A New Distributed Echo State Network Integrated With an Auto-Encoder for Dynamic Soft Sensing

As dynamic industrial processes become increasingly complicated, it tends to be difficult to develop accurate soft sensors. Echo state networks (ESNs) as dynamic neural network (NN) models have been broadly used in developing dynamic soft sensors. However, when facing high-dimensional data, the dimension disaster problem might occur in the input space of ESNs. Furthermore, in ESNs, the number of reservoir nodes is large, causing collinearity between the reservoir outputs. To solve these problems, in this article, a new distributed ESN model integrated with auto-encoder (AE-DESNm) is proposed. In particular, AE-DESNm has distributed and independent input subnets. The dimensionality of each input subnet has been reduced, eliminating the dimension disaster problem. To obtain the distributed and independent input subnets of AE-DESNm, the first integer neighbor clustering hierarchy (FINCH) algorithm is used to cluster the input attributes of high-dimensional data. Each cluster corresponds to one input subnet. In addition, seeking to handle the collinearity issue in the reservoir outputs, auto-encoder (AE) is used to extract features from the reservoir outputs. Finally, the extracted features are modeled by an extreme learning machine (ELM) to estimate key variables. To verify the performance of AE-DESNm, a numerical example and a dataset from one real industrial process named purified terephthalic acid (PTA) production are used. Compared with other methods, the experimental results show that the proposed AE-DESNm can achieve much higher accuracy in soft sensor modeling for dynamic industrial processes.