非线性动态系统中迭代的同步数据协调与显著误差检测的支持向量回归方法

化工厂中过程数据的质量严重影响到来自例如性能监控, 在线优化和控制等活动所获得的效益和性能. 由于许多化工过程通常表现为非线性动态特性, 例如扩展卡尔曼滤波(EKF)和非线性动态数据协调(NDDR)等技术已经被发展出来改进数据的质量. 近期, 迭代非线性动态数据协调(RNDDR)技术已被提出, 该技术结合了EKF和NDDR技术的优点. 但是, RNDDR技术不能够处理具有显著误差的测量值. 本文中, 一种非线性动态系统中迭代的同步数据协调与显著误差检测的支持向量(SV)回归方法被提出. SV回归是一种经验风险和结构风险间的妥协, 并且对于数据协调来说, 其对随机误差和显著误差是鲁棒的．通过将结构风险取代RNDDR中的极大似然估计并使其最小化, 我们的方法不仅可以实现迭代非线性动态数据协调, 还可以同时实现显著误差检测. 本文中的非线性动态系统仿真结果显示出, 所提出的方法在迭代实时估计框架下, 对于非线性动态系统的同步数据协调和显著误差检测是鲁棒、稳定并且精确的. 该方法也可以提供更好的控制性能.     

积分法动态数据校正技术的研究

基于积分法的动态数据校正具有简单、快速和适于在线应用的优点。本文对积分法动态数据校正技术的原理及其应用方法进行了研究。研究结果表明,该方法不要求有状态空间模型,能够充分利用整个时间轴的时间冗余信息;但积分法中的区间长度对其校正精度有影响,因此,采用该方法进行校正时应首先确定适宜的区间长度。将积分法应用于常减压炼油装置拟稳态过程的数据校正,计算结果表明该方法的计算精度高于稳态数据校正。     

Robust, reduced-order, nonstrictly proper state estimation via theoptimal projection equations with guaranteed cost bounds

A state estimation design problem involving parametric plant uncertainties is considered. An estimation error bound suggested by multiplicative white-noise modeling is utilized for guaranteeing robust estimation over a specified range of parameter uncertainties. Necessary conditions that generalize the optimal projection equations for reduced-order state estimation are used to characterize the estimator that minimizes the error bound. The design equations thus effectively serve as sufficient conditions for synthesizing robust estimators. Additional features include the presence of a static estimation gain in conjunction with the dynamic (Kalman) estimator to obtain a nonstrictly proper estimator     

Bias detection and estimation in dynamic data reconciliation

A method for detection and estimation of measurement bias in nonlinear dynamic processes is presented. It employs model-based data reconciliation and requires the examination of the resulting difference between the measured and reconciled values. Since bias is commonly present in process measurements, this technique is an important step toward the ultimate goal of reconciling ‘raw’ process data that may contain bias and gross errors in addition to small random errors. A CSTR example shows that this method does allow for the detection of a single bias in a nonlinear dynamic process whether or not the exact model equations are known.     

一种改进的基于鲁棒估计的动态数据校正方法

针对目前动态数据校正方法存在的缺陷,本文基于鲁棒估计的原理,提出一种新型的鲁棒估计函数,该函数物理概念清晰,参数调节灵活。基于此函数构造的动态数据校正方法(IRDR),在校正随机误差的同时,可以同步对异常点过失误差进行侦破和识别。CSTR仿真实例表明,该方法可以准确识别出系统所含的多个过失误差,校正结果偏差小,曲线平滑,具有较强优越性。     

Robust, reduced-order, nonstrictly proper state estimation via the optimal projection equations with Petersen—Hollot bounds

A state-estimation design problem involving parametric plant uncertainties is considered. An error bound suggested by recent work of Petersen and Hollot is utilized for guaranteeing robust estimation. Necessary conditions which generalize the optimal projection equations for reduced-order state estimation are used to characterize the estimator which minimizes the error bound. The design equations thus effectively serve as sufficient conditions for synthesizing robust estimators. An additional feature is the presence of a static estimation gain in conjunction with the dynamic (Kalman) estimator, i. e., a nonstrictly proper estimator.     

