Controllable centrifugal pendulum

The combustion engine produces huge rotational periodic vibrations that could affect the acoustic comfort of the vehicle. An isolating device is placed after the engine and filters the oscillations in order to deliver a clean averaged torque to the rest of the drive train. The centrifugal pendulum is widely used even though its passive version can quench only one order of vibration. We propose in [3] a design allowing to control the tuning of the pendulum. An actuator delivers an additional force that completes the centrifugal force. This is equivalent to changing the stiffness of a classical vibration absorber. In this paper, we apply to the stiffness an optimal feedback control on a neighbouring extremal path as defined in [1]. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

MV-ALGEBRA VALUED FILTER THEORY

Abstract

Let M be a complete MV-algebra with square roots. Then every M-valued filter can be represented as “intersection” of an appropriate family of maximal M-valued filters. In the case of M = [0,1] maximal [0,1]-valued filters and finitely additive probability measures come to the same thing.     

Decoupling correlated and uncorrelated parametric uncertainty contributions for nonlinear models

For models with correlated parameters, the amount of uncertainty (generally measured by variance) in a model output contributed by a specific parameter encompasses two components: (1) the uncertainty contributed by the variations (used to represent uncertainty in the parameter) correlated with other parameters; and (2) the uncertainty contributed by the variations unique to the parameter of interest (i.e., uncorrelated variations or variations that cannot be explained by any other parameters in the model). A regression-based method has been proposed previously by Xu and Gertner (2008) [1] to decouple the correlated and uncorrelated contributions to uncertainties in model outputs by each parameter for linear models. Based on a modified version of the popular Fourier Amplitude Sensitivity Test (FAST), this paper develops a general approach for the quantification of the correlated and uncorrelated parametric uncertainty contributions in linear, nonlinear and non-monotonic models with linear or nonlinear dependence among parameters. The decoupling of correlated and uncorrelated contributions can help us determine if the uncertainty contributed by a specific parameter results from the uncertainty in itself or from its correlations with other parameters. Thus, this decoupling can be very useful in improving the understanding our modeled systems.     

PFI代数及其P滤子

文「１」引入了ＦＩ代数及其滤子，文「２」讨论了ＦＩ代数与ＭＶ代数的联系，本文在此基础上引入了正关联ＦＩ代数及其正关联滤子，并得到几个重要性质。     

Decoupling inequalities and some mean-value theorems

The purpose of this paper is to present some further applications of the general decoupling theory from [B-D] and [B-D2] to certain diophantine issues. In particular, we consider mean value estimates relevant to the Bombieri- Iwaniec approach to exponential sums and arising in the work of Robert and Sargos [R-S]. Our main input is a new mean-value theorem.     

Frequency and Magnitude Response Design Approximation Problems for Nonlinear-phase Nonrecursive Digital Filters

In this article special (possibly constrained) problems of linear and nonlinear complex approximation are studied with respect to the existence and uniqueness of solutions and the convergence of the approximation errors, where the errors are measured by an arbitrary L p and l p norm respectively. The problems arise in connection with the frequency and magnitude response approximation at the design of nonrecursive digital filters in the frequency domain. Two main results of the article concern the completeness of the functions exp ( m ik y ), k = 0,1,2,… , with respect to a certain space of continuous functions. These results imply that, under usual assumptions and with increasing number of approximating functions exp ( m ik y ), the errors in the frequency and magnitude response approximation problems converge to zero when the design region is not the total interval [0, ~ ] (in case of real coefficients) and not [ m ~ , ~ ] (in case of complex coefficients) which is given for the majority of filter design problems, but that the frequency response errors may not converge to zero when the design region equals [0, ~ ] or [ m ~ , ~ ] respectively.     

