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Manifold embedding stationary subspace analysis for nonstationary process monitoring with industrial applications
Driven by policy incentives and economic pressures, energy-intensive industries are increasingly focusing on energy cost reductions amid the rapid adoption of renewable energy. However, the existing studies often isolate photovoltaic-energy storage system (PV-ESS) configurations from detailed load scheduling, limiting industrial park energy management. To address this, we propose a two-layer cooperative optimization approach (TLCOA). The upper layer employs a genetic algorithm (GA) to optimize the PV capacity and energy storage sizing through natural selection and crossover operations, while the lower layer utilizes mixed integer linear programming (MILP) to derive cost-minimized scheduling strategies under time-of-use tariffs. Multi-process parallel computing accelerates the fitness evaluations, resolving high-dimensional industrial data challenges. Multi-process parallel computing is introduced to accelerate fitness evaluations, effectively addressing the challenges posed by high-dimensional industrial data. Validated with real power market data, the TLCOA demonstrated rapid adaptation to load fluctuations while achieving a 23.68% improvement in computational efficiency, 1.73% reduction in investment costs, 7.55% decrease in power purchase costs, and 8.79% enhancement in renewable energy utilization compared to traditional methods. This integrated framework enables cost-effective PV-ESS deployment and adaptive energy management in industrial facilities, offering actionable insights for renewable integration and scalable energy optimization.
Industrial data often consist of continuous variables (CVs) and binary variables (BVs), both of which provide crucial information about process operating conditions. Due to the coupling between industrial systems or equipment, these hybrid variables are usually high-dimensional and highly correlated. However, existing methods generally model hybrid variables directly in the observation space and assume independence between the variables to overcome the curse of dimensionality. Thus, they are ineffective at capturing dependencies among hybrid variables, and the effectiveness of process monitoring will be compromised. To overcome the limitations, this study proposes to seek a unified subspace for hybrid variables using the probabilistic latent variable (LV) model. By introducing a low-dimensional continuous LV, the proposed method can avoid the curse of dimensionality while capturing the dependencies between hybrid variables. Nevertheless, the inference of LV is analytically intractable and thus time-consuming due to the heterogeneity of CVs and BVs. To accelerate offline learning and online inference procedures, this study originally derives an analytical Gaussian distribution to approximate the true posterior distribution of the LV, based on which an efficient expectation-maximization algorithm is developed for parameter estimation. The Gaussian approximation is simultaneously optimized with the latest parameters to achieve a high approximation accuracy. The LV is then estimated by the posterior mean of the Gaussian approximation. By mapping the heterogeneous variables into a unified subspace, the proposed method defines three monitoring statistics, which are physically interpretable and thoroughly evaluate the probability of hybrid variables being normal. The effectiveness of the proposed method in detecting anomalies in CVs and BVs is shown through a numerically simulated case and a real industrial case.
Broad learning system (BLS), a tri-layer feedforward neural network, has gained widespread recognition for its exceptional scalability and computational efficiency. However, BLS and its derivatives encounter several challenges: 1) overlooking the uncertainty introduced by numerous nonlinear random mappings; 2) failing to cope with the misalignment of model inputs with the output sampling rate; 3) lack of attention to nonstationary scenarios; and 4) absence of theoretical optimization for incremental learning. To overcome these obstacles, we propose a regression modeling and anomaly detection scheme rooted in a temporal kernel stationary BLS (TKS-BLS). We first create a nonlinear kernel broad representation (NKBR) extraction strategy, providing a robust nonlinear foundation for random feature mapping via kernel technology. Following this, we probe the mechanism of temporal matching between model inputs and outputs through a temporal alignment parameter, interpretable under a latent variable relationship. In the integration phase, we establish a Kullback–Leibler divergence objective function to facilitate the capture of stationary relationships within time-series data, in conjunction with the regression error. Subsequently, a double-loop parameter optimization algorithm and an independent incremental learning mechanism are put forth, both backed by comprehensive theoretical analyses. Our method’s superiority is thoroughly confirmed by experimental outcomes from extensive case studies across seven real ironmaking process datasets.
