Estimation of nonstrict Archimedean copulas and its application to quantum networks

Bivariate nonstrict Archimedean copulas form a subclass of Archimedean copulas and are able to model the dependence structure of random variables that do not take on low quantiles simultaneously; i.e. their domain includes a set, the so‐called zero set, with positive Lebesgue measure but zero probability mass. Standard methods to fit a parametric Archimedean copula, e.g. classical maximum likelihood estimation, are either getting computationally more involved or even fail when dealing with this subclass. We propose an alternative method for estimating the parameter of a nonstrict Archimedean copula that is based on the zero set and the functional form of its boundary curve. This estimator is fast to compute and can be applied to absolutely continuous copulas but also allows singular components. In a simulation study, we compare its performance to that of the standard estimators. Finally, the estimator is applied when modeling the dependence structure of quantities describing the quality of transmission in a quantum network, and it is shown how this model can be used effectively to detect potential intruders in this network. Copyright © 2014 John Wiley & Sons, Ltd.     

Data-driven recursive least squares methods for non-affined nonlinear discrete-time systems

Aiming at identifying nonlinear systems, one of the most challenging problems in system identification, a class of data-driven recursive least squares algorithms are presented in this work. First, a full form dynamic linearization based linear data model for nonlinear systems is derived. Consequently, a full form dynamic linearization-based data-driven recursive least squares identification method for estimating the unknown parameter of the obtained linear data model is proposed along with convergence analysis and prediction of the outputs subject to stochastic noises. Furthermore, a partial form dynamic linearization-based data-driven recursive least squares identification algorithm is also developed as a special case of the full form dynamic linearization based algorithm. The proposed two identification algorithms for the nonlinear nonaffine discrete-time systems are flexible in applications without relying on any explicit mechanism model information of the systems. Additionally, the number of the parameters in the obtained linear data model can be tuned flexibly to reduce computation complexity. The validity of the two identification algorithms is verified by rigorous theoretical analysis and simulation studies.     

A self-consistent field method applied to the dynamics of viscous suspensions

A method for the approximate solution of the problem of many bodies of spherical form in a viscous fluid is developed in the Stokes approximation. Using a purely hydrodynamic approach, based on the use of the concept of a self-consistent field, the classical boundary value problem is reduced to a formal procedure for solving a linear system of algebraic equations in the tensor coefficients, which occur in the solution obtained for the velocity field and pressure of the liquid. A procedure for the approximate solution of this system of equations is constructed for the case of dilute suspensions, when the ratio of the size of the dispersed particles to the characteristic distance between them is a small parameter. Finally, the initial boundary value problem is reduced to solving a recurrent system of equations, in which each subsequent approximation for all the required quantities depends solely on the previous approximations. The system of recurrent equations obtained can be solved analytically in any specified approximation with respect to a small parameter. It is shown that this system of equations contains in itself all possible physical formulations of the problems, and, within the frameworks of the mathematical procedure constructed, they are distinguished solely by a set of specified and required functions. The practical possibilities of the method are in no way limited by the number of dispersed particles in the fluid.     

Precomputing strategy for Hamiltonian Monte Carlo method based on regularity in parameter space

Markov Chain Monte Carlo (MCMC) algorithms play an important role in statistical inference problems dealing with intractable probability distributions. Recently, many MCMC algorithms such as Hamiltonian Monte Carlo (HMC) and Riemannian Manifold HMC have been proposed to provide distant proposals with high acceptance rate. These algorithms, however, tend to be computationally intensive which could limit their usefulness, especially for big data problems due to repetitive evaluations of functions and statistical quantities that depend on the data. This issue occurs in many statistic computing problems. In this paper, we propose a novel strategy that exploits smoothness (regularity) in parameter space to improve computational efficiency of MCMC algorithms. When evaluation of functions or statistical quantities are needed at a point in parameter space, interpolation from precomputed values or previous computed values is used. More specifically, we focus on HMC algorithms that use geometric information for faster exploration of probability distributions. Our proposed method is based on precomputing the required geometric information on a set of grids before running sampling algorithm and approximating the geometric information for the current location of the sampler using the precomputed information at nearby grids at each iteration of HMC. Sparse grid interpolation method is used for high dimensional problems. Tests on computational examples are shown to illustrate the advantages of our method.     

ARMA model order and parameter estimation using genetic algorithms

A new method for simultaneously determining the order and the parameters of autoregressive moving average (ARMA) models is presented in this article. Given an ARMA (p, q) model in the absence of any information for the order, the correct order of the model (p, q) as well as the correct parameters will be simultaneously determined using genetic algorithms (GAs). These algorithms simply search the order and the parameter spaces to detect their correct values using the GA operators. The proposed method works on the principle of maximizing the GA fitness value relying on the deviation between the actual plant output, with or without an additive noise, and the estimated plant output. Simulation results show in detail the efficiency of the proposed approach. In addition to that, a practical model identification and parameter estimation is conducted in this article with results obtained as desired. The new method is compared with other well-known methods for ARMA model order and parameter estimation.     

