Mapping polynomial fitting into feedforward neural networks for modeling nonlinear dynamic systems and beyond

Pei, Jin‐Song; Wright, Joseph P.; Smyth, Andrew W.

doi:10.1016/j.cma.2004.12.010

Cited by 38 publications

(22 citation statements)

References 12 publications

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“…A normalized division operation, p 1 ÷ (100p 2 ), of two normalized inputs p 1 and p 2 , can be viewed as a product of p 1 and 1 100p2 , where the two multipliers and multiplication operation are being approximated based on either the authors' analytic work 11,14 or proposed prototypes. 16 Guided by this view of a normalized division operation, Fig.…”

Section: Insights and Condensation Proceduresmentioning

confidence: 99%

“…There are also ranges of values recommended for the weights and biases. 11,14 The approximated surfaces are illustrated in Fig. 1 based on a set of suitable values of weights and biases.…”

Section: Direct Adoption Of Analytic Workmentioning

confidence: 99%

“…This study is part of a continuing development of a heuristic methodology as presented previously. [11][12][13][14][15][16][17] Presented in this paper is a condensed version of another full length paper by the authors. 18 The target functions being studied by the authors are all for the modeling of nonlinear functions in engineering mechanics applications.…”

Section: Introductionmentioning

confidence: 99%

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Mapping some functions and four arithmetic operations to multilayer feedforward neural networks

Pei

Eric

Wright

2008

Health Monitoring of Structural and Biological Systems 2008

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This paper continues the development of a heuristic initialization methodology for designing multilayer feedforward neural networks aimed at modeling nonlinear functions for engineering mechanics applications as presented previously at SPIE 2003SPIE , and 2005SPIE to 2007. Seeking a transparent and domain knowledge-based approach for neural network initialization and result interpretation, the authors examine the efficiency of linear sums of sigmoidal functions while offering constructive methods to approximate functions in engineering mechanics applications. This study provides details and results of mapping the four arithmetic operations (summation, subtraction, multiplication, division) as well as other functions including reciprocal, Gaussian and Mexican hat functions into multilayer feedforward neural networks with one hidden layer. The approximation and training examples demonstrate the efficiency and accuracy of the proposed mapping techniques and details. Future work is also identified. This effort directly contributes to the further extension of the proposed initialization procedure in that it opens the door for the approximation of a wider range of nonlinear functions.

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Section: Insights and Condensation Proceduresmentioning

confidence: 99%

“…There are also ranges of values recommended for the weights and biases. 11,14 The approximated surfaces are illustrated in Fig. 1 based on a set of suitable values of weights and biases.…”

Section: Direct Adoption Of Analytic Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mapping some functions and four arithmetic operations to multilayer feedforward neural networks

Pei

Eric

Wright

2008

Health Monitoring of Structural and Biological Systems 2008

Self Cite

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“…GMDH was developed in the late 1960s by Ivakhnenko (1968) nonlinear relations between input and output variables. In recent years, however, the use of such self-organizing network leads to successful application of GMDH-type algorithm in a broad range area in engineering, science, and economics (Cho, Kim, Seo, H, & Cheng, 2006;de Menezes & Nikolaev, 2006;Huang, Shimizu, Hagihara, & Kobatake, 2003;Nariman-Zadeh, Darvizeh, Jamali, & Moeini, 2005;Oh, Pedrycz, & Park, B. J., 2003;Oh, Pedrycz, & Park, 2005;Park, Oh, & Yoon, 2001;Park, Park, Lee, & Oh, 2004;Pei, Wright, & Smyth, 2005).…”

Section: Introductionmentioning

confidence: 98%

Evolutionary design of hybrid self-organizing fuzzy polynomial neural networks with the aid of information granulation

Park

Pedrycz

2007

Expert Systems with Applications

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“…The common used modeling approaches for dynamical systems are summed up as: 1. Mathematical Modeling [1][2][3]; 2. Dynamic linearization technique (DLT) [4]; 3.…”

Section: Introductionmentioning

confidence: 99%

A Sliding-Window Modeling Approach for Neural Network

Laisheng¹

2014

IJCA

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Mapping polynomial fitting into feedforward neural networks for modeling nonlinear dynamic systems and beyond

Cited by 38 publications

References 12 publications

Mapping some functions and four arithmetic operations to multilayer feedforward neural networks

Mapping some functions and four arithmetic operations to multilayer feedforward neural networks

Evolutionary design of hybrid self-organizing fuzzy polynomial neural networks with the aid of information granulation

A Sliding-Window Modeling Approach for Neural Network

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