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Comprehensive Monitoring of Nonlinear Processes Based on Concurrent Kernel Projection to Latent Structures
Abstract
Projection to latent structures (PLS) and concurrent PLS are approaches for solving quality-relevant process monitoring. In this paper, a new approach called concurrent kernel PLS (CKPLS) is presented to detect faults comprehensively for nonlinear processes. The new model divides the nonlinear process and quality spaces into five subspaces: the co-varying, process-principal, process-residual, quality-principal, and quality-residual subspaces. The co-varying subspace reflects nonlinear relationship between quality variables and original process variables. The process-principal and process-residual subspaces reflect the principal variations and residuals, respectively, in the nonlinear process space. Further, the quality-principal and quality-residual subspaces reflect the principal variations and residuals, respectively, in the quality space. The proposed approach is demonstrated by a numerical simulation and an application of the Tennessee Eastman process.
... Therefore, Li et al [10,11]developed dynamic T-PLS approach to form quality relevant data-driven modeling method for multivariate dynamic process monitoring. When it comes to nonlinear problem, Sheng et al [12] presented a novel method named concurrent kernel PLS (CKPLS), shen et al [13,14] combined locally weighted projection regression (LWPR) with improved PLS to model nonlinear process and design monitoring statistics. Besides PLS type approaches, linear regression methods have also been utilized. ...
... Because it is able to extract ICs from the measured mixed signals, this technique has been widely applied in several fields including process monitoring. Given the measured process variable matrix 12 ...
... The ICs filtering is after performing ICA on the input variable matrix X , by applying OSC to the extracted ICs for removing the quality irrelevant independent components, namely the systematic variation orthogonal to output Y . Suppose the originally extracted independent components are presented as 12 [ ...
Partial least squares (PLS) and linear regression methods have been widely utilized for quality-related fault detection in industrial processes recently. Since these traditional approaches assume that process variables follow Gaussian distribution approximately, their effectiveness will be challenged when facing non-Gaussian processes. To deal with this difficulty, a new quality relevant process monitoring approach based on improved independent component regression (IICR) is presented in this article. Taking high-order statistical information into account, ICA is performed onto process data to produce independent components (ICs). In order to remove irrelevant variation orthogonal to quality variable and keep as much quality-related fault information as possible, a new quality-related independent components selection method is applied to these ICs. Then the regression relationship between filtered ICs and the product quality is built. QR decomposition for regression coefficient matrix is able to give out quality-related and quality-unrelated projectors. After the measured variable matrix is divided into quality relevant and quality irrelevant parts, novel monitoring indices are designed for fault detection. finally, applications to two simulation cases testify the effectiveness of our proposed quality-related fault detection method for non-Gaussian processes.
... where the constraint P T P = I with P ∈ R m×l , µ = 0. According to (3)(4)(5), J loss (P , P M1 , Ω M1 ) is expressed by: ...
... The posterior probability log p (θ|X 1 , X 2 ) is approximated by (3). Similar to Appendix A, Taylor series approximation is applied around θ * M2 and the first order deviation is zero. ...
For multimode processes, one has to establish local monitoring models corresponding to local modes. However, the significant features of previous modes may be catastrophically forgotten when a monitoring model for the current mode is built. It would result in an abrupt performance decrease. Is it possible to make local monitoring model remember the features of previous modes? Choosing the principal component analysis (PCA) as a basic monitoring model, we try to resolve this problem. A modified PCA algorithm is built with continual learning ability for monitoring multimode processes, which adopts elastic weight consolidation (EWC) to overcome catastrophic forgetting of PCA for successive modes. It is called PCA-EWC, where the significant features of previous modes are preserved when a PCA model is established for the current mode. The computational complexity and key parameters are discussed to further understand the relationship between PCA and the proposed algorithm. Numerical case study and a practical industrial system in China are employed to illustrate the effectiveness of the proposed algorithm.
... Qin and Zheng (2013) developed concurrent projection to latent structures (CPLS) to detect the faults that occurred in the covariation subspace, output principal subspace, output residual subspace, input-principal subspace, and input-residual subspace, respectively. In recent years, concurrent kernel PLS (CKPLS) models were developed based on CPLS model to achieve better monitoring performance for large-scale and nonlinear industrial processes (Sheng et al., 2016;Zhang et al., 2015). Based on the experimental results, CKPLS could not only detect the fault accurately in industrial processes, but also identify the fault-relevant direction effectively. ...
... hx,d rawback and make full use of the advantages n CLPS, CKPLS is proposed by Sheng et al. (2016), which concurrently partitions feature space data and output data into five subspaces: a covariance subspace, an input principal subspace, an input residual subspace, an output principal subspace and an output residual subspace. After performing the CKPLS algorithm (Table 2) decomposition, the data matrix ˚ and Y can be expressed as follows: ...
To meet the standards of effluent quality in wastewater treatment processes (WWTPs), a dynamic concurrent kernel partial least squares (DCKPLS) method is proposed for process monitoring. After integrating the augmented matrices and kernel technique, the proposed method can be used to handle the dynamic and nonlinear characteristics of WWTP data simultaneously. Besides, the inherent limitation of PLS decomposition can be overcome by DCKPLS model, which concurrently partitions the feature space data and output variables into five subspaces. Monitoring performance is evaluated by simulated sensor faults of industrial WWTP data. Specifically, the fault detection rates of bias fault and drifting fault using DCKPLS are increased by 22.65 % and 8.06 %, respectively, in comparison with CKPLS. It is also shown that the DCKPLS model provides better monitoring performance than the other counterparts.
... Concurrent PLS was also proposed to solve some drawbacks of the T-PLS. Kernel concurrent PLS was developed by Zhang et al. [176] and Sheng et al. [205]. ...
... Another heuristic is based solely on the dimensionality, such as c = 5m [86][87][88] or c = 500m [66,118,130,204] for the TEP case study. For the TEP alone, many values were used, such as c = 6000 [157,213], c = 1720 [177], c = 4800 [205], c = 3300 [220], and so on. However, note that the appropriate value of c does not depend on the case study, but rather on the characteristics of the data that enters the kernel mapping. ...
Kernel methods are a class of learning machines for the fast recognition of nonlinear patterns in any data set. In this paper, the applications of kernel methods for feature extraction in industrial process monitoring are systematically reviewed. First, we describe the reasons for using kernel methods and contextualize them among other machine learning tools. Second, by reviewing a total of 230 papers, this work has identified 12 major issues surrounding the use of kernel methods for nonlinear feature extraction. Each issue was discussed as to why they are important and how they were addressed through the years by many researchers. We also present a breakdown of the commonly used kernel functions, parameter selection routes, and case studies. Lastly, this review provides an outlook into the future of kernel-based process monitoring, which can hopefully instigate more advanced yet practical solutions in the process industries.
