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

Journal Article · · Neurocomputing
ORCiD logo [1];  [1];  [1];  [2];  [1];  [1]
  1. Northeastern Univ., Shenyang (People's Republic of China)
  2. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
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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.

Research Organization:
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC05-76RL01830
OSTI ID:
1420438
Report Number(s):
PNNL-SA-130982; PII: S0925231218300596
Journal Information:
Neurocomputing, Vol. 285; ISSN 0925-2312
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 21 works
Citation information provided by
Web of Science

Figures / Tables (14)

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Related Subjects

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