A contribution to the real-time simulation of coupled finite element models of machine tools – A numerical comparison

In this paper the real-time simulation of finite element (FE) models of machine tools on a multi-processor architecture is presented. The simulation model is based on several FE component models that are connected by non-linear couplings. These couplings allow relative motions of the components in a wide range. The coupled linear FE models are decomposed at the non-linear coupling nodes and each component is solved locally. The linear structure of the components can be used for efficient simulation methods and the components can be distributed to several processors for a parallel computation. Methods that differ in numerical accuracy and stability, computational effort and real-time capacity will be presented. By means of a complex example, it will be illustrated that a parallel, stable computation can be realized time-deterministically.     

基于非线性传感器智能线性化校正分析方法

详细介绍了有关非线性传感器智能线性化校正的分析方法,以铂电阻非线性特性为例提出三种线性化校正方法,即查表法、数学公式法和比例系数法。可以根据实际测量范围和测量精度的要求选用不同的线性校正方法。在实际电路设计过程中使用前两种方法,得到了很好的线性化结果。在一些应用传感器较多的场合,基于计算机平台完全通过软件开发的虚拟智能线性化传感器,由于其性价比高、使用方便、维护简单、功能扩展容易等优点,非常适合于推广应用。     

Non-linear system identification using the Hammerstein model

An algorithm for the identification of non-linear systems which can be described by a Hammerstein model consisting of a single-valued non-linearity followed by a linear system is presented. Cross-correlation techniques are employed to decouple the identification of the linear dynamics from the characterization of the non-linear element. These results are extended to include the identification of the component subsystems of a feedforward process consisting of a Hammerstein model in parallel with another linear system.     

一种湿度传感器温度补偿的融合算法

针对自动气象站上湿度传感器在实际应用过程中易受温度影响的问题,提出采用RBF神经网络与最小二乘相结合的融合算法实现湿度传感器的温度补偿。该方法将湿度传感器在温度影响下的特性曲线分为两个非线性段和一个线性段,并且自适应的确定线性段和非线性段,在线性段利用最小二乘方法拟合出直线方程,在非线性段利用RBF神经网络补偿温度产生的影响。仿真结果表明,这种方法简单易行,与一般的BP神经网络和最小二乘多项式方法相比,具有拟合训练速度快,补偿精度高的特点,可以有效用于湿度传感器的温度补偿,提高传感器的测量精度和可靠性。     

Finite-dimensional approximation and control of non-linear parabolic PDE systems

This article proposes a rigorous and practical methodology for the derivation of accurate finite-dimensional approximations and the synthesis of non-linear output feedback controllers for non-linear parabolic PDE systems for which the manipulated inputs, the controlled and measured outputs are distributed in space. The method consists of three steps: first, the Karhunen-Loeve expansion is used to derive empirical eigenfunctions of the non-linear parabolic PDE system, then the empirical eigenfunctions are used as basis functions within a Galerkin's and approximate inertial manifold model reduction framework to derive low-order ODE systems that accurately describe the dominant dynamics of the PDE system, and finally, these ODE systems are used for the synthesis of non-linear output feedback controllers that guarantee stability and enforce output tracking in the closed-loop system. The proposed method is used to perform model reduction and synthesize a non-linear dynamic output feedback controller for a rapid thermal chemical vapour deposition process. The controller uses measurements of wafer temperature at five locations to manipulate the power of the top lamps in order to achieve spatially uniform temperature, and thus, uniform deposition of the thin film on the wafer over the entire process cycle. The performance of the non-linear controller is successfully tested through simulations and is shown to be superior to the one of a linear controller.     