... Based on CPLS, Liu et al. developed multiblock CPLS which incorporates process block partition to diagnose faults relevant to process inputs or outputs with a decentralized structure [21] . Sheng et al. extended CPLS to concurrent kernel PLS to detect faults comprehensively for nonlinear processes [22] . Zhang et al. presented kernel CPLS construction method to further diagnose the faults [23] . ...
... P-PL S and CPL S model are shown in Eqs. (22) and (10), respectively, in which T ˆ K and U c are latent score vectors for joint inputoutput subspace, respectively. Thus, the statistics T 2 ˆ K in Eq. (23) for P-PLS and T 2 c in Eq. (12) for CPLS are used to monitor CS in P-PLS and CPLS, respectively. ...
Projection to latent structures(PLS) is widely applied in quality-related process monitoring. Since it is a data-based method, the noise in data will affect PLS model parameter, which may lead to inappropriate space division. In this paper, an approach called parallel projection to latent structures (P-PLS) is proposed. To remove negative effect of the noise, P-PLS firstly updates original correlation matrix obtained by PLS through l 0 minimization. Then process input (i.e., process variables) are divided into two orthogonal subspaces - the output-relevant and the input-relevant subspace by singular value decomposition (SVD) on updated correlation matrix. With respect to process output (i.e., quality variables), the unpredictable part is further decomposed by principal component analysis (PCA). Thus, P-PLS decomposes the whole input and output data space into only 4 subspaces, in which correlation subspace, unpredictable output principal subspace and unpredictable output residual subspace are output-relevant and input-residual subspace is input-relevant. Four fault detection indices are designed for complete monitoring the faults in respective subspaces. Furthermore, the relationships among P-PLS and concurrent PLS models are analyzed in detail. Numerical examples and Tennessee Eastman Process (TEP) are utilized to verify the effectiveness and superiority of proposed P-PLS algorithm.
... For example, principal component analysis (PCA) and its variants have been widely used in industrial processes [13]- [15]. In order to detect quality-related faults, approaches based on partial least square (PLS) have been proposed [16], [17]. When the training data contains both normal and abnormal working condition samples, linear discriminant analysis (LDA) has been developed [18]. ...
With the increasing intelligence and integration, a great number of two-valued variables (generally stored in the form of 0 or 1 value) often exist in large-scale industrial processes. However, these variables cannot be effectively handled by traditional monitoring methods such as LDA, PCA and PLS. Recently, a mixed hidden naive Bayesian model (MHNBM) is developed for the first time to utilize both two-valued and continuous variables for abnormality monitoring. Although MHNBM is effective, it still has some shortcomings that need to be improved. For MHNBM, the variables with greater correlation to other variables have greater weights, which cannot guarantee greater weights are assigned to the more discriminating variables. In addition, the conditional probability must be computed based on the historical data. When the training data is scarce, the conditional probability between continuous variables tends to be uniformly distributed, which affects the performance of MHNBM. Here a novel feature weighted mixed naive Bayes model (FWMNBM) is developed to overcome the above shortcomings. For FWMNBM, the variables that are more correlated to the class have greater weights, which makes the more discriminating variables contribute more to the model. At the same time, FWMNBM does not have to calculate the conditional probability between variables, thus it is less restricted by the number of training data samples. Compared with MHNBM, FWMNBM has better performance, and its effectiveness is validated through the numerical cases of a simulation example and a practical case of Zhoushan thermal power plant (ZTPP), China.
... In the linear situations, the contribution plot is a commonly tool for fault identification (Qin, 2012). Based on the reconfigurability and identifiable conditions of faults, Qin et al. proposed a reconstruction diagnosis method without prior knowledge and a reconstruction diagnosis method with known prior knowledge (Alcala & Qin, 2009;Qin, 2003Qin, , 2012Sheng, Liu, & Qin, 2016). However, since the kernel-based process monitoring methods nonlinearly map the original process variables to the feature space. ...
Blast furnace (BF) ironmaking is one of the most important production links in modern iron-steel making. The operation conditions of BF and the molten iron quality (MIQ) should be monitored and analyzed in real-time to realize high quality with low energy consumption. Aiming at the problems of strong nonlinearity and few fault samples in BF processes, a novel fault identification method for MIQ monitoring based on kernel partial least squares (KPLS) with improved contribution rate is proposed in this paper. First of all, a KPLS model is established with the actual historical data in order to detect the quality-related faults accurately. The T 2 and SPE statistics are used to monitor the operation conditions of process from different aspects. Second, in view of the unclear physical meaning and complex computation of the existing fault identification methods based on KPLS with contribution rate, a scale factor vector is introduced into the new samples to calculate the T 2 and SPE statistics, so as to construct the monitoring indicators functions. By performing Taylor approximation on these constructed functions near the scale factor with the value of 1, two new statistics are obtained from the absolute value of the first-order partial derivative representing the contribution rate of each variable. Finally, in order to further improve the effect of fault identification, the relative contribution rate of each variable is used to identify the final faulty variables. The tests of MIQ monitoring in BF ironmaking process using actual industrial data verify the validity and practicability of the proposed method.
... Table 1 provides the detailed illustrations of advantages and disadvantages of LVMs and kernelbased LVMs. Successful applications have been found in different areas including fault detection, reconstruction, and diagnosis [27][28][29][30][31]. For the prediction model construction, there are also quite a few number of studies. ...
A composite model integrating latent variables of kernel partial least squares with relevance vector machine (KPLS-RVM) has been proposed to improve the prediction performance of conventional soft sensors when facing industrial processes. First, the latent variables are extracted to cope with the high dimensionality and complex collinearity of nonlinear process data by using KPLS projection. Then, the probabilistic method RVM is used to develop predictive function between latent variables and the output variable. The performance of the proposed method is evaluated through two case studies based on subway indoor air quality (IAQ) data and wastewater treatment processes (WWTP) data, respectively. The results show the superiority of KPLS-RVM in prediction performance over the other counterparts including least squares support vector machine (LSSVM), PLS-LSSVM, PLS-RVM, and KPLS-LSSVM. For the prediction of effluent chemical oxygen demand in WWTP data, the coefficient of determination value of KPLS-RVM has been improved by approximately 7.30-19.65% in comparison with the other methods.
... I N THE past years, works on process monitoring [1]- [3] and signal processing [4]- [6] have achieved great success in the modern industry. Recently, a large amount of data are collected in the real processes with the advent of advanced instrumentation and automation systems. ...
