Modeling and monitoring of multimode process based on subspace separation

In the paper, a new process monitoring approach is proposed for handling the multimode monitoring problem in the industrial batch processes. Compared to conventional method, the contributions are as follows: a new method of extracting the common subspace of different modes is proposed based on the subspace separation; after that the two different subspaces are separated, the kernel principal component models is built for the common and specific subspace respectively and the monitoring is carried out in subspace. The monitoring is carried out in the subspaces. The corresponding confidence regions are constructed according to their models respectively.     

Quality‐relevant and process‐relevant fault monitoring with concurrent projection to latent structures

This paper proposes a new concurrent projection to latent structures is proposed in this paper for the monitoring of output‐relevant faults that affect the quality and input‐relevant process faults. The input and output data spaces are concurrently projected to five subspaces, a joint input‐output subspace that captures covariations between input and output, an output‐principal subspace, an output‐residual subspace, an input‐principal subspace, and an input‐residual subspace. Fault detection indices are developed based on these subspaces for various fault detection alarms. The proposed monitoring method offers complete monitoring of faults that happen in the predictable output subspace and the unpredictable output residual subspace, as well as faults that affect the input spaces only. Numerical simulation examples and the Tennessee Eastman challenge problem are used to illustrate the effectiveness of the proposed method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 496–504, 2013     

基于IJB-PCA-ICA算法的故障检测

针对现代工业过程数据的高维性和分布复杂性等问题,提出了一种基于IJB-PCA-ICA（improved Jarque-Bera-principal component analysis-independent component analysis）的故障检测方法。首先采用改进的Jarque-Bera检测方法（J-B test）对原始数据划分高斯与非高斯核心部分,并对其中的高斯性与非高斯性均不明显的变量划分半高斯部分。将半高斯部分通过高斯分布置信概率加权与高斯核心部分和非高斯核心部分分别建立高斯子空间和分高斯子空间,然后对高斯子空间进行相关性划分后采用PCA方法得到高斯子空间的统计量;对非高斯子空间进行主元投影划分后采用ICA方法得到非高斯子空间的统计量,接着通过贝叶斯推断得到的联合统计量进行故障检测。最后通过Tenessee Eastman（TE）仿真实验,有效验证了所提出方法的有效性。     

独立元子空间算法及其在故障检测上的应用

针对高维数据建模问题,提出一种独立元子空间算法(ICSM),作为一种新的集成学习算法,ICSM利用独立元在不同变量上的贡献度来选取子空间,符合了集成学习的要求,具备了明确的物理意义,有效地克服了随机子空间算法(RSM)的主要缺点。在此基础上,进一步将ICSM应用于工业过程监控,提出了一种新的ICSM-PCA故障检测算法。首先在各个子空间内分别建立相应的PCA监测模型,然后根据T~2和SPE统计量的值计算出集成时各自的权重,最后构造两个集成统计量对工业过程进行监测。通过在Tennessee Eastman(TE)模型上的仿真研究,说明提出的算法具有较好的建模效果和故障检测能力。     

基于全变量信息的子空间监控方法

实际化工过程采集得到的数据往往维度较高,直接建模比较复杂。主元分析(principal component analysis,PCA)方法可以提取原始数据主要特征,得到低维数据,但传统的PCA过程监控方法仅保留了方差较大的主元,会造成信息缺失,这将大大影响过程监控性能。针对这一问题,提出了一种新的基于全变量信息(full variable information,FVI)的子空间监控方法。首先,依据每个变量与主元空间(principal component subspace,PCS)和残差空间(residual subspace,RS)相似性的高低,将原始数据空间划分为3个维度较低的子空间,3个子空间保存了全部过程变量,可以更充分地利用过程信息。其次,在每个子空间中,分别建立监控模型,并利用贝叶斯推断整合子空间的监控结果。最后,通过数值仿真及Tennessee Eastman(TE)过程仿真研究验证FVI方法的有效性。     

