A method of local anode effect prediction is proposed for the problem that it is difficult to detect the local anode effect in large aluminum reduction cell in real time. Firstly, a fuzzy classification of local anode effect prediction in terms of fuzziness level is proposed considering various working conditions of anode current in the region. Secondly, a current volatility detection method based on time-sliding window density is designed from the problem of uneven current distribution in the region, and the anode currents in the region are classified and tracked for prediction according to the different current volatility. Thirdly, an improved Gated Recurrent Unit (GRU) neural network structure is proposed to improve the prediction accuracy of fluctuating currents. Finally, simulation experiments are conducted based on actual data, and compared with Long Short-Term Memory (LSTM) and Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM), the proposed method has certain advantages in both prediction time, training time, and the mean absolute error (MAE) and mean square error (MSE), which verifies the effectiveness of the proposed method.

Alumina concentration is an important parameter in the production process of aluminum electrolysis. Due to the complex production environment in the industrial field and the complex physical and chemical reactions in the aluminum reduction cell, nowadays it is still unable to carry out online measurement and real-time monitoring. For solving this problem, a soft-sensing model of alumina concentration based on a deep belief network (DBN) is proposed. However, the soft-sensing model may have some limitations for different cells and different periodic working conditions such as local anode effect, pole changing, and bus lifting in the same cell. The empirical mode decomposition (EMD) and particle swarm optimization (PSO) with the DBN are combined, and an EMD–PSO–DBN method that can denoize and optimize the model structure is proposed. The simulation results show that the improved soft-sensing model improves the accuracy and universality of prediction.

New stability and robust stability results are given based on weaker conservative assumptions. First, new boundary condition is designed. It is less conservative and has broader application range than that has been given. Then, we derive the results which have the same form, but under a weaker conservative assumption. Meanwhile, the process of the proofs has been simplified. Finally, an example is given to illustrate our results. Our results can be extended to the fields of stabilization, filtering and state estimation, and so forth.

Advanced technology for process monitoring and fault diagnosis is widely used in complex industrial processes. An important issue that needs to be considered is the ability to monitor key performance indicators (KPIs), which often cannot be measured sufficiently quickly or accurately. This paper proposes a data-driven approach based on maximizing the coefficient of determination for probabilistic soft sensor development when data are missing. Firstly, the problem of missing data in the training sample set is solved using the expectation maximization (EM) algorithm. Then, by maximizing the coefficient of determination, a probability model between secondary variables and the KPIs is developed. Finally, a Gaussian mixture model (GMM) is used to estimate the joint probability distribution in the probabilistic soft sensor model, whose parameters are estimated using the EM algorithm. An experimental case study on the alumina concentration in the aluminum electrolysis industry is investigated to demonstrate the advantages and the performance of the proposed approach.

Deep learning is an appropriate methodology for modeling complex industrial data in the field of soft sensors, owing to its powerful feature representation capability. Given the nonlinear and dynamic nature of the process industry, the key challenge for soft sensor technology is to effectively mine dynamic information from long sequences and accurately extract features of relevance to quality. A dual temporal attention mechanism-based convolutional long short-term memory network (DTA-ConvLSTM) under an encoder-decoder framework is proposed as a soft sensor model to acquire quality-relevant dynamic features from serial data. Considering different influences of process variables for prediction at multiple time steps and various locations, ConvLSTM and temporal self-attention mechanism are utilized as the encoder to adaptively fuse spatiotemporal features and capture long-term dynamic properties of process in order to capture the trends of industrial variables. Furthermore, a quality-driven temporal attention mechanism is employed throughout the decoding process to dynamically select relevant features to more accurately track quality changes. The encoder-decoder model meticulously analyses the interactions between process and quality variables by incorporating dual-sequence dynamic information to improve the prediction performance. The validity and superiority of the DTA-ConvLSTM model was validated on two industrial case studies of the debutanizer column and sulfur recovery unit. Compared to the traditional LSTM model, the proposed model demonstrated a substantial improvement with the accuracy R² up to 97.3% and 94.9% and the root mean square error reducing to 0.122 and 0.022.