Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking
Abstract
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 amore »
- Authors:
-
[1];
- Northeastern Univ., Shenyang (People's Republic of China)
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Publication Date:
- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1420438
- Report Number(s):
- PNNL-SA-130982
Journal ID: ISSN 0925-2312; PII: S0925231218300596
- Grant/Contract Number:
- AC05-76RL01830
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Neurocomputing
- Additional Journal Information:
- Journal Volume: 285; Journal ID: ISSN 0925-2312
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Modeling error PDF shaping; Wavelet neural network (WNN); Dynamic system modeling; Kernel density estimation (KDE); Gradient descent; Blast furnace ironmaking; Cross thermodetector
Citation Formats
Zhou, Ping, Wang, Chenyu, Li, Mingjie, Wang, Hong, Wu, Yongjian, and Chai, Tianyou. Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking. United States: N. p., 2018.
Web. doi:10.1016/J.NEUCOM.2018.01.040.
Zhou, Ping, Wang, Chenyu, Li, Mingjie, Wang, Hong, Wu, Yongjian, & Chai, Tianyou. Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking. United States. https://doi.org/10.1016/J.NEUCOM.2018.01.040
Zhou, Ping, Wang, Chenyu, Li, Mingjie, Wang, Hong, Wu, Yongjian, and Chai, Tianyou. Wed .
"Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking". United States. https://doi.org/10.1016/J.NEUCOM.2018.01.040. https://www.osti.gov/servlets/purl/1420438.
@article{osti_1420438,
title = {Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking},
author = {Zhou, Ping and Wang, Chenyu and Li, Mingjie and Wang, Hong and Wu, Yongjian and Chai, Tianyou},
abstractNote = {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. However, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.},
doi = {10.1016/J.NEUCOM.2018.01.040},
journal = {Neurocomputing},
number = ,
volume = 285,
place = {United States},
year = {Wed Jan 31 00:00:00 EST 2018},
month = {Wed Jan 31 00:00:00 EST 2018}
}
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Figures / Tables:
Fig. 1: Structure of WNN
Figures / Tables found in this record: