Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

NEUROCOMPUTING

卷:285

Article

Zhou, Ping¹  Wang, Chenyu¹  Li, Mingjie¹  Wang, Hong²  Wu, Yongjian¹  Chai, Tianyou¹ 

[1] Northeastern Univ, State Key Lab Synthet Automat Proc Ind, Shenyang 110819, Liaoning, Peoples R China

[2] Pacific Northwest Natl Lab, Richland, WA 99352 USA

关键词: Modeling error PDF shaping;    Wavelet neural network (WNN);    Dynamic system modeling;    Kernel density estimation (KDE);    Gradient descent;    Blast furnace ironmaking;    Cross thermodetector;   

DOI  :  10.1016/j.neucom.2018.01.040

来源: Elsevier

【 摘 要 】

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) cannot fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, the modeling error PDF by the traditional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow. (C) 2018 Elsevier B.V. All rights reserved.

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