基于鲁棒估计的动态传感数据校正方法

为实现IEEE1451网络化智能传感器输出数据与输入信号随时间的变化曲线保持一致,解决智能传感中的非线性问题,根据数据校正与数据回归的相似性,引入并改进在数据回归中应用较好鲁棒估计方法,结合非线性动态数据校正的DAEs模型,为传感器的校正引擎构建了相应的鲁棒估计目标函数。应用实例可得,校正后的结果与模型值的均方差MSE＆lt;0.003,表明在数据校正方法中引入鲁棒估计方法,可以使目标函数对偏离理想条件的数据不敏感,能显著减小异常数据点对传感数据校正的不利影响,实现高效的数据自校正。     

基于递归神经网络模型预测控制的模型平稳切换

不同生产条件下的控制系统可视多模型控制系统,但多模型控制在模型切换时会引起系统的瞬态响应。采用递归神经网络建立系统的多个模型,基于模型预测控制进行控制模型切换,克服了模型切换时引起的系统瞬态响应,实现系统的平稳切换。并通过仿真表明这种切换策略明显改善了模型切换过程的动态性能。     

Radial basis function neural network for approximation andestimation of nonlinear stochastic dynamic systems

This paper presents a means to approximate the dynamic and static equations of stochastic nonlinear systems and to estimate state variables based on radial basis function neural network (RBFNN). After a nonparametric approximate model of the system is constructed from a priori experiments or simulations, a suboptimal filter is designed based on the upper bound error in approximating the original unknown plant with nonlinear state and output equations. The procedures for both training and state estimation are described along with discussions on approximation error. Nonlinear systems with linear output equations are considered as a special case of the general formulation. Finally, applications of the proposed RBFNN to the state estimation of highly nonlinear systems are presented to demonstrate the performance and effectiveness of the method.     

A structured filter for Markovian switching systems

In this work, a new methodology for the structuring of multiple model estimation schemas is developed. The proposed filter is applied to the estimation and detection of active mode in dynamic systems. The discrete-time Markovian switching systems represented by several linear models, associated with a particular operating mode, are studied. Therefore, the main idea of this work is the subdivision of the models set to some subsets in order to improve the detection and estimation performances. Each subset is associated with sub-estimators based on models of the subset. In order to compute the global estimate and subset probabilities, a global estimator is proposed. Theoretical developments based on a hierarchical decision, leading to more efficiency in detection and state estimation, are proposed. Naturally, these results can be used for fault detection and isolation, using the activation probabilities of operating modes. These results are applied to detect switches in the centre of gravity for vehicle roll dynamics.     

State and parameter estimation for nonlinear biological phenomena modeled by S-systems

Biological pathways can be modeled as a nonlinear system described by a set of nonlinear ordinary differential equations (ODEs). A central challenge in computational modeling of biological systems is the determination of the model parameters. In such cases, estimating these variables or parameters from other easily obtained measurements can be extremely useful. For example, time-series dynamic genomic data can be used to develop models representing dynamic genetic regulatory networks, which can be used to design intervention strategies to cure major diseases and to better understand the behavior of biological systems. Unfortunately, biological measurements are usually highly affected by errors that hide the important characteristics in the data. Therefore, these noisy measurements need to be filtered to enhance their usefulness in practice. This paper addresses the problem of state and parameter estimation of biological phenomena modeled by S-systems using Bayesian approaches, where the nonlinear observed system is assumed to progress according to a probabilistic state space model. The performances of various conventional and state-of-the-art state estimation techniques are compared. These techniques include the extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF), and the developed improved particle filter (IPF). Specifically, two comparative studies are performed. In the first comparative study, the state variables (the enzyme CadA, the transport protein CadB, the regulatory protein CadC and lysine Lys for a model of the Cad System in E. coli (CSEC)) are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error (RMSE) with respect to the noise-free data. In the second comparative study, the state variables as well as the model parameters are simultaneously estimated. In this case, in addition to comparing the performances of the various state estimation techniques, the effect of the number of estimated model parameters on the accuracy and convergence of these techniques is also assessed. The results of both comparative studies show that the UKF provides a higher accuracy than the EKF due to the limited ability of EKF to accurately estimate the mean and covariance matrix of the estimated states through lineralization of the nonlinear process model. The results also show that the IPF provides a significant improvement over PF because, unlike the PF which depends on the choice of sampling distribution used to estimate the posterior distribution, the IPF yields an optimum choice of the sampling distribution, which also accounts for the observed data. The results of the second comparative study show that, for all techniques, estimating more model parameters affects the estimation accuracy as well as the convergence of the estimated states and parameters. However, the IPF can still provide both convergence as well as accuracy related advantages over other estimation methods.     

