A comparison of two hierarchical optimization methods

In this note the interaction prediction method and the goal coordination method for the multi-level optimization of large-scale interconnected dynamical systems with separable quadratic coat functions and linear dynamics are compared. The vehicle for the comparison is a twelth-order complex counter-current example taken from the literature. The computational load for the two methods is compared qualitatively whereas the convergence characteristics arc tested on the example. A simple condition is also given for the convergence of the interaction prediction method. This is also tested on the example.     

Evaluation of methods for estimating aquifer hydraulic parameters

An accurate estimation of aquifer hydraulic parameters is required for groundwater modeling and proper management of vital groundwater resources. In situ measurements of aquifer hydraulic parameters are expensive and difficult. Traditionally, these parameters have been estimated by graphical methods that are approximate and time-consuming. As a result, nonlinear programming (NLP) techniques have been used extensively to estimate them. Despite the outperformance of NLP approaches over graphical methods, they tend to converge to local minima and typically suffer from a convergence problem. In this study, Genetic Algorithm (GA) and Ant Colony Optimization (ACO) methods are used to identify hydraulic parameters (i.e., storage coefficient, hydraulic conductivity, transmissivity, specific yield, and leakage factor) of three types of aquifers namely, confined, unconfined, and leaky from real time–drawdown pumping test data. The performance of GA and ACO is also compared with that of graphical and NLP techniques. The results show that both GA and ACO are efficient, robust, and reliable for estimating various aquifer hydraulic parameters from the time–drawdown data and perform better than the graphical and NLP techniques. The outcomes also indicate that the accuracy of GA and ACO is comparable. Comparing the running time of various utilized methods illustrates that ACO converges to the optimal solution faster than other techniques, while the graphical method has the highest running time.     

On the application of the Wald statistic to order estimation ofARMA models

Consistent criteria for order estimation of autoregressive moving-average (ARMA) processes based on the Wald statistic are presented. The new criteria require only the estimation of the model parameters at the largest order, unlike alternative methods in the literature that require the estimation of the model parameters at all possible orders     

Comparison of methods for estimating the parameters of linear dynamic systems by measurements of short sections of transient processes

Various versions are compared of the multidimensional method of orthogonal regression in the problem of estimating the parameters of linear systems by short sections of transient processes with additive measuring perturbations. The methods are classified by the degree of the use of information on linear links between counts of trajectories of a dynamic object.Translated from Avtomatika i Telemekhanika, No. 3, 2005, pp. 39–47.Original Russian Text Copyright © 2005 by Lomov.This paper was recommended for publication by V.A. Lototskii, a member of the Editorial Board     

An algorithm for estimating the parameters in multiple linear regression model with linear constraints

This paper develops an algorithm for estimating the parameters when the parameters are restricted by linear constraints in a general multiple regression model. The algorithm solves discrete approximation in the Φ error where Φ is a convex and symmetric function. These discrete approximations arise in fitting by polynomials, linear regression and goal programming. Discrete approximation problems in the L₁ norm is a special case. The approaches to the solution of these approximation problems have a long history. The algorithm utilizes certain properties of the problem to significantly reduce the number of iterations to find the approximated solution.     

A comparison of two parametric surface patch methods

The Bézier and Ferguson methods of representing surfaces are compared. Although there are very clear differences in their mode of use they are closely similar in their mathematical basis.     

Practical comparison of two turbulent models

A numerical study of a number of viscous compressible gas flows, using a one-parameter differential turbulence model of Spalart-Olmaras and another, obtained by changing the variables in the two-parameter SST model of Menter, is conducted. Calculations are based on Reynolds averaged two-dimensional Navier-Stokes equations, using a difference scheme of the fifth order of approximation. The problems of a subsonic flat plate, spoon-formed cavern, Jones airfoil overflow, separated flow in front of the angle of compression and dissipation of a single vortex are considered. These results permit me to better define the limits of applicability of the turbulence models considered, and to note their possible shortcomings.     

