非线性过程监测中的数据降维及相关问题研究
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摘要
基于实时测量数据对工业过程实施监测是保障过程安全平稳运行的有效手段。现代工业过程中测量变量众多,但由于潜在的质量、能量平衡及其他操作约束,变量间通常存在严重的线性或非线性相关关系,导致高维过程数据实际上由少量的内在自由变量所驱动。如何基于具有代表性的过程数据有效地使用数据降维方法去除冗余信息,揭示复杂过程数据中的潜在低维结构是过程监测中的基本问题。传统的监测方法大多基于线性多变量统计方法,对广泛存在的非线性过程难以奏效。本文工作从数据降维的角度出发,集中在解决现有非线性过程监测方法中存在的不足和提出更为有效的监测方法,并在标准的TE仿真过程和废水处理实际过程数据上验证了所提出方法的有效性和优越性。本文的研究内容和贡献如下。
Ⅰ.提出使用线性投影近似流形学习方法最大方差展开(MVU)中隐含的非线性降维映射,得到无监督降维方法最大方差展开投影(MVUP),并设计了MVUP非线性故障检测与隔离方法。MVUP继承了MVU在降维后能展开数据中的非线性结构和保持数据分布边界的特性。MVUP监测方法具有很低的在线计算开销且监测效果与当前主流的非线性监测方法相当。
Ⅱ.针对当前流行的基于核无监督降维(KUDR)(如核主元分析(KPCA)、核独立成分分析(KICA)等)的非线性故障检测方法中难以选择最合适核函数的问题,提出一种KUDR通用的核函数自动学习方法。数据中的非线性结构在映射到学习得到的最优核对应的核特征空间中后被尽可能展开为线性,因此KUDR在该核特征空间中实施线性降维方法可以有效地解释数据中的非线性波动,从而带来比使用普通核函数更好的故障检测效果。
Ⅲ.将近年来提出的正交保局投影(OLPP)通过核技巧推广为一种KUDR方法核正交保局投影(KOLPP),并设计了KOLPP非线性故障检测方法。KOLPP显式地考虑了数据中的非线性结构,能同时保持数据中的局部结构和全局结构,比其他流行的KUDR方法具有更强的结构保持能力因此能带来更好的检测效果。
Ⅳ针对当前非线性故障识别降维中由于使用Fisher判别准则存在的不足,提出一种新的有监督降维方法保局判别分析(LPDA)及其核推广核保局判别分析(KLPDA)用于非线性故障识别。不同于Fisher判别准则面向从整体上分开不同故障类的数据,(K)LPDA的降维目标函数直接面向减少局部类间重叠,对于减少误分率更有意义能带来更好的识别效果。
Ⅴ.针对传统方法使用扩充向量利用过程动态信息易造成训练数据相对不足且损失变量结构信息的缺点,提出使用扩充矩阵利用过程动态信息的机制。并将LPDA扩展为能直接对矩阵数据降维的张量保局判别分析(TLPDA),设计了基于扩充矩阵和TLPDA降维的动态故障识别方法。
Ⅵ.以适用于非线性数据集的k-最近邻距离dk作为离群度指标,提出一种快速离群点检测算法近邻修剪(NHP)用于对高维非线性训练数据集的预处理。现有算法仅通过减少对每个数据点dk查询的计算开销来提高算法效率,而NHP算法在每次dk查询过程中能计算出其他点的扩上界用于直接修剪非离群点,能减少dk查询的次数,并通过优化搜索次序提高修剪效果和减少每次dk查询的计算开销。
Process monitoring based on measurement data is very useful for the maintenance of process safety and stability. While numerous variables are measured in modern indus-trial processes, there usually exist severe dependencies among them and high-dimensional process data is actually driven by fewer intrinsic free variables due to the underlying mass/energy balance and other operational constraints. How to effectively perform dimen-sionality reduction to discard redundancy and reveal intrinsic lower-dimensional structure in complex process data is a basic issue in process monitoring. Most traditional monitoring methods are based on linear multivariate statistical methods and not effective for prevalent nonlinear processes. From the perspective of data dimensionality reduction, this disserta-tion focuses on dealing with deficiencies in existing nonlinear process monitoring methods and proposing more effective monitoring methods, and the validity and superiority of the proposed methods are demonstrated on benchmark simulation and real world processes. The contribution of this dissertation is summarized as follows.