Linking groundwater simulation and reservoir system analysis models: The case for California’s Central Valley

Groundwater is an important resource. In many developed basins it meets part or all of the water demands. In addition, the management of groundwater resources directly impacts stream flows through stream-aquifer interactions. Yet many reservoir system analysis models that are used for the management of surface water resources either include a simplified representation of the groundwater flow dynamics or rely on surrogate models (linear response functions, artificial neural networks, etc.) which are trained using more complex groundwater models. These approaches may introduce restrictive, sometimes inaccurate, representation of the groundwater flow dynamics and additional modeling steps. In this study a reservoir system analysis model that utilizes an LP solver is linked directly to a non-linear, three-dimensional, finite element groundwater model. The linked model is a general-purpose model and can be applied to any basin. Some of the features of the linked model are showcased by an application to California's Central Valley.     

电涡流传感器特性曲线拟合的新方法

为了减小电涡流传感器的非线性误差,在最小二乘法的基础上,结合0.618优选法,使拟合方程式中的常数更合理。用这种方法可以求得最佳拟合直线方程和最小的非线性误差。此法适用于各种类型的线性传感器或可以通过适当的变量代换把变量之间的非线性关系化为线性关系的传感器或测量系统。     

基于流体动力学的探空温度传感器太阳辐射误差研究

针对太阳辐射加热导致的误差显著限制了温度测量的准确度的问题,提出了基于流体动力学的太阳辐射误差的修正方法--数值分析法.建立从地面到32 km高空不同气压条件下珠状热敏电阻器探空温度传感器的误差热分析模型,通过计算流体动力学对其进行太阳辐射误差数值模拟分析.着重研究了太阳辐射方向、传感器表面涂层反射率、传感器尺寸等物理参数对太阳辐射误差的影响.研究结果表明:太阳辐射引起的温度测量误差随海拔高度的上升呈现非线性单调递增的变化趋势.当太阳辐射方向垂直于传感器正面时误差最大,增大传感器表面涂层反射率、减小传感器尺寸都能有效降低太阳辐射误差.     

热荧光分析仪温度传感器的研究

采用J型热电偶,设计了一种用于热荧光分析仪加热板温度测量的温度传感器。该传感器的设计主要通过对热电偶分度表进行线性回归分析,根据分析结果搭建热电偶测量电路,实现了±0．4℃的温度测量精度。同时,采用PN结法对热电偶的冷端温度变化进行补偿,通过线性回归分析,对补偿电路的输入一输出特性进行近似化处理,将温度补偿精度由±0．5℃提升到了±0．2℃。设计结果表明,该温度传感器精度高,线性度好,能够满足热荧光分析仪的测温要求。     

基于LS-SVM辨识的温度传感器非线性校正研究

针对人工神经网络等传统方法的不足,提出了一种利用最小二乘支持向量机(LS-SVM)的热电偶非线性校正方法。在该方法中,根据正反馈原理构造形式为幂级数展开模型的非线性补偿器,并利用LS-SVM线性回归算法辨识该补偿器幂级数序列模型的系数。通过该补偿器之后,热电偶可得到理想的线性特性。最后,对铂铑30—铂铑6热电偶(B型)进行非线性校正实验,实验结果表明:在0~1 820℃范围内,校正后系统的线性度小于0.035 3。因此,所提方法有效,且能应用于其他相似系统的非线性校正。     

Constructing NARMAX models using ARMAX models

This paper outlines how it is possible to decompose a complex non-linear modelling problem into a set of simpler linear modelling problems. Local ARMAX models valid within certain operating regimes are interpolated to construct a global NARMAX (non-linear NARMAX) model. Knowledge of the system behaviour in terms of operating regimes is the primary basis for building such models, hence it should not be considered as a pure black-box approach, but as an approach that utilizes a limited amount of a priori system knowledge. It is shown that a large class of non-linear systems can be modelled in this way, and indicated how to decompose the systems range of operation into operating regimes. Standard system identification algorithms can be used to identify the NARMAX model, and several aspects of the system identification problem are discussed and illustrated by a simulation example.     

Quantifying the accuracy of Hammerstein model estimation

This paper investigates the accuracy of the linear component that forms part of an overall Hammerstein model-structure estimate, and a key finding is that the process of estimating the non-linear element can have a strong effect on the associated estimate of the linear dynamics. Furthermore, this effect is not explained simply by way of considering how the input spectrum is changed by the non-linearity. Instead, it arises that the linear model-estimate variability may be dominated by a term that depends on the frequency response of the linear system itself. Amongst other things, the main results derived here have experiment design implications for Hammerstein system estimation.     

