数据局部时空结构特征提取与故障检测方法
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摘要
实时过程监控是保证工业过程安全平稳运行以及产品质量的关键技术和有效手段。现代工业过程每天都生产和存储大量的过程测量数据,这些数据反映了生产过程及设备的运行情况。传统的多变量统计过程监测(MSPM)方法,利用过程数据进行统计建模和特征提取,并基于相应的过程监控算法实时监测,已经成为工业过程综合自动化技术研究的热点和前沿。MSPM大多采用维度约简方法提取数据特征,去除冗余信息,降维算法的数据特征提取能力直接影响到过程监控的性能。传统的维度约简算法,如PCA主要对数据的全局结构特征进行提取,没有考虑数据的局部结构信息。本论文从数据线性降维的角度出发,基于局部流形学习算法NPE的思想,对数据的空间和时序结构特征进行提取,并基于标准TE过程仿真验证本论文提出方法的有效性。
1.将正交保持嵌入(ONPE)通过核方法扩展为核正交保持嵌入算法(KONPE),并将其应用于非线性故障检测。NPE算法从样本的局部空间结构出发,在降维的同时保留了数据的潜在流形结构信息,其正交约束算法ONPE进一步增强了对非线性数据的特征提取和区分能力。KONPE显式地考虑了数据间的非线性结构,提高了对非线性数据的提取能力,比传统的KPCA算法具有更强的空间结构保持能力,因此带来了更好的检测效果。
2.在局部特征提取算法NPE的基础上,提出了基于数据非局部限制的空间局部结构分析方法：基于非局部约束的邻域保持嵌入算法(NSC-NPE)。NPE算法主要关注数据的局部结构特征,没有对非局部数据进行约束,丢失了数据信息。考虑该不足,提出对非邻域内的数据进行约束,据此构建了新的目标函数,给出了平衡数据局部和非局部结构的策略和计算方法。目标是使得数据降维后得到的维度约简空间不仅和原数据具有相似的局部近邻结构,而且其非近邻数据的关系特征也能够得到保留,因此包含了数据整体结构特征信息。同时相比于基于全局结构的方法(如PCA), NSC-NPE针对邻域内和非邻域内的数据分别采用不同的方法进行处理,能够更有效地解释数据的特征信息,因此也具有较好的故障检测效果。
3.利用局部特征提取的方法,提出了针对动态数据的时序结构局部特征提取算法：时间近邻保持嵌入算法(TNPE)。并进一步考虑数据的时序-空间结构特征,提出了时空近邻保持嵌入算法(TSNPE)。实际的工业过程数据一般具有较强的动态相关性,这部分特征反映了数据的时序变化情况,因此在特征提取时需要保留该部分数据关系。传统的仅关注数据空间结构特征的方法不适用于对动态自相关数据的处理,基于此,我们为每个数据点建立基于时间的邻域空间,并对每个数据利用其邻域点进行线性重构,据此来获取数据间的动态相关关系,并在低维空间保留该局部特性。数值仿真和TE过程仿真结果表明了：基于动态相关信息保留的方法,更易于获得数据的本质特性,能够有效提取其时间和空间结构特征。
4.以局部特征提取的线性维度约简算法NPE为例,深入分析了流形学习算法在过程监控领域的应用特点和本质机理。流形学习算法在过程监控领域的应用,经过近几年的发展已经取得了较好的应用效果,但是该类方法在该领域的理论研究还较少。通过分析算法特点、应用条件以及适用范围,对其在过程监控领域应用的适用性进行理论分析。同时对NPE算法的统计量构建问题展开讨论,分析了较于传统方法,局部方法的T2和SPE统计量构建的不同之处。最后对流形学习算法在过程监控领域应用存在的优势和问题进行了总结。
Timely process monitoring plays a critical role in maintaining the process safety and stability, as well as guaranteeing the production quality. In modern chemical process, numerous observations can be well collected and stored, which provide reliable basis for characterizing the process operating conditions. Multivariate statistical process monitoring (MSPM), which only depends on the process data for the feature extraction, process modeling and monitoring, has become one of the research hotspots in industrial process monitoring. MSPM-based methods typically employ dimensionality reduction to discover the underlying data properties and remove redundancy information, thus the performance of dimensionality reduction will directly influence the reliability of the monitoring performance. The conventional global based dimensionality reduction approaches, such as PCA, are mainly performed by the global data features. However, the detailed local neighborhood structure on the data manifold is failed to be discovered. From the perspective of dimensionality reduction, several effective monitoring methods to identify both spatial and temporal relationships among the process data are proposed based on the idea of local information based manifold learning method NPE. The case studies on the Tennessee Eastman process demonstrate the effectiveness of the proposed methods in fault detection.
1. A new nonlinear dimensionality reduction method named kernel orthogonal neighborhood preserving embedding (KONPE) is proposed and applied for nonlinear fault detection, with the application of kernel-trick on the method orthogonal neighborhood preserving embedding (ONPE). As a local space structure based approach, neighborhood preserving embedding (NPE) aims at preserving the latent manifold of data hidden in the high dimensional observations. Imposing orthogonal constraints on NPE, ONPE can effectively improve its discriminating power and the ability of feature extraction. The developed KONPE explicitly considers the low-dimensional structure in data, thus the nonlinear modeling performance is well improved. Simulation results illustrate the superiority of KONPE in process monitoring in comparison with the widely used KPCA.