Spectral compression using subspace clustering

This article describes a subspace clustering strategy for the spectral compression of multispectral images. Unlike standard principal component analysis, this approach finds clusters in several different subspaces of different dimension. Consequently, instead of representing all spectra in a single low‐dimensional subspace of a fixed dimension, spectral data are assigned to multiple subspaces having a range of dimensions from one to eight. In other words, this strategy allows us to distribute spectra into different subspaces thereby obtaining the best fit for each. As a result, more resources can be allocated to those spectra that need many dimensions for accurate representation and fewer resources to those that can be modeled using fewer dimensions. For a given compression ratio, this trade off reduces the overall reconstruction error. In the case of compressing multispectral images, this initial compression method is followed by JPEG2000 compression in order to remove the spatial redundancy in the data as well. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 7–15, 2016     

Quality-relevant and process-relevant fault monitoring based on GNPER and the fault quantification index for industrial processes

Traditional quality-relevant fault monitoring methods focus on extracting the relationship between the global structural features of the process and quality variables but ignore the local features. At the same time, they lack the quantification of quality-relevant faults. To solve these problems, a quality-relevant and process-relevant fault monitoring method and its fault quantification index based on global neighbourhood preserving embedding regression (GNPER) are proposed. First, by seeking the direction of maximum global variance, the global objective function is applied to neighbourhood preserving embedding algorithm, and the global neighbourhood preserving embedding (GNPE) model is established to fully extract the global and local information of process data. Second, on the basis of GNPE, through the idea of projection regression, the GNPER model is established to obtain mapping relationships among process variables and quality variables, and quality-relevant subspace and process-relevant subspace are extracted, the corresponding subspace statistics are established for fault monitoring. Finally, the fault quantification index is established for the faults in the two subspaces, which can provide more meaningful fault monitoring results. A numerical example, the hot rolling mill and the Tennessee Eastman (TE) process, verify the superiority and accuracy of the proposed method.     

基于核T-PLS的化工过程故障检测算法

针对全潜结构投影法（T-PLS）在检测非线性过程故障时误报率和漏报率较高的缺点,提出了基于核函数的全潜结构投影法（KT-PLS）。该算法通过核函数将过程数据从低维输入空间非线性地映射到高维特征空间,实现非线性问题的线性化;然后在质量变量的引导下将特征空间分为与质量直接相关、与质量正交、与质量无关和残差四个子空间;最后分别构建D和Q统计量进行故障检测。将该算法应用到Tennessee Eastman process（TEP）,多种故障模式下的仿真结果表明,KT-PLS比T-PLS更适合监控具有强非线性的生产过程。     

Concurrent phase partition and between‐mode statistical analysis for multimode and multiphase batch process monitoring

The exiting automatic phase partition and phase‐based process monitoring strategies are in general limited to single‐mode multiphase batch processes. In this article, a concurrent phase partition and between‐mode statistical modeling strategy (CPPBM) is proposed for online monitoring of multimode multiphase batch processes. First, the time‐varying characteristics of batch processes are concurrently analyzed across modes so that multiple sequential phases are simultaneously identified for all modes. The feature is that both time‐wise dynamics and mode‐wise variations are considered to get the consistent phase boundaries. Then within each phase, between‐mode statistical analysis is performed where one mode is chosen for the development of reference monitoring system and the relative changes from the reference mode to each alternative mode are analyzed. From the between‐mode perspective, each of the original reference monitoring subspaces, including systematic subspace and residual subspace, are further decomposed into two monitoring subspaces for each alternative mode, which reveal two kinds of between‐mode relative variations. The part which shows significant increases represents the variations that will cause alarm signals if the reference models are used to monitor the alternative modes, whereas the part that shows no increases will not issue alarms. By modeling and monitoring different types of between‐mode relative variations, the proposed CPPBM method can not only efficiently detect faults but also offer enhanced process understanding. It is illustrated with a typical multiphase batch process with multiple modes. © 2013 American Institute of Chemical Engineers AIChE J 60: 559–573, 2014     

Spectra data analysis and calibration modeling method using spectra subspace separation and multiblock independent component regression strategy

In this article, a spectra data analysis and calibration modeling approach is proposed for the estimation of the concentration of sources species in chemical mixture. Based on the multiplicity of underlying spectra characteristics, it designs spectra subspace separation and multiblock independent component regression modeling strategy. It is performed in two steps: The first step aims at an automatic partition of the original wavelength space into different spectra subspaces to reveal the changes of underlying spectra information. In different spectra subspaces, each being well fitted by one independent component analysis (ICA) model, it better explores the existing chemical constituent species of interest. In the second step, multiblock regression system is designed for concentration estimation. The advantage is mainly to allow for easier interpretation and enhanced understanding by zooming into different smaller specific segments and thus well tracking the wavelength‐varying effects on qualities. It is theoretically and experimentally illustrated that the proposed method can result in better predictive power compared with standard ICR (SICR) modeling focusing on the full‐range wavelength. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Model reduction-based optimization using large-scale steady-state simulators