Aiming to solve the problems of the inaccurate dimension reduction of high-dimensional data and insufficient information utilization in traditional manufacturing process monitoring methods—in which mostly only the distance information of pairwise points is used as the similarity index for the data dimension reduction—this paper proposes a data-manifold-based monitoring method that combines the distance information and angle information of pairwise points. First, the intrinsic dimension of manufacturing process data is estimated by combining multiple geometric features on the data manifold. Second, considering the angle information and distance information in the neighborhood of process data, the method to construct local features of the data manifold is given; further, a fusion method of local features and global–local features of manifold data based on the eigendimension is proposed, which constructs the data dimension-reduction mapping matrix to improve the integrity of data information extraction. Then, the data index of process monitoring is given and employed to monitor the manufacturing process. Finally, Tennessee Eastman (TE) process simulation data were used to verify the effectiveness of the proposed method. The results show that compared with other methods, the anomaly detection rate of the proposed method was increased by more than 50%, while the false alarm rate was decreased by 21.4%, which proves that the method can significantly improve the efficiency of manufacturing process anomaly monitoring.
This study investigates nonstationary process monitoring under frequently varying modes, where new modes are allowed to emerge constantly. However, in current multimode process monitoring methods, generally, data are required from all possible modes and mode identification is realized by prior knowledge for multimode nonstationary processes. In contrast, recursive methods update a monitoring model based on the successive data. However, they forget the learned knowledge gracefully and fail to track drastic variations. Aimed at nonstationary data in each mode, this article proposes an adaptive cointegration analysis (CA) to distinguish real faults from normal variations, which updates a model once a normal sample is encountered and adapts to the gradual change in the cointegration relationship. Then, a modified recursive principal component analysis (RPCA) with continual learning ability is developed to deal with the remaining dynamic information, wherein elastic weight consolidation is adopted to consolidate the previously learned knowledge when a new mode appears. The preserved information is beneficial for establishing a more accurate model than traditional RPCA and avoiding drastic performance degradation for future similar modes. In addition, novel statistics are proposed with prior knowledge and thresholds are calculated by recursive kernel density estimation to enhance the performance. An in-depth comparison with recursive CA and recursive slow feature analysis is conducted to emphasize the superiority, in terms of the algorithm accuracy, memory properties, and computational complexity. Compared with state-of-the-art recursive algorithms, the effectiveness of the proposed method is shown by studying on a numerical case and a practical industrial system.
Nonstationary process monitoring is significant to ensure the safety and reliability of industrial processes. However, existing monitoring methods for nonstationary processes usually ignore process uncertainties, caused by random noises and unknown disturbances. Process uncertainties may degrade the monitoring performance for incipient faults, and result in over-fitting of model parameters. To address the problem of monitoring nonstationary industrial processes with uncertainty, a novel algorithm called probabilistic stationary subspace analysis (PSSA) is proposed in this paper. PSSA explicitly models process uncertainties, and distinguishes actual process variations from the uncertainty. The EM algorithm is used to estimate the parameters of PSSA, and the closed-form updates are derived in detail. Based on PSSA, two detection statistics are designed for process monitoring. At last, the effective performance of the proposed method is demonstrated by three case studies, including a numerical example, a continuous stirred tank reactor, and a real power plant.
Operation safety and efficiency are two main concerns in power plants. It is important to detect the anomalies in power plants, and further judge whether they affect key performance indicators (KPIs), such as the thermal efficiency. The two goals can be achieved by KPI-related nonstationary process monitoring. Although the thermal efficiency cannot be accurately measured online, it can be strongly characterized by some online measurable variables, including the exhaust gas temperature and oxygen content of flue gas. These critical variables closely related to the thermal efficiency are termed as output variables. Inspired from nonstationary common trends between input and output variables in thermal power plants, the output-relevant common trend analysis (OCTA) method is proposed to model the input-output relationship. In OCTA, input and output variables are decomposed into nonstationary common trends and stationary residuals, and the model parameters are estimated by solving an optimization problem. It is pointed out that OCTA is a generalized form of partial least squares (PLS). The superior monitoring performance of OCTA is illustrated by case studies on a real power plant in Zhejiang Provincial Energy Group of China. Compared with the other PLS-based recursive algorithms, OCTA can effectively detect the anomalies in power plants and accurately determine whether they have an impact on the thermal efficiency or not.
Robust process monitoring and reliable fault isolation in industrial processes usually encounter different challenges, including process nonlinearity and noise interference. In this brief, a novel method denoising autoencoder and elastic net (DAE-EN) is proposed to solve the aforementioned issues by effectively integrating DAE and EN. The DAE is first trained to robustly capture the nonlinear structure of the industrial data. Then, the encoder network is updated into a sparse model using EN, so that the key variables associated with each neuron can be selected. After that two statistics are developed based on the extracted systematic structure and the retained residual information. In addition, another statistic is also constructed by combining the aforementioned two statistics to provide an overall measurement for the process sample. In this way, a robust monitoring model can be constructed to monitor the abnormal status in industrial processes. After the fault is detected, the faulty neurons are identified by the sparse exponential discriminant analysis, so that the associated faulty variables along each faulty neuron can thus be isolated. Two real industrial processes are used to validate the performance of the proposed method. Experimental results show that the proposed method can effectively detect the abnormal samples in industrial processes and accurately isolate the faulty variables from the normal ones.