2. A nonlocal space structure constrained feature extraction method named nonlocal structure constrained neighborhood preserving embedding (NSC-NPE)is developed, on the basis of the local information based manifold learning approach neighborhood preserving embedding (NPE). NPE mainly focus on preserving the local geometry structure of the process data, and does not give a constraint for the data points outside the neighborhood. As a result, the intrinsic data information may lose. Considering such deficiency, in the new method, the data relationship outside the neighbors is also given constraints. By utilizing the meaningful nonlocal variance information, NSC-NPE constructs a global information based dual-objective optimizations function for modeling the process data. The relationship among the data points in the neighborhood which represents the local structure and the relationships among the data points outside the neighbors which represents the nonlocal structure are both be considered in the objective function. As a result, the global geometrical structure of the data is totally exploited. Different from the global based model PCA, NSC-NPE deals with the global data relation by dealing with the data points in and outside the neighbors with different strategies, respectively. Thus, NSC-NPE can give more faithful representation of the data character and better monitoring performance.
3. With the consideration of autocorrelation among data samples, a novel algorithm named time neighborhood preserving embedding (TNPE) is proposed by utilizing local information. Furthermore, by taking both the temporal and spatial information of the process data into consideration, the method named time and spatial neighborhood preserving embedding (TSNPE) is also given. In industry process, the process variables always have autocorrelation and the system has dynamic properties, such dynamic behavior varied according to specific process condition should be totally extracted. The local space geometry based algorithms may be invalid to deal with the samples with autocorrelation. From this point of view, the neighborhood space is constructed with respect to the time sequence adjacent points of each data point, and the dynamic relationship is represented as a linear combination of its nearest neighbors. The local dynamic character is preserved in the low dimensional space by keeping the reconstruction coefficients. A numerical example and the Tennessee Eastman process indicate the benefit of having process dynamic information included in modeling process. By taking the autocorrelation of the samples in the modeling process, the two methods may be easy to identify the intrinsic data geometry structure and preserve the spatial and temporal relationships effectively.
4. Based on the local information based manifold learning algorithm, NPE, the basic theories and characteristics in applying the manifold learning on process monitoring are discussed. Research on process monitoring based on manifold learning has been well developed recent years, with much good results. However, the theoretical studies of these methods on this field is much few. Thus, the validity of manifold learning is discussed by analyzing the algorithm features, applied conditions, as well as the scope of application. Then, the discussions on the construction of the statistics upon the NPE model are given, which presents the differences between the local based method and the traditional method about the Hotelling's T2and squared prediction error (SPE) statistics. Finally, the advantages as well as the disadvantages of the application in process monitoring by manifold learning are illustrated.
1.将正交保持嵌入(ONPE)通过核方法扩展为核正交保持嵌入算法(KONPE),并将其应用于非线性故障检测。NPE算法从样本的局部空间结构出发,在降维的同时保留了数据的潜在流形结构信息,其正交约束算法ONPE进一步增强了对非线性数据的特征提取和区分能力。KONPE显式地考虑了数据间的非线性结构,提高了对非线性数据的提取能力,比传统的KPCA算法具有更强的空间结构保持能力,因此带来了更好的检测效果。
2.在局部特征提取算法NPE的基础上,提出了基于数据非局部限制的空间局部结构分析方法：基于非局部约束的邻域保持嵌入算法(NSC-NPE)。NPE算法主要关注数据的局部结构特征,没有对非局部数据进行约束,丢失了数据信息。考虑该不足,提出对非邻域内的数据进行约束,据此构建了新的目标函数,给出了平衡数据局部和非局部结构的策略和计算方法。目标是使得数据降维后得到的维度约简空间不仅和原数据具有相似的局部近邻结构,而且其非近邻数据的关系特征也能够得到保留,因此包含了数据整体结构特征信息。同时相比于基于全局结构的方法(如PCA), NSC-NPE针对邻域内和非邻域内的数据分别采用不同的方法进行处理,能够更有效地解释数据的特征信息,因此也具有较好的故障检测效果。
3.利用局部特征提取的方法,提出了针对动态数据的时序结构局部特征提取算法：时间近邻保持嵌入算法(TNPE)。并进一步考虑数据的时序-空间结构特征,提出了时空近邻保持嵌入算法(TSNPE)。实际的工业过程数据一般具有较强的动态相关性,这部分特征反映了数据的时序变化情况,因此在特征提取时需要保留该部分数据关系。传统的仅关注数据空间结构特征的方法不适用于对动态自相关数据的处理,基于此,我们为每个数据点建立基于时间的邻域空间,并对每个数据利用其邻域点进行线性重构,据此来获取数据间的动态相关关系,并在低维空间保留该局部特性。数值仿真和TE过程仿真结果表明了：基于动态相关信息保留的方法,更易于获得数据的本质特性,能够有效提取其时间和空间结构特征。
4.以局部特征提取的线性维度约简算法NPE为例,深入分析了流形学习算法在过程监控领域的应用特点和本质机理。流形学习算法在过程监控领域的应用,经过近几年的发展已经取得了较好的应用效果,但是该类方法在该领域的理论研究还较少。通过分析算法特点、应用条件以及适用范围,对其在过程监控领域应用的适用性进行理论分析。同时对NPE算法的统计量构建问题展开讨论,分析了较于传统方法,局部方法的T2和SPE统计量构建的不同之处。最后对流形学习算法在过程监控领域应用存在的优势和问题进行了总结。
