Incremental Bayesian broad learning system and its industrial application

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Incremental Bayesian broad learning system and its industrial application Ying Liu1,2 · Yifei Wang1,2 · Long Chen1,2,3 · Jun Zhao1,2 · Wei Wang1,2 · Quanli Liu1,2 Accepted: 16 October 2020 © Springer Nature B.V. 2020

Abstract Broad learning system (BLS) is viewed as a class of neural networks with a broad structure, which exhibits an efficient training process through incremental learning. An incremental Bayesian framework broad learning system is proposed in this study, where the posterior mean and covariance over the output weights are both derived and updated in an incremental manner for the increment of feature nodes, enhancement nodes, and input data, respectively, and the hyper-parameters are simultaneously updated by maximizing the evidence function. In such a way, the scale of matrix operations is capable of being effectively reduced. To verify the performance of this proposed approach, a number of experiments by using four benchmark datasets and an industrial case are carried out. The experimental results demonstrate that the proposed method can not only achieve a better outcome compared to the classical BLS and other comparative algorithms but also incrementally remodel the system. Keywords  Broad learning system · Bayesian inference · Incremental learning · Regression

1 Introduction An industrial production process usually involves numerous process variables, and it is of great importance to predict some of them for monitoring the whole process. Through the supervisory control and data acquisition system (SCADA), a large amount of operational data for these variables can be well accumulated and employed for further modeling, prediction, or optimization (Chen et al. 2016a; Jin et al. 2018a). However, industrial data often contain high-level noise, which poses a significant challenge to build an accurate model (Zhao et  al. 2018). Moreover, due to the time-variant characteristic of the production

* Ying Liu [email protected] 1

Key Laboratory of Intelligent Control and Optimization for Industrial Equipment (Dalian University of Technology), Ministry of Education, Dalian 116024, China

2

School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China

3

Dalian University of Technology Artificial Intelligence Institute, Dalian, China



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process, the data-based model might be often invalid so that it is necessary to real-time update the prediction model according to the on-site conditions. Although viewed as a practical method because of their dominant learning and feature extraction abilities, deep networks exhibit the disadvantages of slow convergence, time-consuming issue, and easy to get into local optimum in their training processes (Nguyen et al. 2019; Zhang et al. 2018; Weimer et al. 2016). Different from a deep neural network, Broad learning system (BLS) is a type of network with a broad structure (Chen and Liu 2017), so training a BLS is faster and more efficient. Recently a number of improvements related to the BLS ha