A time-stepping method for non-smooth mechanical systems

Time-stepping algorithms allow a robust simulation of dynamical problems with many unilateral constraints and friction. It's idea is to calculate velocity updates instead of accelerations. As a consequence, contact behaviour and impact can be treated by the same equations. The unilateral constraints are modelled by set-valued force laws. The resulting inequalities can be solved by writing inclusions as non-linear equations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A steepest-descent method for optimization of mechanical systems

Steepest-descent optimal control techniques have been used extensively for dynamic systems in one independent variable and with a full set of initial conditions. This paper presents an extension of the steepest-descent technique to mechanical design problems that are described by boundary-value problems with one or more independent variables. The method is illustrated by solving finite-dimensional problems, problems with distribution of design over one space dimension, and problems with distribution of design over two space dimensions.     

A method for the evaluation of hail suppression

Zusammenfassung Ein Sequenztest-Verfahren wurde für die Prüfung der Annahme entwickelt, dass Hagelverhinderungsversuche die Frequenz der Hageltage verkleinern. Das Verfahren ist auf die Angaben über den Grossversuch II zur Unterdrückung des Hagels in der Magadinoebene (Schweiz) angewandt worden. Funktionen für die Versuchskenngrössen und Stichproben-Mittelwerte sind ebenfalls entwickelt und am selben Beispiel zur Anwendung gebracht worden. Schliesslich werden die Folgerungen, die sich hinsichtlich der Versuchsverfahren und Testergebnisse abzeichnen, erörtert.

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Advisory Committee on Weather Control, Technical Report No. 4.     

Application of the particle-in-cell method for numerical simulation of sheath plasma

We give a survey of papers on the numerical simulation of the sheath plasma using the particle-in-cell method. We study the problem of the behavior of a plasma bounded in the longitudinal direction of an absorbing wall. The model studied contains charged particles (electrons and ions) that move subject to a self-consistent electrostatic field. New pairs of particles are generated in the region of a distributed source. As a numerical model we use the electrostatic “particle-in-cell” method supplemented with the Emmert model for a bulk source and the algorithm of binary Coulomb collisions using a Monte Carlo method. Only electron-ion collisions are taken into account. Translated fromMetody Matematicheskogo Modelirovaniya, 1998, pp. 101–131.     

A numerical method for the servo constraint problem of underactuated mechanical systems

Servo constraints are used in inverse dynamics simulations of discrete mechanical systems, especially for trajectory tracking control problems [1], whose desired outputs are represented by state variables and treated as servo constraints [2]. Servo constraint problems can be classified into fully actuated and underactuated multibody systems, and the equations of motion take the form of differential algebraic equations (DAEs) including holonomic and servo constraints. For fully actuated systems, control inputs can be solved from the equations by model inversion, as the input distribution matrix is nonsingular and invertible. However, underactuated systems have more degrees of freedom than control inputs. The input distribution matrix is not invertible, and in contrast to passive constraints, the realization of servo constraints with the use of control forces can range from orthogonal to tangential [3]. Therefore, it is challenging for the determination of control inputs which force the underactuated system to realize the partly specified motion. For differentially flat underactuated systems, the differentiation index of DAEs may exceed three. Hence we need to apply specific index reduction techniques, such as the projection approach applied in [3], [4], and [6]. The present work applies index reduction by minimal extension [5] to differentially flat underactuated crane systems and shows that the index can be reduced from five to three and even to one. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A regression method for the Monte Carlo evaluation of multidimensional integrals

An investigation is made of some Monte Carlo estimators particularly suited to the application of regression analysis. Sets of estimators are presented which integrate exactly multivariate polynomials of prescribed degree. Application to a number of test integrals shows that economical and accurate results can be obtained as well as reliable error estimates. A comparison is made with some other methods.     

A non-parametric method for fitting ROC curves for evaluation of industrial inspection performance

The use of signal detection theory (SDT) in evaluation of the performance of an inspector on certain tasks requires the identification of the receiver operating characteristic (ROC) curve of the inspector. In this paper a functional form, Y = f(X), for the ROC equation is proposed, and two alternative approaches are developed for estimation of its parameters. This method does not require prior assumptions on the statistical distribution of the noise and signal-plus-noise. The application of the method is illustrated by the use of an example data set.     

A multi-attribute method for choosing among potential alternatives with ordinal evaluation

Some concepts are introduced with a view to dealing with the problem of choosing the “best” potential alternative(s) in a multi-attribute ordinal data context. We assume that we know the possibilistic weights of attributes and ordinal evaluations of each potential alternative on all attributes. We define what we refer to as positive/negative coalitions of attributes and positiveness/negativeness numerical bags associated with each potential alternative. We also define what will be called positional advantage operators and we describe how all these concepts are used to lay the foundation for the choice method appearing in this paper.     

