Design optimization for dynamic response of vibration mechanical system with uncertain parameters using convex model

The concept of uncertainty plays an important role in the design of practical mechanical system. The most common methods for solving uncertainty problems are to model the parameters as a random vector. A natural way to handle the randomness is to admit that a given probability density function represents the uncertainty distribution. However, the drawback of this approach is that the probability distribution is difficult to obtain. In this paper, we use the non-probabilistic convex model to deal with the uncertain parameters in which there is no need for probability density functions. Using the convex model theory, a new method to optimize the dynamic response of mechanical system with uncertain parameters is derived. Because the uncertain parameters can be selected as the optimization parameters, the present method can provide more information about the optimization results than those obtained by the deterministic optimization. The present method is implemented for a torsional vibration system. The numerical results show that the method is effective.     

Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis–Hastings Method

Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.     

Semiclassical quantization of the shell model

The classical limit of the nuclear shell model is shown to be a many-dimensional hamiltonian system in which the coordinates and momenta are the coherent-state parameters of the original quantum system. Several methods for semiclassical quantization of this system are discussed, including surfaces of section and the Birkhoff-Gustavson transformation to action-angle variables. Application to a schematic three-level shell model indicates some of the new problems involved in requantizing multi-dimensional systems which are not present in one-dimensional examples. These include difficulties in finding periodic orbits and the onset of stochasticity.     

四角切圆炉膛三维温度分布优化控制建模研究

炉膛燃烧三维温度分布可视化技术为实现炉内燃烧三维温度分布优化控制奠定了基础。本文采用数值计算的方法建立了炉内不同高度特征截面平均温度及相应的温度中心坐标作为中间被控变量,以各层各角燃烧器燃料量及一次风、二次风量等参数为输入变量的线性模型。检验结果表明该模型能正确反映输入变量的变化对炉内温度分布的影响,为采用自适应遗传算法实施燃烧优化控制创造了条件。     

Interval design point method for calculating the reliability of structural systems

The evaluation of reliability for structural system is important in engineering practices.In this paper,by combining the design point method,JC method,interval analysis theory,and increment load method,we propose a new interval design point method for the reliability of structural systems in which the distribution parameters of random variables are described as interval variables.The proposed method may provide exact probabilistic interval reliability of structures whose random variables can have either a normal or abnormal distribution form.At last,we show the feasibility of the proposed approach through a typical example.     

The accuracy of source distributions measured by using polar correlation

The evaluation of jet noise source distributions as obtained by using the polar correlation technique is discussed. The accuracy with which this, or any other, technique can measure a jet noise source distribution is limited by the analytical model used to describe the source distribution and the statistical estimate which can be made of the randomly fluctuating source strengths. Both these problems are considered and criteria are developed for the accuracy of source location data in terms of the measurement parameters.     

Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables

When a dynamical system is investigated from a time series, one of the most challenging problems is to obtain a model that reproduces the underlying dynamics. Many papers have been devoted to this problem but very few have considered the influence of symmetries in the original system and the choice of the observable. Indeed, it is well known that there are usually some variables that provide a better representation of the underlying dynamics and, consequently, a global model can be obtained with less difficulties starting from such variables. This is connected to the problem of observing the dynamical system from a single time series. The roots of the nonequivalence between the dynamical variables will be investigated in a more systematic way using previously defined observability indices. It turns out that there are two important ingredients which are the complexity of the coupling between the dynamical variables and the symmetry properties of the original system. As will be mentioned, symmetries and the choice of observables also has important consequences in other problems such as synchronization of nonlinear oscillators. (c) 2002 American Institute of Physics.     

A new identification control for generalized Julia sets

In this paper, we propose a new method to realize drive-response system synchronization control and parameter identification for a class of generalized Julia sets. By means of this method, the zero asymptotic sliding variables are applied to control the fractal identification. Furthermore, the problems of synchronization control are solved in the case of a drive system with unknown parameters, and the unknown parameters of the drive system can be identified in the asymptotic synchronization process. The results of simulation examples demonstrate the effectiveness of this new method. Particularly, the basic Julia set is also discussed.     

