A Novel Input Variable Selection and Structure Optimization Algorithm for Multilayer Perceptron-Based Soft Sensors

Hongxun Wang,Fangfang Zhang,Kai Sun,Fengying Ma,Lin Sui,Mengyan Zhang,Adrian Neagu

doi:10.1155/2021/5517289

Abstract

A novel optimization algorithm for multilayer perceptron- (MLP-) based soft sensors is proposed in this paper. The proposed approach integrates input variable selection and hidden layer optimization on MLP into a constrained optimization problem. The nonnegative garrote (NNG) is implemented to perform the shrinkage of input variables and optimization of hidden layer simultaneously. The optimal garrote parameter of NNG is determined by combining cross-validation with Hannan-Quinn information criterion. The performance of the algorithm is demonstrated by an artificial dataset and the practical application of the desulfurization process in a thermal power plant. Comparative results demonstrated that the developed algorithm could build simpler and more accurate models than other state-of-the-art soft sensor algorithms.

Highlights

In complex industrial processes, important process parameters that influence product quality or energy consumption need to be monitored and controlled in real time and with high accuracy
A global optimization algorithm for multilayer perceptron (MLP)-based soft sensor, called GNNG-MLP, is proposed to reduce the redundancy of input and hidden layer simultaneously. e primary strategy of the proposed algorithm is to design a nonlinear quadratic optimization expression with NNG constraint that imposes the shrinkage coefficients on the input and hidden layers of MLP. e GNNG-MLP is implemented with the continuous adjustment of the garrote parameter. e schematic diagram of the proposed algorithm is illustrated in Figure 2, in which the nodes x2 and h2 have null impacts on the model and will be removed from the MLP
Comprehensive simulations are implemented to verify the performance of the proposed algorithm, in which comparisons with other state-of-the-art variable selection algorithms such as SBSMLP [37], NNGEO-MLP [29], and dLASSO-MLP [38] are performed

Summary

Introduction

Important process parameters that influence product quality or energy consumption need to be monitored and controlled in real time and with high accuracy. Sun et al [28] utilized the NNG to compress the input weights of the MLP to achieve nonlinear variable selection, and the superiority of the proposed algorithm was proved through two artificial dataset examples and a real industrial application. Fan et al proposed an algorithm that utilized the least absolute shrinkage and selection operator (LASSO) to perform the selection of input variables and the optimization of the hidden layer of MLP, named dLASSO [33]. A global optimization algorithm for MLP-based soft sensor, called GNNG-MLP, is proposed to reduce the redundancy of input and hidden layer simultaneously. E primary strategy of the proposed algorithm is to design a nonlinear quadratic optimization expression with NNG constraint that imposes the shrinkage coefficients on the input and hidden layers of MLP.

Simulation Results

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