The partial domain adaptation (PDA) challenge is a prevalent issue in industrial fault diagnosis. Current PDA approaches primarily rely on adversarial learning for domain adaptation and use reweighting strategies to exclude source samples deemed outliers. However, the transferability of features diminishes from general feature extraction layers to higher task-specific layers in adversarial learning-based adaptation modules, leading to significant negative transfer in PDA settings. We term this issue the adaptation-discrimination paradox (ADP). Furthermore, reweighting strategies often suffer from unreliable pseudo-labels, compromising their effectiveness. In this work, we propose a novel PDA framework called Interactive Residual Domain Adaptation Networks (IRDAN), which introduces domain-wise models for each domain to provide a new perspective for the PDA challenge. Each domain-wise model is equipped with a residual domain adaptation (RDA) block to preserve the discriminative structure of each domain and mitigate the ADP. Additionally, we introduce a confident information flow via an interactive learning strategy, training the modules of IRDAN sequentially to avoid cross-interference. We also establish a reliable stopping criterion for selecting the best-performing model, ensuring practical usability in real-world applications. Experiments have demonstrated the superior performance of the proposed IRDAN.

Data-driven anomaly detection aims to learn a decision boundary, enveloping the normal region, and separating normal data from abnormal data. However, industrial data are fairly complex due to varying feedstock and unclear transfer processes and chemical reactions. This means the decision boundary will be very complex and even intractable. In addition, process variables are high-dimensional in modern industrial processes, which strengthens the difficulty of boundary extraction. Generally, the boundary should exactly exceed the outermost samples for precisely drawing normal regions. However, what we have in most situations is just normal data contaminated by unknown noises. Hence, conventional solutions that use statistical analysis to define a normal region result in a not-so-accurate decision boundary where missing alarms occur frequently. In addition to the conventional solution based entirely on historical data, i.e., passive fault detection (PAD), an alternative detection method, active fault detection (AAD), can circumvent the above problem by stimulating system performance through the intervention of auxiliary signal. While it results in disruption of the normal operation conditions for the process, its method to enhance output performance through additional signals inspires us. In this paper, we resort to the ability of deep neural networks to fit nonlinear data and perform dimension reduction. A fault data generation strategy is proposed and the artificially generated fault data are used to regulate the model training. The new virtual fault data aids in suppressing the decision boundary closest to the outermost periphery. We propose the principles of data generation and form a network structure, implementing information fusion of genuine normal samples and virtual fault samples. Two cases demonstrate the efficiency of the proposed method.

Systematical measurement errors in industrial sensors should be avoided or rectified, as severe discrepancies in data can impede control, operation, and evaluation. However, some systematical errors are hard to estimate or experiment with. These errors often arise due to the change in external conditions. This means the measurement errors can be ignored when the external conditions remain within the designed scope. Generally, the relationship between the external condition and the systematical error is of complex nonlinearity, which may not be analytically tractable so rectifying the error is challenging. Nonetheless, a general assumption can be made in typical industrial scenarios: most external conditions fall within the design scope so that the corresponding systematical errors are 0. This assumption holds because the sensor is generally installed and calibrated under the most common operating mode. Based on these rationales, we first propose an intermediate sample-enhanced clustering strategy to identify the majority pattern, aiding in figuring out the zero systematical measurement error points. Then, leveraging the zero systematical measurement error information and partly known labels, a semi-supervised learning method is employed for estimating the complex nonlinear mapping from the external condition and the measurement, thereby rectifying the errors. The effectiveness of our approach is demonstrated through the rectification of a density meter in a real industrial aluminum oxide process, validated by the comparison with the laboratory assay outcomes. Note to Practitioners—Measurement instruments in industrial systems are designed to meet the precision requirement under specific conditions. Once the condition x is out of scope, the measurement y will be accompanied by the systematical measurement errors which is the function of x, denoted by$f(x)$. Thus the measurement model is$ y=y_{t}+f(x)+e$, where$y_{t}$is the true value and e is the random measurement error. However, for many scenarios, the errors are complex.$f(x)$is nonlinear and even intractable. From the perspective of engineering practice, the condition x in most of the running period should remain within the design scope to ensure normal use. However, it is also common for the running status to drift from the original designed working points over time. Then, an intolerant systematical measurement error occurs, causing the instrument which can be expensive lose their function. To estimate the systematical measurement error and implement the rectification of the deviated measurement, this paper proposes a data-driven strategy when the condition x is measurable and part of the label for y is available. We demonstrated the effectiveness of the strategy using a real industrial application example.