气冷引线热平衡方程的求解方法

给出了在气冷引线最佳化问题中求解热平衡方程的方法。在寻求终解的过程中,既要解决诸多参量中包含非独立参量的问题,又要解决特解表达式的定义域中既有自变量又有因变量的问题,还要解决多解函数中确定真解定义域的问题。上述问题的解决为最终求出引线温度分布并解决引线最佳化问题奠定了基础。     

加速器驱动次临界系统注入器离子源控制系统

强流质子源及低能传输线是加速器驱动次临界系统(ADS)项目注入器的重要组成部分,为了保证其工作效率设计了一种基于实验物理及工业控制系统(EPICS)架构的远程控制系统。根据被控设备硬件接口的特点及控制需求分别采用可编程控制器(PLC)和串口服务器等作为控制部件,在主控机中使用LabVIEW编程实现了对系统内所有设备的监控,并借助于DSC模块把设备状态和参数等以过程变量的形式进行网络发布。设计的控制系统具有结构简单、工作可靠的特点,已经在系统调试中发挥了重要作用。     

Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization

An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.     

光谱数据解析中的变量筛选方法

如何从海量或高维数据中“提纯”出有用的信息,这是当前数据分析面临的一个巨大的挑战,也是当前研究的一个热点。变量筛选技术能够从众多、复杂的量测数据中提取出特征信息变量,达到简化多元模型乃至提高模型预测性能等目的。在光谱分析中,来自噪声等诸多因素的影响,量测数据会不可避免地包含干扰和无关信息变量,以及变量间存在的多重共线性,这些都会影响模型的稳健性和预测能力。近年来变量（波长）筛选方法在光谱解析领域的研究与应用中取得了较大的进展。结合国内外相关研究文献和作者的研究体会,不仅仅综述了近红外光谱,还综述了中红外光谱、拉曼光谱等众多筛选变量的方法的提出、特点、发展、类别、比较和近五年来在不同领域的应用进展。其中,评价变量重要性的参数及其标准或阈值的选择、搜索变量的策略和途径是变量筛选方法的关键。而且每种方法都具有各自的优势和局限性,实际使用中要根据方法自身特点结合目标体系的特征选择合适的方法。重点内容：（1）对比了光谱数据分析中常用的波长筛选和波段筛选方法;（2）对比了基于PLS模型参数的不同变量筛选方法的原理和特点;（3）根据搜索和筛选变量策略的不同将变量筛选方法进行分类评述。最后,围绕在解析实际复杂体系中变量筛选方法出现的过拟合、不稳定等问题进行了讨论并提出相应的解决措施,同时对变量筛选方法的研究趋势、发展前景和应用方向进行了展望。其中,新的评价变量重要性的判据和搜索变量的策略等工作仍需要展开深入地研究。期望本综述能够对光谱变量筛选的后续研究及应用起到积极的推动作用。     

Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system

Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory,which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.     

Application of the Maximum Entropy Formalism on Sprays Produced by Ultrasonic Atomizers

A recent application of the Maximum Entropy Formalism on liquid atomization problems led to the development of a mathematical volume‐based drop‐size distribution. This function, which depends on three parameters, is a reduction of the four‐parameter generalized Gamma function. The aim of the present work is to investigate the relevance of the three parameters in the characterization of liquid atomization processes. To achieve this, a variety of experimental drop‐size distributions of ultrasonic sprays were analyzed with the mathematical function. Firstly, it is found that the mathematical drop‐size distribution is very suitable to represent the volume‐based drop‐size distribution of ultrasonic sprays. Furthermore, it is seen that when considering the three parameters introduced by the function, one of them is constant for all the situations investigated, and the other two are linked to a non‐dimensional group that includes the main parameters controlling the drop production. These results are very important, since they suggest a possible development of physical models of primary atomization based on the M.E.F., which would allow for the prediction of the spray drop‐size distribution. Thusfar, such a model does not exist.     