Nonstationary variations widely exist in abnormal industrial processes, in which the mean values and variances of the fault nonstationary variables change with time. Thus, the stationary fault information may be buried by nonstationary fault variations resulting in high misclassification rate for fault diagnosis. Besides, the existing fault diagnosis methods do not consider underlying relations among different fault classes, which may lose important classification information. Here, it is recognized that different faults may not only share some common information but also have some specific characteristics. A fault diagnosis strategy with dual analysis of common and specific nonstationary fault variations is proposed here. The nonstationary variables and stationary variables are first separated using Augmented Dickey-Fuller (ADF) test. Then common and specific information is analyzed for fault diagnosis. Two models are developed, in which, the fault-common model is constructed by cointegration analysis (CA) to capture common nonstationary fault variations, and the fault-specific model is built to capture specific fault nonstationary variations of each fault class. With dual consideration of common and specific fault characteristics, the classification accuracy and fault diagnosis performance can be greatly improved. The performance of the proposed method is illustrated with both a well-known benchmark process and a real industrial process.
... After detecting a fault occurs, the most simple reaction is to stop the process, but it may cause huge economic losses and damage to industrial systems. Fault tolerant is an alternative solution and have received amount of attention [25]- [27]. Among the crucial components of industrial system, sensor fault is familiar and always need to be tolerant. ...
... PCA-based methods to inherently nonlinear processes may lead to unreliable and inefficient fault detection, since a linear transformation is hard to tackle the nonlinear relationship between different process variables [10], [11]. To deal with this problem, various nonlinear extensions of PCA have been proposed for fault detection. ...
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the monitored process is linear, nonlinear PCA models, such as autoencoder models and kernel principal component analysis (KPCA), has been proposed and applied to nonlinear process monitoring. However, KPCA-based methods need to perform eigen-decomposition (ED) on the kernel Gram matrix whose dimensions depend on the number of training data. Moreover, prefixed kernel parameters cannot be most effective for different faults which may need different parameters to maximize their respective detection performances. Autoencoder models lack the consideration of orthogonal constraints which is crucial for PCA-based algorithms. To address these problems, this paper proposes a novel nonlinear method, called neural component analysis (NCA), which intends to train a feedforward neural work with orthogonal constraints such as those used in PCA. NCA can adaptively learn its parameters through backpropagation and the dimensionality of the nonlinear features has no relationship with the number of training samples. Extensive experimental results on the Tennessee Eastman (TE) benchmark process show the superiority of NCA in terms of missed detection rate (MDR) and false alarm rate (FAR). The source code of NCA can be found in https://github.com/haitaozhao/Neural-Component-Analysis.git.
... With a huge amount of data collected by distributed control systems, it becomes more and more popular to apply data-driven techniques to process monitoring in modern industries [1, 2, 3]. Statistical process monitoring as a common tool for analysis of correlated data, has been used successfully in fault detection and diagnosis in various processes [4]. ...
Data driven fault detection and diagnosis methods become more and more attractive in modern industries especially process industries. They can not only guarantee safe operation but also greatly improve product quality. For example, dynamic principal component analysis models and reconstruction based contribution are widely applicable in many occasions. However, there is one issue which does not receive enough attention, namely locating the root cause of a fault when it occurs. In this paper, a framework of root cause location is proposed to address this issue, including both stationary faults and nonstationary faults. A case study on Tennessee Eastman process is used to demonstrate the usage and effectiveness of these approaches. Results show the proposed framework is valid.
Nonlinear process is a common phenomenon in industrial processes, which shows a nonlinear relationship between the variables. Generally, PLS and its modifications (Yin et al. in IEEE Trans Industr Electron 62:1651–1658, 2015; Zhou et al. in AIChE J 56:168–178, 2010; Qin and Zheng in AIChE J 59:496–504, 2013) have a high performance when dealing with linear variation among process variables. However, when applied to a nonlinear process, which generally means that there exists a nonlinear relationship between X and Y, or the process data distributed nonlinearly, or both, these methods cannot perform well.
Multivariate monitoring plays an important role in process monitoring. Among the multivariate monitoring methods, the projection to latent structure method (PLS) has been most widely used in the fields of quality control and fault diagnosis. To improve the monitoring capability of traditional PLS methods in nonlinear and non‐Gaussian multivariate systems, this paper proposes an innovative multivariate monitoring strategy, which combines adversarial autoencoder (AAE) and the concurrent projection to latent structure method (CPLS). In the proposed strategy, the original data are mapped to the high‐dimensional space using the AAE method with the Gaussian prior distribution to realize data transformation. The mapped data are linearly divisible and approach the Gaussian distribution. Then, the projection with orthogonality is realized using the CPLS method. In addition, the reconstruction error and distribution properties are used as evaluation indexes of the high‐dimensional mapping performance. The corresponding monitoring strategy is established using the traditional statistical method based on the Gaussian distribution. Finally, the simulations are performed on the Tennessee‐Eastman process platform, and the results show that the proposed method could efficiently extract the principal components, especially in quality‐relevant fault monitoring.
Projection to latent structure (PLS) is a well-known data-based approach widely used in industrial process monitoring. Kernel PLS (KPLS) was proposed in prior studies to apply the PLS in the nonlinear process. However, KPLS-based methods only consider the nonlinear variation of the input and ignore that of the input and output simultaneously. Once the nonlinearity lies in inputs and outputs, the KPLS-based methods cannot accurately describe the nonlinear feature, and result in missing alarms. To provide a common monitoring approach for various nonlinear cases, an input-output kernel PLS (IO-KPLS) model is proposed. The proposed IO-KPLS maps both the original input and output variables into a high-dimensional space. A new nonlinear objective function is then established to extract latent variables. In addition, a nonlinear regression is designed to construct the IO-KPLS model. By constructing statistics, a complete quality-related process monitoring strategy is designed. Driven by the proposed strategy, the nonlinear feature between input and output can be efficiently extracted, and a comprehensive monitoring performance is provided. A numerical example and two industrial benchmarks are performed to demonstrate the efficiency of the proposed method.
Process monitoring, a typical application of Industrial Internet of Things (IIOT), is crucial to ensure the reliable operation of the industrial system. In practice, due to the harsh environment and unreliable sensors and actuators, it is often difficult for IIoT to collect enough tagged and highly reliable data, which further degrades the process monitoring performance and makes the monitoring results not trustworthy. In order to reduce the negative impact of these unreliable factors, a self-weighted dictionary learning process monitoring method is proposed. In particular, a label propagation classifier is implemented from the labeled data to unlabeled data to obtain a credible label prediction. Subsequently, considering the interference of low-quality data and label information, we re-weight the classification loss and label-consistency constraints to enhance the trustworthiness of feature extraction. Finally, a novel iterative optimization algorithm that combines the block coordinate descent method with the alternating direction multiplier method is developed to ensure the convergence speed of the learned classifier and dictionary. Extensive experiments indicate that the proposed method can guarantee the trustworthiness of the process monitoring results.
