With the increasing complexity of industrial systems and process data, deep learning has achieved superior performance in soft sensing but remains constrained by limited interpretability. Most existing interpretability techniques are correlation based, capturing statistical dependencies but providing little insight into underlying mechanisms. Causal modeling, by contrast, offers stronger interpretability by revealing directional and temporal influences, thereby improving both reliability and understanding. Although some recent methods consider time delays, their treatment of lags remains coarse and limited, and cannot adequately capture heterogeneous cross variable delay patterns in industrial time series. To address these limitations, we propose spatio-temporal causal learning with delay annotation (STCLD), which introduces a spatio-temporal delay attention (STDA) module to explicitly learn delay annotated spatio temporal causal graphs for soft sensing. STDA minimizes a maximum mean discrepancy objective to discover causal relations with edge specific delays, while attention path strength and multidimensional dynamic complexity are used to infer causal directions in a model-based way. The learned causal graph and delay information then guide a delay aware prediction module to build a self-interpretable soft sensor. Experiments on two real-world industrial datasets show that STCLD consistently outperforms strong baselines in both predictive accuracy and causal interpretability, providing a robust and general framework for interpretable soft sensor modeling in complex process industries.

In this article, the anti-disturbance switching control approach is proposed for silicon single crystal growth systems with unmeasured states. Initially, the silicon single crystal growth systems are modeled by using the geometrical models of meniscus section, hydrodynamic and heat transfer process of silicon single crystal growth. Since numerous unmeasurable state variables exist in systems and the growth equipments are affected by external and internal disturbances, consideration is given to employing the output feedback control scheme and disturbance observer method in the construction of the anti-disturbance switching controller. Meanwhile, considering the high accuracy of linear systems at equilibrium points, the silicon single crystal growth systems are divided into multiple subsystems using switching control method, that is, multiple equilibrium points are set to enable the systems to switch between different subsystem models, thereby the precision of silicon single crystal growth systems has been improved. Then, using the multiple Lyapunov function method and linear matrix inequality technique, the exponential stability of silicon single crystal growth systems is ensured with the $\boldsymbol {H_{\infty }}$ performance. Finally, the feasibility of designed switching anti-disturbance output feedback control method is verified through actual parameters of silicon single crystal growth systems.

Deep learning-based soft sensors (DLSSs) have been demonstrated to exhibit significantly improved sensing accuracy; however, their vulnerability to adversarial attacks affects their reliability, thus hindering their widespread application. To improve the reliability of DLSSs, in this article, we conducted a systematic investigation of the adversarial attack and defense of DLSSs. By considering the task requirements of DLSSs and the actual scenarios that attackers may encounter, a framework based on black-box attack and proactive defense was proposed to realize the adversarial attack and defense of soft sensors. The adversarial attack was implemented through the proposed knowledge-guided adversarial attack (KGAA) method. By reconstructing the optimization model and introducing the mechanism knowledge into the objective function, the KGAA method could overcome the ill-posed problem of adversarial attack optimization when attacking a regression model. Moreover, based on the KGAA, a corresponding KGAA adversarial training defense method was proposed to achieve proactive defense. The attack and defense methods were verified in terms of the thermal deformation sensing of an air preheater rotor. Compared to other attacks, the KGAA exhibited higher imperceptibility, rationality, and stability; it can thus be considered a practical attack. The implementation of KGAA adversarial training enhances the adversarial robustness of DLSSs, thus aiding the defense of DLSSs to various attacks and improving their reliability.

Multi-furnace scheduling simultaneously is an important part to increase productivity and reduce the production cost in single crystal silicon enterprises. In the restrained power consumption requirements environment, the optimal sequencing of process operation start-time for single crystal furnaces is a challenging problem. To solve this problem, the scheduling model of multi-furnace scheduling is established in this paper to minimize the maximum completion time. Then, an improved DE algorithm called the multi-strategy individual adaptive mutation differential evolution algorithm (MSIADE) is presented to address the scheduling model. In the improved DE algorithm, the different dimensional and multi-strategy mutation operations are adopted to refrain the algorithm from the local optimal, then the different mutation factors are assigned to each individual through the rank of fitness function value to strengthen the exploration ability of the MSIADE algorithm. Simulation experiments results based on the standard test functions and the established scheduling model show the feasibility in the established model and the effectiveness in the proposed algorithm.

