Polynomial filtering for nonlinear stochastic systems with state‐ and disturbance‐dependent noises

This article is concerned with the polynomial filtering problem for a class of nonlinear stochastic systems governed by the Itô differential equation. The system under investigation involves polynomial nonlinearities, unknown‐but‐bounded disturbances, and state‐ and disturbance‐dependent noises ((x,d)‐dependent noises for short). By expanding the polynomial nonlinear functions in Taylor series around the state estimate, a new polynomial filter design method is developed with hope to reduce the conservatism of the existing results. In virtue of stochastic analysis and inequality technique, sufficient conditions in terms of parameter‐dependent linear matrix inequalities (PDLMIs) are derived to guarantee that the estimation error system is input‐to‐state stable in probability. Moreover, the desired polynomial matrix can be obtained by solving the PDLMIs via the sum‐of‐squares approach. The effectiveness and applicability of the proposed method are illustrated by two numerical examples with one concerning the permanent magnet synchronous motor.     

基于标签的矩阵型Gr?bner基算法研究

目前基于标签的Gr?bner基算法大多是Buchberger型的,涉及矩阵型算法的文献往往是为了进行复杂度分析,而不考虑实际的效率。该文从实际应用出发,给出矩阵型Gao-Vol ny-Wan g(GVW)算法的一个实例,提出算法层次的优化设计方法。同时,该文还给出一个高效的约化准则。通过实验,该文比较了算法可用的各项准则及策略。实验结果表明,该文的矩阵型GVW实例在准则和策略的选取上是最优的。并且,矩阵型GVW在某些多项式系统(例如,Cyclic系列和Katsura系列多项式系统)下比Buchberger型GVW要快2~6倍。     

A novel approach based on artificial neural network for calibration of multi-hole pressure probes

Imperfections in the manufacturing process of flow measuring probes affect their measuring behavior. Nevertheless, in order to provide the highest possible accuracy, each individual multi-hole pressure probe has to be calibrated before using them in turbomachinery. This paper presents a novel method based on artificial neural networks (ANN) to predict the flow parameters of multi-hole pressure probes. A two-stage ANN approach using multilayer perceptron (MLP) is proposed in this study. The two-stage prediction approach involves two MLP networks, which represent the calibration data and the prediction error. For a given set of inputs, outputs from both networks are combined to estimate the measured value. The calibration data of a 5-hole probe at RWTH Aachen was used to develop and validate the proposed ANN models and two-stage prediction approach. The results showed that the ANN can predict the flow parameters with high accuracy. Using the two-stage approach, the prediction accuracy was further improved compared to polynomial functions, i.e. a commonly used method in probe calibration. Furthermore, the proposed approach offers high interpolation capabilities while preventing overfitting (i.e. failure to fit new data). Unlike polynomials, it is shown that the ANN based method can provide accurate predictions at intermediate points without large oscillations.     

A continuous network location problem for a single refueling station on a tree

This article considers the continuous version of the refueling station location problem on a tree network, which is a common structure in numerous toll roads worldwide, so as to locate a single alternative-fuel refueling station to maximize the traffic flow covered in round trips/day. Two reduction properties regarding the problem size and some optimality conditions are derived. Based on these conditions, an exact polynomial algorithm is developed to determine the set of optimal locations for the refueling station. A small tree network example is solved to illustrate the algorithm.     

Asymptotic stability for the Lamé system with fractional boundary damping

We consider a Lamé system damped by fractional boundary damping of Neumann type. We prove well-posedness by semigroup theory. Moreover, we prove stabilization by using multipliers method and Rellich type relation combined with the frequency domain method.     

Nonlinear adaptive noise-induced algorithm and its application in penetration signal

A nonlinear adaptive noise induced algorithm with nonlinear weights was proposed to extract rigid body deceleration during penetration events; it has 3rd-order nonlinear weight, which ensures deceleration curve is smooth everywhere (not only continuous) and avoids sharp points (crucial for targets detection). In addition, an autocorrelation algorithm was improved by applying moving window method to be compared with the proposed nonlinear adaptive algorithm. By calculating penetration depth and Power Spectrum Density (PSD) of 4 deceleration time series, we show that the nonlinear adaptive algorithm more effectively reduces noise in deceleration for striking velocities between 538 and 800 m/s compared with Adaptive Paйta Criterion, moving window autocorrelation and wavelet algorithms. It is further shown that the proposed adaptive algorithm is of the same order as the other 3 methods in terms of computational complexity.     

Interference in the Manufacture of Nuclepore Filters

In connection with the manufacture of Nuclepore filters at Vallecitos, considerations that are probabilistic in nature become important. One such consideration deals with the probabilities of interference of circles of uniform radius placed at random on a surface. Such probabilities have been found by several investigators in different contexts. A second consideration is three dimensional in that one must find the probability that cyclinders formed by passing the circles through a plate of given thickness at random angles will intersect completely through the plate. An approximate solution is found to this problem as a function of the ratio of plate thickness to circle radius. Small scale simulations are included to check the adequacy of the approximations.