The development of the Internet of Things, cloud computing, and artificial intelligence has given birth to industrial artificial intelligence (IAI) technology, which enables us to obtain fine perception and in-depth understanding capabilities for the operating conditions of industrial processes, and promotes the intelligent transformation of modern industrial production processes. At the same time, modern industry is facing diversified market demand instead of ultra-large-scale demand, resulting in typical variable conditions, which enhances the nonstationary characteristics of modern industry, and brings great challenges to the monitoring of industrial processes. In this regard, this paper analyzes the complex characteristics of nonstationary industrial operation, reveals the effects on operating condition monitoring, and summarizes the difficulties faced by varying condition monitoring. Furthermore, by reviewing the recent 30 years of development of data-driven methods for industrial process monitoring, we sorted out the evolution of nonstationary monitoring methods, and analyzed the features, advantages and disadvantages of the methods at different stages. In addition, by summarizing the existing related research methods by category, we hope to provide reference for monitoring methods of nonstationary process. Finally, combined with the development trend of industrial artificial intelligence technologies, some promising research directions are given in the field of nonstationary process monitoring.
With the increasing intelligence and integration, a great number of two-valued variables (generally stored in the form of 0 or 1) often exist in large-scale industrial processes. However, these variables cannot be effectively handled by traditional monitoring methods such as linear discriminant analysis (LDA), principal component analysis (PCA) and partial least square (PLS) analysis. Recently, a mixed hidden naive Bayesian model (MHNBM) is developed for the first time to utilize both two-valued and continuous variables for abnormality monitoring. Although the MHNBM is effective, it still has some shortcomings that need to be improved. For the MHNBM, the variables with greater correlation to other variables have greater weights, which can not guarantee greater weights are assigned to the more discriminating variables. In addition, the conditional probability
$P(x_{j}\vert x_{j^{\prime}}, y=k)$
must be computed based on historical data. When the training data is scarce, the conditional probability between continuous variables tends to be uniformly distributed, which affects the performance of MHNBM. Here a novel feature weighted mixed naive Bayes model (FWMNBM) is developed to overcome the above shortcomings. For the FWMNBM, the variables that are more correlated to the class have greater weights, which makes the more discriminating variables contribute more to the model. At the same time, FWMNBM does not have to calculate the conditional probability between variables, thus it is less restricted by the number of training data samples. Compared with the MHNBM, the FWMNBM has better performance, and its effectiveness is validated through numerical cases of a simulation example and a practical case of the Zhoushan thermal power plant (ZTPP), China.
Modern industrial processes are confronted with a large-scale challenge in recent years. In this paper, a novel distributed kernel principal component regression (DKPCR) approach is proposed to study the plant-wide problem of quality-related process monitoring. Along with reducing the scale of abundant measurements, the proposed approach also focuses on the robust issues that arise from the large outliers. In the local phase, every agent of the DKPCR technique processes the data of the partial sections and sends the selected information to the centralized mainframe. The engineer gathers the data from the local agents and then makes a decision based on the Bayesian inference. Additionally, the corresponding weight diagnosis approach is devised to isolate the fault-relevant variables under the smear effect by virtue of the detection results and information. In the end, the Tennessee Eastman case (TEC) and the three-phase flow system (TPFS) are leveraged to demonstrate the detection and diagnosis performance of the proposed approach.
With the rapid advancement of in-process measurements and sensor technology driven by zero-defect manufacturing applications, high-dimensional heterogeneous processes that continuously collect distinct physical characteristics frequently appear in modern industries. Such large-volume high-dimensional data place a heavy demand on data collection, transmission, and analysis in practice. Thus, practitioners often need to decide which informative data streams to observe given the resource constraints at each data acquisition time, which poses significant challenges for multivariate statistical process control and quality improvement. In this article, we propose a generic online nonparametric monitoring and sampling scheme to quickly detect mean shifts occurring in heterogeneous processes when only partial observations are available at each acquisition time. Our innovative idea is to seamlessly integrate the Thompson sampling (TS) algorithm with a quantile-based nonparametric cumulative sum (CUSUM) procedure to construct local statistics of all data streams based on the partially observed data. Furthermore, we develop a global monitoring scheme of using the sum of top-
${r}$
local statistics, which can quickly detect a wide range of possible mean shifts. Tailored to monitoring the heterogeneous data streams, the proposed method balances between exploration that searches unobserved data streams for possible mean shifts and exploitation that focuses on highly suspicious data streams for quick shift detection. Both simulations and a case study are comprehensively conducted to evaluate the performance and demonstrate the superiority of the proposed method.
Note to Practitioners
—This paper is motivated by the critical challenge of online process monitoring by considering the cost-effectiveness and resource constraints in practice (e.g., limited number of sensors, limited transmission bandwidth or energy constraint, and limited processing time). Unlike the existing methodologies which rely on the restrictive assumptions (e.g., normally distributed, exchangeable data streams) or require historical full observations of all data streams to be available offline for training, this paper proposes a novel monitoring and sampling strategy that allows the practitioners to cost-effectively monitor high-dimensional heterogeneous data streams that contain distinct physical characteristics and follow different distributions. To implement the proposed methodology, it is necessary: (i) to identify sample quantiles for each data stream based on historical in-control data offline; (ii) to determine which data streams to observe at each acquisition time based on the resource constraints; and (iii) to automatically screen out the suspicious data streams to form the global monitoring statistic. Experimental results through simulations and a case study have shown that the proposed method has much better performance than the existing methods in reducing detection delay and effectively dealing with heterogeneous data streams.
For nearly a decade, quality-related fault detection algorithms have been widely used in industrial systems. However, the majority of these detection strategies rely on static assumptions of the operating environment. In this paper, taking the time series of variables into consideration, a dynamic kernel entropy component regression (DKECR) framework is proposed to address the instability of quality-related fault detection due to the existing dynamic characteristics. Compared with the typical kernel entropy component analysis method, the proposed method constructs the relationship between process states and quality states to further interpret the direct effect on the product taken by the fault. In the proposed approach, process measurements are converted to a lower-dimensional subspace with a specific angular structure that is more comprehensive than traditional subspace approaches. In addition, the angular statistics and their relevant thresholds are exploited to enhance the quality-related fault detection performance. Finally, the proposed method will be compared with three methods by means of a numerical example and two industrial scenarios to demonstrate its practicality and effectiveness.
With the development of the industrial cyber-physical systems, a small amount of labeled data and a large amount of unlabeled data are collected from the industrial process. Due to the variation of internal operation conditions and external environment, there is a between-mode similarity between data samples. The scarcity of labeled data and the existence of similarity make it challenging to extract data characteristics. In addition, it creates new challenges to process monitoring. To solve these problems, this study proposes a label propagation dictionary learning method. We first establish the connection between atoms and corresponding profiles and realize the propagation of their labels through graph Laplacian regularization. Then, considering the similarity of samples in the same class, the low-rank constraint is added to sparse coding to strengthen the mutual propagation of labels. Finally, an optimization method is designed to obtain the dictionary and classifier simultaneously. When new data samples arrive, we conduct process monitoring and condition prediction based on the learned dictionary and classifier. Experiments show that the proposed method can achieve satisfactory monitoring performance when compared to several state-of-the-art methods, indicating the superiority of the proposed method.
