Optimal Reconstruction of Probabilistic Boolean Networks.

In gene regulatory networks (GRNs), it is important to model gene regulation based on a priori information and experimental data. As a useful mathematical model, probabilistic Boolean networks (PBNs) have been widely applied in GRNs. This article addresses the optimal reconstruction problem of PBNs based on several priori Boolean functions and sampled data. When all candidate Boolean functions are known in advance, the optimal reconstruction problem is reformulated into an optimization problem. This problem can be well solved by a recurrent neural network approach which decreases the computational cost. When parts of candidate Boolean functions are known in advance, necessary and sufficient conditions are provided for the reconstruction of PBNs. In this case, two types of reconstruction problems are further proposed: one is aimed at minimizing the number of reconstructed Boolean functions, and the other one is aimed at maximizing the selection probability of the main dynamics under noises. At last, examples in GRNs are elaborated to demonstrate the effectiveness of the main results.

Adaptive Neural Consensus Observer Networks Design for a Class of Semilinear Parabolic PDE Systems.

This article concerns the investigation on the consensus problem for the joint state-uncertainty estimation of a class of parabolic partial differential equation (PDE) systems with parametric and nonparametric uncertainties. We propose a two-layer network consisting of informed and uninformed boundary observers where novel adaptation laws are developed for the identification of uncertainties. Particularly, all observer agents in the network transmit their information with each other across the entire network. The proposed adaptation laws include a penalty term of the mismatch between the parameter estimates generated by the other observer agents. Moreover, for the nonparametric uncertainties, radial basis function (RBF) neural networks are employed for the universal approximation of unknown nonlinear functions. Given the persistently exciting condition, it is shown that the proposed network of adaptive observers can achieve exponential joint state-uncertainty estimation in the presence of parametric uncertainties and ultimate bounded estimation in the presence of nonparametric uncertainties based on the Lyapunov stability theory. The effects of the proposed consensus method are demonstrated through a typical reaction-diffusion system example, which implies convincing numerical findings.

Hierarchical Self-Attention Network for Industrial Data Series Modeling With Different Sampling Rates Between the Input and Output Sequences.

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.

Quality Prediction Modeling for Industrial Processes Using Multiscale Attention-Based Convolutional Neural Network.

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.

Reinforcement Learning for Blast Furnace Ironmaking Operation With Safety and Partial Observation Considerations.

Making proper decision online in complex environment during the blast furnace (BF) operation is a key factor in achieving long-term success and profitability in the steel manufacturing industry. Regulatory lags, ore source uncertainty, and continuous decision requirement make it a challenging task. Recently, reinforcement learning (RL) has demonstrated state-of-the-art performance in various sequential decision-making problems. However, the strict safety requirements make it impossible to explore optimal decisions through online trial and error. Therefore, this article proposes a novel offline RL approach designed to ensure safety, maximize return, and address issues of partially observed states. Specifically, it utilizes an off-policy actor-critic framework to infer the optimal decision from expert operation trajectories. The "actor" in this framework is jointly trained by the supervision and evaluation signals to make decision with low risk and high return. Furthermore, we investigate a recurrent version of the actor and critic networks to better capture the complete observations, which solves the partially observed Markov decision process (POMDP) arising from sensor limitations. Verification within the BF smelting process demonstrates the improvements of the proposed algorithm in performance, i.e., safety and return.

Error-Triggered Adaptive Sparse Identification for Predictive Control and Its Application to Multiple Operating Conditions Processes.

With the digital transformation of process manufacturing, identifying the system model from process data and then applying to predictive control has become the most dominant approach in process control. However, the controlled plant often operates under changing operating conditions. What is more, there are often unknown operating conditions such as first appearance operating conditions, which make traditional predictive control methods based on identified model difficult to adapt to changing operating conditions. Moreover, the control accuracy is low during operating condition switching. To solve these problems, this article proposes an error-triggered adaptive sparse identification for predictive control (ETASI4PC) method. Specifically, an initial model is established based on sparse identification. Then, a prediction error-triggered mechanism is proposed to monitor operating condition changes in real time. Next, the previously identified model is updated with the fewest modifications by identifying parameter change, structural change, and combination of changes in the dynamical equations, thus achieving precise control to multiple operating conditions. Considering the problem of low control accuracy during the operating condition switching, a novel elastic feedback correction strategy is proposed to significantly improve the control accuracy in the transition period and ensure accurate control under full operating conditions. To verify the superiority of the proposed method, a numerical simulation case and a continuous stirred tank reactor (CSTR) case are designed. Compared with some state-of-the-art methods, the proposed method can rapidly adapt to frequent changes in operating conditions, and it can achieve real-time control effects even for unknown operating conditions such as first appearance operating conditions.