Early detection of incipient faults in industrial processes is increasingly becoming important, as these faults can slowly develop into serious abnormal events, an emergency situation, or even failure of critical equipment. Multivariate statistical process monitoring methods are currently established for abrupt fault detection. Among these, canonical variate analysis (CVA) was proven to be effective for dynamic process monitoring. However, the traditional CVA indices may not be sensitive enough for incipient faults. In this work, an extension of CVA, called the canonical variate dissimilarity analysis (CVDA), is proposed for process incipient fault detection in nonlinear dynamic processes under varying operating conditions. To handle non-Gaussian distributed data, kernel density estimation was used for computing detection limits. A CVA dissimilarity-based index has been demonstrated to outperform traditional CVA indices and other dissimilarity-based indices, namely DISSIM, RDTCSA, and GCCA, in terms of sensitivity when tested on slowly developing multiplicative and additive faults in a CSTR under closed-loop control and varying operating conditions.
Proper monitoring of quality-related variables in industrial processes is nowadays one of the main worldwide challenges with significant safety and efficiency implications. Variational Bayesian mixture of Canonical correlation analysis (VBMCCA)-based process monitoring method was proposed in this paper to predict and diagnose these hard-to-measure quality-related variables simultaneously. Use of Student's t-distribution, rather than Gaussian distribution, in the VBMCCA model makes the proposed process monitoring scheme insensitive to disturbances, measurement noises and model discrepancies. A sequential perturbation method together with derived parameter distribution of VBMCCA is employed to approach the uncertainty levels, which is able to provide confidence interval around the predicted values and give additional control line, rather than just a certain absolute control limit, for process monitoring. The proposed process monitoring framework has been validated in a Wastewater Treatment Plant (WWTP) simulated by Benchmark Simulation Model (BSM) with abrupt changes imposing on a sensor and a real WWTP with filamentous sludge bulking. The results show that the proposed methodology is capable of detecting sensor faults and process faults with satisfactory accuracy.
This paper presents a new nonparametric method to simulate probability density functions of some random variables raised in characterizing an anomaly based intrusion detection system (ABIDS). A group of kernel density estimators is constructed and the criterions for bandwidth selection are discussed. In addition, statistical parameters of these distributions are computed, which can be used directly in ABIDS modeling. Statistical experiments and numerical simulations are used to test these estimators.
Detecting changes in high-dimensional time series is difficult because it
involves the comparison of probability densities that need to be estimated from
finite samples. In this paper, we present the first feature extraction method
tailored to change point detection, which is based on an extended version of
Stationary Subspace Analysis. We reduce the dimensionality of the data to the
most non-stationary directions, which are most informative for detecting state
changes in the time series. In extensive simulations on synthetic data we show
that the accuracy of three change point detection algorithms is significantly
increased by a prior feature extraction step. These findings are confirmed in
an application to industrial fault monitoring.
Identifying temporally invariant components in complex multivariate time series is key to understanding the underlying dynamical system and predict its future behavior. In this Letter, we propose a novel technique, stationary subspace analysis (SSA), that decomposes a multivariate time series into its stationary and nonstationary part. The method is based on two assumptions: (a) the observed signals are linear superpositions of stationary and nonstationary sources; and (b) the nonstationarity is measurable in the first two moments. We characterize theoretical and practical properties of SSA and study it in simulations and cortical signals measured by electroencephalography. Here, SSA succeeds in finding stationary components that lead to a significantly improved prediction accuracy and meaningful topographic maps which contribute to a better understanding of the underlying nonstationary brain processes.
With the rapid development of modern industry and the increasing prominence of artificial intelligence, data-driven process monitoring methods have gained significant popularity in industrial systems. Traditional static monitoring models struggle to represent the new modes that arise in industrial production processes due to changes in production environments and operating conditions. Retraining these models to address the changes often leads to high computational complexity. To address this issue, we propose a multimode process monitoring method based on element-aware lifelong dictionary learning (EaLDL). This method initially treats dictionary elements as fundamental units and measures the global importance of dictionary elements from the perspective of the multimode global learning process. Subsequently, to ensure that the dictionary can represent new modes without losing the representation capability of historical modes during the updating process, we construct a novel surrogate loss to impose constraints on the update of dictionary elements. This constraint enables the continuous updating of the dictionary learning (DL) method to accommodate new modes without compromising the representation of previous modes. Finally, to evaluate the effectiveness of the proposed method, we perform comprehensive experiments on numerical simulations as well as an industrial process. A comparison is made with several advanced process monitoring methods to assess its performance. Experimental results demonstrate that our proposed method achieves a favorable balance between learning new modes and retaining the memory of historical modes. Moreover, the proposed method exhibits insensitivity to initial points, delivering satisfactory results under various initial conditions.