The refinery industry operates as a highly complex system characterized by dynamic interactions among numerous processes, resources, and decision-making strategies. Within this context, production planning and crude oil procurement management are critical to ensuring operational efficiency and profitability. However, traditional optimization approaches often neglect the distinct decision-making time scales of these two functions, limiting their ability to address market dynamics and supply chain complexities effectively. To overcome these challenges, this study introduces an asynchronous multi-agent collaborative optimization framework that enhances the coordination between production planning and crude oil procurement in refinery operations. By enabling production and procurement agents to operate on independent time scales, the framework adapts to fluctuations in crude oil prices and variations in product demand. The study further extends the classical multi-agent reinforcement learning algorithm into an asynchronous paradigm, introducing Async-MAPPO, which allows agents to independently optimize decisions using real-time data. This approach mitigates operational delays and enhances adaptability. Experimental evaluations demonstrate that the proposed method significantly improves production efficiency, reduces operational costs, and strengthens the refinery’s resilience to market fluctuations, underscoring the critical role of asynchronous optimization in refinery operations.

In industrial soft-sensor applications, labeled samples are often scarce and unable to fully represent the dynamic changes in industrial processes. Although semi-supervised methods offer a potential solution to this issue, existing feature-construction-based methods cannot ensure the effectiveness of the feature, and pseudo-label-based methods lack an established confidence evaluation standard. To address these challenges, this article first proposes a novel performance-driven distillation strategy, which designs an innovative siameseLSTM structure for training multiple teacher models. By assigning higher weights to high-performance teacher models and simultaneously leveraging the guidance of the soft sensing task, the student model is guided to learn more effective feature representations. Additionally, a new pseudo label confidence evaluation strategy is introduced, which aims to enhance the generalization of the base soft-sensor model by selecting samples with high-confidence pseudo labels. Finally, By combining the above two strategies, a semi-supervised soft-sensor framework is proposed for the soft sensing of industrial quality variables. The effectiveness of the proposed framework is validated through two real-world datasets from different stages of the alumina production process. Compared with some existing advanced soft sensor frameworks, the prediction results on different datasets show that the root-mean-square error (RMSE) and mean absolute error (MAE) are reduced by an average of 10.76% and 11.18%, respectively, while the correlation coefficient (R2) is averagely increased by 0.1203.

Granger causality has emerged as a valuable tool in comprehending industrial processes and facilitating data modeling by unveiling the inherent relationships within the data. However, the characteristic of causality discovery tasks results in a lack of validation sets, making hyperparameter tuning reliant solely on intuition. Existing nonlinear Granger causality discovery methods suffer from insufficient accuracy and robustness due to the significant impact of hyperparameters. Hence, this article proposes an attribution-aided nonlinear Granger causality discovery method (Attri-NGC) for accurate and robust inference of Granger causality. Attri-NGC comprises two stages. In the first stage, a novel strategy is proposed to assess whether the variability in contributions, derived from deep learning-based attribution, can significantly reflect causality. This assessment transfers the robust advantage of attribution to causal discovery. In the second stage, a sparsity-inducing penalty targeted at ambiguous causality is defined to fine-tune the deep networks used for attribution. Our method transforms the paradigm of Granger causality discovery from a challenging deep networks training problem to a fine-tuning problem, leading to a substantial enhancement in the accuracy and robustness of causality discovery. The effectiveness of the proposed method is comprehensively validated on four public datasets and two industrial process datasets. The superior performance of Attri-NGC in supporting industrial process modeling effectively promotes the integration of Granger causality into practical applications for more interpretable process modeling.

