Faulty Variables Research Articles

Fault Identification of Nonlinear Processes

In this paper, a new kernel partial least-squares (KPLS)-based fault identification method is proposed. Although KPLS is superior to PLS in fault detecting of nonlinear processes, the fault identification methods for KPLS are limited. In this paper, the contributions are (1) The relationship between the input and the output variables are considered and each variable’s contribution is measured using the gradient of kernel function. In the existing work, only input variables are concerned; (2) The complex computation is avoided since the new computation method of the partial derivative in the kernel matrix is introduced. The proposed method has two advantages: the ability to identify faulty variables in nonlinear process and guarantee correct diagnosis of simple sensor faults, compared with PLS using conventional contribution plots. In the end, case study on a numerical example and the electro-fused magnesia furnace (EFMF) is employed to illustrate the effectiveness of the proposed method, where the compari...

Penalized Reconstruction-Based Multivariate Contribution Analysis for Fault Isolation

Contribution analysis in multivariate statistical process monitoring (MSPM) identifies the most responsible variables to the detected process fault. In multivariate contribution analysis, the main challenge of fault isolation is to determine the appropriate variables to be analyzed, and this usually results in a combinatorial optimization problem. Reconstruction-based multivariate contribution analysis (RBMCA) is a generic framework to solve this problem. This paper derives a sufficient condition for the isolatability of faulty variables when using RBMCA. In addition, a penalized RBMCA (PRBMCA) framework is developed to enhance the effectiveness and efficiency of fault isolation, especially for process faults with a small magnitude. In contrast to the original RBMCA, this penalized solution includes two steps. L1-penalized reconstruction is used in the first step to obtain a more compact set of faulty variables. Then, the original RBMCA with a branch and bound algorithm is implemented to further narrow down the faulty variables. The PRBMCA framework is a generic formulation in that it is applicable to various MSPM models. The effectiveness and computational efficiency of the proposed methodology is demonstrated through a numerical example and a benchmark problem of the Tennessee Eastman process.

Multiway independent component analysis mixture model and mutual information based fault detection and diagnosis approach of multiphase batch processes

Batch process monitoring is a challenging task, because conventional methods are not well suited to handle the inherent multiphase operation. In this study, a novel multiway independent component analysis (MICA) mixture model and mutual information based fault detection and diagnosis approach is proposed. The multiple operating phases in batch processes are characterized by non‐Gaussian independent component mixture models. Then, the posterior probability of the monitored sample is maximized to identify the operating phase that the sample belongs to, and, thus, the localized MICA model is developed for process fault detection. Moreover, the detected faulty samples are projected onto the residual subspace, and the mutual information based non‐Gaussian contribution index is established to evaluate the statistical dependency between the projection and the measurement along each process variable. Such contribution index is used to diagnose the major faulty variables responsible for process abnormalities. The effectiveness of the proposed approach is demonstrated using the fed‐batch penicillin fermentation process, and the results are compared to those of the multiway principal component analysis mixture model and regular MICA method. The case study demonstrates that the proposed approach is able to detect the abnormal events over different phases as well as diagnose the faulty variables with high accuracy. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2761–2779, 2013

A novel dynamic bayesian network‐based networked process monitoring approach for fault detection, propagation identification, and root cause diagnosis

A novel networked process monitoring, fault propagation identification, and root cause diagnosis approach is developed in this study. First, process network structure is determined from prior process knowledge and analysis. The network model parameters including the conditional probability density functions of different nodes are then estimated from process operating data to characterize the causal relationships among the monitored variables. Subsequently, the Bayesian inference‐based abnormality likelihood index is proposed to detect abnormal events in chemical processes. After the process fault is detected, the novel dynamic Bayesian probability and contribution indices are further developed from the transitional probabilities of monitored variables to identify the major faulty effect variables with significant upsets. With the dynamic Bayesian contribution index, the statistical inference rules are, thus, designed to search for the fault propagation pathways from the downstream backwards to the upstream process. In this way, the ending nodes in the identified propagation pathways can be captured as the root cause variables of process faults. Meanwhile, the identified fault propagation sequence provides an in‐depth understanding as to the interactive effects of faults throughout the processes. The proposed approach is demonstrated using the illustrative continuous stirred tank reactor system and the Tennessee Eastman chemical process with the fault propagation identification results compared against those of the transfer entropy‐based monitoring method. The results show that the novel networked process monitoring and diagnosis approach can accurately detect abnormal events, identify the fault propagation pathways, and diagnose the root cause variables. © 2013 American Institute of Chemical EngineersAIChE J, 59: 2348–2365, 2013