In this article, a novel time-constrained global and local nonlinear analytic stationary subspace analysis (Tc-GLNASSA) is proposed to enhance blast furnace ironmaking process (BFIP) monitoring. Although the existing analytic stationary subspace analysis method has been available for deriving process consistent relationships. However, the presence of complex nonlinear, periodic nonstationary, and time-varying smelting conditions renders the satisfactory estimation of stationary projections unattainable. To this end, we leverage multiple kernel functions and manifold learning methods to establish a global and local nonlinear structure with time constraints, which will identify the unique nonlinearities excited by periodic nonstationarity. Meanwhile, a singular value decomposition-based modeling efficiency promotion strategy is constructed to reduce the proposed Tc-GLNASSA's computational complexity significantly. The orthogonality of model update scheme is analyzed theoretically, and an overall BFIP monitoring framework is given. Ultimately, practical BFIP case studies fully demonstrate the effectiveness of our proposal.
Load fluctuations, unexpected disturbances, and switching of operating states typically make actual industrial processes exhibit nonstationary. In nonstationary processes, the statistical characteristics of the data will change. It is hard to distinguish process faults and changes in statistical characteristics and hence leads to false alarms. Cointegration analysis (CA) specializes in solving difficulties caused by time-varying means and variances by finding long-term equilibrium relationships among multiple variables. However, components extracted by CA are nonorthogonal, making it difficult to detect incipient faults or having high computational costs. To provide more effective orthogonal components for nonstationary cases, a new process monitoring algorithm called orthogonal stationary component analysis (OSCA) is proposed. The proposed OSCA orthogonalizes the components and subsequently uses a stationary component selection method based on the explained variance to determine the long-run equilibrium of the variables. The performance of OSCA is verified with a closed-loop continuous stirred tank reactor (CSTR) and an actual power plant dataset.
Industrial data generally exhibit nonstationary features due to load changes, external disturbances, etc., which raise great challenges for process monitoring. Most existing methods for nonstationary process monitoring use a two-stage strategy, where stationary series are obtained via preprocessing, followed by feature extraction and modeling for the stationary series. However, the two-stage strategy treats preprocessing and feature extraction separately, which would obtain suboptimal features. This article develops the stationary projective dictionary learning (SPDL) method for monitoring nonstationary industrial processes. Specifically, nonstationary data are projected into a stationary subspace, overcoming the disadvantages of nonstationarity and improving the representation ability of the dictionary. Then, considering process data usually have temporal correlations, a novel self-expression constraint term is added to optimize the features so that it can describe the process data accurately. Finally, an iterative approach is proposed for joint optimization of the projection matrix and the dictionary, and the formulas for parameter estimation are derived in detail. After the projection matrix and the dictionary are obtained, the nonstationary data are projected and reconstructed, and the reconstruction error is adopted to design the monitoring statistic. Case studies on a numerical example, a nonstationary continuous stirred tank reactor (CSTR), and an industrial roasting process reveal that the proposed method is suitable for nonstationary industrial process monitoring.
With the rapid expansion of the scale of modern industrial processes, more and more machine learning approaches using process variables for process monitoring and alarm analysis. The complex correlation of these variables makes a purely process knowledge-based variable division method unsatisfactory for process monitoring. To address this problem, a distributed process monitoring and abnormity root cause analysis model is built from a data-driven perspective. The proposed hierarchical clustering-based multicorrelation block partial least squares (HCMCB-PLS) divides the whole process into several blocks by using hierarchical clustering (HC), and the maximum information coefficient (MIC) is performed to select the correlation variables between the sub-blocks. PLS is conducted in each sub-block for process monitoring. Besides, a modified contribution-based abnormity root cause analysis strategy is developed, which uses an online distributed contribution analysis method to track the root cause variables. The effectiveness of proposed HCMCB-PLS is validated through a case study on the Tennessee-Eastman process. Comparative simulation results indicate that the HCMCB-PLS methodology outperforms other models in both industrial process monitoring and abnormity root cause analysis.
