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.

In [1], to maintain the integrity of the publication and uphold academic standards, a correction is requested for an identified error. Fig. 12 in the article is a duplicate of Fig. 13 due to an inadvertent mistake during the final stages of manuscript preparation.

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.

The growth of data collection in industrial processes has led to a renewed emphasis on the development of data-driven soft sensors. A key step in building an accurate, reliable soft sensor is feature representation. Deep networks have shown great ability to learn hierarchical data features using unsupervised pretraining and supervised fine-tuning. For typical deep networks like stacked auto-encoder (SAE), the pretraining stage is unsupervised, in which some important information related to quality variables may be discarded. In this article, a new quality-driven regularization (QR) is proposed for deep networks to learn quality-related features from industrial process data. Specifically, a QR-based SAE (QR-SAE) is developed, which changes the loss function to control the weights of the different input variables. By choosing an appropriate inductive bias for the weight matrix, the model provides quality-relevant information for predictive modeling. Finally, the proposed QR-SAE is used to predict the quality of a real industrial hydrocracking process. Comparative experiments show that QR-SAE can extract quality-related features and achieve accurate prediction performance.

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.

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.

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.

Accurate prediction of quality variables that are difficult to measure is crucial for industrial process control and optimization. However, the fluctuations in raw material quality and production conditions may cause industrial process data to be distributed in multiple working conditions. The data under the same working condition show similar characteristics, which are often defined as one data mode. Hence, the overall process data exhibit multimode characteristics, which brings great challenges in developing a uniform prediction model. Besides, the noninterpretability of the existing data-driven prediction models brings great resistance to their practical application. To address these issues, this article proposes a novel data mode related interpretable transformer network (DMRI-Former) for predictive modeling and key sample analysis in industrial processes. In DMRI-Former, a novel data mode related interpretable self-attention mechanism is designed to enhance the homomode perceptual ability of each individual mode while also capturing cross-mode features of different modes. Moreover, the key samples under different modes can be discovered using DMRI-Former, which further improves the interpretability of the modeling process. Finally, the superiority of the proposed DMRI-Former is verified in two real-world industrial processes compared to other state-of-the-art methods.

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 development of high-throughput technologies for gene analysis, the biclustering method has attracted much attention. However, existing methods have problems with high time and space complexity. This paper proposes a biclustering method, called Row and Column Structure-based Biclustering (RCSBC), with low time and space complexity to find checkerboard patterns within microarray data. First, the paper describes the structure of bicluster by using the structure of rows and columns. Second, the paper chooses the representative rows and columns with two algorithms. Finally, the gene expression data are biclustered on the space spanned by representative rows and columns. To the best of our knowledge, this paper is the first to exploit the relationship between the row/column structure of a gene expression matrix and the structure of biclusters. Both the synthetic datasets and the real-life gene expression datasets are used to validate the effectiveness of our method. It can be seen from the experiment results that the RCSBC outperforms the state-of-the-art algorithms both on clustering accuracy and time/space complexity. This study offers new insights into biclustering the large-scale gene expression data without loading the whole data into memory.

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.

Multivariate analysis is an important kind of method in process monitoring and fault detection, in which the canonical correlation analysis (CCA) makes use of the correlation change between two groups of variables to distinguish the system status and has been greatly studied and applied. For the monitoring of nonlinear dynamic systems, the deep neural network-aided CCA (DNN-CCA) has received much attention recently, but it lacks a general definition and comparative study of different network structures. Therefore, this article first introduces four deep neural network (DNN) models that are suitable to combine with CCA, and the general form of DNN-CCA is given in detail. Then, the experimental comparison of these methods is conducted through three cases, so as to analyze the characteristics and distinctions of CCA aided by each DNN model. Finally, some suggestions on method selection are summarized, and the existed open issues in the current DNN-CCA form and future directions are discussed.

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.

In industrial processes, inferential sensors have been extensively applied for prediction of quality variables that are difficult to measure online directly by hard sensors. Deep learning is a recently developed technique for feature representation of complex data, which has great potentials in soft sensor modeling. However, it often needs a large number of representative data to train and obtain a good deep network. Moreover, layer-wise pretraining often causes information loss and generalization degradation of high hidden layers. This greatly limits the implementation and application of deep learning networks in industrial processes. In this article, a layer-wise data augmentation (LWDA) strategy is proposed for the pretraining of deep learning networks and soft sensor modeling. In particular, the LWDA-based stacked autoencoder (LWDA-SAE) is developed in detail. Finally, the proposed LWDA-SAE model is applied to predict the 10% and 50% boiling points of the aviation kerosene in an industrial hydrocracking process. The results show that the LWDA-SAE-based soft sensor is superior to multilayer perceptron, traditional SAE, and the SAE with data augmentation only for its input layer (IDA-SAE). Moreover, LWDA-SAE can converge at a faster speed with a lower learning error than the other methods.

Soft sensor has been extensively utilized in industrial processes for prediction of key quality variables. To build an accurate virtual sensor model, it is very significant to model the dynamic and nonlinear behaviors of process sequential data properly. Recently, a long short-term memory (LSTM) network has shown great modeling ability on various time series, in which basic LSTM units can handle data nonlinearities and dynamics with a dynamic latent variable structure. However, the hidden variables in the basic LSTM unit mainly focus on describing the dynamics of input variables, which lack representation for the quality data. In this paper, a supervised LSTM (SLSTM) network is proposed to learn quality-relevant hidden dynamics for soft sensor application, which is composed of basic SLSTM unit at each sampling instant. In the basic SLSTM unit, the quality and input variables are simultaneously utilized to learn the dynamic hidden states, which are more relevant and useful for quality prediction. The effectiveness of the proposed SLSTM network is demonstrated on a penicillin fermentation process and an industrial debutanizer column.