Numerical modeling of the trajectories of plastic granules in a tribo-aero-electrostatic separator

A tribo-aero-electrostatic separator has been recently patented for the selective sorting of granular plastics mixtures generated during the recycling of waste electrical and electronic equipments (WEEE). The plastics are tribo-charged in a parallelepiped fluidized bed device, two opposite walls of which being the electrodes that generate the electric field that performs the separation. In two previous papers, different sets of operating parameters of this separator have been studied by hundreds of experiments, in order to improve the efficiency of the process and the purity of the products. The aim of the present paper is to complement these studies by establishing a model for computing the trajectory of plastics granules in such separator. The distribution of electric field and the profile of the airflow between electrodes were expressed using simple analytical formulas, which were introduced in the system of differential equations that served for the calculation of granule trajectories under the action of the various electric and mechanical forces. The computations were performed for various operating parameters: applied-voltage, granule size, charge density. The model can guide the design of industrial tribo-aero-electrostatic separators and the choice of the optimum values of the operating variables of such equipment.     

The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant

In this paper, the extended Pad'e approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter varepsilon is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values.     

Exploiting dynamical coherence: A geometric approach to parameter estimation in nonlinear models

Parameter estimation in nonlinear models is a common task, and one for which there is no general solution at present. In the case of linear models, the distribution of forecast errors provides a reliable guide to parameter estimation, but in nonlinear models the facts that predictability may vary with location in state space, and that the distribution of forecast errors is expected not to be Normal, means that parameter estimation based on least squares methods will result in systematic errors. A new approach to parameter estimation is presented which focuses on the geometry of trajectories of the model rather than the distribution of distances between model forecast and the observation at a given lead time. Specifically, we test a number of candidate trajectories to determine the duration for which they can shadow the observations, rather than evaluating a forecast error statistic at any specific lead time(s). This yields insights into both the parameters of the dynamical model and those of the observational noise model. The advances reported here are made possible by extracting more information from the dynamical equations, and thus improving the balance between information gleaned from the structural form of the equations and that from the observations. The technique is illustrated for both flows and maps, applied in 2-, 3-, and 8-dimensional dynamical systems, and shown to be effective in a case of incomplete observation where some components of the state are not observed at all. While the demonstration of effectiveness is strong, there remain fundamental challenges in the problem of estimating model parameters when the system that generated the observations is not a member of the model class. Parameter estimation appears ill defined in this case.     

Development of particle multiplicity distributions using a general form of the grand canonical partition function

Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a,x,z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba–Nielson–Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given.     

Oceanographic inverse problems

Oceanographic inverse problems are generalizations of the concept of linear regression to encompass the fitting of numerical models based on the partial-diffential equations of fluid dynamics to oceanic data by adjusting surface fluxes, initial conditions, and/or transport parameters. The limited resolution of the data requires some sort of regularizing assumptions similar to those needed for spatial interpolation. Computationally, they are nonlinear-least-squares problems involving very many variables. These problems can be ill-conditioned due to the indirect nature of the observations, to the way the dynamics enter, and to the effect of the regularizing assumptions. Solving such large optimization problems requires efficient computation of derivatives of functions defined by computational codes. The adjoint method provides derivatives with respect to all the code's many adjustable inputs for roughly the same cost as computing a single model simulation. Although computationally difficult, model fitting offers the promise of dynamically consistent multivariate analyses of oceanographic data.     

抛物方程的多重非均匀网格模型及其应用

提出了抛物方程的多重非均匀网格模型,以准确求解三维空间存在多辐射源的电波传播问题。通过对不同辐射源建立不同的坐标系,并对其仿真空间采用不同的非均匀网格划分,构建了抛物方程的多重非均匀网格模型。在此基础上,实现了三维多辐射源问题的并行计算。实例仿真了空间存在四个辐射源的电波传播特性。结果表明,抛物方程的多重非均匀网格模型能够准确求解多源的空间电磁场分布特性,且在该算例中,并行技术使得抛物方程的计算速度提升了2.41倍,极大地提高了抛物方程对三维多源问题的求解效率。