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

2006 ◽  
Author(s):  
Jin-Song Pei ◽  
Eric C. Mai
Keyword(s):  
Neural Network ◽  
Nonlinear Functions ◽  
Initialization Scheme ◽  
Engineering Mechanics

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

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
Jin-Song Pei ◽  
Eric C. Mai
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Feedforward Neural Networks ◽  
Nonlinear Functions ◽  
Neural Network Architecture ◽  
New Approach ◽  
Restoring Forces ◽  
Multilayer Feedforward Neural Network ◽  
Engineering Mechanics

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.

The Fault Diagnosis of Tower Crane Based on Genetic Algorithm and BP Neural Network

2011 ◽  
Vol 368-373 ◽  
pp. 3163-3166 ◽  
Author(s):  
Si Cong Yuan ◽  
Jing Qiang Shang ◽  
Xiao Yu Wang ◽  
Chao Li
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Fault Diagnosis ◽  
Bp Neural Network ◽  
Architectural Engineering ◽  
Tower Crane ◽  
Monitoring And Diagnosis ◽  
Engineering Mechanics

As the most important architectural engineering mechanics in the processing of architectural construction, the progress of construction will be put off by the appearance of the fault of Tower Crane, so it is absolutely crucial to take the monitoring and diagnosis of the condition. BP Neural Network ,which is optimized by Genetic Algorithm, is constructed to have the prediction and identification of the fault of Tower Crane, and it proved that it is effectively and precisely to justify the fault of Tower Crane through using the structure of improving BP Neural Network.

scholarly journals Neutrosophic Compound Orthogonal Neural Network and Its Applications in Neutrosophic Function Approximation

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 147 ◽  
Author(s):  
Jun Ye ◽  
Wenhua Cui
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Learning Algorithm ◽  
Learning Performance ◽  
Uncertain Information ◽  
Sigmoid Function ◽  
Nonlinear Functions ◽  
Single Output ◽  
Classification Pattern ◽  
Hidden Layer

Neural networks are powerful universal approximation tools. They have been utilized for functions/data approximation, classification, pattern recognition, as well as their various applications. Uncertain or interval values result from the incompleteness of measurements, human observation and estimations in the real world. Thus, a neutrosophic number (NsN) can represent both certain and uncertain information in an indeterminate setting and imply a changeable interval depending on its indeterminate ranges. In NsN settings, however, existing interval neural networks cannot deal with uncertain problems with NsNs. Therefore, this original study proposes a neutrosophic compound orthogonal neural network (NCONN) for the first time, containing the NsN weight values, NsN input and output, and hidden layer neutrosophic neuron functions, to approximate neutrosophic functions/NsN data. In the proposed NCONN model, single input and single output neurons are the transmission notes of NsN data and hidden layer neutrosophic neurons are constructed by the compound functions of both the Chebyshev neutrosophic orthogonal polynomial and the neutrosophic sigmoid function. In addition, illustrative and actual examples are provided to verify the effectiveness and learning performance of the proposed NCONN model for approximating neutrosophic nonlinear functions and NsN data. The contribution of this study is that the proposed NCONN can handle the approximation problems of neutrosophic nonlinear functions and NsN data. However, the main advantage is that the proposed NCONN implies a simple learning algorithm, higher speed learning convergence, and higher learning accuracy in indeterminate/NsN environments.

scholarly journals Formation Tracking for Nonaffine Nonlinear Multiagent Systems Using Neural Network Adaptive Control

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Tongjuan Zhao ◽  
Jiuhe Wang ◽  
Jianhua Zhang
Keyword(s):  
Neural Network ◽  
Multiagent Systems ◽  
Tracking Control ◽  
Feedback System ◽  
Nonlinear Functions ◽  
Adaptive Tracking Control ◽  
Formation Tracking ◽  
Adaptive Law ◽  
Consensus Tracking ◽  
Time Form

Adaptive tracking control for distributed multiagent systems in nonaffine form is considered in this paper. Each follower agent is modeled by a nonlinear pure-feedback system with nonaffine form, and a nonlinear system is unknown functions rather than constants. Radial basis function neural networks (NNs) are employed to approximate the unknown nonlinear functions, and weights of NNs are updated by adaptive law in finite-time form. Then, the adaptive finite NN approach and backstepping technology are combined to construct the consensus tracking control protocol. Numerical simulation is presented to demonstrate the efficacy of suggested control proposal.

NEURAL NETWORK ANALYSIS OF THERMAL IMAGE DATA

1992 ◽  
Vol 03 (02) ◽  
pp. 199-207
Author(s):  
Shahram Hejazi ◽  
Stephen M. Bauer ◽  
Robert A. Spangler
Keyword(s):  
Neural Network ◽  
Image Data ◽  
Nonlinear Functions ◽  
Data Set ◽  
Truncation Errors ◽  
The Neural Network ◽  
Radiation Distribution ◽  
Algebraic Treatment ◽  
Experimental Errors ◽  
Planck’S Law

Thermal images of the human body, when obtained at different wavelengths of infrared radiation, offer a means of eliminating several sources of error which can occur in single-wavelength thermal imaging procedures. Algebraic treatment of image data, however, utilizing nonlinear functions derived from integration over Planck’s law of radiation distribution, proves to be extremely sensitive to experimental errors in measurement and truncation errors in computation. The neural network backpropagation algorithm has been applied to thermal data processing which has resulted in a more stable and error-tolerant method of data reduction. Trained on a computed ideal data set, this algorithm has been shown to more reliably process actual data.

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