Parallel Computing and SGD-Based DPMM For Soft Sensor Development With Large-Scale Semisupervised Data

Abstract

Soft sensors based on Gaussian mixture models (GMM) have been widely used in industrial process systems for modeling the nonlinearity, non-Gaussianity, and uncertainties. However, there are still some challenging issues in developing high-accuracy GMM-based soft sensors. First, labeled samples are usually scarce due to technical or economical limitations, causing traditional supervised GMM-based soft sensing methods fail to provide satisfactory performance. Second, tremendous amounts of unlabeled samples are gathered, nevertheless, how to fully exploit those unlabeled samples in terms of improving both the predictive accuracy and computational efficiency remains unresolved. In this paper, in order to deal with these issues, two computationally efficient soft sensing methods, namely the parallel computing-based semisupervised Dirichlet process mixture models (P-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DPMM) and stochastic gradient descent-based S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DPMM (SGD-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DPMM), are proposed. The S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DPMM is first developed to mine information contained in both labeled and unlabeled samples for predictive accuracy enhancement, and subsequently is extended to the P-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DPMM and SGD-S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> DPMM to handle large-scale process data with sufficient and limited computing resources, respectively. Two case studies are carried out on real-world industrial processes, and the results obtained demonstrate the effectiveness of the proposed methods.