工业过程监测：基于小波和统计学的方法
摘要
保障生产安全和减小产品质量波动一直是过程工业的两个主题。只有密
切地监督生产过程的运行状态，不断地检测过程的变化和故障信息，才能有
效防止灾难性事故的发生，同时减少产品质量的波动，提高产品的竞争力。
而流程工业具有规模大、结构复杂，以及现场环境恶劣等特点，使得过程监
测的理论研究与实践成为过程控制领域中最具挑战性的热点课题之一。虽然
基于精确数学模型的过程监测方法在理论上比不依赖数学模型的方法更成
熟，但是由于流程工业的上述特点，使得前者难以在实际工程中应用。因此，
本文研究的是不依赖数学模型的监测方法，此类方法一般均为“数据驱动”
或“基于知识”的。
本文所采用的两个主要分析工具，即小波和统计学理论，都是从不依赖
于数学模型的角度来实现对过程的监测。其中小波是从信号处理和函数逼近
的角度来处理过程数据；而多元统计分析则用于建立过程监测模型，这是通
过对过程数据的统计分析来实现的。这两种方法相互配合，在整个过程监测
系统中承担着不同的任务。本文的主要内容包括如下几个方面：
①系统地介绍了过程监测的基本概念和内容，对基于数学模型和不依
赖于数学模型的故障诊断方法进行了比较，指出了后者在流程工业监测中的
优越性。
②针对过程变量的多率采样问题，提出了一种基于小波多尺度分析理
论的误差递阶补偿算法，实现对高频采样信号的重构。并给出了算法的精度
分析。此算法具有能克服噪声影响、重构精度高和物理意义明确的特点。
③指出了过程数据滤波的特点及要求，阐述了小波阈值滤波和鲁棒小
波分解的思想。对数据在线多尺度分解中的关键技术进行了研究，给出了平
移不变小波分解和区间小波分解的算法实现。
④采用小波阈值密度估计器研究了过程数据的概率密度函数逼近问
题。给出了适合工业应用的估计器网格结构、平滑参数和系数阈值的确定方
法。提出利用Q-Q图迭代检验以消除粗差数据对密度估计的影响。
Xll 浙江大学博士学位论文
⑤对PCA监测方法的特点及其内涵进行了研究。通过分别导出户和
SPE统计量均值与过程数据统计参数之间的关系，分析了影响PCA检测行
为的因素，以及工况变化与故障在PCA下的不同被检测行为。指出了通常
关于PCA检测行为的一些不正确的结论。
③提出了一种改进的PCA方法（MPCA），采用主元相关变量残差统
计量（Pop）代替通常的平方预测误差SPE统计量，用于对工业过程的监测。
MPCA避免了SPE统计量检验的保守性，能够提供更详细的过程变化信息，
从而有效识别正常工况改变与过程故障引起的户图变化。此外在主元子空间
和残差子空间中分别讨论了故障可检测性的充分和必要条件。采用故障临界
幅值的概念对故障在MPCA下的被检测行为进行了分析，并给出了一种新的
主元确定方法。
①基于MPCA监测方法，对故障的重构、识别以及分离等重要问题进
行了系统和定量的分析。给出了MPCA在主元空间中故障的可重构性、可分
离性，以及识别的充分和必耍条件。利用获得的结果对双效蒸发过程进行了
仿真监测，研究了传感器故障的重构与识别问题。
③从过程监测的角度出发，阐述了化工过程有向图模型的基本概念，
归纳了已有的各种传感器设置方法。并结合故障子空间方法的特点，定性地
研究了考虑故障可观性与分辨率时的传感器网络设置问题。
③研究了过程趋势的暂态事件定义和三角形原语描述，以及过程信号
的多尺度特征提取的实现方法。提出了一个针对过程工业实际情况的、集成
的过程监测系统框架体系，并阐述了其中各主要模块的功能。
最后对过程监测中的方法论进行了讨论，阐述了作者在该问题上的观
点。并对未来的研究课题进行了展望。
The safety of production procedure and consistency of product quality are
always two themes of the process industry. To avoid disastrous accidents and
decrease fluctuations of product quality so that products are competitive, the
process conditions must be under closely monitoring and faults should be timely
detected. However, the large scale and complex structure of industrial process, as
well as the uncertainty of real environment, makes the theoretic research and
implementation of process monitoring system as one of challenges in the field of
process control. The model-based monitoring methods are much maturer in
theory in comparison with the model-free one, but the former has great
difficulties when applied in the real plants due to the previously mentioned
characteristics of industrial process. Therefore, the topic of this thesis focuses on
the model-free monitoring method, which is more practicable for its data-driven
or knowledge-based characteristics.