Temporal feature representation is critical for soft sensor modeling in industrial time sequences. Deep learning networks like long short-term memory are often used to model the temporal dynamics of data sequences. However, the data collected from industrial plants are usually sampled with irregular frequency, making it challenging for traditional methods to handle these temporally changeable relationships. Therefore, a Gaussian-based interval-aware transformer (GIA-Trans) with interval embedding is proposed in this article to model industrial data with irregular sampling frequency. In GIA-Trans, positional and temporal embedding layers are established to take positional distances and time intervals of samples into account. Then, Gaussian-based time-aware attention is proposed to tackle the changeable time intervals with adaptive weights. In this way, the temporal correlations between samples can be adaptively captured. The GIA-Trans is applied to an industrial hydrocracking process to predict the C5 and C6 content of light naphtha.

Accurate feature extraction and quality variable prediction are critical problems for time sequences in industrial processes. However, industrial samples often exhibit strong temporal correlations with each other that have different positional distances, making it challenging for conventional data-driven models like long short-term memory (LSTM) and Vanilla transformer to capture these underlying features. In this article, a difference metric attention with position distance-based weighting is proposed for transformer (DMA-trans) in industrial time series modeling. First, the DMA is established to calculate the difference of query-key vector pair in transformer to measure the spatial similarity. In this fashion, the difference can accurately represent the spatial similarity of vectors, compared with the original dot product directly on two vectors. Then, positional distance-based weights are designed to capture the sample relevance that has different positional distances. This may help to extract more potential features because the closer samples tend to have higher relevance while there may be weak correlations if two samples are far in positional distance. The effectiveness of the DMA-trans model is validated in industrial hydrocracking processes for C5 content of the light naphtha and the final boiling point of the jet fuel.

Traditional industrial production processes, such as nonferrous metallurgy, are mostly based on complex, cascading, large-scale equipment. Many soft sensing approaches are rendered inapplicable due to the particularity of this physical structure, which involves uncertain time delay and extreme imbalance between the input and output dimensions. To alleviate this problem, this article first proposes a time-delay analysis strategy to preliminarily reduce the input dimensions of the process variables. Then, a new orthogonal self-attention (OSA) mechanism is proposed to capture nonlinear features related to quality variables along both spatial and temporal dimensions, thus solving the problem of uncertainty of the time delays of process variables affecting quality variables. In addition, a new long short-term memory (LSTM) structure called differential-cross LSTM is proposed, which is incorporated in a cascading manner differential-cross cascade LSTM (DCCLSTM) to emulate the physical structure of the industrial process. Therefore, the soft-sensor framework called OSA-DCCLSTM is constructed, where data from each major equipment undergo the time-delay analysis strategy and the OSA computation and is subsequently input into the corresponding differential-cross LSTM module. Extensive experiments on a real-world alumina evaporation process datasets show the effectiveness of the proposed framework. Compared with some existing state-of-the-art methods, the root-mean-squared error and mean absolute error are on average decreased by 0.3742 and 0.2234, while the correlation coefficient is on average increased by 0.1389.

For industrial processes, it is significant to carry out the dynamic modeling of data series for quality prediction. However, there are often different sampling rates between the input and output sequences. For the most traditional data series models, they have to carefully select the labeled sample sequence to build the dynamic prediction model, while the massive unlabeled input sequences between labeled samples are directly discarded. Moreover, the interactions of the variables and samples are usually not fully considered for quality prediction at each labeled step. To handle these problems, a hierarchical self-attention network (HSAN) is designed for adaptive dynamic modeling. In HSAN, a dynamic data augmentation is first designed for each labeled step to include the unlabeled input sequences. Then, a self-attention layer of variable level is proposed to learn the variable interactions and short-interval temporal dependencies. After that, a self-attention layer of sample level is further developed to model the long-interval temporal dependencies. Finally, a long short-term memory network (LSTM) network is constructed to model the new sequence that contains abundant interactions for quality prediction. The experiment on an industrial hydrocracking process shows the effectiveness of HSAN.

