基于机器学习的软测量技术理论与应用
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摘要
世界是普遍联系的,并且以某种形式表现出来,这是本课题研究的基本哲学基础。这种普遍联系在数学家的眼里就是一种映射关系,或者说是函数关系。在信息时代里,这种映射关系蕴涵于成千上万的数据中。本文研究的软测量技术就是要寻找埋藏于数据中的各种函数关系。在当今以信息技术带动工业化发展的时代,仪器仪表和测试技术是信息科学技术的重要组成部分。现代社会,随着人们对产品质量要求的提高和人们安全意识与环保意识的提高,对各类测试仪器、检测仪器和分析仪器的需求日益增加。软测量技术是各类综合指标测试仪器、检测仪器和分析仪器的基础技术。此外,作为传统仪器仪表的重要补充,软测量技术在工业测控领域也具有广阔的应用前景。软测量技术研究对仪器仪表和测控技术的发展具有重要意义。
通常,实际工业过程具有复杂非线性特性和存在大量噪声干扰,这限制了基于机理分析、多元线性回归和神经网络等传统软测量技术的应用。为了克服传统方法的局限性,本课题着重研究基于机器学习理论的、具有好的泛化能力和鲁棒性的非线性软测量建模方法。在保证模型泛化能力和鲁棒性的前提下,研究可以提高建模效率的改进实现算法。本课题的主要研究工作和成果有:
(1)对传统k-最近邻(kNN)算法进行近邻距离定义的改进,用属性加权距离取代标准欧氏距离。进而,基于改进kNN算法提出了一种数据集剪辑算法,用于滤除矛盾数据样本。针对中大规模数据集提出了一种快速kNN算法,运行速度仅与最近邻数k值和数据集维数n值有关。通常,运行速度较传统算法可提高几倍至十几倍。对于局部学习算法的研究,最近邻子集的快速搜索算法研究具有普遍意义。
(2)研究基于多神经网络的软测量建模方法,旨在提高工业环境下软测量模型的鲁棒性和泛化能力。提出了一种以聚类子簇数据作为验证数据集(而非训练数据集)的多神经网络,并将其用于构造两层结构多神经网络模型。针对纸浆Kappa值数据集,使用单一神经网络、两类单层多神经网络和两层多神经网络等四种模型进行软测量建模对比实验。实验结果表明,两层多神经网络模型的鲁棒性和泛化能力优于其他三种模型。
(3)将软间隔支持向量机回归算法用于软测量建模。给出了两个版本的ε-SVMR算法,同时给出了该算法的通用二次规划(QP)解算器和序贯最小优化(SMO)两种实现方法。针对纸浆Kappa值数据集进行两个仿真实验,分别研究ε-SVMR算法的自由参数对模型预测性能的影响和ε-SVMR算法两种实现方法的建模效率。主要结论是,基于SMO算法的SVM方法尤其适用于中大规模实际工业过程的软测量建模。
(4)研究了时间序列的两种预测建模方法,即样本扩展TDNN方法和特征扩展SVM方法。两种建模方法分别基于过程时间序列的样本扩展数据集和特征扩展数据集。对于制浆蒸煮过程时间序列的仿真实验表明:多步预测的性能优于单步预测的性能,尤其对于样本序列较少的情形;特征扩展SVM方法的性能优于样本扩展TDNN方法的性能,尤其对于单序列输入的情形。
(5)对过程神经网络(PNN)进行理论研究,揭示了过程神经元和传统神经元间的联系。指出了过程神经元可用传统神经元进行无限逼近,给出了两个逼近定理和证明,以及相关的两个推论。针对模拟产生的正弦波编码信号集进行仿真实验,研究过程神经网络的预测建模性能。实验得出的主要结论是,过程神经网络对于白噪声具有很好的抑制作用,从而增加了模型的鲁棒性。但其使用需要选取用于基展开的正交基函数系。
(6)引入信号内积和范数的定义,提出了一种新的过程式输入学习算法,即过程支持向量机(PSVM)。针对模拟产生的正弦波编码信号集进行仿真实验,并将实验结果和过程神经网络的实验结果进行比较。PSVM方法的使用比较方便,可以避开正交基函数系的选择问题。当噪声幅度较小时,PSVM方法的表现优于PNN方法;当噪声幅度变大时,PSVM方法的表现稍差于PNN方法,但可通过对信号进行类似于PNN方法的基展开截频处理提高其预测性能。关于PNN和PSVM学习方法的研究为过程式输入的软测量建模提供必要的理论基础。
本课题研究取得的创造性成果有:(1)提出了一种基于改进kNN算法的数据集剪辑算法,用于滤除数据集中的大误差样本。(2)提出了一种快速kNN算法,对于局部学习(消极学习)算法的研究具有普遍意义。(3)提出了一种以聚类子簇数据作为验证数据集(而非训练数据集)的多神经网络模型,用于构建泛化能力好的预测模型。(4)提出了过程神经元的两个逼近定理并给出了证明,揭示了过程神经元和传统神经元的内在联系。(5)提出了一种新的过程式输入学习算法,即过程支持向量机。
总之,本课题以基于机器学习的软测量技术理论和应用作为主要研究内容,展开深入研究,取得了一些有益的成果。文中提出的软测量建模方法既丰富了软测量建模理论,也促进了软测量技术的工业实用化。后两章比较侧重理论研究,取得的理论成果不仅对软测量理论的发展具有重要作用,而且对机器学习理论的发展也有一定的促进作用。由于作者水平有限,文中难免有错误或不妥之处,恳请各位专家和读者批评指正。
Relations exist universally in nature and are expressed in certain forms, which is the basic philosophy foundation of this research subject. In mathematicians’view, this kind of relations is a kind of mappings, or mapping functions. In the information age, these mapping relations are contained within many thousands of data. The soft sensing technology (SST), being researched in this dissertation, aims at finding various mapping functions hidden in data. Today, in the age that industrialization is driven by the information technology (IT), the instrumentation and measurement technology is an important part of the information science and technology. With people requiring higher quality and enhancing security awareness and environment protection, various testing, measuring and analyzing instruments are demanded increasingly. Furthermore, as an emerging technology, the SST is widely applied in the industrial measurement and control field. Therefore, research on the SST is very important to the development of instrumentation and measurement technology.