ADP-Based Event-Triggered Constrained Optimal Control on Spatiotemporal Process: Application to Temperature Field in Roller Kiln.

The precise control of the spatiotemporal process in a roller kiln is crucial in the production of Ni-Co-Mn layered cathode material of lithium-ion batteries. Since the product is extremely sensitive to temperature distribution, temperature field control is of great significance. In this article, an event-triggered optimal control (ETOC) method with input constraints for the temperature field is proposed, which takes up an important position in reducing the communication and computation costs. A nonquadratic cost function is adopted to describe the system performance with input constraints. First, we present the problem description of the temperature field event-triggered control, where this field is described by a partial differential equation (PDE). Then, the event-triggered condition is designed according to the information of system states and control inputs. On this basis, a framework of the event-triggered adaptive dynamic programming (ETADP) method that is based on the model reduction technology is proposed for the PDE system. A critic network is used to approach the optimal performance index by a neural network (NN) together with that an actor network is used to optimize the control strategy. Furthermore, an upper bound of the performance index and a lower bound of interexecution times, as well as the stabilities of the impulsive dynamic system and the closed-loop PDE system, are also proved. Simulation verification demonstrates the effectiveness of the proposed method.

Multiscale Feature Fusion and Semi-Supervised Temporal-Spatial Learning for Performance Monitoring in the Flotation Industrial Process.

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.

Multi-scale feature selection network for lightweight image super-resolution.

Recently, many super-resolution (SR) methods based on convolutional neural networks (CNNs) have achieved superior performance by utilizing deep and heavy models, which may not be suitable for real-world low-budget devices. To address this issue, we propose a novel lightweight SR network called a multi-scale feature selection network (MFSN). As the basic building block of MFSN, the multi-scale feature selection block (MFSB) is presented to extract the rich multi-scale features from a coarse-to-fine receptive field level. For a better representation ability, a wide-activated residual unit is adopted in each branch of MFSB except the last one. In MFSB, the scale selection module (SSM) is designed to effectively fuse the features from two adjacent branches by adjusting receptive field sizes adaptively. Further, a comprehensive channel attention mechanism (CCAM) is integrated into SSM to learn the dynamic selection weight by considering the local and global inter-channel dependencies. Extensive experimental results illustrate that the proposed MFSN is superior to other lightweight methods.

A Spatial-Temporal Variational Graph Attention Autoencoder Using Interactive Information for Fault Detection in Complex Industrial Processes.

Modern industry processes are typically composed of multiple operating units with reaction interaction and energy-mass coupling, which result in a mixed time-varying and spatial-temporal coupling of process variables. It is challenging to develop a comprehensive and precise fault detection model for the multiple interconnected units by simple superposition of the individual unit models. In this study, the fault detection problem is formulated as a spatial-temporal fault detection problem utilizing process data of multiple interconnected unit processes. A spatial-temporal variational graph attention autoencoder (STVGATE) using interactive information is proposed for fault detection, which aims to effectively capture the spatial and temporal features of the interconnected unit processes. First, slow feature analysis (SFA) is implemented to extract temporal information that reveals the dynamic relevance of the process data. Then, an integration method of metric learning and prior knowledge is proposed to construct coupled spatial relationships based on temporal information. In addition, a variational graph attention autoencoder (VGATE) is suggested to extract temporal and spatial information for fault detection, which incorporates the dominances of variational inference and graph attention mechanisms. The proposed method can automatically extract and deeply mine spatial-temporal interactive feature information to boost detection performance. Finally, three industrial process experiments are performed to verify the feasibility and effectiveness of the proposed method. The results demonstrate that the proposed method dramatically increases the fault detection rate (FDR) and reduces the false alarm rate (FAR).