In industrial processes, frequent communication failures and information corruption may result in the loss of entire blocks of industrial process data, which is also known as blackout missing data. The imperfect data of industrial time series impede the performance of subsequent modeling and control tasks. However, traditional matrix factorization or supervised learning data imputation methods are hardly applicable to the challenging task of recovering blackout missing data. The difficulty in imputing the blackout data stems from two major factors: the imputation process lacks the reference of co- evolutionary variables, and the blackout data have strong autocorrelation and drift in distribution. To address these issues, this paper develops a novel hierarchical imputation framework for recovering blackout data based on the masked transformer network (Masked-Former). First, a reconstruction block strategy with random masked points is innovatively proposed to improve the ability of the model to recover missing values under different working conditions for incomplete datasets. Then, based on the masked incomplete data set, the proposed method utilizes the local feature capture capability of convolutional networks and the sample-level long-range dependency capture capability of the self-attention mechanism to complete coarse-grained and fine-grained missing data imputation, respectively. Finally, extensive experiments are conducted to verify the superior performance of the proposed method on two real-world industrial data sets. Note to Practitioners—Inspired by the phenomenon that industrial process data often have missing data, this paper proposes a novel hierarchical imputation Masked-Former method for blackout missing data recovery. The method combines local data features with long-term time series dependency performance to improve completion performance. Then, the obtained completed data can help practitioners monitor the status of industrial field conditions. In addition, it is helpful to perform subsequent quality prediction and process monitoring tasks, allowing practitioners to quickly take preventative measures to avoid disasters and take corrective operations to return the plant to its normal operating range.

In conventional process monitoring, a latent variable model (LVM) is first learned in offline training and the statistics related to extracted latent features and residuals are then used for online monitoring. However, such a practice ignores the dynamic interaction between modeling and monitoring, rendering useful online samples underexplored. This study proposes a novel LVMs-based monitoring framework that exploits the interaction using a weighting strategy and the maximum likelihood method to improve the monitoring performance with online information. The key idea is to integrate a weighting vector to components which contribute to the fault detection indices for more effective online fault information extraction. We use the maximum likelihood ratio to optimize the weighting vector and construct a new fault detection index accordingly. Case studies on a numerical example and a three-phase flow facility demonstrate the effectiveness of our approach.Note to Practitioners—A large number of anomaly detection methods in industrial systems has emerged in recent years. Latent variable models are the dominant branch of anomaly detection methods with substantial research and practice. However, fault detection performance is still unexpected especially for some minor faults that cause underwhelming fluctuation. Based on LVM models, we investigate the performance maximization method of industrial fault detection. The main mechanism is a weighting strategy that connects the normal data and the online sample to be monitored. We do not attach any additional conditions besides the existing requirements for LVM models. Also, it is the class of LVM methods that can be benefited from this novel strategy rather than a specific approach, which has been verified using principal component analysis and canonical correlation analysis. Moreover, the fault detection performance has boosted for all kinds of fault types. Notice we use general linear LVM models for deriving the methodology. Extension to nonlinear methods is still an open question for the sake of the introduced non-convex optimization.