Nowadays, how to select the kernel function and their parameters for ensuring high-performance indicators in fault diagnosis applications remains as two open research issues. This paper provides a comprehensive literature survey of kernel-preprocessing methods in condition monitoring tasks, with emphasis on the procedures for selecting their parameters. Accordingly, twenty kernel optimization criteria and sixteen kernel functions are analyzed. A kernel evaluation framework is further provided for helping in the selection and adjustment of kernel functions. The proposal is validated via a KPCA-based monitoring scheme and two well-known benchmark processes.
Key performance indicator (KPI)‐relevant fault detection method has been raised for decades to hugely increase the economic interest of modern industries. However, the typical data‐driven approaches like the kernel principal component analysis (KPCA) and the kernel entropy analysis (KECA) are inefficient to consider the influence taken by the fault factor on the KPI. Thus, in this work, an algorithm called the kernel entropy regression (KECR) is proposed to enhance the interpretability between the fault and the KPI. The proposed algorithm captures the information relevant to the KPI state in the subspace and rewords the decomposition of the KECA method. The angular structure of the KECR method achieves an accurate partition for process variables to hugely decrease false detection results. In the end, an industrial case is utilized to demonstrate the effectiveness of the KECR method.
Frequent and wide changes in operation conditions are quite common in real process industry, resulting in typical wide-range nonstationary and transient characteristics along time direction. The considerable challenge is, thus, how to solve the conflict between the learning model accuracy and change complexity for analysis and monitoring of nonstationary and transient continuous processes. In this work, a novel condition-driven data analytics method is developed to handle this problem. A condition-driven data reorganization strategy is designed which can neatly restore the time-wise nonstationary and transient process into different condition slices, revealing similar process characteristics within the same condition slice. Process analytics can then be conducted for the new analysis unit. On the one hand, coarse-grained automatic condition-mode division is implemented with slow feature analysis to track the changing operation characteristics along condition dimension. On the other hand, fine-grained distribution evaluation is performed for each condition mode with Gaussian mixture model. Bayesian inference-based distance (BID) monitoring indices are defined which can clearly indicate the fault effects and distinguish different operation scenarios with meaningful physical interpretation. A case study on a real industrial process shows the feasibility of the proposed method which, thus, can be generalized to other continuous processes with typical wide-range nonstationary and transient characteristics along time direction.
Note to Practitioners
—Industrial processes in general have nonstationary characteristics which are ubiquitous in real world data, often reflected by a time-variant mean, a time-variant autocovariance, or both resulting from various factors. The focus of this study is to develop a universal analytics and monitoring method for wide-range nonstationary and transient continuous processes. Condition-driven concept takes the place of time-driven thought. For the first time, it is recognized that there are similar process characteristics within the same condition slice and changes in the process correlations may relate to its condition modes. Besides, the proposed method can provide enhanced physical interpretation for the monitoring results with concurrent analysis of the static and dynamic information which carry different information, analogous to the concepts of “position” and “velocity” in physics, respectively. The static information can tell the current operation condition, while the dynamic information can clarify whether the process status is switching between different steady states. It is noted that the condition-driven concept is universal and can be extended to other applications for industrial manufacturing applications.
Just-in-time learning (JITL) scheme has been employed as an efficient tool of online soft sensor. It requires current measured data with high accuracy. However, in real industrial environments, it is difficult to ensure that no disturbance is added to the measurement. To solve this problem, this article proposes an improved JITL scheme, which employs leverage calculation to trim the weight of variables and abate the affect of disturbances. On this basis, an online modeling and output prediction algorithm is further presented. The experiment on a typical nonlinear system shows the better robustness and accuracy of the presented algorithm in comparison with conventional JITL-based approaches. Moreover, an online fault detection strategy for nonlinear systems is proposed based on JITL and partial least squares (PLS), for the purpose of simplifying the parameter setting and reducing the computational load of conventional fault detection approaches for nonlinear systems. Four statistic indexes are designed, including conventional
$T^2$
and SPE for fault detection,
$T^2_h$
and
$T^2_t$
of two orthogonal decomposition input subspaces for fault birth subspace observation. A numerical nonlinear system and an industrial benchmark of Tennessee Eastman process are employed for fault detection experiments, testifying the effectiveness of the proposed strategy.
Most industrial systems frequently switch their operation modes due to various factors, such as the changing of raw materials, static parameter setpoints, and market demands. To guarantee stable and reliable operation of complex industrial processes under different operation modes, the monitoring strategy has to adapt different operation modes. In addition, different operation modes usually have some common patterns. To address these needs, this article proposes a structure dictionary learning-based method for multimode process monitoring. In order to validate the proposed approach, extensive experiments were conducted on a numerical simulation case, a continuous stirred tank heater (CSTH) process, and an industrial aluminum electrolysis process, in comparison with several state-of-the-art methods. The results show that the proposed method performs better than other conventional methods. Compared with conventional methods, the proposed approach overcomes the assumption that each operation mode of industrial processes should be modeled separately. Therefore, it can effectively detect faulty states. It is worth to mention that the proposed method can not only detect the faulty of the data but also classify the modes of normal data to obtain the operation conditions so as to adopt an appropriate control strategy.
Data-driven fault detection and root cause analysis methods have become popular in modern industrial production, as they can guarantee the safety and stability of the process operation if the process monitoring technology is implemented for fault detection and the root cause of the faults is analyzed in a timely manner. This approach is beneficial for maintaining and improving the quality of the upcoming batches. This paper proposes a framework for fault detection and root cause analysis to address the aforementioned issue, particularly for batch processes. First, a new algorithm called KECA-DISSIM, which combines the kernel entropy component analysis (KECA) and the dissimilarity analysis (DISSIM), is proposed to realize batch process monitoring. The KECA can effectively extract the nonlinear characteristics of a batch process based on nonlinear mapping. Subsequently, the dissimilarity indices between the normal reference datasets and testing datasets can be calculated. If the KECA-DISSIM detects that a testing dataset is a nonnormal batch, a novel root cause analysis named the comparative Granger causality analysis (CGC) is introduced to enable root cause analysis. The testing dataset is decomposed into a series of data slices via a moving window along the time domain. A series of causality values for each pair of variables is obtained by performing the Granger causality analysis on these time slices. Last, case studies based on a typical seven-variable nonlinear numerical process and a benchmark fed-batch penicillin fermentation process are performed to illustrate the practicality and effectiveness of the proposed framework.