Memory Shapelet Learning for Early Classification of Streaming Time Series.

Early classification predicts the class of the incoming sequences before it is completely observed. How to quickly classify streaming time series without losing interpretability through early classification method is a challenging problem. A novel memory shapelet learning framework for early classification is proposed in this article. First, a memory distance matrix is introduced to store the historical characteristics of streaming time series, which can alleviate repetitive calculations caused by the growing length of time series. Second, early interpretable shapelets are extracted in the proposed method by optimizing both accuracy objective and earliness objective simultaneously. The proposed method employs end-to-end learning, which allows the model to directly learn early shapelets without the necessity of searching for numerous candidate shapelets. Third, an objective function of memory shapelet learning is proposed by overall considering accuracy and earliness, which can be optimized by gradient descent algorithm. Finally, experiments are conducted on benchmark dataset UCR, Tennessee Eastman process, and real-world aluminum electrolysis process in China. Comparable results with other state-of-the-art methods demonstrate the superior performance of the proposed method in interpretability, accuracy, earliness, and time complexity.

EaLDL: Element-Aware Lifelong Dictionary Learning for Multimode Process Monitoring.

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.

A Multi-Featured Factor Analysis and Dynamic Window Rectification Method for Remaining Useful Life Prognosis of Rolling Bearings.

Currently, the research on the predictions of remaining useful life (RUL) of rotating machinery mainly focuses on the process of health indicator (HI) construction and the determination of the first prediction time (FPT). In complex industrial environments, the influence of environmental factors such as noise may affect the accuracy of RUL predictions. Accurately estimating the remaining useful life of bearings plays a vital role in reducing costly unscheduled maintenance and increasing machine reliability. To overcome these problems, a health indicator construction and prediction method based on multi-featured factor analysis are proposed. Compared with the existing methods, the advantages of this method are the use of factor analysis, to mine hidden common factors from multiple features, and the construction of health indicators based on the maximization of variance contribution after rotation. A dynamic window rectification method is designed to reduce and weaken the stochastic fluctuations in the health indicators. The first prediction time was determined by the cumulative gradient change in the trajectory of the HI. A regression-based adaptive prediction model is used to learn the evolutionary trend of the HI and estimate the RUL of the bearings. The experimental results of two publicly available bearing datasets show the advantages of the method.

VAE-Based Interpretable Latent Variable Model for Process Monitoring.

Latent variable-based process monitoring (PM) models have been generously developed by shallow learning approaches, such as multivariate statistical analysis and kernel techniques. Owing to their explicit projection objectives, the extracted latent variables are usually meaningful and easily interpretable in mathematical terms. Recently, deep learning (DL) has been introduced to PM and has exhibited excellent performance because of its powerful presentation capability. However, its complex nonlinearity prevents it from being interpreted as human-friendly. It is a mystery how to design a proper network structure to achieve satisfactory PM performance for DL-based latent variable models (LVMs). In this article, a variational autoencoder-based interpretable LVM (VAE-ILVM) is developed for PM. Based on Taylor expansions, two propositions are proposed to guide the design of appropriate activation functions for VAE-ILVM, allowing nondisappearing fault impact terms contained in the generated monitoring metrics (MMs). During threshold learning, the sequence of counting that test statistics exceed the threshold is considered a martingale, a representative of weakly dependent stochastic processes. A de la Peña inequality is then adopted to learn a suitable threshold. Finally, two chemical examples verify the effectiveness of the proposed method. The use of de la Peña inequality significantly reduces the minimum required sample size for modeling.

LSTMED: An uneven dynamic process monitoring method based on LSTM and Autoencoder neural network.

Due to the complicated production mechanism in multivariate industrial processes, different dynamic features of variables raise challenges to traditional data-driven process monitoring methods which assume the process data is static or dynamically consistent. To tackle this issue, this paper proposes a novel process monitoring method based on the long short-term memory (LSTM) and Autoencoder neural network (called LSTMED) for multivariate process monitoring with uneven dynamic features. First, the LSTM units are arranged in the encoder-decoder form to construct an end-to-end model. Then, the constructed model is trained in an unsupervised manner to capture long-term time dependency within variables and dominant representation of high dimensional process data. Afterward, the kernel density estimation (KDE) method is performed to determine the control limit only based on the reconstruction error from historical normal data. Finally, effective online monitoring for uneven dynamic process can be achieved. The performance and advantage of the process monitoring method proposed are explained through typical cases, including the numerical simulation and Tennessee Eastman (TE) benchmark process, and comparative experimental analysis with state-of-the-art methods.

