非线性测量模型的合成标准不确定度公式探讨

在ISO/IEC Guide 98—3:2008《测量不确定度——第3部分:测量不确定度表示指南(GUM:2008)》中和JJF 1059.1—2012《测量不确定度评定与表示》中,给出了所有输入量均服从正态分布且互不相关的非线线测量模型含高阶项的合成标准不确定度计算公式。本文推导了输入量均服从对称分布且互不相关的非线性测量模型含高阶项的合成标准不确定度通用公式,并对其适用条件进行了研讨。

非线性测量误差模型的影响分析(英文)

本文对非线性测量误差模型给出了统一的诊断方法,并证明了数据删除模型与均值漂移模型的等价性,由此出发得到了Cook距离、残差、杠杆值等诊断统计量.本文还讨论了非线性测量误差模型的局部影响分析,并给出了一个具体应用实例.推广了Zhao & Lee(1995)的结果.

一类非线性测量误差模型的保形法曲率及其局部影响

保形法曲率是Poon W Y和Poon Y S(1997)从微分几何的观点出发提出来的诊断模型局部影响的一种统计量,它将影响曲率标准化在[0,1]范围内,并提供了判定局部影响大小的阙值,可看作Cook(1986)局部影响方法的进一步推广。本文采用保形法曲率方法来诊断具有正态先验分布的非线性测量误差模型的局部影响,并对常见的两种扰动模型给出了局部影响的计算公式。最后通过实例分析验证了文中诊断统计量的有效性。

亥姆霍兹线圈原理分析及测量不确定度评定

以比奥-萨伐尔定律为基础,首先,计算了微电流矢量在空间任意点的磁场;然后,推算出单个圆形线圈产生的磁场;最后,推导出亥姆霍兹线圈在中间点的磁场表达式,建立起测量模型,用蒙特卡罗法进行了测量不确定度分析。详细地论述了计算公式与测量模型的关系,以及使用Matlab计算软件进行计算的流程和数据处理方案。使用蒙特卡罗法避免了不确定度评定中的非线性测量模型问题,并在不确定度分量估算时考虑了实际使用所带来的影响,从而增加了评定结果的可信性,具有一定的参考价值。

电压驻波比测量不确定度的评定和表述

电压驻波比是无线电领域表征反射特性的传统参量,目前仍有应用场景,然而一些实验室对电压驻波比测量不确定度的报告是不完善的。比较了GUM法线性模型、GUM法非线性模型和蒙特卡洛法对电压驻波比测量不确定度的评定结果,给出了一种在常规测量条件下可代替蒙特卡洛法的快速估算方法,并将该方法推广到一元非线性测量模型。

基于HHT的转动惯量测量技术研究

为提高扭摆法测量大型回转体转动惯量的测量精度,克服线性转动惯量测量模型及周期法转动惯量计算的弊端,开展了基于希尔伯特-黄变换(HHT)的转动惯量测量技术研究。建立了考虑摩擦阻力矩的非线性转动惯量测量模型,在此基础上,通过经验模态分解提取了角位移主分量,利用希尔伯特变换识别了扭摆系统的瞬时阻尼系数和瞬时无阻尼固有频率,最后利用最小二乘法拟合得到非线性模型参数,精确求解了转动惯量。研制了一套大型回转体转动惯量测量系统,对不同组合的标准件进行转动惯量测量试验,验证了基于HHT的转动惯量计算方法的可行性。大量试验测量结果表明,本系统转动惯量测量相对误差小于0.2%,测量精度显著优于传统的周期法测量结果。

Nonlinear Model Predictive Control Based on Support Vector Machine with Multi-kernel

Multi-kernel-based support vector machine （SVM） model structure of nonlinear systems and its specific identification method is proposed, which is composed of a SVM with linear kernel function followed in series by a SVM with spline kernel function. With the help of this model, nonlinear model predictive control can be transformed to linear model predictive control, and consequently a unified analytical solution of optimal input of multi-step-ahead predictive control is possible to derive. This algorithm does not require online iterative optimization in order to be suitable for real-time control with less calculation. The simulation results of pH neutralization process and CSTR reactor show the effectiveness and advantages of the presented algorithm.

Assimilating Amounts of Precipitation Using a New Four-Dimensional Variational Method

Observations of accumulated precipitation are extremely valuable for effectively improving rainfall analysis and forecast. It is, however, difficult to use such observations directly through sequential assimilation methods, such as three-dimensional variational data assimilation or an Ensemble Kalman Filter. In this study, the authors illustrate a new approach that makes effective use of precipitation data to improve rainfall forecast. The new method directly obtains an optimal solution in a reduced space by fitting observations with historical time series generated by the model; it also avoids the implementation of tangent linear model and its adjoint. A lot of historical samples are produced as the ensemble of precipitation observations with the fully nonlinear forecast model. The results show that the new approach is capable of extracting information from precipitation observations to improve the analysis and forecast. This method provides comparable performance with the standard fourdimensional variational data assimilation at a much lower computational cost.

Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models

This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a non-linear model. On the basis of the error definition,this paper puts forward a new adjustment criterion, SGPE.Last,this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.