This article studies the performance monitoring problem for the potassium chloride flotation process, which is a critical component of potassium fertilizer processing. To address its froth image segmentation problem, this article proposes a multiscale feature extraction and fusion network (MsFEFNet) to overcome the multiscale and weak edge characteristics of potassium chloride flotation froth images. MsFEFNet performs simultaneous feature extraction at multiple image scales and automatically learns spatial information of interest at each scale to achieve efficient multiscale information fusion. In addition, the potassium chloride flotation process is a multistage dynamic process with massive unlabeled data. To overcome its dynamic time-varying and working condition spatial similarity characteristics, a semi-supervised froth-grade prediction model based on a temporal-spatial neighborhood learning network combined with Mean Teacher (MT-TSNLNet) is proposed. MT-TSNLNet designs a new objective function for learning the temporal-spatial neighborhood structure of data. The introduction of Mean Teacher can further utilize unlabeled data to promote the proposed prediction model to better track the concentrate grade. To verify the effectiveness of the proposed MsFEFNet and MT-TSNLNet, froth image segmentation and grade prediction experiments are performed on a real-world potassium chloride flotation process dataset.

Soft sensors have been increasingly applied for quality prediction in complex industrial processes, which often have different scales of topology and highly coupled spatiotemporal features. However, the existing soft sensing models usually face difficulties in extracting the multiscale local spatiotemporal features in multicoupled complex process data and harnessing them to their full potential to improve the prediction performance. Therefore, a multiscale attention-based CNN (MSACNN) is proposed in this article to alleviate such problems. In MSACNN, convolutional kernels of different sizes are first designed in parallel in the convolutional layers, which can generate feature maps containing local spatiotemporal features at different scales. Meanwhile, a channel-wise attention mechanism is designed on the feature maps in parallel to get their attention weights, representing the significance of the local spatiotemporal feature at different scales. The superiority of the proposed MSACNN over the other state-of-the-art methods is validated through the performance evaluation in two real industrial processes.

Few-sample modes are easy to appear when a new working condition is triggered in industrial processes especially during the early stages of the new working mode. However, monitoring the early behavior of a new mode is important because engineers and operators are less knowledgeable with such a new mode. Considering the few-sample challenge in this problem, a new multisource transfer learning framework is proposed that leverages historical data under various operating conditions to enrich process monitoring over new mode data. In contrast to existing transfer learning-related work, a new unsupervised domain adaptation framework is designed. The historical modes as the source provide precious knowledge and reference to the new mode so that the features of the new mode are robust to noise and insufficient samples. Mathematically, the historical features play the role of a regularizer for the feature learning in the target domain. A geometrical illustration is given and an iterative optimization algorithm is developed with the convergence analysis. Except for the features guided by historical modes, individual features of the new mode are also extracted from the residual part to form a complete monitoring framework. Finally, the effectiveness of the proposed method is validated through a numerical experiment and a real industrial hydrocracking process.

In complex process industries, multivariate time sequences are omnipresent, whose nonlinearities and dynamics present two major challenges for soft sensing of important quality variables. Consequently, due to the potent representational capabilities, nonlinear dynamic models like gated recurrent unit (GRU) and long short-term memory (LSTM) networks have been used for data sequence modeling. Though it is a common occurrence in many industrial plants, data series with heterogeneous sample intervals and missing values cannot be directly handled by these dynamic algorithms. To this end, attention-based interval-aided networks (AIA-Net) are proposed in this article to adaptively model the temporal information for heterogeneous sampling sequences with missing values in the processes industry. It includes two main mechanisms, which are named attention-based time-aware dynamic imputation and interval-aided time-aware network, respectively. The reduction rate is introduced by the attention-based time-aware dynamic imputation to apply the effects of time intervals and is used in the imputation of missing data. The interval-aided time-aware network includes time intervals in the model structure and uses a sampling interval gate to correct the temporal correlations in time series. The proposed AIA-Net is successfully applied to a real hydrocracking process to predict the C5 and C6 content in the light naphtha.