Dusty Supersonic Flow Past a Blunt Body: Viscous and Nonstationary Effects

High‐speed space‐ or aircrafts travelling through a dusty atmosphere may meet dust clouds in which the particles are often distributed very nonuniformly. Such nonuniformities may result in the onset of unsteady effects in the shock and boundary layer and (that is of prime interest) unsteady heat fluxes at the stagnation region of the vehicle. In the nearwall region of high‐speed dusty‐gas flow, there may take place regimes with and without particle inertial deposition, which require essentially different mathematical models for describing the heat transfer [1]. The present paper deals with two problems, considered within the framework of the two‐fluid model of dusty gas [2]: (i) determination of the limits of the particle inertial deposition regime and the distribution of dispersed‐phase parameters near the frontal surface of a sphere immersed in dusty supersonic flow (Mach number M = 6) at moderate flow Reynolds numbers (10² ≤ Re ≤ ∞); (ii) effect of free‐stream nonuniformities in the concentration of low inertial (non‐depositing) particles on the friction and heat transfer at the stagnation point of the body at high Re and M.     

Optimization approach to the design of frequency sampling filters

Many digital signal processing applications require linear phase filtering. For applications that require narrow-band linear phase filtering, frequency sampling filters can implement linear phase filters more efficiently than the commonly used direct convolution filter. In this paper, a technique is developed for designing linear phase frequency sampling filters. A frequency sampling filter approximates a desired frequency response by interpolating a frequency response through a set of frequency samples taken from the desired frequency response. Although the frequency response of a frequency sampling filter passes through the frequency samples, the frequency response may not be well behaved between the specific samples. Linear programming is commonly used to control the interpolation errors between frequency samples. The design method developed in this paper controls the interpolation errors between frequency samples by minimizing the mean square error between the desired and actual frequency responses in the stopband and passband. This design method describes the frequency sampling filter design problem as a constrained optimization problem which is solved using the Lagrange multiplier optimization method. This results in a set of linear equations which when solved determine the filter's coefficients.This work was partially funded by The National Supercomputing Center for Energy and the Environment, University of Nevada Las Vegas, Las Vegas, Nevada and by NSF Grant MIP-9200581.     

加权U—统计量的一个重对数律

证明了关于独立同分布随机变量序列的加权Ｕ－统计量的一个重对数律,类似于献「３」证明了一个加权Ｕ－统计量的解耦不等式。     

Parameter identification of dynamical systems

This paper deals with the problem of identification of the unknown parameters of a dynamical system. Our work in this paper largely simulation related, follows the approach suggested by Kim and Lee [IEEE Int. Conf. Neural Networks (1993) 438–443] and it depends on the introduction of auxiliary polynomial. The merit of our work lies on the facts that no assumptions are placed on the stability of auxiliary polynomial and also that it does not require the a priori knowledge of the stability of the dynamical system, in question. Our method applies to both linear and quasi-linear dynamical systems. The results obtained involve the construction of appropriate neural networks. A variety of configurations of the dynamical systems are considered for simulation.     

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons; 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst I 2003;50(6):805–9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan’s root-locus. Int J Control 2006;79(7):822–9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL. The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf.     

Three revenue-sharing variants: their significant performance differences under system-parameter uncertainties

In the widely studied ‘revenue sharing’ (hereafter [RS]) contract format, the manufacturer of a product not only charges the retailer a unit wholesale price w, but also requires the retailer to share part of the product's revenue (ie, the unit retail price p) with him. For a product with price-dependent demand, it is well known that if a dominant manufacturer knows the system parameters deterministically, then [RS] gives him the perfect power of simultaneously coordinating the channel and allocating profit arbitrarily. Unfortunately, [RS]'s power deteriorates as the manufacturer's knowledge of the system parameters becomes increasingly uncertain. This paper shows that this deterioration can be substantially reduced by using slightly modified versions of [RS]; these modifications roughly amount to sharing a retailer's gross profit instead of revenue. In other words, this paper presents simple modifications to the classical [RS], leading to contract formats that perform substantially better under system-parameter uncertainty.     