Deep learning is a recently developed feature representation technique for data with complicated structures, which has great potential for soft sensing of industrial processes. However, most deep networks mainly focus on hierarchical feature learning for the raw observed input data. For soft sensor applications, it is important to reduce irrelevant information and extract quality-relevant features from the raw input data for quality prediction. To deal with this problem, a novel deep learning network is proposed for quality-relevant feature representation in this article, which is based on stacked quality-driven autoencoder (SQAE). First, a quality-driven autoencoder (QAE) is designed by exploiting the quality data to guide feature extraction with the constraint that the potential features should largely reconstruct the input layer data and the quality data at the output layer. In this way, quality-relevant features can be captured by QAE. Then, by stacking multiple QAEs to construct the deep SQAE network, SQAE can gradually reduce irrelevant features and learn hierarchical quality-relevant features. Finally, the high-level quality-relevant features can be directly applied for soft sensing of the quality variables. The effectiveness and flexibility of the proposed deep learning model are validated on an industrial debutanizer column process.

Deep learning has been recently introduced for soft sensors in industrial processes. However, most of the existing deep networks, such as stacked autoencoder, are pretrained in a layerwise unsupervised way to learn feature representations for the raw input data itself. For soft sensors, it is necessary to extract quality-relevant features for quality prediction. Thus, a deep layerwise supervised pretraining framework is proposed for quality-relevant feature extraction and soft sensor modeling in this article, which is based on stacked supervised encoder-decoder (SSED). In SSED, hierarchical quality-relevant features are successively learned by a number of supervised encoder-decoder (SED) models. For each SED, the features from the previous hidden layer are served as new inputs to generate the high-level features that are learned with the constraint of predicting the quality data as good as possible at the output layer of this SED. With this new structure, the SED can learn quality-relevant features that can largely improve the prediction performance. By stacking multiple SEDs, hierarchical quality-relevant features can be progressively learned, and irrelevant information is gradually reduced by deep SSED network. The effectiveness of the proposed model is demonstrated on a numerical example and an industrial process of the debutanizer column.

Nowadays, data-driven soft sensors have been developed to estimate the quality variables which are difficult-to-measure in industrial processes. Feature representation plays a significant role in constructing accurate soft sensors. Recently, deep learning has been introduced for feature representation in process data modeling. However, traditional deep networks cannot capture quality-related features for output prediction. To handle this problem, a nonlinear variable-wise weighted stacked autoencoder (NVW-SAE) is proposed to learn deep quality-related features in this paper. By measuring the nonlinear Kendall correlations of input or feature variables with the quality variable in each autoencoder, a corresponding weighted reconstruction objective function is designed to learn quality-related features layer by layer in NVW-SAE. Finally, the proposed NVW-SAE based soft sensor method is applied to a debutanizer column to estimate the concentration of butane, which shows its effectiveness and superiority.

Recommender systems are effective in predicting the most suitable products for users, such as movies and books. To facilitate personalized recommendations, the quality of item ratings should be guaranteed. However, a few ratings might not be accurate enough due to the uncertainty of user behavior and are referred to as natural noise. In this article, we present a novel fuzzy clustering‐based method for detecting noisy ratings. The entropy of a subset of the original ratings dataset is used to indicate the data‐driven uncertainty, and evaluation metrics are adopted to represent the prediction‐driven uncertainty. After the repetition of resampling and the execution of a recommendation algorithm, the entropy and evaluation metrics vectors are obtained and are empirically categorized to identify the proportion of the potential noise. Then, the fuzzy C‐means‐based denoising (FCMD) algorithm is performed to verify the natural noise under the assumption that natural noise is primarily the result of the exceptional behavior of users. Finally, a case study is performed using two real‐world datasets. The experimental results show that our proposal outperforms previous proposals and has an advantage in dealing with natural noise.

In modern industrial processes, soft sensors have played an important role for effective process control, optimization, and monitoring. Feature representation is one of the core factors to construct accurate soft sensors. Recently, deep learning techniques have been developed for high-level abstract feature extraction in pattern recognition areas, which also have great potential for soft sensing applications. Hence, deep stacked autoencoder (SAE) is introduced for soft sensor in this paper. As for output prediction purpose, traditional deep learning algorithms cannot extract high-level output-related features. Thus, a novel variable-wise weighted stacked autoencoder (VW-SAE) is proposed for hierarchical output-related feature representation layer by layer. By correlation analysis with the output variable, important variables are identified from other ones in the input layer of each autoencoder. The variables are assigned with different weights accordingly. Then, variable-wise weighted autoencoders are designed and stacked to form deep networks. An industrial application shows that the proposed VW-SAE can give better prediction performance than the traditional multilayer neural networks and SAE.

Just-in-time learning (JITL) is a commonly used technique for industrial soft sensing of nonlinear processes. However, traditional JITL approaches mainly focus on equal sample sizes between process (input) variables and quality (output) variables, which may not be practical in industrial processes since quality variables are usually much harder to obtain than other process variables. In order to handle unequal length dataset with only a few labeled data, a novel semisupervised JITL framework is proposed for soft sensor modeling for nonlinear processes, which is based on semisupervised weighted probabilistic principal component regression (SWPPCR). In the new semisupervised JITL framework, traditional Mahalanobis distance and a new proposed scaled Mahalanobis distance are used for similarity measurement and weight assignment. By selecting the most relevant labeled and unlabeled samples and assigning them with the corresponding weights, a local SWPPCR can be built to estimate the output variables of the query sample. Case studies are carried out to evaluate the prediction performance of the proposed semisupervised JITL framework on a numerical example and an industrial process. The effectiveness and flexibility of the proposed method are demonstrated by the prediction results.