Most engineering systems can be accurately simulated using models consisting of Partial Differential Equations. Thus the challenging problem of PDE-constrained optimization arises naturally in engineering design. Issues surface due to the high number of variables involved and the use of specialized software for simulation which may not include an optimization option. In this work we present a methodology for the steady-state optimization of systems for which an input/output steady-state simulator is available. The proposed method is efficient for dissipative systems and is based on model reduction. This framework employs a two-step projection scheme, first onto the low-dimensional, adaptively computed, dominant subspace of the system and second onto the subspace of independent variables. Hence only low order Jacobian and Hessian matrices are used in this formulation, computed efficiently with directional perturbations.     

Two-dimensional Bayesian monitoring method for nonlinear multimode processes

Nonlinear and multimode are two common behaviors in modern industrial processes, monitoring research studies have been carried out separately for these two natures in recent years. This paper proposes a two-dimensional Bayesian method for monitoring processes with both nonlinear and multimode characteristics. In this method, the concept of linear subspace is introduced, which can efficiently decompose the nonlinear process into several different linear subspaces. For construction of the linear subspace, a two-step variable selection strategy is proposed. A Bayesian inference and combination strategy is then introduced for result combination of different linear subspaces. Besides, through the direction of the operation mode, an additional Bayesian combination step is performed. As a result, a two-dimensional Bayesian monitoring approach is formulated. Feasibility and efficiency of the method are evaluated by the Tennessee Eastman (TE) process case study.     

Quality‐relevant fault diagnosis with concurrent phase partition and analysis of relative changes for multiphase batch processes

Multiplicity of phases as indicated by changes of process characteristics is an inherent nature of many batch processes for both normal and fault cases. To more efficiently perform online fault diagnosis via reconstruction for multiphase batch processes, the phase nature and the relationship between normal and fault cases within each phase should be deeply addressed. This article proposes a quality‐relevant fault diagnosis strategy with concurrent phase partition and analysis of relative changes for multiphase batch processes. First, a concurrent phase partition algorithm is developed. The basic idea is to track the changes of process characteristics at normal and fault statuses jointly so that multiple sequential modeling phases are identified simultaneously for both normal and fault cases. Then, the relative changes from the normal status to each fault case are analyzed in each phase to reveal the specific fault effects more efficiently. The fault effects are decomposed in two different monitoring subspaces, principal subspace, and residual subspace, by capturing their different roles in removing out‐of‐control signals. The significant increases relative to the normal case are judged to be responsible for the concerned alarm monitoring statistics in each phase. The others are composed of general variations that are deemed to still follow normal rules and thus insignificant to remove alarm monitoring statistics. Those alarm‐responsible fault deviations are then used to develop reconstruction models which can more efficiently recover the fault‐free part for online fault diagnosis. The proposed algorithm is illustrated with a typical multiphase batch process with one normal case and three fault cases. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2048–2062, 2014     

A quadratic programming technique with application to kinetic rate constant determination

A technique for the solution of the quadratic programming problem by a series of unconstrained optimizations in subspaces of the original space is developed. This technique uses a previously known transformation to convert the problem into an optimization in the non-negative orthant. The optimization can then be solved by optimizations in subspaces. The algorithm is shown to always decrease the objective function and to converge in a finite number of iterations. The algorithm is easily programmed on a computer.An example, previously used by others, is solved with this technique in a fewer number of iterations. An illustration of this technique for kinetic rate constant determination is included. Other applications for this simple quadratic programming scheme are discussed.     

