A heuristic neural network initialization scheme for modeling nonlinear functions in engineering mechanics

Pei, Jin‐Song; Eric, C.

doi:10.1117/12.658916

Cited by 4 publications

(6 citation statements)

References 16 publications

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“…The two options for prototypes shown in Fig. 2 for the approximation of a fractional power nonlinearity have been presented in Reference [26]. There appears to be a many-to-many relationship between types of nonlinearities and prototypes, which should be confirmed in future studies.…”

Section: Multiple Options In Selecting Prototypes and Variantsmentioning

confidence: 91%

“…All ten types of nonlinearities were successfully trained using the proposed methodology. While typical examples of directly adopting the proposed prototypes can be found in References [25,26,27], the way to utilize the proposed decomposition technique is the focus of this section. All training was carried out using the Matlab Neural Network Toolbox [19] with batch training mode and the Levenberg-Marquardt backpropagation algorithm [28].…”

Section: Training Examplesmentioning

confidence: 99%

“…Additionally, the fractional power nonlinearity (Type V in Fig. 2) can also be trained using a decomposition approach as presented in Reference [26].…”

Section: Approximating One-variable Functions By Combining Prototypesmentioning

confidence: 99%

“…4(a), a wave form is spatially partitioned into several individual cycles, each of which can be approximated independently using Prototype #3 after some detailed treatment under Stage III transformation. The training results have been presented in References[25,26]. InFig.…”

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confidence: 99%

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Constructing Multilayer Feedforward Neural Networks to Approximate Nonlinear Functions in Engineering Mechanics Applications

Pei

Eric

2008

Journal of Applied Mechanics

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This paper presents a major step in the development and validation of a systematic prototype-based methodology for designing multilayer feedforward neural networks to model nonlinearities common in engineering mechanics. The applications of this work include (but are not limited to) system identification of nonlinear dynamic systems and neural-network-based damage detection. In this and previous studies (Pei, J. S., 2001, “Parametric and Nonparametric Identification of Nonlinear Systems,” Ph.D. thesis, Columbia University; Pei, J. S., and Smyth, A. W., 2006, “A New Approach to Design Multilayer Feedforward Neural Network Architecture in Modeling Nonlinear Restoring Forces. Part I: Formulation,” J. Eng. Mech., 132(12), pp. 1290–1300; Pei, J. S., and Smyth, A. W., 2006, “A New Approach to Design Multilayer Feedforward Neural Network Architecture in Modeling Nonlinear Restoring Forces. Part II: Applications,” J. Eng. Mech., 132(12), pp. 1301–1312; Pei, J. S., Wright, J. P., and Smyth, A. W., 2005, “Mapping Polynomial Fitting Into Feedforward Neural Networks for Modeling Nonlinear Dynamic Systems and Beyond,” Comput. Methods Appl. Mech. Eng., 194(42–44), pp. 4481–4505), the authors do not presume to provide a universal method to approximate any arbitrary function. Rather the focus is given to the development of a procedure which will consistently lead to successful approximations of nonlinear functions within the specified field. This is done by examining the dominant features of the function to be approximated and exploiting the strength of the sigmoidal basis function. As a result, a greater efficiency and understanding of both neural network architecture (e.g., the number of hidden nodes) as well as weight and bias values is achieved. Through the use of illuminating mathematical insights and a large number of training examples, this study demonstrates the simplicity, power, and versatility of the proposed prototype-based initialization methodology. A clear procedure for initializing neural networks to model various nonlinear functions commonly seen in engineering mechanics is provided. The proposed methodology is compared with the widely used Nguyen–Widrow initialization to demonstrate its robustness and efficiency in the specified applications. Future work is also identified.

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Section: Multiple Options In Selecting Prototypes and Variantsmentioning

confidence: 91%

Section: Training Examplesmentioning

confidence: 99%

“…Additionally, the fractional power nonlinearity (Type V in Fig. 2) can also be trained using a decomposition approach as presented in Reference [26].…”

Section: Approximating One-variable Functions By Combining Prototypesmentioning

confidence: 99%

mentioning

confidence: 99%

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Constructing Multilayer Feedforward Neural Networks to Approximate Nonlinear Functions in Engineering Mechanics Applications

Pei

Eric

2008

Journal of Applied Mechanics

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“…Commonly used methods in data mining comprise: Artificial NNs: NNs are biologically inspired predictive models (mimicking the functioning of human brain) that can learn and map linear and nonlinear functions14; Generalized rule induction: generates rules about significant relationships, rather than just predicting a class value5; Top‐down induction of decision trees: induces classification rules in the intermediate form of a tree structure15; k ‐Nearest neighbor: it classifies unlabeled data instances with a majority class of the k most similar data instances in the training set6; Other methods comprise genetic algorithms16 used for the optimization of data mining algorithms, rough sets, fuzzy set approaches for classification,5 Bayesian classification,5 etc. …”

Section: Knowledge Discovery and Data Miningmentioning

confidence: 99%

An overview of the use of neural networks for data mining tasks

Stahl

Jordanov

2012

WIREs Data Min & Knowl

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In the recent years, the area of data mining has been experiencing considerable demand for technologies that extract knowledge from large and complex data sources. There has been substantial commercial interest as well as active research in the area that aim to develop new and improved approaches for extracting information, relationships, and patterns from large datasets. Artificial neural networks (NNs) are popular biologically-inspired intelligent methodologies, whose classification, prediction, and pattern recognition capabilities have been utilized successfully in many areas, including science, engineering, medicine, business, banking, telecommunication, and many other fields. This paper highlights from a data mining perspective the implementation of NN, using supervised and unsupervised learning, for pattern recognition, classification, prediction, and cluster analysis, and focuses the discussion on their usage in bioinformatics and financial data analysis tasks.

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Demonstration and validation of constructive initialization method for neural networks to approximate nonlinear functions in engineering mechanics applications

Pei

Masri

2014

Nonlinear Dyn

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A heuristic neural network initialization scheme for modeling nonlinear functions in engineering mechanics

Cited by 4 publications

References 16 publications

Constructing Multilayer Feedforward Neural Networks to Approximate Nonlinear Functions in Engineering Mechanics Applications

Constructing Multilayer Feedforward Neural Networks to Approximate Nonlinear Functions in Engineering Mechanics Applications

An overview of the use of neural networks for data mining tasks

Demonstration and validation of constructive initialization method for neural networks to approximate nonlinear functions in engineering mechanics applications

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