Non-linear dynamics of flexible multibody systems

In this work we set to examine several important issues pertinent to currently very active research area of the finite element modeling of flexible multibody system dynamics. To that end, we first briefly introduce three different model problems in non-linear dynamics of flexible 3D solid, a rigid body and 3D geometrically exact beam, which covers the vast majority of representative models for the particular components of a multibody system. The finite element semi-discretization for these models is presented along with the time-discretization performed by the mid-point scheme. In extending the proposed methodology to modeling of flexible multibody systems, we also present how to build a systematic representation of any kind of joint connecting two multibody components, a typical case of holonomic contraint, as a linear superposition of elementary constraints. We also indicate by a chosen model of rolling contact, an example of non-holonomic constraint, that the latter can also be included within the proposed framework. An important aspect regarding the reduction of computational cost while retaining the consistency of the model is also addressed in terms of systematic use of the rigid component hypothesis, mass lumping and the appropriate application of the explicit-implicit time-integration scheme to the problem on hand. Several numerical simulations dealing with non-linear dynamics of flexible multibody systems undergoing large overall motion are presented to further illustrate the potential of presented methodology. Closing remarks are given to summarize the recent achievements and point out several directions for future research.     

Adaptive hierarchical tuning of fuzzy controllers

Fuzzy controller design includes both linear and non-linear dynamic analysis. The knowledge base parameters associated within the fuzzy rule base influence the non-linear control dynamics while the linear parameters associated within the fuzzy output signal influence the overall control dynamics. For distinct identification of tuning levels, an equivalent linear controller output and a normalized non-linear controller output are defined. A linear proportional-integral-derivative (PID) controller analogy is used for determining the linear tuning parameters. Non-linear tuning is derived from the locally defined control properties in the non-linear fuzzy output. The non-linearity in the fuzzy output is then represented in a graphical form for achieving the necessary non-linear tuning. Three different tuning strategies are evaluated. The first strategy uses a genetic algorithm to simultaneously tune both linear and non-linear parameters. In the second strategy the non-linear parameters are initially selected on the basis of some desired non-linear control characteristics and the linear tuning is then performed using a trial and error approach. In the third method the linear tuning is initially performed off-line using an existing linear PID law and an adaptive non-linear tuning is then performed online in a hierarchical fashion. The control performance of each design is compared against its corresponding linear PID system. The controllers based on the first two design methods show superior performance when they are implemented on the estimated process system. However, in the presence of process uncertainties and external disturbances these controllers fail to perform any better than linear controllers. In the hierarchical control architecture, the non-linear fuzzy control method adapts to process uncertainties and disturbances to produce superior performance.     

Infrared thermometer sensor dynamic error compensation using Hammerstein neural network

A novel dynamic neural network structure based on Hammerstein model is proposed and applied to dynamic error compensation for infrared thermometer sensor in this paper. First, the devices of dynamic calibration for infrared thermometer sensor are designed and the calibration experiments with continuous excitation are carried out. Then, the non-linear inverse system of the sensor dynamic compensator is expressed by a non-linear static subunit followed by a linear dynamic subunit—Hammerstein model. A novel neural network structure is designed, the weights in which are corresponding with the parameters of Hammerstein model. Finally, The iterative algorithm is derived, through which the non-linear static and linear dynamic subunit in Hammerstein model can be optimised and the coefficients of the dynamic compensator are gotten. The dynamic calibration data of the uIRt/c sensor are used to test and the experiment results show that the stabilizing time of the sensor is reduced less than 6 ms from 26 ms and the dynamic characteristic is obviously improved after compensation.     

