Broad learning system (BLS) is a novel neural network with effective and efficient learning ability. BLS has attracted increasing attention from many scholars owing to its excellent performance. This article proposes a weighted BLS (WBLS) based on BLS to tackle the noise and outliers in an industrial process. WBLS provides a unified framework for easily using different methods of calculating the weighted penalty factor. Using the weighted penalty factor to constrain the contribution of each sample to modeling, the normal and abnormal samples were allocated higher and lower weights to increase and decrease their contributions, respectively. Hence, the WBLS can eliminate the bad effect of noise and outliers on the modeling. The weighted ridge regression algorithm is used to compute the algorithm solution. Weighted incremental learning algorithms are also developed using the weighted penalty factor to tackle the noise and outliers in the additional samples and quickly increase nodes or samples without retraining. The proposed weighted incremental learning algorithms provide a unified framework for using different methods of computing weights. We test the feasibility of the proposed algorithms on some public data sets and a real-world application. Experiment results show that our method has better generalization and robustness.

Production quality indices of complex industrial processes are usually hard to be measured in real time, which leads to unavailability of closed-loop operational optimization and control. Therefore, data-driven modeling techniques have been extensively employed to estimate production quality indices online. However, the conventional data-driven modeling methods often fail to achieve good performance because of interference from outliers. To solve the above-mentioned problem, this paper proposes an improved random vector functional link network (RVFLN) using a novel training method, which adopts a ridge regularized model with weighted factor for each training sample to evaluate the output weights. The robustness of the model has been achieved by employing a nonparametric kernel density estimation method to assign the weighted factors according to the training sample. To ensure the quality and computational load of the network in online applications, various online learning versions are presented according to the scope of data sampling. The improved RVFLN called robust regularized RVFLN has been validated using UCI, Statlib standard data sets, and an industrial grinding operation data. Results show that our proposed modeling technique perform favorably, and demonstrate its good potential for real world applications.

Aiming at simplifying the network structure of broad learning system (BLS), this article proposes a novel simplification method called compact BLS (CBLS). Groups of nodes play an important role in the modeling process of BLS, and it means that there may be a correlation between nodes. The proposed CBLS not only focuses on the compactness of network structure but also pays closer attention to the correlation between nodes. Learning from the idea of Fused Lasso and Smooth Lasso, it uses the $L_{1}$ -regularization term and the fusion term to penalize each output weight and the difference between adjacent output weights, respectively. The $L_{1}$ -regularization term determines the correlation between the nodes and the outputs, whereas the fusion term captures the correlation between nodes. By optimizing the output weights iteratively, the correlation between the nodes and the outputs and the correlation between nodes are attempted to be considered in the simplification process simultaneously. Without reducing the prediction accuracy, finally, the network structure is simplified more reasonably and a sparse and smooth output weights solution is provided, which can reflect the characteristic of group learning of BLS. Furthermore, according to the fusion terms used in Fused Lasso and Smooth Lasso, two different simplification strategies are developed and compared. Multiple experiments based on public datasets are used to demonstrate the feasibility and effectiveness of the proposed methods.

As the large-scale integration of renewable energy into the power grid, coal-fired power units have to undertake the task of load-frequency regulation, the optimization control of the coal-fired power units is becoming increasingly important. Reinforcement learning is being used for optimization control of the process increasingly but may encounter high learning costs. In this paper, a process model-assisted optimization control framework called PMA-OC is proposed to achieve the optimization control of coal-fired power unit. In this framework, a low-precision process model developed by process operation knowledge is employed to achieve the initial control based on model predictive control algorithm (MPC) and improve the dynamic characteristics of the coordinated control system. Then the deep reinforcement learning algorithm (DRL) is utilized to improve the initial control continuously, through constantly interacting with the improved process. With the full mining of process knowledge from the power unit, the improved process offers the better training samples for DRL, reduces the learning complexity of DRL, and strengthens the learning efficiency of DRL. Finally, the proposed control framework is employed to achieve the optimization control of the coordinated control system, and simulation results indicate that the proposed control framework outperforms the existing standalone MPC and DRL methods in terms of anti-interference ability, dynamic response time, and performs well control capability. Note to Practitioners —The flexible and stable operation of coal-fired power units is of great significance to the peak load regulation and supply guarantee of the power grid. For practitioners of the coal-fired power unit, this paper proposes a process model-assisted optimization control framework to promote the process knowledge utilization. In this framework, process knowledge is used to implement preliminary control on coal-fired power units to reduce the complex dynamic characteristics of coal-fired power units. Then, the reinforcement learning algorithm is used to continuously improve the control performance of coal-fired power units by interacting with the improved process. Finally, the effectiveness of the proposed method is verified by a supercritical unit. Although the proposed method is applied to the optimal control of coal-fired power units, its ideas can be used for the reference in other complex industrial processes.