Usually, a practical industrial process has a complex nonlinearity and is polluted by lots of noises, which limits the applications of traditional SSTs based on the mechanism analysis, multivariate linear regression (MLR) and artificial neural network (ANN). To overcome the limitations of the traditional SSTs, our research puts emphasis on studying the nonlinear soft sensor modeling methods that have good generalization capability and strong robustness. The research work is based on the machine learning (ML) theory. Under the precondition of guaranteeing the model’s generalization capability (GC) and robustness, some modified algorithms are studied and developed to improve the modeling efficiency. Main research work and productions are listed as follows:
(1) Modify the distance definition of traditional k-nearest neighbors (kNN) algorithm by replacing the standard Euclidian distance with attribute-weighted distance. And develop a dataset editing algorithm based on the modified kNN algorithm for filtering inconsistent samples. Propose a fast kNN algorithm for medium- or large-scale datasets. Its running efficiency is only affected by the neighbor number k and the dimension of dataset n. Usually, it runs several up to twenty times faster than the traditional algorithm. As for developing the locally-approximated learning, there is universal sense to study the algorithms that can fast search for the kNN sub-dataset.
(2) Research the soft sensor modeling methods based on multiple neural networks (MNN), which aims at improving the model’s GC and robustness in the industrial environment. Propose an MNN model that uses clustering sub-datasets as validation datasets (not training datasets), based on which a two-layer MNN model is built. Two comparison experiments are performed over the pulp Kappa dataset for four different models, including single ANN, ensemble MNN, modular MNN and two-layer MNN. Experiment results show that the two-layer MNN model outperforms other three models on the robustness and GC.
(3) Apply the soft margin SVM regression algorithm to the soft sensor modeling. Give two versions of theε-SVMR algorithm and its two implementing methods, i.e., the universal quadratic programming solver and sequential minimal optimization (SMO) algorithm. Over the pulp Kappa dataset, two experiments are performed to study how free parameters to impact the performance of theε-SVMR algorithm and to compare the modeling efficiency of two implementing methods. The main conclusion is that the SVMR method, especially the SMO algorithm, is fit for soft sensor modeling of practical industrial processes.
