基于多模型方法的工业过程辨识研究
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摘要
现代社会对工业过程提出了越来越高的要求，由于工业过程中对于控制和优化等方面的研究均以数学模型为基础，因此针对工业过程的辨识研究有着重要的理论意义和实际价值，也受到了越来越多研究人员和工程师的关注。
工业过程中常出现非线性、不确定性、时间延迟、遗失数据以及数据采样频率不同等问题，传统基于单个线性模型的辨识方法存在一定的局限性。因此，本文针对这类相关的问题展开了深入研究，推导其过程模型，并通过一系列的仿真试验以及小规模实验验证所提辨识方法的有效性。论文的主要研究工作包括以下几个方面：
(1)研究了工业过程中具有时间延迟且不同数据采样频率的线性系统辨识问题。推导出基于离散化技术的慢速率状态空间模型，提出了基于比传统方法计算负荷低的状态增广策略的卡尔曼滤波方法来解决时间延迟系统的状态估计，并应用随机梯度算法或递推最小二乘算法估计参数，通过仿真例子和三容水箱系统实验验证了所提方法的有效性。
(2)研究了工业过程中具有单个不确定调度变量的非线性系统辨识问题，其中调度变量的动态特性通过状态空间方程来表达，并分别考虑线性和非线性的不同工况。选取带外加输入的自回归模型(AutoRegressive model with eXogenous input,ARX)作为局部模型，在每个工作点附近辨识局部ARX模型，应用归一化的指数函数作为权函数，全局模型为局部模型及其权函数的组合，应用期望最大化(Expectation Maximization, EM)算法同时估计ARX模型以及权函数的未知参数。为了求解EM算法中的积分问题，对于具有线性动态特性的调度变量，应用卡尔曼平滑算法估计隐藏调度变量的分布；对于具有非线性动态特性的调度变量，应用粒子平滑算法。通过连续搅拌反应釜和精馏塔的仿真例子以及混杂水箱系统实验对所提方法的有效性进行了验证。
(3)研究了工业过程中具有多个互相关调度变量的非线性系统辨识问题。在不同工作点空间内辨识局部ARX模型，应用归一化的指数函数将局部模型整合成全局非线性系统。提出了基于多模型方法及EM算法的辨识方法，使得局部模型及其权函数的参数被同时估计，通过具有两个互相关调度变量的非线性系统的仿真例子验证了所提方法的有效性。
(4)研究了工业过程中具有多个互相关调度变量的非线性系统，其中真实的调度变量为隐藏变量，调度变量的动态特性通过状态空间方程来表达，并考虑当观测到的调度变量含有遗失数据以及调度变量模型中含有未知参数的情况下非线性系统的辨识问题。提出了基于多模型方法及EM算法的辨识方法来同时估计局部ARX模型的参数、权函数的参数和调度变量状态空间方程的参数，通过数值仿真和精馏塔的仿真例子以及三容水箱系统实验对所提方法的有效性进行了验证。
(5)研究了工业过程中具有不确定调度变量且含有未知时间延迟的非线性系统辨识问题，提出了基于多模型方法及EM算法的辨识方法，使得局部模型的参数、权函数的参数以及未知的时间延迟被同时估计，通过连续搅拌反应釜仿真例子验证了所提算法的有效性。
Industrial processes have seen an astonishing increase in their requirements, and mostof the research on industrial process control and optimization are based on the processmathematical models. Therefore, researches on industrial process identifcation have im-portant theoretical signifcance and practical values, and have drew more attentions byindustrial practitioners as well as academic researchers.
Industrial processes usually exhibit nonlinearity, uncertainty, time delay, missing dataand diferent sampling rates between the inputs and outputs, and traditional identifcationmethods based on single linear model have some limitations for identifying the process-es. Therefore, this thesis focuses on the research on the industrial process identifcationproblems; the process models are derivatived, and several simulation examples as wellas pilot-scale experimental study are considered to illustrate the efcacy of the proposedmethod. The major work of this thesis includes:
(1) Identifcation of dual-rate linear system with time delay. The slow-rate model of thedual-rate system with time delay is derived by using the discretization technique.The states are estimated by using Kalman flter, and the parameters are estimatedbased on the stochastic gradient algorithm or recursive least squares algorithm.When concerning state estimate of the dual-rate system with time delay, the stateaugmentation method is employed with lower computational load than that of theconventional one. Simulation examples and an experimental study on a pilot-scalemultitank system are given to illustrate the proposed algorithm.
