【作者】 陈爱军；

【导师】 宋执环；

【作者基本信息】 浙江大学 ， 控制科学与工程， 2006， 博士

【摘要】 传统的工业过程建模大多基于精确的数学模型，这种方法适用于运行机理和过程特性已知的工业系统。对于结构复杂、非线性、时变的工业系统，透彻分析其过程机理并建立精确数学模型是相当困难的，常常需要付出很大的人力和物力。在许多实际生产过程中，对系统机理和数学模型知之甚少的工程技术人员，通过观察和经验总结仍然对系统进行良好的手动控制。因此，采用机器学习的方法来模拟人类的这种行为是一种有效的技术方法。研究小样本下的分类或回归估计问题，研究者们提出了统计学习理论。统计学习理论作为机器学习一个分支，由于其优异的特性及应用前景受到越来越多的关注。支持向量机(SVM)衍生于统计学习理论，能够在最小化训练误差和模型复杂度之间找到最佳平衡点，是一种比较经典的机器学习方法。由于秉承了统计学习理论的主要思想(如结构风险最小化、VC维)，支持向量机可以在有限样本下得到全局最优，从而避免局部最优问题。1999年Suykens与Vandewalle将支持向量机的二次规划问题替换为一组线性等式，提出了最小二乘支持向量机(LS-SVM)。与采用线性或非线性规划方法的其它支持向量机算法相比，LS-SVM具有降低计算复杂度的优点。因此，最小二乘支持向量机在许多分类或回归估计问题中取得了很好的应用效果。本文以最小二乘支持向量机在建模、预测和控制方面的应用为背景开展研究工作，提出一些适用于动态系统特征提取、建模、预测和控制的最小二乘支持向量机改进算法。本文的主要贡献如下：1．在支持向量机回归估计中，输入样本间的自相关或互相关的特性会恶化支持向量机的泛化性能。因此对支持向量机的输入数据进行特征提取，是解决该问题的一个重要步骤。本文提出一种基于动态独立分量分析(DICA)的特征提取方法，由于从自相关和互相关的输入变量中提取独立分量，DICA更适用于动态过程变量的特征提取。将DICA方法分别应用于广义支持向量机或最小二乘支持向量机回归估计，构成多层支持向量回归估计器。第一层为降低分析复杂性，提高回归估计鲁棒性的DICA特征提取层；第二层为实现系统动态建模的SVM或LSSVM层。将DICA-LSSVM辨识器用于TE过程组分浓度估计与建模，仿真结果表明：DICA-LSSVM的估计精度优于不采用特征提取的LSSVM估计器，以及基于PCA、DPCA、ICA特征提取方法的估计器。2．为提高LS-SVM动态建模的实时性，本文提出一种基于限定、增长和缩减记忆模式下的递推最小二乘支持向量机算法(RLS-SVM)。三种记忆模式算法无需求逆，使最小二乘支持向量机的在线建模速度更加快捷。进一步合理运用三种建模模式，又提出了以最小化预报误差为目标的自适应建模方法，使得LS-SVM更适用于在线学习与预报的工业应用场合。仿真算例和自来水厂投药系统的仿真实例验证了该方法的有效性和优越性。3．使最小二乘支持向量机的解具有稀疏性，本文提出一种稀疏解算法——矢量基学习。通过引入基矢量、基矢量集与解空间的概念，从分析新样本矢量与解空间的夹角入手，推导出该样本是否为基矢量的判断准则。随着新样本的到来，在线判别支持向量，从而使LS-SVM的支持向量具有稀疏性。为改进基于矢量基学习的LS-SVM动态建模实时性，进一步提出了适用于矢量基学习的增长记忆模式递推公式。仿真算例及水处理厂的应用实例验证了该方法的可行性和有效性。4．考虑‘过度拟合’和‘野值点’对辨识模型的影响，应用正态分布函数的一些特性，本文提出基于正态分布加权的最小二乘支持向量机。根据预测误差的统计特性，以确定加权规则的参数，从而赋予训练样本不同的权值。由于考虑了生产过程中样本的一些特性，因此相对已有的加权方法，基于正态分布加权的最小二乘支持向量机更具有鲁棒性和实用性。5．基于上述研究结论，提出基于LS-SVM自适应建模的预测控制(MPC)方法。建立MPC-PID串级控制结构：内环采用PID方法，以抗扰性为目标，具有算法简单、高速采样、快速抗扰的特点；外环采用MPC方法，以鲁棒性为目标，具有提升闭环控制系统鲁棒性的特点。以一个聚合反应器为研究对象，进行仿真研究，实验结果验证了该控制结构具有很好的控制性能。更多还原