Ⅰ. A new unsupervised dimensionality reduction method named maximum variance unfolding projections (MVUP) and MVUP-based nonlinear fault detection and iso-lation methods are proposed. MVUP approximates the underlying nonlinear dimen-sionality reduction mapping of the manifold learning method maximum variance un-folding (MVU) by linear projection, inheriting its nonlinear structure unfolding and distribution boundary preserving features. The MVUP-based monitoring method has very low online computational cost and comparable effectiveness to state-of-the-art nonlinear monitoring methods.
Ⅱ. A kernel function learning method is proposed for kernel unsupervised dimensional-ity reduction (KUDR) (e.g. KPCA, KICA) methods which have been widely used in nonlinear fault detection. Nonlinear structure in data is unfolded to be linear in the kernel feature space corresponding to the learned optimal kernel. Therefore, KUDR using the optimal kernel can effectively explain data variation by performing a linear method in the kernel feature space, leading to improved detection performance.
Ⅲ. A new KUDR method named kernel orthogonal locality preserving projections (KOLPP) and KOLPP-based fault detection method are proposed. KOLPP is the kernel gen-eralization of OLPP method and explicitly consider the underlying nonlinear struc-ture in data. KOLPP has more structure preserving power than other popular KUDR methods, leading to better detection performance.
Ⅳ. To overcome the drawbacks of existing fault recognition methods due to using the Fisher's criterion, a new supervised dimensionality reduction method named local-ity preserving discriminant analysis (LPDA) and its kernel generalization KLPDA are proposed for nonlinear fault recognition. (K)LPDA directly target at minimizing local overlapping among different classes and can provide better recognition perfor-mance than existing methods.
Ⅴ. To overcome the drawbacks of using extended vector for incorporating process dy-namic information, an extended matrix-based scheme is proposed. LPDA is extended to Tensor LPDA (TLPDA) which can deal with matrices directly. A dynamic fault recognition method based on extended matrix and TLPDA is proposed.
Ⅵ. With theκ-nearest neighbor distance (dκ) as outlying measure which is effective for nonlinear data set, a fast outlier detection algorithm named NeighborHood Pruning (NHP) is proposed for preprocessing training data. NHP derives upper bounds of dk for other data points when performing each dκquery, which are used for pruning non-outliers and reducing the number of dκqueries. The searching order is optimized to increase the number of pruning and reduce the computational cost of each dκquery.
Ⅰ.提出使用线性投影近似流形学习方法最大方差展开(MVU)中隐含的非线性降维映射,得到无监督降维方法最大方差展开投影(MVUP),并设计了MVUP非线性故障检测与隔离方法。MVUP继承了MVU在降维后能展开数据中的非线性结构和保持数据分布边界的特性。MVUP监测方法具有很低的在线计算开销且监测效果与当前主流的非线性监测方法相当。
Ⅱ.针对当前流行的基于核无监督降维(KUDR)(如核主元分析(KPCA)、核独立成分分析(KICA)等)的非线性故障检测方法中难以选择最合适核函数的问题,提出一种KUDR通用的核函数自动学习方法。数据中的非线性结构在映射到学习得到的最优核对应的核特征空间中后被尽可能展开为线性,因此KUDR在该核特征空间中实施线性降维方法可以有效地解释数据中的非线性波动,从而带来比使用普通核函数更好的故障检测效果。
Ⅲ.将近年来提出的正交保局投影(OLPP)通过核技巧推广为一种KUDR方法核正交保局投影(KOLPP),并设计了KOLPP非线性故障检测方法。KOLPP显式地考虑了数据中的非线性结构,能同时保持数据中的局部结构和全局结构,比其他流行的KUDR方法具有更强的结构保持能力因此能带来更好的检测效果。
Ⅳ针对当前非线性故障识别降维中由于使用Fisher判别准则存在的不足,提出一种新的有监督降维方法保局判别分析(LPDA)及其核推广核保局判别分析(KLPDA)用于非线性故障识别。不同于Fisher判别准则面向从整体上分开不同故障类的数据,(K)LPDA的降维目标函数直接面向减少局部类间重叠,对于减少误分率更有意义能带来更好的识别效果。
Ⅴ.针对传统方法使用扩充向量利用过程动态信息易造成训练数据相对不足且损失变量结构信息的缺点,提出使用扩充矩阵利用过程动态信息的机制。并将LPDA扩展为能直接对矩阵数据降维的张量保局判别分析(TLPDA),设计了基于扩充矩阵和TLPDA降维的动态故障识别方法。
Ⅵ.以适用于非线性数据集的k-最近邻距离dk作为离群度指标,提出一种快速离群点检测算法近邻修剪(NHP)用于对高维非线性训练数据集的预处理。现有算法仅通过减少对每个数据点dk查询的计算开销来提高算法效率,而NHP算法在每次dk查询过程中能计算出其他点的扩上界用于直接修剪非离群点,能减少dk查询的次数,并通过优化搜索次序提高修剪效果和减少每次dk查询的计算开销。