(2) Identifcation of nonlinear systems with an uncertain scheduling variable. A multiplemodel approach is developed; wherein, a set of local auto regressive exogenous(ARX) models are frst identifed at diferent process operating points, and are thencombined to describe the complete dynamics of a nonlinear system. An expectation-maximization (EM) algorithm is used for simultaneous identifcation of local ARXmodels, and for computing the probability associated with each of the local ARXmodels taking efect. A smoothing algorithm is used to estimate the distributionof the hidden scheduling variables in the EM algorithm. If the dynamics of thescheduling variables are linear, Kalman smoother is used; whereas, if the dynamicsare nonlinear, sequential Monte-Carlo method is used. Several simulation examples,including a continuous stirred tank reactor and a distillation column, are consideredto illustrate the efcacy of the proposed method. Furthermore, to highlight thepractical utility of the developed identifcation method, an experimental study on apilot-scale hybrid tank system is also provided.
(3) Identifcation of nonlinear systems with multiple and correlated scheduling variables.Multiple ARX models are identifed on diferent process operating conditions, and anormalized exponential function as the probability density function associated witheach of the local ARX models taking efect is then used to combine all the localmodels to represent the complete dynamics of a nonlinear system. The parametersof the local ARX models and the exponential functions are estimated simultaneouslyunder the framework of the EM algorithm. A numerical example of two correlatedscheduling variables is applied to demonstrate the proposed identifcation method.
(4) Identifcation of nonlinear processes in the presence of noise corrupted and corre-lated multiple scheduling variables with missing data. The dynamics of the hiddenscheduling variables are represented by a state-space model with unknown parame-ters. To assure generality, it is assumed that multiple correlated scheduling variablesare corrupted with unknown disturbances and the identifcation data-set is incom-plete with missing data. A multiple model approach under the framework of theEM algorithm is proposed to formulate and solve the identifcation problem of non-linear systems. The parameters of the local process models and scheduling variablesmodels as well as the hyperparameters of the weighting function are simultaneouslyestimated. The particle smoothing technique is adopted to handle the computationof expectation functions. Identifcation of a numerical example and a distillationcolumn are considered to demonstrate the efciency of the proposed method. Theadvantages of the proposed method are further illustrated through an experimentalstudy on a pilot-scale multitank system.
(5) Identifcation of nonlinear systems with a noisy scheduling variable, and the mea-surement of the system has an unknown time delay. ARX models are selected as thelocal models, and multiple local models are identifed along the process operatingpoints. The dynamics of a nonlinear system are represented by associating a nor-malized exponential function with each of the ARX models; therein, the normalizedexponential function is acted as the probability density function. The parameters ofthe ARX models and the exponential functions as well as the unknown time delay areestimated simultaneously under the EM algorithm using the retarded input-outputdata. A continuous stirred tank reactor example is given to verify the proposedidentifcation approach.
工业过程中常出现非线性、不确定性、时间延迟、遗失数据以及数据采样频率不同等问题，传统基于单个线性模型的辨识方法存在一定的局限性。因此，本文针对这类相关的问题展开了深入研究，推导其过程模型，并通过一系列的仿真试验以及小规模实验验证所提辨识方法的有效性。论文的主要研究工作包括以下几个方面：
(1)研究了工业过程中具有时间延迟且不同数据采样频率的线性系统辨识问题。推导出基于离散化技术的慢速率状态空间模型，提出了基于比传统方法计算负荷低的状态增广策略的卡尔曼滤波方法来解决时间延迟系统的状态估计，并应用随机梯度算法或递推最小二乘算法估计参数，通过仿真例子和三容水箱系统实验验证了所提方法的有效性。
(2)研究了工业过程中具有单个不确定调度变量的非线性系统辨识问题，其中调度变量的动态特性通过状态空间方程来表达，并分别考虑线性和非线性的不同工况。选取带外加输入的自回归模型(AutoRegressive model with eXogenous input,ARX)作为局部模型，在每个工作点附近辨识局部ARX模型，应用归一化的指数函数作为权函数，全局模型为局部模型及其权函数的组合，应用期望最大化(Expectation Maximization, EM)算法同时估计ARX模型以及权函数的未知参数。为了求解EM算法中的积分问题，对于具有线性动态特性的调度变量，应用卡尔曼平滑算法估计隐藏调度变量的分布；对于具有非线性动态特性的调度变量，应用粒子平滑算法。通过连续搅拌反应釜和精馏塔的仿真例子以及混杂水箱系统实验对所提方法的有效性进行了验证。
(3)研究了工业过程中具有多个互相关调度变量的非线性系统辨识问题。在不同工作点空间内辨识局部ARX模型，应用归一化的指数函数将局部模型整合成全局非线性系统。提出了基于多模型方法及EM算法的辨识方法，使得局部模型及其权函数的参数被同时估计，通过具有两个互相关调度变量的非线性系统的仿真例子验证了所提方法的有效性。
(4)研究了工业过程中具有多个互相关调度变量的非线性系统，其中真实的调度变量为隐藏变量，调度变量的动态特性通过状态空间方程来表达，并考虑当观测到的调度变量含有遗失数据以及调度变量模型中含有未知参数的情况下非线性系统的辨识问题。提出了基于多模型方法及EM算法的辨识方法来同时估计局部ARX模型的参数、权函数的参数和调度变量状态空间方程的参数，通过数值仿真和精馏塔的仿真例子以及三容水箱系统实验对所提方法的有效性进行了验证。
(5)研究了工业过程中具有不确定调度变量且含有未知时间延迟的非线性系统辨识问题，提出了基于多模型方法及EM算法的辨识方法，使得局部模型的参数、权函数的参数以及未知的时间延迟被同时估计，通过连续搅拌反应釜仿真例子验证了所提算法的有效性。
Industrial processes have seen an astonishing increase in their requirements, and mostof the research on industrial process control and optimization are based on the processmathematical models. Therefore, researches on industrial process identifcation have im-portant theoretical signifcance and practical values, and have drew more attentions byindustrial practitioners as well as academic researchers.
