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Nonlinear system modeling via knot-optimizing B-spline networks.
1Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong.
IEEE Transactions on Neural Networks
|February 6, 2008
Summary
This study introduces a new knot-optimizing B-spline network for nonlinear system modeling. The method optimizes knot points and coefficients using simulated annealing, effectively improving system approximation.
Area of Science:
- Engineering
- Computer Science
- Applied Mathematics
Background:
- B-spline networks are used for nonlinear system modeling.
- Selecting optimal knot points for B-spline networks is challenging due to limited theoretical guidance.
- Existing methods struggle to achieve optimal network structures for minimizing error criteria.
Purpose of the Study:
- To propose a novel knot-optimizing B-spline network for approximating general nonlinear system behavior.
- To address the difficulty in selecting appropriate knot points for effective B-spline network design.
- To improve the accuracy and efficiency of nonlinear system modeling using B-spline networks.
Main Methods:
- A novel B-spline network where knot points are treated as independent variables.
- Optimization of both knot points and B-spline expansion coefficients.
- Utilizing the simulated annealing algorithm for network training to avoid local minima.
Main Results:
- The proposed method effectively approximates general nonlinear system behavior.
- Demonstrated effectiveness in modeling dynamic systems with up to six input dimensions.
- Successful optimization of B-spline network structures for improved performance.
Conclusions:
- The knot-optimizing B-spline network offers a robust approach to nonlinear system modeling.
- Simulated annealing is an effective optimization algorithm for training B-spline networks.
- The method provides a significant improvement over existing techniques for complex system approximation.
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