Adaptive Multimode Process Monitoring Based on Mode-Matching and Similarity-Preserving Dictionary Learning.

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.

Event-Triggered Optimal Control for Temperature Field of Roller Kiln Based on Adaptive Dynamic Programming.

Temperature field control is crucial for the comprehensive performance of Ni-Co-Mn layered cathode material that is the most important part of lithium-ion batteries. Starting from the aspect of a class of distributed parameter systems described by highly dissipative partial differential equations (PDEs), an event-triggered optimal control (ETOC) method based on adaptive dynamic programming (ADP) for the roller kiln temperature field is proposed. First, we formulate the event-triggered control problem of the temperature field under the general framework of PDE systems. Then, an event-triggered condition is designed based on the stability of the closed-loop PDE system, which also guarantees the upper bound of the performance index. Subsequently, ADP technology is adopted to realize the ETOC, where the critic network is employed to approximate the optimal value function. Since the studied system can be regarded as an impulsive dynamic system with flow dynamics and jump dynamics simultaneously, the stability of the impulsive dynamic system combined with the ADP-based closed-loop PDE system is proved. Finally, simulation results on the temperature field verify the effectiveness of the proposed method.

Weak Stabilization of Boolean Networks Under State-Flipped Control.

In this brief, stabilization of Boolean networks (BNs) by flipping a subset of nodes is considered, here we call such action state-flipped control. The state-flipped control implies that the logical variables of certain nodes are flipped from 1 to 0 or 0 to 1 as time flows. Under state-flipped control on certain nodes, a state-flipped-transition matrix is defined to describe the impact on the state transition space. Weak stabilization is first defined and then some criteria are presented to judge the same. An algorithm is proposed to find a stabilizing kernel such that BNs can achieve weak stabilization to the desired state with in-degree more than 0. By defining a reachable set, another approach is proposed to verify weak stabilization, and an algorithm is given to obtain a flip sequence steering an initial state to a given target state. Subsequently, the issue of finding flip sequences to steer BNs from weak stabilization to global stabilization is addressed. In addition, a model-free reinforcement algorithm, namely the Q -learning ( [Formula: see text]) algorithm, is developed to find flip sequences to achieve global stabilization. Finally, several numerical examples are given to illustrate the obtained theoretical results.

Toward Robust Fault Identification of Complex Industrial Processes Using Stacked Sparse-Denoising Autoencoder With Softmax Classifier.

This article proposes a robust end-to-end deep learning-induced fault recognition scheme by stacking multiple sparse-denoising autoencoders with a Softmax classifier, called stacked spare-denoising autoencoder (SSDAE)-Softmax, for the fault identification of complex industrial processes (CIPs). Specifically, sparse denoising autoencoder (SDAE) is established by integrating a sparse AE (SAE) with a denoising AE (DAE) for the low-dimensional but intrinsic feature representation of the CIP monitoring data (CIPMD) with possible noise contamination. SSDAE-Softmax is established by stacking multiple SDAEs with a layerwise pretraining procedure, and a Softmax classifier with a global fine-tuning strategy. Furthermore, SSDAE-Softmax hyperparameters are optimized by a relatively new global optimization algorithm, referred to as the state transition algorithm (STA). Benefiting from the deep learning-based feature representation scheme with the STA-based hyperparameter optimization, the underlying intrinsic characteristics of CIPMD can be learned automatically and adaptively for accurate fault identification. A numeric simulation system, the benchmark Tennessee Eastman process (TEP), and a real industrial process, that is, the continuous casting process (CCP) from a top steel plant of China, are used to validate the performance of the proposed method. Experimental results show that the proposed SSDAE-Softmax model can effectively identify various process faults, and has stronger robustness and adaptability against the noise interference in CIPMD for the process monitoring of CIPs.

Imputation of Missing Values in Time Series Using an Adaptive-Learned Median-Filled Deep Autoencoder.

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.