Minimum bias priors for estimating parameters of additive terms instate-space models

We treat the problem of estimating parameters of additive terms, sometimes called bias terms, in state-space models. We consider models that depend linearly on the state but possibly nonlinearly on the parameters, where both the state and observation are corrupted by additive noise. A prior density for the parameters is introduced that, when combined with the likelihood function to form a posterior density, minimizes the bias of the posterior mean. The result is a useful prior based on ignorance. Two examples and simulations illustrate the use of the prior     

A comparison of two methods for accelerating the convergence of Fourier series

We compare the epsilon algorithm of Wynn with a generalization of summation by parts for accelerating slowly convergent Fourier series. The series considered are

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and four series that arise from the numerical inversion Summation by parts is shown to be advantageous in the acceleration of Fourier sine series. Both acceleration techniques are shown to lead to approximately the same accuracy in accelerating the series that come from the Laplace transform examples.     

Recursive computation of inner bounds for the parameters of linear models

Minimum-volume ellipsoidal outer bounds on the parameters of linear regression-type models with bounded model-output error can be computed by an established algorithm. A complementary algorithm to compute maximum-volume ellipsoidal inner bounds is derived. It is little more complicated than the existing outer-bounding algorithm. In conjunction with that algorithm, it allows parameter values to be classified as acceptable, dubious or unacceptable. It is also found to be effective in determining output-error bounds by trial and error during development of parameter-bounding models.     

A comparison of two optimization methods for mesh quality improvement

We compare inexact Newton and block coordinate descent optimization methods for improving the quality of a mesh by repositioning the vertices, where the overall quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.

A comparison of two sampling methods for global sensitivity analysis

We compare the convergence properties of two different quasi-random sampling designs – Sobol?s quasi-Monte Carlo, and Latin supercube sampling in variance-based global sensitivity analysis. We use the non-monotonic V-function of Sobol? as base case-study, and compare the performance of both sampling strategies at increasing sample size and dimensionality against analytical values. The results indicate that in almost all cases investigated here, the Sobol? design performs better. This, coupled with the fact that effective Latin supercube sampling requires a priori knowledge of the interaction properties of the function, leads us to recommend Sobol? sampling in most practical cases.     

Using linear models in optimizing parameters of time-triggered protocols

A mechanism of synchronization of components of distributed systems in which communications are based on a common time schedule for all system components is illustrated by examples of simple Time-Triggered Protocols. For parametric linear models of synchronization, the optimization problem is considered for a parameter that should exclude the overlapping of messages in communication channels. The results of using numeric methods for estimation of the optimal value of this parameter are described. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 24–32, May–June 2006.     

一维时间序列分形维数算法对比分析

分形维数在一维时间序列的分形特性分析中应用非常广泛,其计算方法多种多样,但是相关计算方法的全面对比鲜见文献报道。针对常用的八种一维时间序列分形维数计算方法,以WCF合成时间序列为研究对象,分别就算法的准确性和效率,对数据长度的依赖性进行分析对比。结果表明：准确性较好的三种算法是FA,DFA和Higuchi算法;而运算效率最高的是Sevcik,Katz和Castiglioni算法,但是它们的准确性偏低,而FA和Higuchi算法在计算时间上略微增加,但准确性比较高;在数据长度为4 096点时,各算法的计算值基本稳定,尤其是FA、Higuchi和DFA算法,在数据长度为4 096点时,计算值与理论值比较吻合。由此可以得出结论,Higuchi和DFA算法在计算一维时间序列的分形维数时性能优越,在相关的计算中优先选择。     

Optimal aircraft landing-approach trajectories: A comparison of two dynamic models

Sequential quadratic programming is used to solve a minimum-noise aircraft landing-approach problem for two dynamic models. The “exact” model features the usual point-mass equations of motion for flight in a vertical plane. The other model is based on two simplifying assumptions:

• 1.(1) small angle of attack and flight path angle and
• 2.(2) no flight path angle dynamics (lift equals weight).

Range is used to replace time as the independent variable. The resulting models are of order three and two, respectively; each model involves two control functions. The primary objective is to compare the solutions for each model with regard to accuracy and computational effort. Numerical results are presented for a variety of boundary conditions and path constraints.     