Process monitoring based on measurement data is very useful for the maintenance of process safety and stability. While numerous variables are measured in modern indus-trial processes, there usually exist severe dependencies among them and high-dimensional process data is actually driven by fewer intrinsic free variables due to the underlying mass/energy balance and other operational constraints. How to effectively perform dimen-sionality reduction to discard redundancy and reveal intrinsic lower-dimensional structure in complex process data is a basic issue in process monitoring. Most traditional monitoring methods are based on linear multivariate statistical methods and not effective for prevalent nonlinear processes. From the perspective of data dimensionality reduction, this disserta-tion focuses on dealing with deficiencies in existing nonlinear process monitoring methods and proposing more effective monitoring methods, and the validity and superiority of the proposed methods are demonstrated on benchmark simulation and real world processes. The contribution of this dissertation is summarized as follows.
Ⅰ. A new unsupervised dimensionality reduction method named maximum variance unfolding projections (MVUP) and MVUP-based nonlinear fault detection and iso-lation methods are proposed. MVUP approximates the underlying nonlinear dimen-sionality reduction mapping of the manifold learning method maximum variance un-folding (MVU) by linear projection, inheriting its nonlinear structure unfolding and distribution boundary preserving features. The MVUP-based monitoring method has very low online computational cost and comparable effectiveness to state-of-the-art nonlinear monitoring methods.
Ⅱ. A kernel function learning method is proposed for kernel unsupervised dimensional-ity reduction (KUDR) (e.g. KPCA, KICA) methods which have been widely used in nonlinear fault detection. Nonlinear structure in data is unfolded to be linear in the kernel feature space corresponding to the learned optimal kernel. Therefore, KUDR using the optimal kernel can effectively explain data variation by performing a linear method in the kernel feature space, leading to improved detection performance.
Ⅲ. A new KUDR method named kernel orthogonal locality preserving projections (KOLPP) and KOLPP-based fault detection method are proposed. KOLPP is the kernel gen-eralization of OLPP method and explicitly consider the underlying nonlinear struc-ture in data. KOLPP has more structure preserving power than other popular KUDR methods, leading to better detection performance.
Ⅳ. To overcome the drawbacks of existing fault recognition methods due to using the Fisher's criterion, a new supervised dimensionality reduction method named local-ity preserving discriminant analysis (LPDA) and its kernel generalization KLPDA are proposed for nonlinear fault recognition. (K)LPDA directly target at minimizing local overlapping among different classes and can provide better recognition perfor-mance than existing methods.
Ⅴ. To overcome the drawbacks of using extended vector for incorporating process dy-namic information, an extended matrix-based scheme is proposed. LPDA is extended to Tensor LPDA (TLPDA) which can deal with matrices directly. A dynamic fault recognition method based on extended matrix and TLPDA is proposed.
Ⅵ. With theκ-nearest neighbor distance (dκ) as outlying measure which is effective for nonlinear data set, a fast outlier detection algorithm named NeighborHood Pruning (NHP) is proposed for preprocessing training data. NHP derives upper bounds of dk for other data points when performing each dκquery, which are used for pruning non-outliers and reducing the number of dκqueries. The searching order is optimized to increase the number of pruning and reduce the computational cost of each dκquery.
引文
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