For industrial processes, operating conditions tend to be time varying, leading to the time-varying nonstationary characteristics. In this paper, an active nonstationary variables selection-based just-in-time co-integration analysis and slow feature analysis monitoring approach is proposed to explore the real-time variations in dynamic processes. To this end, by analyzing the time-varying stationarity of online data, active nonstationary variables are selected. Meanwhile, a just-in-time strategy is used to update the offline model. On this basis, co-integration analysis and slow feature analysis are developed for extracting long-run equilibrium relationships and slowly varying features. A comprehensive statistic is generated by Bayesian inference to monitor the operation status. With the active nonstationary information extraction, the proposed method emphasizes the online nonstationary characteristics, which allows the monitoring model to effectively capture the dynamic variations. Two case studies on benchmark processes show the advantages and feasibility of the proposed method.
In real industrial processes, factors, such as the change in manufacturing strategy and production technology lead to the creation of multimode industrial processes and the continuous emergence of new modes. Although the industrial SCADA system has accumulated a large amount of historical data, which can be used for modeling and monitoring multimode processes to a certain extent, it is difficult for the model learned from historical data to adapt to emerging modes, resulting in the model mismatch. On the other hand, updating the model with data from new modes allows the model to continuously match the new modes, but it may cause the model to lose the ability to represent the historical modes, resulting in "catastrophic forgetting." To address these problems, this article proposed a jointly mode-matching and similarity-preserving dictionary learning (JMSDL) method, which updated the model by learning the data of new modes, so that the model can adaptively match the newly emerged modes. At the same time, a similarity metric was put forward to guarantee the representation ability of the proposed method for historical data. A numerical simulation experiment, the CSTH process experiment, and an industrial roasting process experiment indicated that the proposed JMSDL method can match new modes while maintaining its performance on the historical modes accurately. In addition, the proposed method significantly outperforms the state-of-the-art methods in terms of fault detection and false alarm rate.
Dimensionality reduction methods based on manifold learning are widely adopted for industrial process monitoring. However, in many situations, these methods fail to preserve manifold intrinsic features in low-dimensional space, resulting in reduced process monitoring efficacy. To overcome this problem, a modified locality preserving projection (MLPP) based on the Riemannian metric is put forward. First, the Riemannian metric, which embodies a manifold’s geometric information, is estimated from process data. Then, the low dimensional embedding coordinates obtained from LPP are supplemented with an estimate of the Riemannian metric. Finally, a process monitoring model is developed, and kernel density estimation is utilized to approximate confidence bounds for and SPE statistics. The proposed MLPP method is applied to the feature extraction of Twin-Peaks dataset, fault detection of hot strip mill, steam turbine system and Tennessee Eastman processes. The effectiveness of MLPP method is compared with both the manifold learning and deep learning approaches. In addition, the proposed method is evaluated under various noisy conditions. The average fault detection rate of 98.9%, 99.6% and 84.4% in hot strip mill, steam turbine system and Tennessee Eastman processes, respectively, are higher than the existing methods. Quantitative results indicate the superiority of the proposed MLPP method.
Practical industrial processes usually have nonstationary properties, which make the monitoring more challenging because the fault information may be buried by nonstationary trends. For nonstationary processes, many methods have been proposed for fault detection based on continuous variables. However, binary variables may appear together with continuous variables in modern industrial processes. To address the issue of process monitoring with hybrid variables and nonstationarity, a model named recursive hybrid variable monitoring (RHVM) is proposed in this paper. For RHVM, recursive strategy is utilized to suppress nonstationary trend and to reveal fault information. In addition, RHVM has the ability of model self-updating with arriving samples. The closed-form updates of required parameters are derived in detail and the improvement of performance is analyzed. At last, the superiority of the proposed model is demonstrated by a simulation example and a practical nonstationary process of a power plant.
Principal Component Analysis (PCA) is a widely used technique in process monitoring, fault diagnosis, and soft sensing of industrial systems. Despite its popularity, PCA suffers from the limitations of poor interpretability and robustness. In order to improve the PCA model, this article considers a structured sparse method--Laplace sparse principal component analysis (LSPCA), by integrating domain knowledge and sparsity constraint in the form of Laplace matrix and elastic net regularization constraint. Different from previous work, this article focuses on the advantages brought by the Laplace matrix and sparsity constraint on revealing the true latent process structure. When variable correlations are known in advance, the Laplace matrix can help extract sparse principal components that are consistent with the variable correlations. The increased accuracy of extracted latent process structure enhances the capability of PCA in soft sensing. The performance of the proposed method is verified by a simulation example and an application study to a distillation process.