不确定系统的不确定项观测器设计

为了克服常规用不确定项的界估计来设计控制器带来的保守性和动态性能差的弊端,本文就连续的和离散的不确定系统,分别提出了不确定项的观测器设计方案.通过引入分布和离散加权平均的概念,对这两种观测器的观测误差精度进行了分析估算,从数学上证明了所得的观测值在加权平均意义下是无偏的.此外,通过适当选择观测器反馈增益,可以得到满意的误差估计精度.把该方法应用到一个控制系统中,仿真结果表明所提出的观测器能很好的估计不确定项和改进闭环系统动态性能.     

Pseudo-state approach to observer based optimal discrete-timeestimation

A frequency-domain-based solution of the optimal linear estimation problem is obtained using a polynomial system representation. The H₂ optimal filter can be realized using an observer based structure estimating pseudo-state variables that are fed back through a dynamic gain control block. There are normally fewer pseudo-states than the total order of the system. The dynamic gain for the model based observer is computed from diophantine equations and the observer provides both pseudo state and output estimates. The approach can deal with improper plant transfers and singular measurements     

Data reconciliation for real-time optimization of an industrial coke-oven-gas purification process

Online optimization is more and more used in the chemical industry to run a process near its optimum operating condition by providing real-time computed optimal set-points to the distributed control system. Process measurements are necessary for these applications to determine the actual state of the process and to increase the accuracy of the model with parameter estimation techniques. However, these measurements usually contain random as well as gross errors which have to be identified and eliminated before the measurements are used for online optimization. In this contribution, a data reconciliation approach was integrated into an online optimization framework for the ammonia hydrogen sulfide circulation scrubbing, a common industrial coke-oven-gas purification process. We used a rigorous rate-based model to describe this reactive absorption and desorption process. To increase the accuracy of the model, we estimated several process parameters using a sequential parameter estimation approach. Data reconciliation was performed based on simple component balances to achieve model-consistent data and to identify measurement biases. The model was then validated online on a pilot plant by connecting the estimation package through the process control system. Based on the online measured data, operating cost minimization was carried out and the computed optimal set-points realized real-time. A satisfactory agreement between measured data and optimization was achieved.     

典型炼油装置数据校正技术的研究

化工过程测虽数据作为反映装置运行状况的特征信息,是实现计算机过程控制、模拟、优化和生产管理的基本依据.研究过程数据校正技术,对实现装置优化控制与管理具有重要理论意义和现实意义.现有理论研究大都采用传统统计检验和线性化处理方法,在实际应用有较大局限性.本文在对已有数据校正技术分析的基础上,提出将修正的时间序列分析法用于测量数据校正.综合考虑数据的窄间冗余和时间冗余,充分利用过程的历史数据,建立了时间序列概率模型,并针对含随机误差数据和含过失误差数据两种情况,从时序法平均值、阶跃过程模型等方面详细探讨数据校正方法.将新的数据校正方法用于典型常减压蒸馏装置,结果表明,新方法能够侦破出数据中含有的过失误差;校正值与真值的平均偏差非常小,具有足够的精度保证数据的准确性;修正的时间序列分析法用于数据校正能克服传统方法的局限性.     