(4) Study two prediction modeling methods using time series (TS) sampled from a process, i.e., the temporal difference trained neural network (TDNN) and SVMR algorithm. Two methods train prediction models over the sample-expanding dataset and feature-expanding dataset, respectively. Two experiments are carried out on the TSs of the kraft pulping process. The experiment results show the multi-step expanding prediction exceeds the single-step prediction, especially for the small-sized TS set. And the feature-expanding SVMR method exceeds the sample-expanding TDNN method, especially for the single-sequence TS set.
(5) Do theoretical research on the process neural network (PNN) and reveal the relationship between the process neuron and the traditional neuron. Point out that the process neuron can be approximated infinitely using the traditional neuron, present two approximating theorems and their detailed proof, and give two related corollaries. Experiments are performed to validate the PNN method over a set of function-generated sine wave coded signals. The experiments prove that the PNN can suppress white noises and enhance the robustness of the model. However, applying the PNN need choose a certain function orthogonal basis.
(6) Define the inner product and norm of signals (functions), and propose a novel process learning algorithm, i.e., the process SVM (PSVM). Experiments are carried out to compare the PSVM with the PNN over the same set of signals as above. Avoid choosing a function orthogonal basis, which makes the PSVM more convenient to be applied than the PNN. When the noise amplitude is small, the PSVM model outperforms the PNN model; when the noise amplitude is rather large, the PSVM model performs a little worse than the PNN model. But its performance can be improved by representing signal samples with finite basis functions.
Creative achievements obtained in our research include: (1) Propose a dataset editing method based on the modified kNN algorithm for filtering inconsistent samples in a dataset. (2) Present a fast kNN algorithm, which has a universal sense for studying local learning (lazy learning) methods. (3) To improve the generalization ability of a model, present an MNN model that uses clustering sub-datasets as validation datasets. (4) Propose two approximating theorems to the process neuron, which reveal the relationship between the process neuron and the traditional neuron. (5) Present a novel process learning algorithm, namely, the PSVM. In conclusion, this research work focuses on studying theories and applications of the SST based on the machine learning. After doing in-depth research work, we obtain some useful achievements. The soft sensing approaches proposed in the dissertation not only enrich the soft sensing theory, but also promote the industrial utilization of the SST. The last two chapters pay attention to theoretical research. The theoretical fruits will push the development of the soft sensing theory as well as the ML theory. Limit to the author’s knowledge and experience, mistakes and faults are hard to avoid in the dissertation. Please point them out and give some comments or suggestions.