Optimal eigenvectors of spectral datasets: sequential selection from one set vs a collection from two sets

In this paper, the influence of spectral datasets and the method of selection of the corresponding feature vectors on the compression and reconstruction of data is scrutinised. To fulfil this aim, two different sets of reflectance data with the least spectral similarity are selected from different sets of spectral databases and the most optimal eigenvectors are chosen using different strategies. Six and 12 arrangements of eigenvectors obtained from different individual or combined databases are then used for the compression of reflectance spectra of learning sets, as well as those that have not been used in extraction of eigenvectors. The validity of the desired reduced subspaces is assessed by computing the spectral errors between the actual and the reconstructed spectra of samples of learning sets. Moreover, the efficiencies of designed compressed subspaces are evaluated through the numbers of out‐of‐range reconstructed spectra, as well as the spectral and colorimetric deviations between the actual and compressed‐reconstructed reflectance spectra of samples of datasets that were not employed in learning sequence. The results show that in the restricted subspaces, i.e. six‐dimensional subspace, the most effective results are achieved when the reduced subspace is created from a collection of two separate sets of eigenvectors of two different datasets with the maximum degree of dissimilarity, and the reduced spaces that have been made from six eigenvectors of individual datasets lead to higher errors.     

A new optimization model and a customized solution method for natural gas production network design and operation

This article proposes to tackle integrated design and operation of natural gas production networks under uncertainty, using a new two‐stage stochastic programming model, a novel reformulation strategy, and a customized global optimization method. The new model addresses material balances for multiple key gas components, pressure flow relationships in gas wells and pipelines, and compressor performance. This model is a large‐scale nonconvex mixed‐integer nonlinear programming problem that cannot be practically solved by existing global optimization solvers or decomposition‐based optimization methods. With the new reformulation strategy, the reformulated model has a better decomposable structure, and then a new decomposition‐based global optimization method is developed for efficient global optimization. In the case study of an industrial naturals production system, it is shown that the proposed modeling and optimization methods enable efficient solution, and the proposed optimization method is faster than a state‐of‐the‐art decomposition method by at least an order of magnitude. © 2016 American Institute of Chemical Engineers AIChE J, 63: 933–948, 2017     

Process monitoring method based on correlation variable classification and vine copula

Chemical processes are becoming increasingly complicated, leading to an increase in process variables and more complex relationships among them. The vine copula has a significant advantage in portraying the dependence of high-dimensional variables. However, as the dimensions increase, the vine copula model incurs a high computational load; such pressure greatly reduces model efficiency. Relationships among variables in the industrial process are complex. Different variables may be strongly or weakly associated or even independent. This paper proposes a process monitoring method based on correlation variable classification and vine copula. The weighted correlation measure is first used to divide variables into a correlated subspace and weakly correlated subspace. Then, two vine structures, C-vine and D-vine, are applied to the correlated and weakly correlated subspaces, respectively. This method takes advantage of C-vine for correlated variables and the flexibility of D-vine for weakly correlated variables. Finally, comprehensive statistics are established based on different subspaces. Monitoring results of the numerical system and the Tennessee Eastman process demonstrate the effectiveness and validity of the proposed method.     

Efficient structure synthesis of reactive distillation processes using the IDEAS approach

A new synthesis method for reactive distillation processes is proposed. At each stage of a column, vapor–liquid equilibrium (VLE) is assumed and kinetically controlled reaction in liquid phase is considered. First, the liquid composition space is divided into small subspaces. Then, for each subspace a representative liquid composition is decided and assigned to a module corresponding to a stage of a distillation column. Then, after the calculation of the VLE and the reaction rate, the distribution network (superstructure) connecting all modules by vapor and liquid flow paths is constructed. The feature of the proposed model is that all constraints are linear to the optimization variables: the liquid and vapor flow rate and the liquid hold-up. The developed method was applied to the metathesis reaction of 2-pentene, and a completely new process structure was obtained. The effectiveness of the implied structure was confirmed through a comparison with conventional structures.     

Comparison of global optimization algorithms for the design of water-using networks

We address a special class of bilinear process network problems with global optimization algorithms iterating between a lower bound provided by a mixed-integer linear programming (MILP) formulation and an upper bound given by the solution of the original nonlinear problem (NLP) with a local solver. Two conceptually different relaxation approaches are tested, piecewise McCormick envelopes and multiparametric disaggregation, each considered in two variants according to the choice of variables to partition/parameterize. The four complete MILP formulations are derived from disjunctive programming models followed by convex hull reformulations. The results on a set of test problems from the literature show that the algorithm relying on multiparametric disaggregation with parameterization of the concentrations is the best performer, primarily due to a logarithmic as opposed to linear increase in problem size with the number of partitions. The algorithms are also compared to the commercial solvers BARON and GloMIQO through performance profiles.