具有包容关系的结构异质DEA效率评价方法

指标结构同质是数据包络分析（DEA）方法的基本假设之一;然而,现实问题的复杂性使得该假设常常难以完全被满足.针对具有包容关系的产出结构异质问题,通过解析决策单元（DMU）之间生产结构的内在关系来构建一种分阶段的DEA效率评价方法.该方法充分考虑了不同结构DMU的主观偏好,较好地规避了传统DEA方法在结构异质DMU效率评价过程中的不公平性.随后,该方法分别被拓展至投入结构异质和多重结构异质的情境中.最后,通过两个算例来说明本文方法的有效性与实用性.     

An approximate method for analysing stochastic mechanical systems

An approximate method for analysing diffusion processes in a natural mechanical system when there are perturbing forces similar to normal white noise is proposed. It is based on orthogonal expansions of the one-dimensional probability density of the state vector in a suitable Hubert space of functions which are square-integrable with respect to a certain measure in the phase space (manifold) of the system. The method consists of solving a special system of linear ordinary differential equations for the expansion coefficients, and is suitable for computer implementation. The method is rigorously proved. The motion of a two-dimensional mathematical pendulum in a random medium is investigated as an example.     

综合评价中一种新的指标选择方法

文章首先概述了指标选择方法的现状,并指出现有方法在全面性和代表性上的问题。接着提出了一种用聚类分析、非参数检验等构成的指标动态筛选方法,有效的解决了全面性和代表性的问题。最后通过实例说明了该方法的应用。     

A theoretical approximation scheme for Stackelberg problems

We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985.     

A theoretical description for solitons in polyacetylene

The bond-alternation domain walls or the solitons in the dimerized polyacetylene are analyzed theoretically. The width of the soliton is many times the period of the chain, so that the soliton can be reasonably well described by a continuum model. Because of the existence of the bond-alternation domain walls, the electron density is different definitely. Thus the electron density can be used to describe the formation of the domain walls, and a self-trapped potential is discussed and introduced in the Hamiltonian. It is shown that the envelope of the wave functions of the chain is governed by the nonlinear Schr?dinger equation which has soliton solutions. Then the shape of the soliton is determined analytically which is in accordance with the numerical calculations by Su, Schrieffer and Heeger. This implies that the bond-alternation domain wall or the soliton is observed as the envelope of the wave function.     

Some theoretical properties of Silverman's method for Smoothed functional principal component analysis

Principal component analysis (PCA) is one of the key techniques in functional data analysis. One important feature of functional PCA is that there is a need for smoothing or regularizing of the estimated principal component curves. Silverman’s method for smoothed functional principal component analysis is an important approach in a situation where the sample curves are fully observed due to its theoretical and practical advantages. However, lack of knowledge about the theoretical properties of this method makes it difficult to generalize it to the situation where the sample curves are only observed at discrete time points. In this paper, we first establish the existence of the solutions of the successive optimization problems in this method. We then provide upper bounds for the bias parts of the estimation errors for both eigenvalues and eigenfunctions. We also prove functional central limit theorems for the variation parts of the estimation errors. As a corollary, we give the convergence rates of the estimations for eigenvalues and eigenfunctions, where these rates depend on both the sample size and the smoothing parameters. Under some conditions on the convergence rates of the smoothing parameters, we can prove the asymptotic normalities of the estimations.     

基于公共权重的区间DEA效率评价及其排序方法研究

针对传统区间数据包络分析方法,在确定每一个决策单元区间效率的上界和下界时,存在的评价尺度不一致且计算复杂等问题,本文提出了一种同时最大化所有决策单元的效率上界和下界的公共权重区间DEA模型,并给出了一种考虑决策者偏好信息的可能度排序方法,用以解决区间效率的全排序问题。最后,以中国大陆11个沿海省份工业生产效率测算为例说明了所提方法的有效性和实用性。     

Characterizations of a game theoretical cost allocation method

In the 1930's the Tennessee Valley Authority developed several methods to allocate the costs of multipurpose water projects. One of these methods is the alternate cost avoided method. This paper provides two characterizations of the alternate cost avoided method, one on a class of cost games with a fixed player set, the other on a class of cost games with a variable player set using a reduced game property.The author is indebted to P. Borm, T. Driessen, Y. Funaki, S. Tijs and J. Zarzuelo for helpful discussions and useful suggestions.