Modified unscented recursive nonlinear dynamic data reconciliation for constrained state estimation

In state estimation problems, often, the true states satisfy certain constraints resulting from the physics of the problem, that need to be incorporated and satisfied during the estimation procedure. Amongst various constrained nonlinear state estimation algorithms proposed in the literature, the unscented recursive nonlinear dynamic data reconciliation (URNDDR) presented in [1] seems to be promising since it is able to incorporate constraints while maintaining the recursive nature of estimation. In this article, we propose a modified URNDDR algorithm that gives superior performance when compared with the basic URNDDR. The improvements are obtained via better constraint handling and are demonstrated on representative case studies [2], [3]. In addition to this modification, an efficient strategy combining basic unscented Kalman filter (UKF), URNDDR and modified URNDDR is also proposed in this article for solving large scale state estimation problems at relatively low computational cost. The utility of the proposed strategy is demonstrated by applying it to the Tennessee Eastman challenge process [4].     

Model and distribution uncertainty in multivariate GARCH estimation: A Monte Carlo analysis

Multivariate GARCH models are in principle able to accommodate the features of the dynamic conditional covariances; nonetheless the interaction between model parametrization of the second conditional moment and the conditional density of asset returns adopted in the estimation determines the fitting of such models to the observed dynamics of the data. Alternative MGARCH specifications and probability distributions are compared on the basis of forecasting performances by means of Monte Carlo simulations, using both statistical and financial forecasting loss functions.     

A novel real-time adaptive suboptimal recursive state estimation scheme for nonlinear discrete dynamic systems with non-Gaussian noise

A real-time state filtering and prediction scheme which is adaptive, recursive, and suboptimal is proposed for discrete time nonlinear dynamic systems with either Gaussian or non-Gaussian noise. The proposed scheme (PR) estimates states adaptively whenever both the observation is available and there exists a non-zero and finite number of real state roots of the observation model, otherwise the PR estimates states non-adaptively. The PR state transition and observation functions are as general as the state transition and observation functions for particle filters. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple hypothesis testing. The PR first detects state estimate divergence points along the time axis, and then state estimate divergences are prevented by introducing new admissible state quantization levels; whereas the extended Kalman filter (EKF), sampling importance resampling (SIR) particle filter (bootstrap filter), and auxiliary sampling importance resampling (ASIR) particle filter produce diverging state estimates from actual state values for many dynamic models. The PR uses state transition functions in order to calculate transition probabilities from gates to gates. If these transition probabilities are somehow available, then state transition functions are not needed for state estimation with the PR; whereas state transition functions are necessary for state estimation with both particle filters and the EKF. The PR is very suitable for state estimation with either constraints imposed on state estimates or missing observations. The PR is more general than grid-based estimation approaches. Monte Carlo simulations have shown the effectiveness of the PR, that is, the PR performance is better than the performances of the EKF, SIR, and ASIR particle filters for many nonlinear models with white Gaussian noise, four examples of which are presented in the paper.     

Shape and nonrigid motion estimation through physics-basedsynthesis

A physics-based framework for 3-D shape and nonrigid motion estimation for real-time computer vision systems is presented. The framework features dynamic models that incorporate the mechanical principles of rigid and nonrigid bodies into conventional geometric primitives. Through the efficient numerical simulation of Lagrange equations of motion, the models can synthesize physically correct behaviors in response to applied forces and imposed constraints. Applying continuous Kalman filtering theory, a recursive shape and motion estimator that employs the Lagrange equations as a system model is developed. The system model continually synthesizes nonrigid motion in response to generalized forces that arise from the inconsistency between the incoming observations and the estimated model state. The observation forces also account formally for instantaneous uncertainties and incomplete information. A Riccati procedure updates a covariance matrix that transforms the forces in accordance with the system dynamics and prior observation history. Experiments involving model fitting and tracking of articulated and flexible objects from noisy 3-D data are described     

Dynamic Bayesian beta models

We develop a dynamic Bayesian beta model for modeling and forecasting single time series of rates or proportions. This work is related to a class of dynamic generalized linear models (DGLMs), although, for convenience, we use non-conjugate priors. The proposed methodology is based on approximate analysis relying on Bayesian linear estimation, nonlinear system of equations solution and Gaussian quadrature. Intentionally we avoid MCMC strategy, keeping the desired sequential nature of the Bayesian analysis. Applications to both real and simulated data are provided.