A maximum a posteriori estimator for trajectories of diffusion processes

Let x _t be a diffusion process observed via a noisy sensor, whose output is y_t We consider the problem of evaluating the maximum a posteriori trajectory {x_s0≤ s ≤ t Based on results of Stratonovich [1] and Ikeda-Watanabe [2], we show that this estimator is given by the solution of an appropriate variational problem which is a slight modification of the "minimum energy" estimator. We compare our results to the non-linear filtering theory and show that for problems which possess a finite dimensional solution, our approach yields also explicit filters. For linear diffusions observed via linear sensors, these filters are identical to the Kalman-filter     

灰色系统模型的优化岭回归算法

文献[1]指出了目前用普通最小二乘法估计灰微分方程参数的方法由于方程组的病态问题很难求解得合理的参数;文献[2]指出了根据初值求解灰色系统模型的时间响应式的方法由于初值的误差使所求得时间响应式产生系统误差.为了克服灰色模型的上述两个缺点,本文设计了一种求解灰色系统模型的优化岭回归算法,计算一个广泛引用的算例演示了这种算法的优越性.     

A Decomposition Method for Some Biharmonic Problems

In this paper we consider two biharmonic problems [13] which will be conventionally indicated as "simply supported" and "clamped plate" problem. We construct a decomposition method [16], [19] related to the partition of the plate in two, or more, subdomains. We carry on the numerical treatment of the method first decoupling these fourth order problems into two second order problems, then discretizing these problems by mixed linear finite element and obtaining an algebraic system. Moreover, we present an iterative block algorithm for solving the foregoing system, which can be efficiently developed on parallel computers.In the end, we extend the method to the respective biharmonic variational inequalities [10].     

Linearly implicit time discretization for free surface problems

Deeper investigation of time discretization for free surface problems is a widely neglected problem. Many existing approaches use an explicit decoupling which is only conditionally stable. Only few unconditionally stable methods are known, and known methods may suffer from too strong numerical dissipativity. They are also usually of first rder only [1, 9]. We are therefore looking for unconditionally stable, minimally dissipative methods of higher order. Linearly implicit Runge-Kutta (LIRK) methods are a class of one-step methods that require the solution of linear systems in each time step of a nonlinear system. They are well suited for discretized PDEs, e.g. parabolic problems [7]. They have been used successfully to solve the incompressible Navier-Stokes equations [5]. We suggest an adaption of these methods for free surface problems and compare different approximations to the Jacobian matrix needed for such methods. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Families of two-step fourth order P-stable methods for second order differential equations

This paper deals with a class of symmetric (hybrid) two-step fourth order P-stable methods for the numerical solution of special second order initial value problems. Such methods were proposed independently by Cash [1] and Chawla [3] and normally require three function evaluations per step. The purpose of this paper is to point out that there are some values of the (free) parameters available in the methods proposed which can reduce this work; we study two classes of such methods. The first is the class of ‘economical’ methods (see Definition 3.1) which reduce this work to two function evaluations per step, and the second is the class of ‘efficient’ methods (see Definition 3.2) which reduce this work with respect to implementation for nonlinear problems. We report numerical experiments to illustrate the order, acuracy and implementational aspects of these two classes of methods.     

Tensile-bending coupling in the limitting 1D beam equations resulting from the frictional contact

The asymptotic dimension reduction for beam contact problems without friction leads to decoupled ODE systems in the longitudinal variable, see [4]. This decoupling is due to the fact that friction is not taken into account. In this work we extend [2] by an alternative scaling of the tensile force in the 3D formulation that permits us to reduce the dimension of a contact problem with friction in tensile direction, too. The tension and the bending component in the direction of the contact normal are coupled due to the friction. The coupling of the displacement components is illustrated by a numerical example. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimum calibration points estimating distribution functions

The calibration method has been widely discussed in the recent literature on survey sampling, and calibration estimators are routinely computed by many survey organizations. The calibration technique was introduced in [12] to estimate linear parameters as mean or total. Recently, some authors have applied the calibration technique to estimate the finite distribution function and the quantiles. The computationally simpler method in [14] is built by means of constraints that require the use of a fixed value t₀. The precision of the resulting calibration estimator changes with the selected point t₀. In the present paper, we study the problem of determining the optimal value t₀ that gives the best estimation under simple random sampling without replacement. A limited simulation study shows that the improvement of this optimal calibrated estimator over possible alternatives can be substantial.