Finding GM-estimators with global optimization techniques

In this note we address the problem of finding the GM-estimator for the location parameter of a univariate random variable. When this problem is non-convex but d.c. one can use a standard covering method, which, in the one-dimensional case has a simple form. In this paper we exploit the structure of the problem in order to obtain d.c. decompositions with certain optimality properties in the application of the algorithm. Numerical results show that this general-purpose algorithm outperforms previous ad-hoc methods for this problem.     

Modified Landweber tterations in a multilevel setting applied to the determination of nonlinear material parameters in piezoelectricity

An efficient solution of the inverse problem of identifying nonlinear dependencies in hyperbolic systems of PDEs, here piezoelectric material parameter curves, is the aim of this work. The dominant material tensor entries in the coupled field equations which describe the electromechanical interplay are approximated by functions depending on the physical field quantities electric field or mechanical stress. In order to solve this nonlinear and ill-posed problem of parameter curve identification efficiently, modified Landweber iterations (steepest descent and minimal error) will be studied. A multilevel approach is expedient due to the discretization of the unknown parameter curves and high computational efforts solving the forward problem (transient, nonlinear FEM computations). Theoretical investigations concerning convergence and regularization properties of the methods in a multilevel scenario will be presented, along with numerical results from an example in piezoelectricity. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于遗传算法的LuGre轮胎模型参数辨识研究

LuGre轮胎模型是一种动态轮胎摩擦力模型,该模型能够精确描述轮胎摩擦环节的动态特性,但由其高度非线性使得参数辨识非常困难.针对LuGre轮胎模型,提出一种基于遗传算法的模型参数两步辨识方法.首先由PD控制辨识出静态参数;然后由PID控制辨识出动态参数.在每一步辨识中,均采用遗传算法作为优化工具,从而避免了采用拟和辨识方法中误差较大,试验条件难以控制的缺点.该算法仅仅使用轮胎转速数据,而转速传感器是汽车防滑刹车控制系统(ABS)的基本组成部分,因此该算法可以与ABS结合工作,低成本的实现LuGre轮胎模型参数辨识.     

Analytical solutions for heat transfer on fractal and pre-fractal domains

Fractals can be used to represent intricate self-similar geometries, but their application to the representation of physical systems is beset with difficulties which stem from an inability to define traditionally derived-physical quantities such as stress, pressure, strain, heat etc. This paper describes a method for the determination of analytical heat-transfer solutions on pre-fractal and fractal domains. The approach requires the construction of maps from pre-fractal domains to the continuum, which facilitate the application of traditional continuum solution methods. Solutions on fractal domains are achievable with this approach, and are defined to be the limit solution of analytical solutions obtained on the pre-fractals approximating the fractal of interest. This approach avoids many of the complications and technical difficulties arising from the use of measure theory and fractional derivatives, but also infers that the governing heat transfer equations are valid on all pre-fractals. The fractals considered are necessarily deterministic and relatively simple in form to demonstrate the solution methodology. The solutions presented are limited to one and two-dimensional domains and, in 1-D, are applied to an idealised composite material consisting of relatively small particles of infinitely low thermal conductivity embedded in a relatively large matrix of infinitely high thermal conductivity. The fractal composite system is thus not truly representative of a realistic physical system, but the methods presented do serve to demonstrate how analytical solutions can be attained on dust-like fractal domains. It is demonstrated that a measurable temperature is possible on a fractal structure along with finite measures of heat flux and energy. Transient and steady state thermal solutions are presented. The solutions on a selection of the pre-fractals are compared against finite element predictions to reinforce the validity of the approach.     

产品可靠度的E-Bayes估计

提出了参数估计的一种新方法——E-Bayes估计法.对Pascal分布,给出了可靠度的E-Bayes估计的定义(在先验分布中有一个超参数情形),在此基础上给出了可靠度的E-Bayes估计,并给出了可靠度的E-Bayes估计性质——E-Bayes估计和多层Bayes估计的关系.最后,给出了模拟算例,结果表明本文提出的E-Bayes估计法可行且便于工程应用.     

Parameter estimation in general state-space models using particle methods

Particle filtering techniques are a set of powerful and versatile simulation-based methods to perform optimal state estimation in nonlinear non-Gaussian state-space models. If the model includes fixed parameters, a standard technique to perform parameter estimation consists of extending the state with the parameter to transform the problem into an optimal filtering problem. However, this approach requires the use of special particle filtering techniques which suffer from several drawbacks. We consider here an alternative approach combining particle filtering and gradient algorithms to perform batch and recursive maximum likelihood parameter estimation. An original particle method is presented to implement these approaches and their efficiency is assessed through simulation.     

An alternative to ratio method in sample surveys

Summary This paper examines a simple transformation which enables the use of product method in place of ratio method. The convenience with the former, proposed by Murthy [3], is that expressions for bias and mean square error (mse) can be exactly evaluated. The optimum situation in the minimum mse sense and allowable departures from this optimum are indicated. The procedure requires a good guess of a certain parameter, which does not seem very restrictive for practice. Two methods for dealing with the bias of the estimator are mentioned. An extension to use multiauxiliary information is outlined.     