In this paper, a novel supervised nonlinear process monitoring method named comprehensive kernel principal component regression (C-KPCR) is proposed to monitor the quality-related/unrelated additive/multiplicative faults. Firstly, mutual information is used to classify the process variables into quality-related part and quality-unrelated part. Secondly, the original variables matrix and the variables variance matrix are constructed and the data is mapped into high-dimensional feature space to deal with the nonlinear problem. Then the quality-related additive and multiplicative faults can be detected based on the regression model using original variables matrix and variables variance matrix, respectively. Afterwards, the monitoring result of quality-unrelated fault is obtained through combining the quality-unrelated information in the regression model and the quality-unrelated process variables. Finally, the effectiveness of the proposed method is demonstrated by a numerical example and the Tennessee Eastman process.
The efficient mitigation of the detrimental effects of a fault in complex systems requires online fault diagnosis techniques that are able to identify the cause of an observable anomaly. However, an individual diagnosis model can only acquire a limited diagnostic effect and may be insufficient for a particular application. In this paper, a Bayesian network-based probabilistic ensemble learning (PEL-BN) strategy is proposed to address the aforementioned issue. First, an ensemble index is proposed to evaluate the candidate diagnosis models in a probabilistic manner so that the diagnosis models with better diagnosis performance can be selected. Then, based on the selected classifiers, the architecture of the Bayesian network can be constructed using the proposed three types of basic topologies. Finally, the advantages of different diagnosis models are integrated using the developed Bayesian network, and thus, the fault causes of the observable anomaly can be accurately inferred. In addition, the proposed method can effectively capture the mixed fault characteristics of multifaults (MFs) by integrating decisions derived from different diagnosis models. Hence, this method can also provide a feasible solution for diagnosing MFs in real industrial processes. A simulation process and a real industrial process are adopted to verify the performance of the proposed method, and the experimental results illustrate that the proposed PEL-BN strategy improves the diagnosis performance of single faults and is a feasible solution for MF diagnosis.
Note to Practitioners
—The focus of this paper is to develop a probabilistic ensemble learning strategy based on the Bayesian network (PEL-BN) to diagnose different kinds of faults in industrial processes. The PEL-BN strategy can automatically select the base classifiers to establish the architecture of the Bayesian network. In this way, the conclusions of these base classifiers can be effectively integrated to provide better diagnosis performance. In addition, the proposed method is also a feasible technique for diagnosing MFs resulted from the joint effects of multiple faults.
Concurrent monitoring schemes that achieve simultaneous process and quality-relevant monitoring have recently attracted much attention. In this paper we formulate a {\em supervised fault diagnosis} framework based on canonical correlation analysis (CCA) with regularization, which includes quality-relevant and quality-irrelevant fault diagnosis. Monitoring indices based on regularized concurrent CCA models are introduced to perform quality-relevant, potentially quality-relevant, and quality-irrelevant monitoring. Additionally, contribution plots and generalized reconstruction-based contribution methods are developed, along with their implications for the diagnosis based on the various monitoring indices. Finally, the Tennessee Eastman process is used to illustrate the supervised monitoring and diagnosis of quality-relevant and quality-irrelevant disturbances, and the 15 known disturbances are classified into two categories based on whether they have an impact on product quality variables.
Gas component perception plays an important role of robot for environment detection. The reinforced nonlinear model with update-driven is proposed for gas component perception. When new data are collected, the update-driven strategy constructs two concatenations to modify the proposed model without using the old data, where two concatenations are the loading matrices of the old model concatenated to new collected data. Considering the nonlinear characteristics between the independent variables and the dependent variables, there are two types of the proposed method (TypeI and TypeII). For TypeI, partial least squares (PLS) is performed on the concatenations, and the inner linear function of PLS is replaced by the neural network, where the radial basis function neural network (RBFNN) and the back propagation neural network (BPNN) are, respectively, employed for TypeI (TypeI-RBFNN and TypeI-BPNN). For TypeII, the radial basis function network extends the independent variables of the concatenations, and PLS is performed on the concatenations to extract the nonlinear principle components, which are the inputs of two feedforward neural networks. The residuals error matrices of the concatenations are, respectively, used as the outputs of two feedforward neural networks. Two real experimental data sets, which are gas-fired plant data set and coal-fired plant data set, are used for estimating the proposed method. The experimental results show that the proposed method can realize gas component perception and TypeI-RBFNN of the proposed method has a better prediction accuracy for different components.
The prediction accuracy of the traditional kernel with data-driven regression methods strongly depends on the appropriate selection of the kernel function and aims at solving the nonlinearity of the input space. In this paper, a self-learning kernel regression model is proposed. A special kernel space from the measured data is learned and designed, so that combined with dimension reductions on the input variables, the regression behavior between the projected input variables and the output variable is found. The model is posed as a semidefinite programming problem with the objective function to find the maximum variance between the learned manifolds. The kernel is data dependent and can be generated online whenever a new data point is available. The effectiveness of the proposed algorithm is demonstrated through the case studies on a simple nonlinear system and a real semiconductor process. IEEE
In data-driven state estimation and process monitoring, the correctness of results mainly rely on the accuracy of measurement. Actually, noises, outliers and measured errors always exist in real industrial systems. Just-in-time learning (JITL) is an useful on-line learning method and can be applied for data-based state estimation. Due to the reality of inaccurate measurement, an improved JITL method with strengthen robustness is necessary to be studied. In this paper, a robust version of just-in-time learning strategy is proposed. It is inspired from the leverage weight. By calculating the leverage impact, the outliers in high leverage cases are treated to reduce their weight and affect less on output prediction. A typical nonlinear system experiment is employed to prove the robust and veracity of the proposed strategy. Finally, the robust JITL is implemented for fault detection on a three-tank system to verify its applicability.
The practitioners are concerned with strip-thickness relevant faults of steel-making cold-rolling continuous annealing process (CAP) which is a typical dynamic nonlinear process. In this paper, a novel data-driven dynamic concurrent kernel canonical correlation analysis (DCKCCA) approach is proposed for the diagnosis of the CAP strip thickness relevant faults. First, a DCKCCA algorithm is proposed to capture dynamic nonlinear correlations between strip thickness and process variables. Strip thickness specific variations, process-specific variations, and thickness-process covariations are monitored respectively. Secondly, a multi-block extension of DCKCCA is designed to compute the contributions according to block partition of lagged variables, in order to help localize faults relevant to abnormal strip thickness. Finally, the proposed methods are illustrated by the application to a real continuous annealing process.
Projection to latent structures (PLS) model has been widely used in quality-related process monitoring, as it can establish a mapping relationship between process variables and quality index variables. To enhance the adaptivity of PLS, kernel PLS (KPLS) as an advanced version has been proposed for nonlinear processes. In this paper, we discuss a new total kernel PLS (T-KPLS) for nonlinear quality-related process monitoring. The new model divides the input spaces into four parts instead of two parts in KPLS, where an individual subspace is responsible in predicting quality output, and two parts are utilized for monitoring the quality-related variations. In addition, fault detection policy is developed based on the T-KPLS model, which is more well suited for nonlinear quality-related process monitoring. In the case study, a nonlinear numerical case, the typical Tennessee Eastman Process (TEP) and a real industrial hot strip mill process (HSMP) are employed to access the utility of the present scheme.