Nonlinear state estimation for fermentation process using cubature Kalman filter to incorporate delayed measurements

State estimation of biological process variables directly influences the performance of on-line monitoring and op- timal control for fermentation process. A novel nonlinear state estimation method for fermentation process is proposed using cubature Kalman filter （CKF） to incorporate delayed measurements. The square-root version of CI（F （SCKF） algorithm is given and the system with delayed measurements is described. On this basis, the sample-state augmentation method for the SCKF algorithm is provided and the implementation of the proposed algorithm is constructed. Then a nonlinear state space model for fermentation process is established and the SCKF algorithm incorporating delayed measurements based on fermentation process model is presented to implement the nonlinear state estimation. Finally, the proposed nonlinear state estimation methodology is applied to the state estimation for penicillin and industrial yeast fermentation processes. The simulation results show that the on-fine state estimation for fermentation process can be achieved by the proposed method with higher esti- mation accuracy and better stability.

Nonlinear model predictive control based on support vector machine and genetic algorithm

This paper presents a nonlinear model predictive control(NMPC) approach based on support vector machine(SVM) and genetic algorithm(GA) for multiple-input multiple-output(MIMO) nonlinear systems.Individual SVM is used to approximate each output of the controlled plant Then the model is used in MPC control scheme to predict the outputs of the controlled plant.The optimal control sequence is calculated using GA with elite preserve strategy.Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection.

An Algorithm for Parameter Identification of UAS from Flight Data

The aim of the present work is to realize an identification algorithm especially devoted to UAS （unmanned aerial systems）. Because UAS employ low cost sensor, very high measurement noise has to be taken into account. Therefore, due to both modelling errors and atmospheric turbulence, noticeable system noise has also to be considered. To cope with both the measurement and system noise, the identification problem addressed in this work is solved by using the FEM （filter error method） approach. A nonlinear mathematical model of the subject aircraft longitudinal dynamics has been tuned up through semi-empirical methods, numerical simulations and ground tests. To take into account model nonlinearities, an EKF （extended Kalman filter） has been implemented to propagate the state. A procedure has been tuned up to determine either aircraft parameters or the process noise. It is noticeable that, because the system noise is treated as unknown parameter, it is possible to identify system affected by noticeable modelling errors. Therefore, the obtained values of process noise covariance matrix can be used to highlight system failure. The obtained results show that the algorithm requires a short computation time to determine aircraft parameter with noticeable precision by using low computation power. The present procedure could be employed to determine the system noise for various mechanical systems, since it is particularly devoted to systems which present dynamics that are difficult to model. Finally, the tuned up off-line EKF should be employed to on-line estimation of either state or unmeasurable inputs like atmospheric turbulence.

On all-propulsion design of integrated orbit and attitude control for inner-formation gravity field measurement satellite

The inner-formation gravity field measurement satellite （IFS） is a novel pure gravitational orbiter. It aims to measure the Earth＇s gravity field with unprecedented accuracy and spatial resolution by means of precise orbit determination （POD） and relative state measurement. One of the key factors determining the measurement level is the outer-satellite control used for keeping the inner-satellite flying in a pure gravitational orbit stably. In this paper the integrated orbit and attitude control of IFS during steady-state phase was investigated using only thrusters. A six degree-of-freedom translational and rotational dynamics model was constructed considering nonlinearity resulted from quaternion expression and coupling induced by community thrusters. A feasible quadratic optimization model was established for the integrated orbit and attitude control using con- strained nonlinear model predictive control （CNMPC） techniques. Simulation experiment demonstrated that the presented CNMPC aigorithm can achieve rapid calculation and overcome the non-convexity of partial constraints. The thruster layout is rational with low thrust consumption, and the mission requirements of IFS are fully satisfied.

Tracking with nonlinear measurement model by coordinate rotation transformation

A new filtering method is proposed to accurately estimate target state via decreasing the nonlinearity between radar polar measurements(or spherical measurements in three-dimensional(3D) radar) and target position in Cartesian coordinate. The degree of linearity is quantified here by utilizing correlation coefficient and Taylor series expansion. With the proposed method, the original measurements are converted from polar or spherical coordinate to a carefully chosen Cartesian coordinate system that is obtained by coordinate rotation transformation to maximize the linearity degree of the conversion function from polar/spherical to Cartesian coordinate. Then the target state is filtered along each axis of the chosen Cartesian coordinate. This method is compared with extended Kalman filter(EKF), Converted Measurement Kalman filter(CMKF), unscented Kalman filter(UKF) as well as Decoupled Converted Measurement Kalman filter(DECMKF). This new method provides highly accurate position and velocity with consistent estimation.

Nonabelian Gauged Linear Sigma Model

The gauged linear sigma model （GLSM for short） is a 2d quantum field theory introduced by Witten twenty years ago. Since then, it has been investigated extensively in physics by Hori and others. Recently, an algebro-geometric theory （for both abelian and nonabelian GLSMs） was developed by the author and his collaborators so that he can start to rigorously compute its invariants and check against physical predications. The abelian GLSM was relatively better understood and is the focus of current mathematical investigation. In this article, the author would like to look over the horizon and consider the nonabelian GLSM. The nonabelian case possesses some new features unavailable to the ahelian GLSM. To aid the future mathematical development, the author surveys some of the key problems inspired by physics in the nonabelian GLSM.