A new fault diagnosis method of multimode processes using Bayesian inference based Gaussian mixture contribution decomposition

This paper presents a novel Bayesian inference based Gaussian mixture contribution (BIGMC) method to isolate and diagnose the faulty variables in chemical processes with multiple operating modes. The statistical confidence intervals of traditional principal component analysis (PCA) based T2 and SPE diagnostics rely upon the assumption that the operating data follow a multivariate Gaussian distribution approximately and therefore may not be able to determine the faulty variables in multimode non-Gaussian processes accurately. As an alternative solution, the proposed BIGMC method first identifies the multiple Gaussian modes corresponding to different operating conditions and then integrates the Mahalanobis distance based variable contributions across all the Gaussian clusters through Bayesian inference strategy. The derived BIGMC index is of probabilistic feature and includes all operation scenarios with posterior probabilities as weighting factors. The Tennessee Eastman process (TEP) is used to demonstrate the utility of the proposed BIGMC method for fault diagnosis of multimode processes. The comparison of the single-PCA and multi-PCA based contribution approaches shows that the BIGMC method can effectively identify the leading faulty variables with superior diagnosis capability.

Fault diagnosis using contribution plots without smearing effect on non-faulty variables

Isolating faulty variables to provide additional information about a process fault is a crucial step in the diagnosis of a process fault. There are two types of data-driven approaches for isolating faulty variables. One is the supervised method, which requires the datasets of known faults to define a fault subspace or an abnormal operating region for each faulty mode. This type of approach is not practical for an industrial process, since the known event lists might not exist for some industrial processes. The counterpart is to isolate faulty variables without a priori knowledge, using, for example, a contribution plot, which is a popular tool in the unsupervised category. However, it is well known that this approach suffers from the smearing effect, which may mislead the faulty variables of the detected faults. In the presented work, a contribution plot without the smearing effect on non-faulty variables was derived based on missing data analysis. Two benchmark examples, the continuous stirred tank reactor (CSTR) and the Tennessee Eastman (TE) process, were provided to compare the fault isolation performances of the alternatives using the missing data approach.

Reconstruction-based multivariate contribution analysis for fault isolation: A branch and bound approach

Identification of faulty variables is an important component of multivariate statistical process monitoring (MSPM); it provides crucial information for further analysis of the root cause of the detected fault. The main challenge is the large number of combinations of process variables under consideration, usually resulting in a combinatorial optimization problem. This paper develops a generic reconstruction based multivariate contribution analysis (RBMCA) framework to identify the variables that are the most responsible for the fault. A branch and bound (BAB) algorithm is proposed to efficiently solve the combinatorial optimization problem. The formulation of the RBMCA does not depend on a specific model, which allows it to be applicable to any MSPM model. We demonstrate the application of the RBMCA to a specific model: the mixture of probabilistic principal component analysis (PPCA mixture) model. Finally, we illustrate the effectiveness and computational efficiency of the proposed methodology through a numerical example and the benchmark simulation of the Tennessee Eastman process.

Fault diagnosis of continuous annealing processes using a reconstruction-based method

The continuous annealing process line (CAPL) has complex process characteristics, such as strong correlation of a large number of process variables and interconnected multi-subsystems and multiple operation zones. Practitioners are concerned with typical process faults, such as strip-break and roll-slippage, whose effects are often confined in a specific zone. Considering the large-scale process characteristics and fault characteristics, a multi-block fault diagnosis method is proposed. A novel reconstruction-based block contribution (RBBC) is first proposed in order to diagnose the faulty block. The reconstruction-based variable contribution (RBVC) within a block is also proposed to determine the faulty variables. The proposed RBBC–RBVC hierarchical scheme is applied successfully to a real CAPL on two fault cases. A finite state machine is utilized to diagnose strip-break and reconstructed combined index is studied to diagnose roll-slippage.