Timely process monitoring plays a critical role in maintaining the process safety and stability, as well as guaranteeing the production quality. In modern chemical process, numerous observations can be well collected and stored, which provide reliable basis for characterizing the process operating conditions. Multivariate statistical process monitoring (MSPM), which only depends on the process data for the feature extraction, process modeling and monitoring, has become one of the research hotspots in industrial process monitoring. MSPM-based methods typically employ dimensionality reduction to discover the underlying data properties and remove redundancy information, thus the performance of dimensionality reduction will directly influence the reliability of the monitoring performance. The conventional global based dimensionality reduction approaches, such as PCA, are mainly performed by the global data features. However, the detailed local neighborhood structure on the data manifold is failed to be discovered. From the perspective of dimensionality reduction, several effective monitoring methods to identify both spatial and temporal relationships among the process data are proposed based on the idea of local information based manifold learning method NPE. The case studies on the Tennessee Eastman process demonstrate the effectiveness of the proposed methods in fault detection.
1. A new nonlinear dimensionality reduction method named kernel orthogonal neighborhood preserving embedding (KONPE) is proposed and applied for nonlinear fault detection, with the application of kernel-trick on the method orthogonal neighborhood preserving embedding (ONPE). As a local space structure based approach, neighborhood preserving embedding (NPE) aims at preserving the latent manifold of data hidden in the high dimensional observations. Imposing orthogonal constraints on NPE, ONPE can effectively improve its discriminating power and the ability of feature extraction. The developed KONPE explicitly considers the low-dimensional structure in data, thus the nonlinear modeling performance is well improved. Simulation results illustrate the superiority of KONPE in process monitoring in comparison with the widely used KPCA.
2. A nonlocal space structure constrained feature extraction method named nonlocal structure constrained neighborhood preserving embedding (NSC-NPE)is developed, on the basis of the local information based manifold learning approach neighborhood preserving embedding (NPE). NPE mainly focus on preserving the local geometry structure of the process data, and does not give a constraint for the data points outside the neighborhood. As a result, the intrinsic data information may lose. Considering such deficiency, in the new method, the data relationship outside the neighbors is also given constraints. By utilizing the meaningful nonlocal variance information, NSC-NPE constructs a global information based dual-objective optimizations function for modeling the process data. The relationship among the data points in the neighborhood which represents the local structure and the relationships among the data points outside the neighbors which represents the nonlocal structure are both be considered in the objective function. As a result, the global geometrical structure of the data is totally exploited. Different from the global based model PCA, NSC-NPE deals with the global data relation by dealing with the data points in and outside the neighbors with different strategies, respectively. Thus, NSC-NPE can give more faithful representation of the data character and better monitoring performance.
3. With the consideration of autocorrelation among data samples, a novel algorithm named time neighborhood preserving embedding (TNPE) is proposed by utilizing local information. Furthermore, by taking both the temporal and spatial information of the process data into consideration, the method named time and spatial neighborhood preserving embedding (TSNPE) is also given. In industry process, the process variables always have autocorrelation and the system has dynamic properties, such dynamic behavior varied according to specific process condition should be totally extracted. The local space geometry based algorithms may be invalid to deal with the samples with autocorrelation. From this point of view, the neighborhood space is constructed with respect to the time sequence adjacent points of each data point, and the dynamic relationship is represented as a linear combination of its nearest neighbors. The local dynamic character is preserved in the low dimensional space by keeping the reconstruction coefficients. A numerical example and the Tennessee Eastman process indicate the benefit of having process dynamic information included in modeling process. By taking the autocorrelation of the samples in the modeling process, the two methods may be easy to identify the intrinsic data geometry structure and preserve the spatial and temporal relationships effectively.
4. Based on the local information based manifold learning algorithm, NPE, the basic theories and characteristics in applying the manifold learning on process monitoring are discussed. Research on process monitoring based on manifold learning has been well developed recent years, with much good results. However, the theoretical studies of these methods on this field is much few. Thus, the validity of manifold learning is discussed by analyzing the algorithm features, applied conditions, as well as the scope of application. Then, the discussions on the construction of the statistics upon the NPE model are given, which presents the differences between the local based method and the traditional method about the Hotelling's T2and squared prediction error (SPE) statistics. Finally, the advantages as well as the disadvantages of the application in process monitoring by manifold learning are illustrated.
引文
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