The increased dynamics and complexity of wireless sensor networks (WSNs) raise higher requirements on the flexibility and applicability of data collection algorithms. Therefore, a novel distributed optimization framework for data collection with energy harvesting in duty-cycle (DC) WSNs is developed in this article, which employs the mobile collector (called SenCar) to collect data from the selected sensors (called anchors) to circumvent the bottlenecks caused by the variations of energy distribution. In order to guarantee the optimality of mobile data collection, it is divided into two steps: first, a method for calculating the optimal number of anchors is developed and then an adaptive anchor selection algorithm is proposed to determine those anchors. Second, the mobile data collection problem of DC WSNs is formulated as a delay optimization problem constrained by flow conversation, congestion control, and energy balance. Then, we focus on designing the distributed algorithm to resolve that optimization problem, in which each sensor node only needs to communicate with its neighbors to make decisions without any global information and can locally adjust the information weight of its neighbors. Besides, the accelerated distributed algorithm with the uncoordinated step size is also proposed to improve the convergence rate. Furthermore, the explicit convergence analysis of the proposed algorithm is provided in this article. Finally, the numerical results show that our algorithm can quickly converge to the optimal solution and has obvious superiority in adjusting link flow, storing energy, and extending network lifetime.

For deep learning-based soft sensors, the lack of interpretability and the consequent unreliability has become one of the most important problems. In this article, a neural network scheme called the deep multiple attention soft sensor (DMASS), which consists solely of attention mechanisms, is proposed to develop a self-interpretable soft sensor. DMASS was established to ensure the self-interpretability of data selection and sensor modeling and try to integrate these originally independent phases into the single scheme. First, the existing attention mechanisms’ core implementation steps are summarized as a unified form, and then the variable attention mechanism and time lag attention mechanism are proposed. When DMASS's training is completed, the obtained attention weights provide the self-interpretable data selection results. Then, a self-attention activation structure (SAAS) is proposed to extract the nonlinear spatio-temporal features of data. The mathematical expression for the extracted feature, the SAAS's attention matrix, the information path diagram for DMASS's training, and the uncertainty-aware interval prediction show the self-interpretability of sensor modeling. Finally, DMASS was applied to predict the thermal deformation of the air preheater rotor, and the validity of DMASS's self-interpretability is verified by the known mechanism analysis and information bottleneck theory. Meanwhile, DMASS's great sensing performance was confirmed through comparison with other novel soft sensors.

Shape fitting, including straight line and ellipse fitting, plays an important role in the (cylinder-) shape control system of silicon single crystal growth, because the straight lines and ellipse in the crystal image contain the important horizontal circle center and diameter information. This information can be used as control variables so that the grown crystal approximates to a perfect cylinder, and thus can be used as high-quality source materials. In this paper, we develop new straight line and ellipse fitting algorithms. The key points are as follows. We formulate the two-dimensional (2-D) binary image into a single-snapshot array signal of a virtual sensor array, and casts the angle estimation problem of straight lines into the direction finding one of virtual incoming sources. Based on the virtual array manifold and potential incoming angles, the relevant over-complete dictionary is constructed, and thus a sparse regression problem is formed. To solve such a regression problem, we introduce the weight vector sparsity term into the conventional linear least-squares support vector regression framework to estimate the angles of these straight lines. Based on the estimated angles and potential offsets, another over-complete dictionary is constructed, and thus the image can be looked upon as the sparse representation of these dictionary atoms. Since the constructed dictionary is of the same size as the image, we use the compressed sensing theory to reduce the relevant dimensionality and then apply the aforementioned sparse regression method to obtain the relevant offsets of these straight lines. We derive a new second-order polynomial of ellipse equation to obtain the ellipse parameters to avoid the trival solution from the conventional polynomial model. Some simulation and experimental examples are given to illustrate the effectiveness of the proposed algorithms.

Ellipse fitting is widely applied in the fields of computer vision and automatic industry control, in which the procedure of ellipse fitting often follows the preprocessing step of edge detection in the original image. Therefore, the ellipse fitting method also depends on the accuracy of edge detection besides their own performance, especially due to the introduced outliers and edge point errors from edge detection which will cause severe performance degradation. In this paper, we develop a robust ellipse fitting method to alleviate the influence of outliers. The proposed algorithm solves ellipse parameters by linearly combining a subset of ("more accurate") data points (formed from edge points) rather than all data points (which contain possible outliers). In addition, considering that squaring the fitting residuals can magnify the contributions of these extreme data points, our algorithm replaces it with the absolute residuals to reduce this influence. Moreover, the norm of data point errors is bounded, and the worst case performance optimization is formed to be robust against data point errors. The resulting mixed l1-l2 optimization problem is further derived as a second-order cone programming one and solved by the computationally efficient interior-point methods. Note that the fitting approach developed in this paper specifically deals with the overdetermined system, whereas the current sparse representation theory is only applied to underdetermined systems. Therefore, the proposed algorithm can be looked upon as an extended application and development of the sparse representation theory. Some simulated and experimental examples are presented to illustrate the effectiveness of the proposed ellipse fitting approach.