“In the past, we mined gold with electromechanical machines; In the Knowledge Economy age, we are to mine gold with learning machines. Our gold mines are the databases stored in factories and enterprises.”
通常,实际工业过程具有复杂非线性特性和存在大量噪声干扰,这限制了基于机理分析、多元线性回归和神经网络等传统软测量技术的应用。为了克服传统方法的局限性,本课题着重研究基于机器学习理论的、具有好的泛化能力和鲁棒性的非线性软测量建模方法。在保证模型泛化能力和鲁棒性的前提下,研究可以提高建模效率的改进实现算法。本课题的主要研究工作和成果有:
(1)对传统k-最近邻(kNN)算法进行近邻距离定义的改进,用属性加权距离取代标准欧氏距离。进而,基于改进kNN算法提出了一种数据集剪辑算法,用于滤除矛盾数据样本。针对中大规模数据集提出了一种快速kNN算法,运行速度仅与最近邻数k值和数据集维数n值有关。通常,运行速度较传统算法可提高几倍至十几倍。对于局部学习算法的研究,最近邻子集的快速搜索算法研究具有普遍意义。
(2)研究基于多神经网络的软测量建模方法,旨在提高工业环境下软测量模型的鲁棒性和泛化能力。提出了一种以聚类子簇数据作为验证数据集(而非训练数据集)的多神经网络,并将其用于构造两层结构多神经网络模型。针对纸浆Kappa值数据集,使用单一神经网络、两类单层多神经网络和两层多神经网络等四种模型进行软测量建模对比实验。实验结果表明,两层多神经网络模型的鲁棒性和泛化能力优于其他三种模型。
(3)将软间隔支持向量机回归算法用于软测量建模。给出了两个版本的ε-SVMR算法,同时给出了该算法的通用二次规划(QP)解算器和序贯最小优化(SMO)两种实现方法。针对纸浆Kappa值数据集进行两个仿真实验,分别研究ε-SVMR算法的自由参数对模型预测性能的影响和ε-SVMR算法两种实现方法的建模效率。主要结论是,基于SMO算法的SVM方法尤其适用于中大规模实际工业过程的软测量建模。
(4)研究了时间序列的两种预测建模方法,即样本扩展TDNN方法和特征扩展SVM方法。两种建模方法分别基于过程时间序列的样本扩展数据集和特征扩展数据集。对于制浆蒸煮过程时间序列的仿真实验表明:多步预测的性能优于单步预测的性能,尤其对于样本序列较少的情形;特征扩展SVM方法的性能优于样本扩展TDNN方法的性能,尤其对于单序列输入的情形。
(5)对过程神经网络(PNN)进行理论研究,揭示了过程神经元和传统神经元间的联系。指出了过程神经元可用传统神经元进行无限逼近,给出了两个逼近定理和证明,以及相关的两个推论。针对模拟产生的正弦波编码信号集进行仿真实验,研究过程神经网络的预测建模性能。实验得出的主要结论是,过程神经网络对于白噪声具有很好的抑制作用,从而增加了模型的鲁棒性。但其使用需要选取用于基展开的正交基函数系。
(6)引入信号内积和范数的定义,提出了一种新的过程式输入学习算法,即过程支持向量机(PSVM)。针对模拟产生的正弦波编码信号集进行仿真实验,并将实验结果和过程神经网络的实验结果进行比较。PSVM方法的使用比较方便,可以避开正交基函数系的选择问题。当噪声幅度较小时,PSVM方法的表现优于PNN方法;当噪声幅度变大时,PSVM方法的表现稍差于PNN方法,但可通过对信号进行类似于PNN方法的基展开截频处理提高其预测性能。关于PNN和PSVM学习方法的研究为过程式输入的软测量建模提供必要的理论基础。
本课题研究取得的创造性成果有:(1)提出了一种基于改进kNN算法的数据集剪辑算法,用于滤除数据集中的大误差样本。(2)提出了一种快速kNN算法,对于局部学习(消极学习)算法的研究具有普遍意义。(3)提出了一种以聚类子簇数据作为验证数据集(而非训练数据集)的多神经网络模型,用于构建泛化能力好的预测模型。(4)提出了过程神经元的两个逼近定理并给出了证明,揭示了过程神经元和传统神经元的内在联系。(5)提出了一种新的过程式输入学习算法,即过程支持向量机。
总之,本课题以基于机器学习的软测量技术理论和应用作为主要研究内容,展开深入研究,取得了一些有益的成果。文中提出的软测量建模方法既丰富了软测量建模理论,也促进了软测量技术的工业实用化。后两章比较侧重理论研究,取得的理论成果不仅对软测量理论的发展具有重要作用,而且对机器学习理论的发展也有一定的促进作用。由于作者水平有限,文中难免有错误或不妥之处,恳请各位专家和读者批评指正。
Relations exist universally in nature and are expressed in certain forms, which is the basic philosophy foundation of this research subject. In mathematicians’view, this kind of relations is a kind of mappings, or mapping functions. In the information age, these mapping relations are contained within many thousands of data. The soft sensing technology (SST), being researched in this dissertation, aims at finding various mapping functions hidden in data. Today, in the age that industrialization is driven by the information technology (IT), the instrumentation and measurement technology is an important part of the information science and technology. With people requiring higher quality and enhancing security awareness and environment protection, various testing, measuring and analyzing instruments are demanded increasingly. Furthermore, as an emerging technology, the SST is widely applied in the industrial measurement and control field. Therefore, research on the SST is very important to the development of instrumentation and measurement technology.