Two primary mathematical tools used in our proposed monitoring strategy
are wavelets and statistics. Both of them are model-free methods when applied to
the process monitoring. Specifically, the wavelet theory deals with process data as
a signal processing or function approximation tool, and statistics (here we
actually refer to the multivariate statistical analysis) is used to build the process
monitoring model which is realized by statistically analyze process data. The
wavelets and statistics play different but complementary roles in the whole
process monitoring strategy.
The main contributions of this thesis are as follows:
?The elementary concepts and scope of process monitoring are
systematically introduced. The model-based and model-free monitoring methods
are compared, and the latter is shown more suitable and practicable for industrial
applications.
?A wavelet-based rnultiscale hierarchical error-compensation algorithm
xIv
is presented to treat the multi-rate issues of process variables. The proposed
method is used to reconstruct a low sampling rate signal to a higher one. The
reconstruction errors are given and derived results are justified. This algorithm
has the advantages of noise-free, high reconstruction accuracy and explicit
physical background.
?The character and requirement of the filtering of process data are
illustrated, and the ideas of wavelet thresholding filtering and robust wavelet
decomposition are introduced. Further, key techniques of multiscale on-line
process data decomposition are studied and the implementation of shift-invariant
decomposition and interval wavelet decomposition algorithms are presented.
(~) The probability density function of process variable is estimated by
using wavelet thresholding density estimator (WTDE). The parameters of WTDE
as the grid structure, smoothing parameter, and thresholds are selected by the
proposed criteria. The iterative Q-Q plot is used to eliminate the influence of
gross errors to the density estimation procedure.
?The characteristics and fault detection behavior of PCA are explored,
and the relations of expectations of ~ and SPE statistics to the statistical
parameters of process data are presented. These relationships reveal the influence
factors to the detection behavior of PCA and can be used to differentiate the
process change from fault. Some default conclusions conflicting with the real root
cause and thus l
切地监督生产过程的运行状态，不断地检测过程的变化和故障信息，才能有
效防止灾难性事故的发生，同时减少产品质量的波动，提高产品的竞争力。
而流程工业具有规模大、结构复杂，以及现场环境恶劣等特点，使得过程监
测的理论研究与实践成为过程控制领域中最具挑战性的热点课题之一。虽然
基于精确数学模型的过程监测方法在理论上比不依赖数学模型的方法更成
熟，但是由于流程工业的上述特点，使得前者难以在实际工程中应用。因此，
本文研究的是不依赖数学模型的监测方法，此类方法一般均为“数据驱动”
或“基于知识”的。
本文所采用的两个主要分析工具，即小波和统计学理论，都是从不依赖
于数学模型的角度来实现对过程的监测。其中小波是从信号处理和函数逼近
的角度来处理过程数据；而多元统计分析则用于建立过程监测模型，这是通
过对过程数据的统计分析来实现的。这两种方法相互配合，在整个过程监测
系统中承担着不同的任务。本文的主要内容包括如下几个方面：
①系统地介绍了过程监测的基本概念和内容，对基于数学模型和不依
赖于数学模型的故障诊断方法进行了比较，指出了后者在流程工业监测中的
优越性。
②针对过程变量的多率采样问题，提出了一种基于小波多尺度分析理
论的误差递阶补偿算法，实现对高频采样信号的重构。并给出了算法的精度
分析。此算法具有能克服噪声影响、重构精度高和物理意义明确的特点。
③指出了过程数据滤波的特点及要求，阐述了小波阈值滤波和鲁棒小
波分解的思想。对数据在线多尺度分解中的关键技术进行了研究，给出了平
移不变小波分解和区间小波分解的算法实现。
④采用小波阈值密度估计器研究了过程数据的概率密度函数逼近问
题。给出了适合工业应用的估计器网格结构、平滑参数和系数阈值的确定方
法。提出利用Q-Q图迭代检验以消除粗差数据对密度估计的影响。
Xll 浙江大学博士学位论文
⑤对PCA监测方法的特点及其内涵进行了研究。通过分别导出户和
SPE统计量均值与过程数据统计参数之间的关系，分析了影响PCA检测行
为的因素，以及工况变化与故障在PCA下的不同被检测行为。指出了通常
关于PCA检测行为的一些不正确的结论。
③提出了一种改进的PCA方法（MPCA），采用主元相关变量残差统
计量（Pop）代替通常的平方预测误差SPE统计量，用于对工业过程的监测。
MPCA避免了SPE统计量检验的保守性，能够提供更详细的过程变化信息，
从而有效识别正常工况改变与过程故障引起的户图变化。此外在主元子空间
和残差子空间中分别讨论了故障可检测性的充分和必要条件。采用故障临界
幅值的概念对故障在MPCA下的被检测行为进行了分析，并给出了一种新的
主元确定方法。
①基于MPCA监测方法，对故障的重构、识别以及分离等重要问题进
行了系统和定量的分析。给出了MPCA在主元空间中故障的可重构性、可分
离性，以及识别的充分和必耍条件。利用获得的结果对双效蒸发过程进行了
仿真监测，研究了传感器故障的重构与识别问题。
