the estimators are derived and analyzed. The effect of departure of the errors from normality is also studied.     

火电厂智能化远程管理云平台系统设计

为优化火力发电的生产,解决传统服务器在存储和挖掘大数据能力上的不足,该文采用云存储和云计算技术,将爆发式增长的火电机组生产数据存储在云端,通过对云端数据库的访问,搭建在线的火电厂远程管理平台,对生产数据进行远程监督和规范化存储。智能化云平台系统通过果蝇算法优化的广义回归神经网络(FOA-GRNN),设计一种锅炉热效率实时软测量模型。通过实验验证,云平台相比于传统服务器,在保证预测精度的前提下,有着更加高效的数据处理能力。     

基于特征值分解的随机子空间算法研究

针对基于数据驱动的随机子空间法计算效率低下的问题,提出一种基于特征值分解的随机子空间算法,该方法通过对ＣＨ矩阵的特征值分解得到扩展可观测矩阵Ｔｍｉ,进而识别出系统模态参数。相比于传统算法,该算法免去了对Ｈａｎｋｌ矩阵的ＱＲ分解及投影矩阵的ＳＶＤ运算,从而大大节省了内存和计算时间。通过一个７自由度的数值仿真和重庆朝天门大桥模型的实例分析证明该方法在保持计算精度的情况下大幅度地提升了计算效率。     

Extraction of parameters and their error distributions from cyclic voltammograms using bootstrap resampling enhanced by solution maps: Computational study

The conventional determination of model parameter errors in least-squares regression of experimental cyclic voltammetric data assumes validity of local approximations (e.g., linearization) in the parameter space and normal distributions of the data and parameter errors. Such assumptions may not always be satisfied in practice. Bootstrap resampling techniques present a more universally applicable approach to error estimation, which until now has not been used in cyclic voltammetric studies, owing to the high costs of the required voltammogram simulations. We demonstrate that the burden of computing voltammograms can be significantly reduced by the use of high-dimensional model representation (HDMR) solution mapping techniques, thereby making it feasible to apply the bootstrap data analysis in cyclic voltammetry. We perform computational experiments with bootstrap resampling, enhanced by HDMR maps, for a typical cyclic voltammetric model (i.e., the Eqrev Cirr Eqrev reaction mechanism at a planar macroelectrode under semi-infinite, pure diffusion transport conditions). The experiments reveal that the bootstrap distributions of the estimated parameters provide a satisfactory quantification of the parameter errors and can also be used for detecting statistical correlations of the parameters.     

基于模糊非线性回归算法的图像复原

为了利用多幅具有相似降质特性的退化图像信息恢复出原图像,提出了一种新的基于模糊参量非线性回归估计的图像盲复原算法。 该算法充分利用多幅图像具有的相似降质特征,首先给出一种非理想光照分布参数的模糊非线性回归估计方法,然后通过估计出的参数得到与原图同样大小的非理想光照分布图,最后通过观测图像与非理想光照分布图相消的方法,对退化图像进行复原。 实验结果表明,该算法运算快速,对边缘细节及平滑区域均有良好的修复能力,在修复效果上明显优于一般图像修复算法。     

新安江模型参数有效优化及不确定性评估

应用新安江模型进行水文模拟时,由于模型本身的不足及参数多、信息量少等原因,会出现率定的最优参数组不唯一、不稳定等问题。考虑到以往的参数优选,都只得出一个参数组,不能反映出其不确定性状况。提出应用基于马尔可夫链蒙特卡罗(MCMC)理论的SCEM-UA算法,通过双牌流域以1 h为时段间隔的36场典型洪水数据对新安江模型参数进行优选和不确定性评估。结果表明,该算法能很好地推出新安江模型参数的后验概率分布;率定和检验结果分析也表明,应用SCEM-UA算法对新安江模型进行优选和不确定评估是有效和可行的。     

A genetic programming based fuzzy regression approach to modelling manufacturing processes

Fuzzy regression has demonstrated its ability to model manufacturing processes in which the processes have fuzziness and the number of experimental data sets for modelling them is limited. However, previous studies only yield fuzzy linear regression based process models in which variables or higher order terms are not addressed. In fact, it is widely recognised that behaviours of manufacturing processes do often carry interactions among variables or higher order terms. In this paper, a genetic programming based fuzzy regression GP-FR, is proposed for modelling manufacturing processes. The proposed method uses the general outcome of GP to construct models the structure of which is based on a tree representation, which could carry interaction and higher order terms. Then, a fuzzy linear regression algorithm is used to estimate the contributions and the fuzziness of each branch of the tree, so as to determine the fuzzy parameters of the genetic programming based fuzzy regression model. To evaluate the effectiveness of the proposed method for process modelling, it was applied to the modelling of a solder paste dispensing process. Results were compared with those based on statistical regression and fuzzy linear regression. It was found that the proposed method can achieve better goodness-of-fitness than the other two methods. Also the prediction accuracy of the model developed based on GP-FR is better than those based on the other two methods.     

The Horseracing Simulation algorithm for evaluation of small failure probabilities

Over the past decade, the civil engineering community has ever more realized the importance and perspective of reliability-based design optimization (RBDO). Since then several advanced stochastic simulation algorithms for computing small failure probabilities encountered in reliability analysis of engineering systems have been developed: Subset Simulation (Au and Beck (2001) [2]), Line Sampling (Schuëller et al. (2004) [3]), The Auxiliary Domain Method (Katafygiotis et al. (2007) [4]), ALIS (Katafygiotis and Zuev (2007) [5]), etc. In this paper we propose a novel advanced stochastic simulation algorithm for solving high-dimensional reliability problems, called Horseracing Simulation (HRS). The key idea behind HS is as follows. Although the reliability problem itself is high-dimensional, the limit-state function maps this high-dimensional parameter space into a one-dimensional real line. This mapping transforms a high-dimensional random parameter vector, which may represent the stochastic input load as well as any uncertain structural parameters, into a random variable with unknown distribution, which represents the uncertain structural response. It turns out that the corresponding cumulative distribution function (CDF) of this random variable of interest can be accurately approximated by empirical CDFs constructed from specially designed samples. The generation of samples is governed by a process of “racing” towards the failure domain, hence the name of the algorithm. The accuracy and efficiency of the new method are demonstrated with a real-life wind engineering example.