Usually, a practical industrial process has a complex nonlinearity and is polluted by lots of noises, which limits the applications of traditional SSTs based on the mechanism analysis, multivariate linear regression (MLR) and artificial neural network (ANN). To overcome the limitations of the traditional SSTs, our research puts emphasis on studying the nonlinear soft sensor modeling methods that have good generalization capability and strong robustness. The research work is based on the machine learning (ML) theory. Under the precondition of guaranteeing the model’s generalization capability (GC) and robustness, some modified algorithms are studied and developed to improve the modeling efficiency. Main research work and productions are listed as follows:
(1) Modify the distance definition of traditional k-nearest neighbors (kNN) algorithm by replacing the standard Euclidian distance with attribute-weighted distance. And develop a dataset editing algorithm based on the modified kNN algorithm for filtering inconsistent samples. Propose a fast kNN algorithm for medium- or large-scale datasets. Its running efficiency is only affected by the neighbor number k and the dimension of dataset n. Usually, it runs several up to twenty times faster than the traditional algorithm. As for developing the locally-approximated learning, there is universal sense to study the algorithms that can fast search for the kNN sub-dataset.
(2) Research the soft sensor modeling methods based on multiple neural networks (MNN), which aims at improving the model’s GC and robustness in the industrial environment. Propose an MNN model that uses clustering sub-datasets as validation datasets (not training datasets), based on which a two-layer MNN model is built. Two comparison experiments are performed over the pulp Kappa dataset for four different models, including single ANN, ensemble MNN, modular MNN and two-layer MNN. Experiment results show that the two-layer MNN model outperforms other three models on the robustness and GC.
(3) Apply the soft margin SVM regression algorithm to the soft sensor modeling. Give two versions of theε-SVMR algorithm and its two implementing methods, i.e., the universal quadratic programming solver and sequential minimal optimization (SMO) algorithm. Over the pulp Kappa dataset, two experiments are performed to study how free parameters to impact the performance of theε-SVMR algorithm and to compare the modeling efficiency of two implementing methods. The main conclusion is that the SVMR method, especially the SMO algorithm, is fit for soft sensor modeling of practical industrial processes.
(4) Study two prediction modeling methods using time series (TS) sampled from a process, i.e., the temporal difference trained neural network (TDNN) and SVMR algorithm. Two methods train prediction models over the sample-expanding dataset and feature-expanding dataset, respectively. Two experiments are carried out on the TSs of the kraft pulping process. The experiment results show the multi-step expanding prediction exceeds the single-step prediction, especially for the small-sized TS set. And the feature-expanding SVMR method exceeds the sample-expanding TDNN method, especially for the single-sequence TS set.
(5) Do theoretical research on the process neural network (PNN) and reveal the relationship between the process neuron and the traditional neuron. Point out that the process neuron can be approximated infinitely using the traditional neuron, present two approximating theorems and their detailed proof, and give two related corollaries. Experiments are performed to validate the PNN method over a set of function-generated sine wave coded signals. The experiments prove that the PNN can suppress white noises and enhance the robustness of the model. However, applying the PNN need choose a certain function orthogonal basis.
(6) Define the inner product and norm of signals (functions), and propose a novel process learning algorithm, i.e., the process SVM (PSVM). Experiments are carried out to compare the PSVM with the PNN over the same set of signals as above. Avoid choosing a function orthogonal basis, which makes the PSVM more convenient to be applied than the PNN. When the noise amplitude is small, the PSVM model outperforms the PNN model; when the noise amplitude is rather large, the PSVM model performs a little worse than the PNN model. But its performance can be improved by representing signal samples with finite basis functions.
Creative achievements obtained in our research include: (1) Propose a dataset editing method based on the modified kNN algorithm for filtering inconsistent samples in a dataset. (2) Present a fast kNN algorithm, which has a universal sense for studying local learning (lazy learning) methods. (3) To improve the generalization ability of a model, present an MNN model that uses clustering sub-datasets as validation datasets. (4) Propose two approximating theorems to the process neuron, which reveal the relationship between the process neuron and the traditional neuron. (5) Present a novel process learning algorithm, namely, the PSVM. In conclusion, this research work focuses on studying theories and applications of the SST based on the machine learning. After doing in-depth research work, we obtain some useful achievements. The soft sensing approaches proposed in the dissertation not only enrich the soft sensing theory, but also promote the industrial utilization of the SST. The last two chapters pay attention to theoretical research. The theoretical fruits will push the development of the soft sensing theory as well as the ML theory. Limit to the author’s knowledge and experience, mistakes and faults are hard to avoid in the dissertation. Please point them out and give some comments or suggestions.
“In the past, we mined gold with electromechanical machines; In the Knowledge Economy age, we are to mine gold with learning machines. Our gold mines are the databases stored in factories and enterprises.”
引文
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