A comparison of two training methods for improving warning symbol comprehension

This study compared the effectiveness of two different types of training in improving comprehension of warning symbols by younger (aged 20-35 years) and older adults (aged 50-70 years). The verbal label training paired the symbol with a label describing its meaning while the accident scenario training further expanded on the nature of the hazard, the required/prohibited actions, as well as the possible consequences of failing to comply. Contrary to prior research (e.g., [Lesch, M.F., 2003. Comprehension and memory for warning symbols: age-related differences and impact of training. J. Safety Res. 34, 495-505]), there was no difference in comprehension for younger and older adults prior to training, with both groups only obtaining about 40% correct responses. Both types of training improved performance on a subsequent comprehension test. However, the accident scenario training produced a higher percentage of correct responses, greater confidence in those responses, as well as a longer-lasting reduction of reaction times. In order to further improve symbol design, as well as training to address comprehension difficulties, future research should more closely examine symbol characteristics that influence comprehension.     

A comparison between two photographic methods for the determination of relative bidirectional reflectance

Two simple photographic methods have recently been proposed for the measurement of relative bidirectional reflectance (Lillesand and Kiefer 1979, Curran 1980). These two methods were used to calculate the relative bidirectional reflectance of ten contrasting surfaces. The photographic relative bidirectional reflectance so recorded, was then compared with the radiometric bidirectional reflectance for each surface. Two conclusions were drawn: first, that relative bidirectional reflectance can be measured using these simple photographic techniques, and second, that there was no significant difference between the Lillesand and Kiefer and Curran methods for photographically deriving relative bidirectional reflectance.     

A comparison of three parallelisation methods for 2D flood inundation models

For many applications two-dimensional hydraulic models are time intensive to run due to their computational requirements, which can adversely affect the progress of both research and industry modelling projects. Computational time can be reduced by running a model in parallel over multiple cores. However, there are many parallelisation methods and these differ in terms of difficulty of implementation, suitability for particular codes and parallel efficiency. This study compares three parallelisation methods based on OpenMP, message passing and specialised accelerator cards. The parallel implementations of the codes were required to produce near identical results to a serial version for two urban inundation test cases. OpenMP was considered the easiest method to develop and produced similar speedups (of ～3.9×) to the message passing code on up to four cores for a fully wet domain. The message passing code was more efficient than OpenMP, and remained over 90% efficient on up to 50 cores for a completely wet domain. All parallel codes were less efficient for a partially wet domain test case. The accelerator card code was faster and more power efficient than the standard code on a single core for a fully wet domain, but was subject to longer development time (2 months compared to <2 week for the other methods).     

Efficient methods for estimating constrained parameters with applications to lasso logistic regression

Fitting logistic regression models is challenging when their parameters are restricted. In this article, we first develop a quadratic lower-bound (QLB) algorithm for optimization with box or linear inequality constraints and derive the fastest QLB algorithm corresponding to the smallest global majorization matrix. The proposed QLB algorithm is particularly suited to problems to which the EM-type algorithms are not applicable (e.g., logistic, multinomial logistic, and Cox’s proportional hazards models) while it retains the same EM ascent property and thus assures the monotonic convergence. Secondly, we generalize the QLB algorithm to penalized problems in which the penalty functions may not be totally differentiable. The proposed method thus provides an alternative algorithm for estimation in lasso logistic regression, where the convergence of the existing lasso algorithm is not generally ensured. Finally, by relaxing the ascent requirement, convergence speed can be further accelerated. We introduce a pseudo-Newton method that retains the simplicity of the QLB algorithm and the fast convergence of the Newton method. Theoretical justification and numerical examples show that the pseudo-Newton method is up to 71 (in terms of CPU time) or 107 (in terms of number of iterations) times faster than the fastest QLB algorithm and thus makes bootstrap variance estimation feasible. Simulations and comparisons are performed and three real examples (Down syndrome data, kyphosis data, and colon microarray data) are analyzed to illustrate the proposed methods.     

Robust likelihood inference for regression parameters in partially linear models

A robust likelihood approach is proposed for inference about regression parameters in partially-linear models. More specifically, normality is adopted as the working model and is properly corrected to accomplish the objective. Knowledge about the true underlying random mechanism is not required for the proposed method. Simulations and illustrative examples demonstrate the usefulness of the proposed robust likelihood method, even in irregular situations caused by the components of the nonparametric smooth function in partially-linear models.