Transient analysis of flexible multi-body systems. Part I: Dynamics of flexible bodies

The formulation for the dynamic analysis of undamped linear structural systems using the finite element method results in two element matrices; the mass and stiffness matrices, that describe the element inertia and stiffness properties. However, these matrices are not sufficient to describe the dynamics of structures that undergo large rigid-body motion. Other element matrices, in addition to the mass and stiffness matrices, are required to account for the inertia coupling between gross motion and elastic deformation. These matrices are time-invariant and can be generated and assembled in the same manner as the mass and stiffness matrices are assembled in linear structural dynamics. An inherent relation between these matrices and the deformable body mean axes exists. This paper is the first of two parts. It presents the two-dimensional and three-dimensional formulation of the system equations of motion of inertia-variant flexible bodies. In particular, Euler parameters are employed to describe the rotations of the body reference in the spatial analysis. In Part II [13], this formulation is applied to the impact analysis of a large-scale constrained flexible aircraft which are modeled as a multi-body system consisting of interconnected rigid and flexible components.     

Admittance and Impedance Representations of Friction Based on Implicit Euler Integration

Modeling of friction force is cumbersome because of its discontinuity at zero velocity. This paper presents a set of discrete-time friction models for the purpose of haptic rendering and virtual environment construction. These models allow friction to be treated as an admittance-type or impedance-type element of a virtual environment. They are derived from implicit Euler integration of Coulomb-like discontinuous friction and linear mass-spring-damper dynamics, and have closed-form expressions. They include rate-dependent friction laws, and their extension to multidimensional cases is easy in most practical cases. The validity of the models is demonstrated through numerical examples and implementation experiments     

Solving Non-Linear Models with Saddle-Path Instabilities

Economic models derived from optimizing behavior are typically characterized by the properties of non-linearity and saddle-path instability. The typical solution method involves deriving the stable arm of the saddle-path and calculating suitable “jumps” to bring the path of endogenous variables onto this stable arm. The solution for the stable arm can be determined using a range of different approaches. In this paper we examine the extent to which the success of these alternative approaches can be evaluated. Any method of evaluation will be dependent upon the amount of information that is known about a particular model solution. For some deterministic models the only information known with certainty about the path of the model solution are values taken by steady-state solutions; the rest of the path must be approximated in some way based on numerical solutions derived from non-linear ordinary differential equations. In some special cases it is possible to derive a closed-form solution of the entire path. As an example of a model with a closed-form solution, we consider a simple linear model with two stable complex-valued eigenvalues and one unstable real-valued eigenvalue. The model is then employed as a benchmark to compare the properties of model solutions derived using two well-known solution algorithms. Because the model has complex-valued eigenvalues it will have cyclic dynamics and thus problems encountered in solving these dynamics will likely coincide with some of the problems that solution algorithms have in solving non-linear models. Since the entire solution path of the model is known, it is possible to derive deeper insights into the factors that are likely to ensure the success or failure of different solution approaches than would be the case if less information about the solution path was available.An earlier version of this paper was presented to the Ninth International Conference on Computing in Economics and Finance organized by the Society of Computational Economics, University of Washington at Seattle, July 11–13, 2003. Earlier versions of this paper have also been presented at seminars and workshops at the University of Oxford, at the University of Canterbury at Christchurch, and at the University of Melbourne. JEL Classifications: C63, E17     

Geometrically non-linear formulation for the three dimensional solid-shell transition finite elements

This paper presents a geometrically non-linear formulation using total lagrangian approach for the solid-shell transition finite elements. Such transition finite elements are necessary in geometrically non-linear analysis of structures modelled with three dimensional solid elements and the curved shell elements. These elements are an essential connecting link between the solid elements and the shell elements. The element formulation presented here is derived using the properties of the three dimensional solid elements and the curved shell elements. No restrictions are imposed on the magnitude of the nodal rotations. Thus the element formulation is capable of handling large rotations between two successive load increments. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate their behavior, accuracy and applications in three dimensional stress analysis.

It is shown that the selection of different stress and strain components at the integration points do not effect the overall linear response of the element. However, in geometrically non-linear applications it may be necessary to select appropriate stress and the strain components at the integration points for stable and converging element behavior. Numerical examples illustrate various characteristics of the element.