A nonlinear kernel Gaussian mixture model based inferential monitoring approach for fault detection and diagnosis of chemical processes

A nonlinear kernel Gaussian mixture model (NKGMM) based inferential monitoring method is proposed in this article for chemical process fault detection and diagnosis. Aimed at the multimode non-Gaussian process with within-mode nonlinearity, the developed NKGMM approach projects the operating data from the raw measurement space into the high-dimensional kernel feature space. Thus the Gaussian mixture model can be estimated in the feature space with each component satisfying multivariate Gaussianity. As a comparison, the conventional independent component analysis (ICA) searches for the non-Gaussian subspace with maximized negentropy, which is not equivalent to the multi-Gaussianity in multimode process. The regular Gaussian mixture model (GMM) method, on the other hand, assumes the Gaussianity of each cluster in the original data space and thus cannot effectively handle the within-mode nonlinearity. With the extracted kernel Gaussian components, the geometric distance driven inferential index is further derived to monitor the process operation and detect the faulty events. Moreover, the kernel Gaussian mixture based inferential index is decomposed into variable contributions for fault diagnosis. For the simulated multimode wastewater treatment process, the proposed NKGMM approach outperforms the ICA and GMM methods in early detection of process faults, minimization of false alarms, and isolation of faulty variables of nonlinear and non-Gaussian multimode processes.

Improved algorithm for calculating contributions to D-statistic

D-statistic contribution analysis has been frequently used in practice for fault diagnosis. Existing algorithms for computing contributions to D-statistic tend to distribute cross-term contribution equally between two correlated variables. This leads to increased variance in contribution estimation and hence poor separability of faulty and normal variables. A new method for contribution calculation to D-statistic is proposed here which introduces a weighting scheme capable of distinguishing the contributions of two correlated variables. Simulation examples show that the proposed approach achieves improved resolution for distinguishing faulty and normal conditions.

Data‐driven fault detection and isolation for multimode processes

AbstractContribution plots of the monitored statistics, Q and T2, are investigated to locate faulty variables when the statistics are out of their control limits. It is a popular method for fault isolation; however, it is well known that the smearing out of contributions leads to misdiagnose the faulty variables. Alternatively, the reconstruction‐based contribution approach is claimed to guarantee correct diagnosis. It has been examined in this paper that the approach fails to locate faulty variables when encountering multiple sensor faults. A fault isolation chart on principal component subspace is provided to locate faulty variables for a process with multiple operating regions. The results of an industrial application show that the proposed approach locates faulty variables precisely, whereas the root causes of the abnormalities have been successfully identified. Copyright © 2011 Curtin University of Technology and John Wiley & Sons, Ltd.

Fault Diagnosis of Continuous Annealing Processes Using Reconstruction-based Block Contribution

AbstractContinuous annealing process line (CAPL) has complex process characteristics, such as strong correlation of large number of process variables, and the coexistence of multi- subsystems and multi-operation zones. Practitioners are concerned with process faults, such as strip-break fault and roll slippage fault, whose effects often confine in a specific zone. Considering the process characteristics and fault characteristics, a fault diagnosis method is proposed. Reconstruction-based variable contribution (RBVC) is extended to reconstruction-based block contribution (RBBC) for principal component analysis (PCA) method in order to find the faulty block, and RBVC is used to determine the faulty variable. Simulation results show the effectiveness of the proposed methods, and it is applied successfully to a practical CAPL.

A branch and bound method for isolation of faulty variables through missing variable analysis

Fault detection and diagnosis is a critical approach to ensure safe and efficient operation of manufacturing and chemical processing plants. Although multivariate statistical process monitoring has received considerable attention, investigation into the diagnosis of the source or cause of the detected process fault has been relatively limited. This is partially due to the difficulty in isolating multiple variables, which jointly contribute to the occurrence of fault, through conventional contribution analysis. In this work, a method based on probabilistic principal component analysis is proposed for fault isolation. Furthermore, a branch and bound method is developed to handle the combinatorial nature of problem involving finding the contributing variables, which are most likely to be responsible for the occurrence of fault. The efficiency of the method proposed is shown through benchmark examples, such as Tennessee Eastman process, and randomly generated cases.

Operational Performance Assessment and Fault Isolation for Multimode Processes

Industrial processes are usually operated under normal conditions during daily production. For the purpose of improving product quality and productivity, the process engineers need to realize where the process variations come from. In this paper, according to the geometric shapes of clusters on the principal component (PC) subspace, the major variations along variable directions can be identified using a Pareto diagram and the 80/20 rule. In addition, fault isolation charts on the PC subspace are proposed to locate faulty variables when detecting abnormal events. A simulation example is demonstrated where the proposed approach is capable of locating the faulty variables without a smearing effect even in the case of multiple sensor faults. An industrial application of assessing operational performance and isolating faulty variables is presented. The results show that the faulty variables are highly correlated to the variables dominating the data variations in the normal operations, i.e., process-related abnormalities can be prevented by reducing the process variations during normal operations.