This paper summarizes recent results on applying the method of par-tial least squares (PLS) in a reproducing kernel Hilbert space (RKHS). A previously proposed nonlinear kernel-based PLS regression model has proven to be competitive with other regularized regression methods in RKHS. In this paper the use of kernel PLS for discrimination is discussed. A new methodology for classification is then proposed. This is based on kernel PLS dimensionality reduction of the original data space followed by a support vector classifier. Good results using this method on a two-class classification problem are reported here.
A family of regularized least squares regression models in a reproducing kernel Hilbert space is extended by the kernel Partial Least Squares (PLS) regression model. Similar to Principal Components Regression (PCR), PLS is a method based on the projection of input (explanatory) varibles to the latent variables (components). However, in contrast to PCR, PLS creates the components by modeling the relationship between input and output variables while maintaining most of the information in the input variables. PLS is useful in situations where the number of explanatory variables exceeds the number of observations and/or a high level of multicollinearity among those variables is assumed. Motivated by this fact we will provide a kernel PLS algorithm for construction of nonlinear regression models in possibly high-dimensional feature spaces. We give the theoretical description of the kernel PLS algorithm and we experimentally compare the algorithm with the existing kernel PCR and kernel ridge regression techniques. We will demonstrate that on the data sets employed kernel PLS achieves the same results as kernel PCR but uses significantly fewer, qualitatively different components.
This paper discusses the embedding of neural networks into the framework of the PLS (partial least squares) modeling method resulting in a neural net PLS modeling approach. By using the universal approximation property of neural networks, the PLS modeling method is genealized to a nonlinear framework. The resulting model uses neural networks to capture the nonlinearity and keeps the PLS projection to attain robust generalization property. In this paper, the standard PLS modeling method is briefly reviewed. Then a neural net PLS (NNPLS) modeling approach is proposed which incorporates feedforward networks into the PLS modeling. A multi-input-multi-output nonlinear modeling task is decomposed into linear outer relations and simple nonlinear inner relations which are performed by a number of single-input-single-output networks. Since only a small size network is trained at one time, the over-parametrized problem of the direct neural network approach is circumvented even when the training data are very sparse. A conjugate gradient learning method is employed to train the network. It is shown that, by analysing the NNPLS algorithm, the global NNPLS model is equivalent to a multilayer feedforward network. Finally, applications of the proposed NNPLS method are presented with comparison to the standard linear PLS method and the direct neural network approach. The proposed neural net PLS method gives better prediction results than the PLS modeling method and the direct neural network approach.
In this paper, a data-driven multiblock concurrent projection to latent structures (CPLS) method is proposed for monitoring large-scale manufacturing lines, particularly for cold rolling continuous annealing processes (CAPs) fault diagnosis. The proposed method provides decentralized process monitoring and helps localize faults in both input variables and output variables concurrently. First, the CPLS-based process monitoring method is briefly reviewed. Second, a multiblock CPLS algorithm, which incorporates process block partition, is proposed to diagnose faults relevant to process inputs or outputs with a decentralized structure. For the CAP line application, tension-specific variations, roll-specific variations, and tension–roll covariations are analyzed in each partitioned block. Furthermore, within the roll-specific subspace of an abnormal block, a delay-alignment scheme based on strip transportation delay is proposed to diagnose defective processing materials.
In this paper, the use of multiple variable spaces is proposed for monitoring modern industrial processes where data for a large number of process variables may be collected from different sources to reveal different characteristics. The easiest method of modeling a process is to treat all variables in a single data space, but then the information inherent in different types of variables would be mixed together and there would be no local view of each variable space. An extended algorithm based on the concept of total projection to latent structures, which we call multispace T-PLS (MsT-PLS), is thus developed to treat variables in multiple data spaces. Multiple variable spaces that are separated from the measurement space are composed of different sets of process variables measured at the same time and responsible for the same response data. Using the proposed algorithm, the relationships among multiple variable spaces are studied under the supervision of quality characteristics. Thus, comprehensive information decomposition is obtained in each variable space, which can be separated into four systematic subspaces in response to the cross-space common and specific process variability and one final residual subspace. The theoretical support for MsT-PLS is analyzed in detail and its statistical characteristics are compared with those of single-space T-PLS (SsT-PLS) algorithm. A process monitoring strategy is developed based on the MsT-PLS subspace decomposition result and applied to the Tennessee Eastman process for illustration purposes.
Process monitoring and fault diagnosis of the continuous annealing process lines (CAPLs) have been a primary concern in industry. Stable operation of the line is essential to final product quality and continuous processing of the upstream and downstream materials. In this paper, a multilevel principal component analysis (MLPCA)-based fault diagnosis method is proposed to provide meaningful monitoring of the underlying process and help diagnose faults. First, multiblock consensus principal component analysis (CPCA) is extended to MLPCA to model the large scale continuous annealing process. Secondly, a decentralized fault diagnosis approach is designed based on the proposed MLPCA algorithm. Finally, experiment results on an industrial CAPL are obtained to demonstrate the effectiveness of the proposed method.
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
Feature extraction and dimensionality reduction are important tasks in many
fields of science dealing with signal processing and analysis. The relevance of
these techniques is increasing as current sensory devices are developed with
ever higher resolution, and problems involving multimodal data sources become
more common. A plethora of feature extraction methods are available in the
literature collectively grouped under the field of Multivariate Analysis (MVA).
This paper provides a uniform treatment of several methods: Principal Component
Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis
(CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions
derived by means of the theory of reproducing kernel Hilbert spaces. We also
review their connections to other methods for classification and statistical
dependence estimation, and introduce some recent developments to deal with the
extreme cases of large-scale and low-sized problems. To illustrate the wide
applicability of these methods in both classification and regression problems,
we analyze their performance in a benchmark of publicly available data sets,
and pay special attention to specific real applications involving audio
processing for music genre prediction and hyperspectral satellite images for
Earth and climate monitoring.
This paper provides a state-of-the-art review of the methods and applications of data-driven fault detection and diagnosis that have been developed over the last two decades. The scope of the problem is described with reference to the scale and complexity of industrial process operations, where multi-level hierarchical optimization and control are necessary for efficient operation, but are also prone to hard failure and soft operational faults that lead to economic losses. Commonly used multivariate statistical tools are introduced to characterize normal variations and detect abnormal changes. Further, diagnosis methods are surveyed and analyzed, with fault detectability and fault identifiability for rigorous analysis. Challenges, opportunities, and extensions are summarized with the intent to draw attention from the systems and control community and the process control community.