Missing data is a common phenomenon in the industrial field. The recovery of missing data is crucial to enhance the reliability of subsequent data-driven monitoring and control of industrial processes. Most existing methods are limited by the confined scope of feature extraction, which makes it impossible to rely on global information to impute missing data. In addition, they usually assume that industrial data is a uniform distribution across all working conditions, ignoring the differences in data evolution patterns across different conditions. To address these issues, this paper proposes an innovative scope-free global multi-condition-aware imputation framework based on diffusion transformer (SGMCAI-DiT). First, it extends the diffusion model by introducing conditional probability to capture the condition distribution of the entire data. Then, a noise prediction model is designed based on a novel double-weighted attention mechanism (DW-SA) to broaden the horizons of feature extraction. By discerning the inter-conditional interactions and the intra-conditional local information, the missing data imputation performance can be improved. Finally, the effectiveness and suitability of the proposed SGMCAI-DiT are verified on four real datasets sourced from industrial processes and two public non-industrial datasets. Extensive experimental results demonstrate that the proposed method outperforms several state-of-the-art methods in different missing data scenarios.

Despite remarkable advancements in graph contrastive learning techniques, the identification of interdependent relationships when maximizing cross-view mutual information remains a challenging issue, primarily due to the complexity of graph topology. In this study, we propose to formulate cross-view interdependence from the innovative perspective of information flow. Accordingly, IDEAL, a simple yet effective framework, is proposed for interdependence-adaptive graph contrastive learning. Compared with existing methods, IDEAL concurrently addresses same-node and distinct-node interdependence, circumvents the reliance on additional distribution mining techniques, and is augmentation-aware. Besides, the objective of IDEAL takes advantage of both contrastive and generative learning objectives and is thus capable of learning a uniform embedding distribution while retaining essential semantic information. The effectiveness of IDEAL is validated by extensive empirical evidence. It consistently outperforms state-of-the-art self-supervised methods by considerable margins across seven benchmark datasets with diverse scales and properties and, at the same time, showcases promising training efficiency.

The occurrence of abnormal operating conditions in industrial flotation processes adversely influences flotation concentrate yields and quality. It is imperative to prioritize the maintenance of normal operating conditions within the flotation process for process optimization. Considering the influence of the operation variable adjustment of different flotation cells on the final production indicators and the difficulty of establishing an adequate mathematical model, an intelligent collaborative decision-making plan based on multiple flotation cells is proposed in this study. First, multimodal data from industrial flotation sites are collected to emulate the comprehensive perceptual capabilities exhibited by human operators. Then, based on the concept of collaborative optimization, an intelligent collaborative decision-making plan for adjusting operating parameters is proposed. Finally, a series of experiments are conducted using actual industrial data. The results demonstrate the efficacy of the proposed intelligent collaborative decision-making plan in enhancing abnormal operation conditions, thereby establishing its promising potential for practical implementation in the industrial flotation process.

Multiple modes are ubiquitous in current industrial processes, and the amount of historical data contained in different modes may vary considerably. Insufficient data can easily lead to cold start problems when building a fault detection model for a particular mode. To solve this problem, while considering the similarity and differences between multiple modes, a deep model using domain adaptation based on feature separation is proposed for nonlinear process monitoring with few samples. The model extracts common features from modes and the data deficiency is compensated by transferring the domain knowledge from the source to the common features. On the other hand, to avoid missing useful information by focusing only on common features, the model also extracts the specific features of the target domain. Thus, monitoring performance is improved with the help of domain adaptation while taking into account the specific characteristics of the target domain. Furthermore, three detection indices are designed to monitor the common feature subspace, the specific feature subspace, and the residual subspace, respectively. The benefit of this is allowing more diagnostic information to be obtained when a fault occurs. The proposed method was tested with a numerical example and a real industrial hydrocracking process to verify the detection effectiveness.