For real industrial processes, time-varying behaviors are quite common. Consequently, industrial processes usually possess nonstationary characteristics, which makes conventional monitoring methods suffer from the model mismatch problem. In this article, an exponential analytic stationary subspace analysis (EASSA) algorithm is proposed to develop an adaptive strategy for nonstationary process monitoring. It is recognized that although covered by nonstationary trends, some underlying components of the process may remain stationary, which can be used for reliable process monitoring. For this, an EASSA algorithm is first developed to estimate the stationary sources more accurately and numerically stably. Then, a monitoring strategy is developed on the estimated stationary sources to provide reliable monitoring results. Considering that the relationships between process variables are driven to change slowly by time-varying behaviors, an update strategy and an adaptive monitoring scheme are designed to accurately track the trajectory of nonstationary processes while reducing the update frequency as much as possible. To meet the need of the EASSA algorithm, the minimum update unit has been expanded from one sample to one batch and the update conditions are given, by which the model is prevented from erroneously adapting to incipient faults to a certain extent. Case study on both a simulation process and a real thermal power plant process demonstrates that the proposed method can distinguish the real faults from normal changes while being robust to the disturbances in the nonstationary process.
For large-scale process monitoring, traditional decentralized monitoring methods fail to discriminate real faults from normal operation deviations. This paper proposes a novel decentralized method for monitoring large-scale industrial processes by exploring serial correlations and local manifold structures of the data. A block division strategy based on maximal information coefficient-spectral clustering is proposed, which can divide the measured variables into several blocks without any prior knowledge. To extract inter-block relevance, multiblock principal component analysis is introduced to whiten the original variables. On this basis, we develop a new dimensionality reduction algorithm named manifold regularized slow feature analysis (MRSFA) to capture the temporal dynamics and local structure information in each block. Monitoring statistics are constructed based on the captured feature information to concurrently monitor the operation deviations and anomalous dynamics. To achieve decision fusion, the monitoring results derived from all blocks are combined through Bayesian inference. Two case studies on the Tennessee Eastman process and a real industrial process are carried out and the experimental results demonstrate the effectiveness of the proposed method.
Complex industrial processes are commonly characterized with multiple operation modes. The existing manifold learning-based process monitoring methods describe each mode individually without capturing the connections among different modes, which may deteriorate the monitoring capability. This paper proposes a novel dimensionality reduction model referred as to multi-manifold joint projections (MMJP) to monitor the multimode processes, where the intra-mode and the inter-mode adjacency matrices are constructed to reflect the underlying features within each mode and among different modes, respectively. The neighboring and non-neighboring structures of data within each mode are captured by the distance and angle information of pairwise points to reveal the intrinsic structure of the original data, thus offering a more faithful representation of multimodal data and further enhancing monitoring performance. During online monitoring, a point to manifold distance (PMD) criterion is proposed to determine the running-on mode of new samples. Two case studies demonstrated the superior performance of the proposed approach in multimode process monitoring.
In real industrial applications, process data may get corrupted due to failure of the measurement devices or errors in data management. Besides, incipient faults, which may evolve into serious accidents, are generally more difficult to be detected because of its small magnitudes. In this study, a robust canonical variate dissimilarity analysis (CVDA) method is proposed to detect incipient faults for industrial processes with missing value. According to the low-rank characteristic, the low-rank matrix decomposition (LRMD) method is applied to recover the missing elements and reduce the ambient noise for process data. The output results of LRMD model consist of a low-rank component and a sparse component, which indicate main variance and residual information of the inputted data, respectively. For each component, a canonical variate analysis (CVA) model is developed to extract the temporal correlation in the process data. Based on the obtained features, a total of three monitoring statistics are established to reflect the operation status of the online sample. Among them, a statistic is used to measure the static deviation of this sample, and other two indices are applied to evaluate the dissimilarity between the past and future canonical variates. A simulated process and a real industrial process are adopted to illustrate the performance of the proposed method. Experimental results show that the proposed model can be well developed with incomplete training data and robustly detects the incipient faults for industrial applications.
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.
The main challenge for complex industrial processes is that the distribution of new process data is different from that of old process data, resulting in poor performance when monitoring the new process (target domain) using the model established by the old process (source domain) data. Moreover, new process data is often unlabeled, which is more common in actual industrial processes. Therefore, this paper proposes a novel fault diagnosis method for complex industrial processes based on Manifold Distribution Adaptation (MDA) to cope with this challenge. Specifically, in order to avoid feature degradation caused by feature transformation directly in the original feature space, MDA first maps source domain data and target domain data to Grassmann manifold through geodesic flow kernel. Second, dynamic distribution adaptation and source domain instance re-weighting are performed simultaneously on the Grassmann manifold to reduce the shift between the domains. Then, the base classifier trained by the adaptive source domain data can achieve accurate classification of the target domain data. Finally, the superiority of MDA is verified on the public transfer learning datasets and the actual industrial process datasets.