In this paper, a statistical approach to fault detection and isolation (FDI) of robot manipulators is presented. It is based on a statistical method called partial least squares (PLS) and on the inverse dynamic model of a robot. PLS is a well-established linear technique in process control for identifying and monitoring industrial plants. Since a robot inverse dynamics can be represented as a linear static model in the dynamical parameters, it is possible to use algorithms and confidence regions developed in statistical decision theory. This approach has several advantages with respect to standard FDI modules: It is strictly related to the algorithm used for identifying the dynamical parameters, it does not need to solve at run time a set of nonlinear differential equations, and the design of a nonlinear observer is not required. This method has been tested on a PUMA 560 simulator, and results of the simulations are discussed.
In this paper, new monitoring approach, hierarchical kernel partial least squares (HKPLS), is proposed for the batch processes. The advantages of HKPLS are: (1) HKPLS gives more nonlinear information compared to hierarchical partial least squares (HPLS) and multi-way PLS (MPLS) and (2) a new batch process monitoring using HKPLS does not need to estimate or fill in the unknown part of the process variable trajectory deviation from the current time until the end. The proposed method is applied to the penicillin process and continuous annealing process and is compared with MPLS and HPLS monitoring results. Applications of the proposed approach indicate that HKPLS effectively capture the nonlinearities in the process variables and show superior fault detectability.
Frank, I.E., 1990. A nonlinear PLS model. Chemometrics and Intelligent Laboratory Systems, 8: 109–119.A nonlinear extension of the PLS (partial least squares regression) method is introduced. The algorithm connects the predictor and response latent variables by a smooth but otherwise unrestricted nonlinear function. Similarities and differences between the linear and nonlinear PLS models are discussed. The performance of the new nonlinear PLS method is illustrated on three chemical data sets with different covariance structures.
This paper describes a model of an industrial chemical process for the purpose of developing, studying and evaluating process control technology. This process is well suited for a wide variety of studies including both plant-wide control and multivariable control problems. It consists of a reactor/ separator/recycle arrangement involving two simultaneous gas—liquid exothermic reactions of the following form:A(g) + C(g) + D(g) → G(liq), Product 1,A(g) + C(g) + E(g) → H(liq), Product 2. Two additional byproduct reactions also occur. The process has 12 valves available for manipulation and 41 measurements available for monitoring or control.The process equipment, operating objectives, process control objectives and process disturbances are described. A set of FORTRAN subroutines which simulate the process are available upon request.The chemical process model presented here is a challenging problem for a wide variety of process control technology studies. Even though this process has only a few unit operations, it is much more complex than it appears on first examination. We hope that this problem will be useful in the development of the process control field. We are also interested in hearing about applications of the problem.
Partial least squares or projection to latent structures (PLS) has been used in multivariate statistical process monitoring similar to principal component analysis. Standard PLS often requires many components or latent variables (LVs), which contain variations orthogonal to Y and useless for predicting Y. Further, the X-residual of PLS usually has quite large variations, thus is not proper to monitor with the Q-statistic. To reduce false alarm and missing alarm rates of faults related to Y, a total projection to latent structures (T-PLS) algorithm is proposed in this article. The new structure divides the X-space into four parts instead of two parts in standard PLS. The properties of T-PLS are studied in detail, including its relationship to the orthogonal PLS. Further study shows the space decomposition on X-space induced by T-PLS. Fault detection policy is developed based on the T-PLS. Case studies on two simulation examples show the effectiveness of the T-PLS based fault detection methods. © 2009 American Institute of Chemical Engineers AIChE J, 2010
A generic preprocessing method for multivariate data, called orthogonal projections to latent structures (O-PLS), is described. O-PLS removes variation from X (descriptor variables) that is not correlated to Y (property variables, e.g. yield, cost or toxicity). In mathematical terms this is equivalent to removing systematic variation in X that is orthogonal to Y. In an earlier paper, Wold et al. (Chemometrics Intell. Lab. Syst. 1998; 44: 175–185) described orthogonal signal correction (OSC). In this paper a method with the same objective but with different means is described. The proposed O-PLS method analyzes the variation explained in each PLS component. The non-correlated systematic variation in X is removed, making interpretation of the resulting PLS model easier and with the additional benefit that the non-correlated variation itself can be analyzed further. As an example, near-infrared (NIR) reflectance spectra of wood chips were analyzed. Applying O-PLS resulted in reduced model complexity with preserved prediction ability, effective removal of non-correlated variation in X and, not least, improved interpretational ability of both correlated and non-correlated variation in the NIR spectra. Copyright © 2002 John Wiley & Sons, Ltd.
Projection to latent structures or partial least squares (PLS) produces output-supervised decomposition on input X, while principal component analysis (PCA) produces unsupervised decomposition of input X. In this paper, the effect of output Y on the X-space decomposition in PLS is analyzed and geometric properties of the PLS structure are revealed. Several PLS algorithms are compared in a geometric way for the purpose of process monitoring. A numerical example and a case study are given to illustrate the analysis results.
PLS-regression (PLSR) is the PLS approach in its simplest, and in chemistry and technology, most used form (two-block predictive PLS). PLSR is a method for relating two data matrices, X and Y, by a linear multivariate model, but goes beyond traditional regression in that it models also the structure of X and Y. PLSR derives its usefulness from its ability to analyze data with many, noisy, collinear, and even incomplete variables in both X and Y. PLSR has the desirable property that the precision of the model parameters improves with the increasing number of relevant variables and observations.This article reviews PLSR as it has developed to become a standard tool in chemometrics and used in chemistry and engineering. The underlying model and its assumptions are discussed, and commonly used diagnostics are reviewed together with the interpretation of resulting parameters.Two examples are used as illustrations: First, a Quantitative Structure–Activity Relationship (QSAR)/Quantitative Structure–Property Relationship (QSPR) data set of peptides is used to outline how to develop, interpret and refine a PLSR model. Second, a data set from the manufacturing of recycled paper is analyzed to illustrate time series modelling of process data by means of PLSR and time-lagged X-variables.
Kernel principal component analysis (kernel-PCA) is an elegant nonlinear extension of one of the mostly used data analysis and dimensionality reduction techniques, the principal component analysis. In this paper, we propose an online algorithm for kernel-PCA. To this end, we examine a kernel-based version of Oja's rule, initially put forward to extract a linear principal axe. As with most kernel-based machines, the model order equals the number of available observations. To provide an online scheme, we propose to control the model order. We discuss theoretical results, such as an upper bound on the error of approximating the principal functions with the reduced-order model. We derive a recursive algorithm to discover the first principal axe, and extend it to multiple axes. Experimental results demonstrate the effectiveness of the proposed approach, both on synthetic dataset and on images of handwritten digits, with comparison to classical kernel-PCA and iterative kernel-PCA.