Advances in Interval Methods for Deterministic Global Optimization in Chemical Engineering

In recent years, it has been shown that strategies based on an interval-Newton approach can be used to reliably solve a variety of nonlinear equation solving and optimization problems in chemical process engineering, including problems in parameter estimation and in the computation of phase behavior. These strategies provide a mathematical and computational guarantee either that all solutions have been located in an equation solving problem or that the global optimum has been found in an optimization problem. The primary drawback to this approach is the potentially high computational cost. In this paper, we consider strategies for bounding the solution set of the linear interval equation system that must be solved in the context of the interval-Newton method. Recent preconditioning techniques for this purpose are reviewed, and a new bounding approach based on the use of linear programming (LP) techniques is presented. Using this approach it is possible to determine the desired bounds exactly (within round out), leading to significant overall improvements in computational efficiency. These techniques will be demonstrated using several global optimization problems, with focus on problems arising in chemical engineering, including parameter estimation and molecular modeling. These problems range in size from under ten variables to over two hundred, and are solved deterministically using the interval methodology.     

Parameter estimation for fractional Ornstein–Uhlenbeck processes at discrete observation

This paper deals with the problem of estimating the parameters for fractional Ornstein–Uhlenbeck processes from discrete observations when the Hurst parameter H is known. Both the drift and the diffusion coefficient estimators of discrete form are obtained based on approximating integrals via Riemann sums with Hurst parameter H ∈ (1/2, 3/4). By adapting the stochastic integral representation to the fractional Brownian motion, these two estimators can be efficiently computed by the use of computer software. Numerical examples are presented to examine the performance of our method. An application to real data is also presented to show how to apply this method in practice.     

地基-结构相互作用系统的时域参数识别

提出地基-结构相互作用系统的时域参数识别方法．在建立地基-结构相互作用的计算模式和运动方程的基础上,运用扩展的卡尔曼滤波技术,将相互作用系统中的参数作为增加的状态变量,建立了该系统的时域参数识别方法．并依据大型振动台条件下的层状地基-贮仓结构相互作用系统的模型试验数据,实施了地基-结构相互作用系统时域参数识别的全过程．计算结果表明,该方法产生良好的参数估计．     

Simulation Based Determination of Piezoelectric Material Parameters

The exact numerical simulation of piezoelectric transducers needs the knowledge of all material tensors that occur in the piezoelectric constitutive relations. The determination of these tensors is achieved by a simulation based algorithm which adjusts the 3D - FEM simulated data with electrical measurements of a piezoelectric transducer. Its advantage compared to the standards (see [1], [2]) lies in the fact that a determination of the complete set of material parameters from one arbitrarily shaped specimen with a high precision is possible. The reconstruction of the material tensors is formulated as a parameter identification problem for a system of PDEs. Since unique solvability of this inverse problem may hardly be verified, the system of equations we have to solve for recovering the material tensor entries can be rank deficient and therefore requires application of appropriate regularization strategies. For this purpose, we use inexact Newton methods. The material parameters are assumed to be complex-valued which allows to account for mechanical, dielectric and piezoelectric losses. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An algorithm to construct Monte Carlo confidence intervals for an arbitrary function of probability distribution parameters

We derive a new algorithm for calculating an exact confidence interval for a parameter of location or scale family, based on a two-sided hypothesis test on the parameter of interest, using some pivotal quantities. We use this algorithm to calculate approximate confidence intervals for the parameter or a function of the parameter of one-parameter continuous distributions. After appropriate heuristic modifications of the algorithm we use it to obtain approximate confidence intervals for a parameter or a function of parameters for multi-parameter continuous distributions. The advantage of the algorithm is that it is general and gives a fast approximation of an exact confidence interval. Some asymptotic (analytical) results are shown which validate the use of the method under certain regularity conditions. In addition, numerical results of the method compare well with those obtained by other known methods of the literature on the exponential, the normal, the gamma and the Weibull distribution.     

Quantifying the risk using copulae with nonparametric marginals

We show that copulae and kernel estimation can be mixed to estimate the risk of an economic loss. We analyze the properties of the Sarmanov copula. We find that the maximum pseudo-likelihood estimation of the dependence parameter associated with the copula with double transformed kernel estimation to estimate marginal cumulative distribution functions is a useful method for approximating the risk of extreme dependent losses when we have large data sets. We use a bivariate sample of losses from a real database of auto insurance claims.     

Associative memory approach to the identification of structural and mechanical systems

This paper presents a new method for identification of parameters in nonlinear structural and mechanical systems in which the initial guesses of the unknown parameter vectors may be far from their true values. The method uses notions from the field of artificial neural nets and, using an initial set of training parameter vectors, generates in an adaptive fashion other relevant training vectors to yield identification of the parameter vector in a recursive fashion. The simplicity and power of the technique are illustrated by considering three highly nonlinear systems. It is shown that the technique presented here yields excellent estimates with only a limited amount of response data, even when each element of the set comprising the initial training parameter vectors is far from its true value—in fact, sufficiently far that the usual recursive identification schemes fail to converge.