③从过程监测的角度出发，阐述了化工过程有向图模型的基本概念，
归纳了已有的各种传感器设置方法。并结合故障子空间方法的特点，定性地
研究了考虑故障可观性与分辨率时的传感器网络设置问题。
③研究了过程趋势的暂态事件定义和三角形原语描述，以及过程信号
的多尺度特征提取的实现方法。提出了一个针对过程工业实际情况的、集成
的过程监测系统框架体系，并阐述了其中各主要模块的功能。
最后对过程监测中的方法论进行了讨论，阐述了作者在该问题上的观
点。并对未来的研究课题进行了展望。
The safety of production procedure and consistency of product quality are
always two themes of the process industry. To avoid disastrous accidents and
decrease fluctuations of product quality so that products are competitive, the
process conditions must be under closely monitoring and faults should be timely
detected. However, the large scale and complex structure of industrial process, as
well as the uncertainty of real environment, makes the theoretic research and
implementation of process monitoring system as one of challenges in the field of
process control. The model-based monitoring methods are much maturer in
theory in comparison with the model-free one, but the former has great
difficulties when applied in the real plants due to the previously mentioned
characteristics of industrial process. Therefore, the topic of this thesis focuses on
the model-free monitoring method, which is more practicable for its data-driven
or knowledge-based characteristics.
Two primary mathematical tools used in our proposed monitoring strategy
are wavelets and statistics. Both of them are model-free methods when applied to
the process monitoring. Specifically, the wavelet theory deals with process data as
a signal processing or function approximation tool, and statistics (here we
actually refer to the multivariate statistical analysis) is used to build the process
monitoring model which is realized by statistically analyze process data. The
wavelets and statistics play different but complementary roles in the whole
process monitoring strategy.
The main contributions of this thesis are as follows:
?The elementary concepts and scope of process monitoring are
systematically introduced. The model-based and model-free monitoring methods
are compared, and the latter is shown more suitable and practicable for industrial
applications.
?A wavelet-based rnultiscale hierarchical error-compensation algorithm
xIv
is presented to treat the multi-rate issues of process variables. The proposed
method is used to reconstruct a low sampling rate signal to a higher one. The
reconstruction errors are given and derived results are justified. This algorithm
has the advantages of noise-free, high reconstruction accuracy and explicit
physical background.
?The character and requirement of the filtering of process data are
illustrated, and the ideas of wavelet thresholding filtering and robust wavelet
decomposition are introduced. Further, key techniques of multiscale on-line
process data decomposition are studied and the implementation of shift-invariant
decomposition and interval wavelet decomposition algorithms are presented.
(~) The probability density function of process variable is estimated by
using wavelet thresholding density estimator (WTDE). The parameters of WTDE
as the grid structure, smoothing parameter, and thresholds are selected by the
proposed criteria. The iterative Q-Q plot is used to eliminate the influence of
gross errors to the density estimation procedure.
?The characteristics and fault detection behavior of PCA are explored,
and the relations of expectations of ~ and SPE statistics to the statistical
parameters of process data are presented. These relationships reveal the influence
factors to the detection behavior of PCA and can be used to differentiate the
process change from fault. Some default conclusions conflicting with the real root
cause and thus l
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