【Abstract】 The traditional approaches of industrial process modeling are mainly based on analytical models. This kind of method is suitable for the systems that we had known clearly how they work. For complex, nonlinear and dynamic industrial system, it is usually hard to analysis the mechanism of processes and to build up the mathematic models, moreover it will take us unbearable staff cost and financial cost. In most real production processes, an experienced human operator may have little knowledge about a complex system, but can still regulate control systems satisfactorily by observing the signals of inputs and outputs. Therefore, this behavior of mimicking the human ability by machine learning is an effective technique means.Studying the statistical classification or regression problem based on a given finite amount of samples, the researchers proposed the statistical learning theory (SLT). As a new technique for machine learning, the statistical learning theory is gaining more popularity due to distinguished properties and promising application performance. Support vector machine (SVM), one of novel machine learning methods, is to find a fine balance between the training error and the complexity of the learning machine. Because the formulation of SVM is guided by the statistical learning theory (i.e., structure risk minimization principle, Vapnik-Chervonenkis theory), these properties ensure that SVM can obtain global solutions instead of trapping in local optimal solutions under finite samples.In 1999, Suykens and Vandewalle proposed a modified version of SVM for classification, which is called least square support vector machine (LS-SVM) and resulted in a set of linear equations instead of a convex quadratic programming (QP) problem. Especially, LS-SVM has a significant advantage of the lower computational complexity than the other support vector machine formulations using linear or nonlinear mathematical programming. Therefore, Least squares support vector machine has shown an excellent classification or regression performance in many applications.In this thesis, the investigations are mainly focused on the application performances of LS-SVM, which involve the feature extraction, modeling, prediction and control problems. Several modification algorithms for LS-SVM are proposed here, that can be used to resolve the dynamic system issues respectively. The main contributions of the dissertation are as follows:1. In developing a SVM regression, the auto-relative or correlated features of input data could deteriorate the generalization performance of SVM. To resolve this problem, the first important step is feature extraction. A new feature extraction method, called dynamic independent component analysis (DICA), is proposed in this paper. This method is able to remove the major dynamics from the process, and to find statistically independent components from auto- and cross-correlatedvariables. To deal with the regression estimation, we combine the DICA with traditional support vector regression or least square support vector regression to construct multi-layer support vector regression. The first layer is feature extraction that has the advantages of robust performance and reduction of analysis complexity. The second layer is the SVM or LSSVM that makes the dynamic regression estimation. This modeling method is applied to estimation of process compositions in the simulation benchmark of the Tennessee Eastman (TE) plant. The simulation results clearly show that the estimator by feature extraction using DICA can perform better than that without feature extraction and with PCA, ICA, DPCA methods for feature extraction.2. To improve the modeling speed of LS-SVM, a recursive algorithm for training least squares support vector regression is presented in this paper. The recursive algorithm is based on the fixed, increased and decreased memory modes. Because three kinds of recursive modeling expression dispense with the need for calculating the matrix inversion, the online modeling speed of LS-SVM is accelerated in particular. Based on the criteria of minimizing the estimated error, a new adaptive modeling method is also proposed here. This modeling method adapted the LS-SVM to online learning problems and modeling of real industry modeling issue. Simulation analysis and the modeling of a typical plant for water treatment are also given .3. Because of equality instead of inequality constrains, the LS-SVM solutions lost the sparseness. To obtain a sparseness of support vector for least squares support vector regression, an algorithm called vector base learning (VBL) is proposed in this paper. And the concepts of base vector (BV), base vector set (BVS) and vector space are also introduced here. By calculating the angle between new sample vector and vector space, the criteria whether the measurement vector is one of the BVS is derived. As getting the new sample, the proposed algorithm on-line determines that the measurement is the support vector or not. This makes the solutions of LS-SVM have the feature of sparsity. Improving the modeling speed of LS-SVM, a recursive algorithm of increased memory mode for VBL algorithm is also proposed. Simulation analysis and the modeling of a typical plant for water treatment clearly illustrated the validity and feasibility of the presented method.4. Considering the impacts of ’excessive fitting’ and ’unusual point’ on identification, a weighted least squares support vector machine which based on the normal distribution function is proposed in this thesis. Its weighted rules mainly apply some statistical characteristics of the normal distribution faction. Confirming the parameters of the weighted rules according to the prediction errors, we can determine different weighted factor on each training variables. Because of emphasizing the real time properties of the sample, the weighted LS-SVM based on the normal distribution function has better robust and practicable ability than the known methods.5. Summarizing the results of the preceding chapters, a kind of nonlinear predictive control scheme based on the adaptive LS — SVM model is presented. A MPC-PID cascade control structure is built up. The inner control loop is PID controller, which has the performance of resisting the disturbance. As we know, PID has the characteristics of simple algorithm, fast sampling, and rapid noise immunity. The outer control loop is MPC controller, which lets the close control loop have the ability of higher robust. A simulation of CSTR process is given to prove the validity of the proposed method. The simulation results show that the nonlinear predictive control strategy based on LS — SVM model has a satisfactory performance.更多还原