Industrial processes usually exhibit nonlinearity, uncertainty, time delay, missing dataand diferent sampling rates between the inputs and outputs, and traditional identifcationmethods based on single linear model have some limitations for identifying the process-es. Therefore, this thesis focuses on the research on the industrial process identifcationproblems; the process models are derivatived, and several simulation examples as wellas pilot-scale experimental study are considered to illustrate the efcacy of the proposedmethod. The major work of this thesis includes:
(1) Identifcation of dual-rate linear system with time delay. The slow-rate model of thedual-rate system with time delay is derived by using the discretization technique.The states are estimated by using Kalman flter, and the parameters are estimatedbased on the stochastic gradient algorithm or recursive least squares algorithm.When concerning state estimate of the dual-rate system with time delay, the stateaugmentation method is employed with lower computational load than that of theconventional one. Simulation examples and an experimental study on a pilot-scalemultitank system are given to illustrate the proposed algorithm.
(2) Identifcation of nonlinear systems with an uncertain scheduling variable. A multiplemodel approach is developed; wherein, a set of local auto regressive exogenous(ARX) models are frst identifed at diferent process operating points, and are thencombined to describe the complete dynamics of a nonlinear system. An expectation-maximization (EM) algorithm is used for simultaneous identifcation of local ARXmodels, and for computing the probability associated with each of the local ARXmodels taking efect. A smoothing algorithm is used to estimate the distributionof the hidden scheduling variables in the EM algorithm. If the dynamics of thescheduling variables are linear, Kalman smoother is used; whereas, if the dynamicsare nonlinear, sequential Monte-Carlo method is used. Several simulation examples,including a continuous stirred tank reactor and a distillation column, are consideredto illustrate the efcacy of the proposed method. Furthermore, to highlight thepractical utility of the developed identifcation method, an experimental study on apilot-scale hybrid tank system is also provided.
(3) Identifcation of nonlinear systems with multiple and correlated scheduling variables.Multiple ARX models are identifed on diferent process operating conditions, and anormalized exponential function as the probability density function associated witheach of the local ARX models taking efect is then used to combine all the localmodels to represent the complete dynamics of a nonlinear system. The parametersof the local ARX models and the exponential functions are estimated simultaneouslyunder the framework of the EM algorithm. A numerical example of two correlatedscheduling variables is applied to demonstrate the proposed identifcation method.
(4) Identifcation of nonlinear processes in the presence of noise corrupted and corre-lated multiple scheduling variables with missing data. The dynamics of the hiddenscheduling variables are represented by a state-space model with unknown parame-ters. To assure generality, it is assumed that multiple correlated scheduling variablesare corrupted with unknown disturbances and the identifcation data-set is incom-plete with missing data. A multiple model approach under the framework of theEM algorithm is proposed to formulate and solve the identifcation problem of non-linear systems. The parameters of the local process models and scheduling variablesmodels as well as the hyperparameters of the weighting function are simultaneouslyestimated. The particle smoothing technique is adopted to handle the computationof expectation functions. Identifcation of a numerical example and a distillationcolumn are considered to demonstrate the efciency of the proposed method. Theadvantages of the proposed method are further illustrated through an experimentalstudy on a pilot-scale multitank system.
(5) Identifcation of nonlinear systems with a noisy scheduling variable, and the mea-surement of the system has an unknown time delay. ARX models are selected as thelocal models, and multiple local models are identifed along the process operatingpoints. The dynamics of a nonlinear system are represented by associating a nor-malized exponential function with each of the ARX models; therein, the normalizedexponential function is acted as the probability density function. The parameters ofthe ARX models and the exponential functions as well as the unknown time delay areestimated simultaneously under the EM algorithm using the retarded input-outputdata. A continuous stirred tank reactor example is given to verify the proposedidentifcation approach.
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