Missing values are ubiquitous in industrial data sets because of multisampling rates, sensor faults, and transmission failures. The incomplete data obstruct the effective use of data and degrade the performance of data-driven models. Numerous imputation algorithms have been proposed to deal with missing values, primarily based on supervised learning, that is, imputing the missing values by constructing a prediction model with the remaining complete data. They have limited performance when the amount of incomplete data is overwhelming. Moreover, many methods have not considered the autocorrelation of time-series data. Thus, an adaptive-learned median-filled deep autoencoder (AM-DAE) is proposed in this study, aiming to impute missing values of industrial time-series data in an unsupervised manner. It continuously replaces the missing values by the median of the input data and its reconstruction, which allows the imputation information to be transmitted with the training process. In addition, an adaptive learning strategy is adopted to guide the AM-DAE paying more attention to the reconstruction learning of nonmissing values or missing values in different iteration periods. Finally, two industrial examples are used to verify the superior performance of the proposed method compared with other advanced techniques.

Data modeling and online monitoring are two critical stages for data-driven anomaly detection. Regarding data modeling, deep neural networks (DNNs) can learn good decision boundaries to separate the anomaly and normal regions, due to their flexible model structures and excellent fitting ability. However, DNNs, using nonlinear activations with specific boundaries, may indirectly cause a limited anomaly detection margin, especially when there are samples far from centroids. Moreover, an anomaly detection model with a narrow detection margin is deemed insensitive to general faults. An anomaly detection model with a tight detection margin will suffer a severe performance degradation. To mitigate the intrinsic drawbacks of DNNs, we develop a new regularizer based on the maximum likelihood of complete data (i.e., observations and latent variables). The regularizer is neuronwise and mathematically acts as compressing neurons, dragging the marginal points into the centroids. Combining the regularizer with the encoding–decoding structure networks, we perform an industrial case study to verify the superiority of the proposed method.

Since the change of operation condition is common in industrial processes, it could cause historical process data multimodal characteristics. When the working conditions are switched, the new mode will suffer small sample problem in the initial stage of the working mode switching, which brings difficulties to the monitoring of the new mode. Different from traditional modeling method which only considers the new mode data, this paper proposes a novel multi-source transfer learning method that considers both the historical multimode and new mode data. First, the common features of historical multimode data are extracted. Then, the extracted features are transformed into the model of new mode data. In order to alleviate the problem of insufficient samples of the current working mode, the common subspace of the new mode is obtained by combining the common features of the historical multimode with the new mode data. Finally, a numerical case and a real industrial hydrocracking process are used to validate the effectiveness of the proposed method.

Due to the existence of complex disturbances and frequent switching of operational conditions characteristics in the real industrial processes, the process data under different operational conditions subject to different distributions, which means there exist different manifold structures under broad operations. Globally, the entire process data are distributed in a multimanifold structure. Nevertheless, the existing data-driven quality prediction methods do not consider the relationships among different manifolds of data and just treats the process data as a single manifold. How to extract effective multimanifold structure feature representation from complex process data and enhance online prediction ability are still challenging in the field of real industrial processes. To this end, in this article, a novel stacked multimanifold autoencoder (S-MMAE) is proposed for feature extraction and quality prediction. Especially, by introducing a new multimanifold regularization into the original loss function of stacked autoencoder at each layer, the intrinsic multimanifold structure information of data is utilized to guide the feature learning procedure. In this way, the learned features can offer a more comprehensive representation of original data and help enhance the prediction performance. At last, the application results in a practical hydrocracking process demonstrate that the proposed S-MMAE can achieve excellent prediction accuracy, which outperforms other state-of-the-art methods.