Fault Detection and Isolation for Multimode Processes with Recursive Principal Component Analysis

Contribution plots of the monitored statistics, Q and T2, are investigated to locate faulty variables when the statistics are out of their control limits. It is a popular method for fault isolation; however, it is well known that the smearing out of contributions leads to misdiagnose the faulty variables. Alternatively, the reconstruction-based contribution approach is claimed to guarantee correct diagnosis. It has been examined in this paper that the approach fails to precisely locate faulty variables when encountering multiple sensor faults. A fault isolation chart on principal component (PC) subspace is provided to locate faulty variables for a process with multiple operating regions. The results of the quadruple-tank process simulation show the proposed approach successfully locate faulty variables in a case of multiple sensor faults, as long as the process behavior can be depicted by the scores on the PC subspace.

Nonstationary fault detection and diagnosis for multimode processes

AbstractFault isolation based on data‐driven approaches usually assume the abnormal event data will be formed into a new operating region, measuring the differences between normal and faulty states to identify the faulty variables. In practice, operators intervene in processes when they are aware of abnormalities occurring. The process behavior is nonstationary, whereas the operators are trying to bring it back to normal states. Therefore, the faulty variables have to be located in the first place when the process leaves its normal operating regions. For an industrial process, multiple normal operations are common. On the basis of the assumption that the operating data follow a Gaussian distribution within an operating region, the Gaussian mixture model is employed to extract a series of operating modes from the historical process data. The local statistic T2 and its normalized contribution chart have been derived for detecting abnormalities early and isolating faulty variables in this article. © 2009 American Institute of Chemical Engineers AIChE J, 2010

Total PLS Based Contribution Plots for Fault Diagnosis

摘要: 多变量统计过程监控对于复杂工业过程是一种有效的故障检测和诊断技术. 最小二乘(或称潜空间投影)模型是多变量统计过程监控中常用的一种投影模型, 能够同时对过程数据和质量数据进行建模. 讨论了一种新的基于全潜空间投影模型的故障诊断技术. 全潜空间投影模型中有4个检测统计量. 提出了一种新的T2贡献图计算方法, 对于所有检测统计量, 得到了相应的贡献图算法. 为了确定一个变量是否发生了故障, 计算所有变量贡献图的控制限. 该技术可以将辨识到的故障变量分为与Y有关和与Y无关的两类. 基于Tennessee Eastman过程的案例研究表明了该技术的有效性. 关键词: 数据驱动 / 全潜空间投影 / 贡献图 / 故障诊断

High-Dimensional Process Monitoring and Fault Isolation via Variable Selection

Both process monitoring and fault isolation are important and challenging tasks for quality control and improvement in high-dimensional processes. Under a practical assumption that not all variables would shift simultaneously, this paper proposes a variable-selection-based multivariate statistical process control (SPC) procedure for process monitoring and fault diagnosis. A forward-selection algorithm is first utilized to screen out potential out-of-control variables; a multivariate control chart is then set up to monitor suspicious variables. Therefore, detection of faulty conditions and isolation of faulty variables can be achieved in one step. Both simulation studies and a real example have shown the effectiveness of the proposed procedure.

Total PLS Based Contribution Plots for Fault Diagnosis

Multivariate statistical process monitoring (MSPM) is an efficient data-driven fault detection and diagnosis approach for complex industrial processes. Partial least squares or projection to latent structures (PLS) is one of the latent projection structures used in MSPM, which uses process data X and quality data Y together. In this paper, we discuss a new fault diagnosis approach based on total projection to latent structures (T-PLS). Four kinds of monitoring statistics are used in T-PLS, and a new definition of variable contributions to T 2 of PLS is proposed. Then, definitions of variable contributions to all statistics are derived to identify the faults. Control limits for contribution plots are calculated to identify whether a variable is in abnormal situation or not. Further, the proposed method separates the identified variables into faulty variables related to Y and unrelated to Y more clearly than conventional method. A case study on Tennessee Eastman process (TEP) indicates the efficiency of the proposed approach.

Fault Detection and Identification Using Modified Bayesian Classification on PCA Subspace

A novel process monitoring method based on modified Bayesian classification on PCA subspace is proposed. Fault detection and identification are the major steps to diagnose root causes of a process fault. However, before the faulty variables from the abnormal operations are identified, the different operating states need to be clustered from the historical data. The proposed approach modifies the Bayesian classification method to cluster data into groups. Therefore, a new fault identification index is derived based on cluster center and covariance. An industrial compressor process is used to demonstrate the effectiveness of the proposed approach. In the example, process-insight-based variables were monitored along with the measured variables. The capability of fault diagnosis has been improved, since the fault identification indices are directly related to the variables with process characteristics.