Closed-loop control is widely used in modern industrial processes to ensure that process performance such as product quality and waste discharge are maintained at the predefined set-points. However, control actions which may compensate the disturbances on process performance and result in obvious process dynamics cause great challenges to process monitoring. The influences of control actions on process performance and dynamics for process monitoring have not been fully investigated before. Thus, a performance-relevant full decomposition of slow feature analysis termed PFDSFA here, is proposed for process monitoring under closed-loop control by simultaneously considering the influences of process variations on process performance and dynamics. First, the new algorithm extracts variations which are closely relevant to performance variables using canonical correlation analysis. Based on it, process variable space can be decomposed into performance-relevant subspace and process-relevant subspace. Then, both static and dynamic variations of each subspace are extracted to design monitoring statistics which can distinguish normal operating condition deviations from dynamic anomalies incurred by real faults. The proposed PFDSFA algorithm offers a fine-scale decomposition of process variations and achieves comprehensive process monitoring of process static and dynamic characteristics. Besides, it is efficient in indicating whether disturbances make influence on process performance and dynamics. Finally, two case studies are employed to illustrate the applicability and efficacy of the proposed algorithm in comparison with some other monitoring approaches.
Fault diagnosis, which identifies the root cause of the observed out-of-control status, is essential to the counteraction or elimination of faults in industrial processes. Many conventional data driven fault diagnosis methods ignore the fault tendency of abnormal samples, and need a complete retraining process to include the newly collected abnormal samples or fault classes. In this study, a broad convolutional neural network (BCNN) is designed with incremental learning capability for solving the aforementioned issues. The proposed method combines several consecutive samples as a data matrix, and then extracts both fault tendency and nonlinear structure from the obtained data matrix using convolutional operation. After that, weights in fully connected layer can be trained based on the obtained features and their corresponding fault labels. Because of the architecture of this network, the diagnosis performance of BCNN model can be improved by adding newly generated additional features. Finally, the incremental learning capability of the proposed method is also designed, so that BCNN model can update itself to include new coming abnormal samples and fault classes. Experimental results illustrate that it can better capture the characteristics of the fault process, and effectively update diagnosis model to include new coming abnormal samples and fault classe.
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.
A new kind process monitoring method which based on global–local manifold analysis is proposed in this article. Firstly, this method models the global–local manifold structure of the process in the off-line stage, and then detects the changes in the global–local manifold structure when new observation samples are used for on-line monitoring. In addition, conventional algorithms that based on global–local manifold structure may lose accuracy when monitor the process since the Gaussian assumption is not easily satisfied. In this new method, a novel score variable which approximately follows Gaussian distribution regardless of the original is derived. Besides, the incorporation of statistical local approach also reveals conspicuous detection sensitivity. We also propose a visual fault diagnosis method based on the global–local manifold structure analysis. The proposed process monitoring method is well examined through a numerical example and the TE process benchmark.
Learning under non-stationarity can be achieved by decomposing the data into a subspace that is stationary and a non-stationary one (stationary subspace analysis (SSA)). While SSA has been used in various applications, its robustness and computational efficiency has limits due to the difficulty in optimizing the Kullback-Leibler divergence based objective. In this paper we contribute by extending SSA twofold: we propose SSA with (a) higher numerical efficiency by defining analytical SSA variants and (b) higher robustness by utilizing the Wasserstein-2 distance (Wasserstein SSA). We show the usefulness of our novel algorithms for toy data demonstrating their mathematical properties and for real-world data (1) allowing better segmentation of time series and (2) brain-computer interfacing, where the Wasserstein-based measure of non-stationarity is used for spatial filter regularization and gives rise to higher decoding performance.
This paper introduces a technique to monitor chemical processes that are driven by a set of serially correlated nonstationary and stationary factors. The approach relies on (i) identifying and separating the common stationary and nonstationary factors, (ii) modeling these factors using multivariate time series models and (iii) incorporating a compensation scheme to directly monitor these factors without being compromised by the effect of forecast recovery. Based on the residuals of the time series models, the technique yields two distinct test statistics to monitor both types of factors individually. Different from existing work, the paper highlights that the technique is sensitive to any fault condition and can extract and describe both, stationary and non-stationary trends. These benefits are illustrated by a simulation example and the application to an industrial semi-batch process describing nonstationary emptying and filling cycles.