Process complexities are characterized by strong nonlinearities, dynamics, and uncertainties. Monitoring such a complex process requires a high-quality model describing the corresponding nonlinear dynamic behavior. The proposed model is constructed using deep neural networks (DNNs) to represent the state transition and observation generation, both of which constitute a stochastic nonlinear state-space model. A new bidirectional recurrent neural network (RNN), creating a connection of the hidden layer between a forward RNN and a backward RNN, is proposed to generate the filtering estimation and the smoothing estimation of process states which further generate observations with DNN-based process models. The smoothing estimator and the process model are first learned offline with all collected samples. Then the filtering estimator is fine-tuned by the learned smoother and process models to achieve real-time monitoring since the filter state is estimated based on the past and the current observations. Two indices are designed based on the learned model for monitoring the process anomaly. The proposed process monitoring model can deal with complex nonlinearities, process dynamics, and process uncertainties, all of which can be very challenging for the existing methods, such as kernel mapping and stacked auto-encoder. Two case studies validate that the effectiveness of the proposed method outperforms the other comparative methods by at least 10% when using the averaged fault detection rate in the industrial experimental data.

Multimodal data are common in industrial processes because of switched operating conditions, varying feedstocks and changed product designs and so on. To guarantee process safety and improving process performance, a variable-wise weighted parallel stacked auto-encoder model is proposed for nonlinear multimode process monitoring. Considering the similarity and difference between multiple operating modes with complex process nonlinearities, mode-common and mode-specific deep features are parallelly extracted with the proposed new model. Since each variable distinctly contributes to the mode-common features, variable-wise weights are designed with an optimal transport distance between modes when the mode-common features are learned. Moreover, different from designing a unified monitoring index for all modes, three asymmetric indices are designed to not only trigger an alarm for an anomaly, but also indicate whether the anomaly is caused by mode-common factors, mode-specific factors or others. Thus, the real-time monitoring results, together with some diagnosis information are simultaneously presented. A numerical example and a real industry application are used to validate the monitoring efficacy of the proposed model.

Batch process quality prediction is an important application in manufacturing and chemical industries. The complexity of batch processes is characterized by multiphase, nonlinearity, dynamics, and uneven durations so that modeling of these batch processes is rather difficult. Moreover, there are other challenges in the face of quality prediction. Specifically, the process trajectories over the whole running duration potentially make specific contributions to the final targets so that the prediction issue embraces tremendously high-dimensional inputs but very low-dimensional outputs. This means that the prediction suffers from a severe dimensional imbalance between inputs and outputs. Motivated by these difficulties, this paper proposes a new deep learning-based framework for complex feature representative and quality prediction. Long short-term memory (LSTM) is used to extract comprehensive quality-relevant hidden features from a long-time sequence in each phase, significantly reducing the predictor dimensions. And these features from different phases are further integrated and compressed by a stacked auto-encoder (SAE). A practical industrial example testifies to the efficacy of the proposed framework.

Most data-driven process monitoring approaches consider the fault detection as a binary classification issue: normal or abnormal. All deviations from the nominal operating condition can trigger the same alarms. They fail to distinguish different fluctuation patterns and locate the positions of anomalies, such as the normal deviations in operating conditions, sensors faults, actuator faults, and process faults. A new process monitoring strategy based on orthogonal decomposition (OD) is proposed for the concurrent detection and location of different deviation patterns. OD is performed to discriminate the dynamics of data driven by measured disturbances and unmeasured disturbances in the same control system. This way, the original variable space is decomposed into the deterministic subspace and stochastic subspace. A dynamic principal component analysis-based subspace identification technique is used to construct the monitoring indices in the deterministic and stochastic subspaces, respectively. Two case studies show the validity of the OD-based process monitoring approach. Note to Practitioners-Fault diagnosis based on process data models always focused on analyzing variables' contributions to the anomaly in the past practice. But it is frequently difficult to decide the root causes just using the variables' contributions because different faults may induce a similar variation of the same variable. This paper provides a new scheme to locate the faulty components, including the sensor faults, actuator faults, process faults, and disturbance variations. It is more pertinent to learn about the fault locations than variables' contributions. Moreover, by locating faults first and then figuring out variables' contributions to a specific location, more detailed and precise diagnosis conclusions can be drawn when being compared with the results of using the variables' contributions in a global system. This new method is purely data driven and it has no demand for complex process knowledge.