It is a big challenge to identify the most effective features for enhancement of fault classification accuracy in rotating machines due to nonstationary and nonlinear vibration characteristics of the machines under varying operating conditions. To find discriminative features, a novel dimension reduction algorithm, referred to as the nearest and farthest distance preserving projection (NFDPP), is proposed for machine fault feature extraction and classification. With the NFDPP, both the nearest and farthest samples of the data manifold can be analyzed simultaneously to identify features leading to fault classification. Additionally, we denoise the features directly in the feature space to save computation time and storage space, and prove its equivalence to denoising the signals in the time domain. Through analysis of measured vibration data for bearings with different defects, it is demonstrated that the proposed NFDPP approach can effectively classify different bearing faults and identify the severity of the bearing ball defect, and the direct denoising of features yield a significant improvement in fault classification. The effectiveness of the proposed method is further validated in identifying compound faults in locomotive bearings in an industrial setting.
A novel dimensionality reduction algorithm named “global–local preserving projections” (GLPP) is proposed. Different from locality preserving projections (LPP) and principal component analysis (PCA), GLPP aims at preserving both global and local structures of the data set by solving a dual-objective optimization function. A weighted coefficient is introduced to adjust the trade-off between global and local structures, and an efficient selection strategy of this parameter is proposed. Compared with PCA and LPP, GLPP is more general and flexible in practical applications. Both LPP and PCA can be interpreted under the GLPP framework. A GLPP-based online process monitoring approach is then developed. Two monitoring statistics, i.e., D and Q statistics, are constructed for fault detection and diagnosis. The case study on the Tennessee Eastman process illustrates the effectiveness and advantages of the GLPP-based monitoring method.
This paper introduces cointegration testing method for nonstationary process monitoring, which yields a long-run dynamic equilibrium relationship for nonstationary process systems. The process variables are examined, and then a cointegration model of the tested nonstationary variables is identified. The residual sequence of the cointegration model describes the dynamic equilibrium errors of the nonstationary process system and can be further analyzed for condition monitoring and fault detection purposes. The autocorrelated residual sequence is filtered with AR model first, then compensated to keep the fault signatures from being distorted by the filtering process. An application case study to an industrial distillation unit with a nonstatioanry process shows that a tidy cointegration model can describe the dynamic equilibruim state of the unit and correctly detect abnormal behavior of the process.
Non-stationary effects are ubiquitous in real world data. In many settings, the observed signals are a mixture of underlying stationary and non-stationary sources that cannot be measured directly. For example, in EEG analysis, electrodes on the scalp record the activity from several sources located inside the brain, which one could only measure invasively. Discerning stationary and non-stationary contributions is an important step towards uncovering the mechanisms of the data generating system. To that end, in Stationary Subspace Analysis (SSA), the observed signal is modeled as a linear superposition of stationary and non-stationary sources, where the aim is to separate the two groups in the mixture. In this paper, we propose the first SSA algorithm that has a closed form solution. The novel method, Analytic SSA (ASSA), is more than 100 times faster than the state-of-the-art, numerically stable, and guaranteed to be optimal when the covariance between stationary and non-stationary sources is time-constant. In numerical simulations on wide range of settings, we show that our method yields superior results, even for signals with time-varying group-wise covariance. In an application to geophysical data analysis, ASSA extracts meaningful components that shed new light on the Pi 2 pulsations of the geomagnetic field.
The theory of many multivariate chemometrical methods is based on the measurement of distances. The Mahalanobis distance (MD), in the original and principal component (PC) space, will be examined and interpreted in relation with the Euclidean distance (ED). Techniques based on the MD and applied in different fields of chemometrics such as in multivariate calibration, pattern recognition and process control are explained and discussed.
While principal component analysis (PCA) has found wide application in process monitoring, slow and normal process changes often occur in real processes, which lead to false alarms for a fixed-model monitoring approach. In this paper, we propose two recursive PCA algorithms for adaptive process monitoring. The paper starts with an efficient approach to updating the correlation matrix recursively. The algorithms, using rank-one modification and Lanczos tridiagonalization, are then proposed and their computational complexity is compared. The number of principal components and the confidence limits for process monitoring are also determined recursively. A complete adaptive monitoring algorithm that addresses the issues of missing values and outlines is presented. Finally, the proposed algorithms are applied to a rapid thermal annealing process in semiconductor processing for adaptive monitoring.