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Related Concept Videos

Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Approximate Integration01:24

Approximate Integration

In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Newton’s Method01:30

Newton’s Method

Newton’s Method is a powerful iterative technique for approximating the roots of real-valued, differentiable functions, particularly when analytical solutions are impractical. This approach is widely used in scientific computing, engineering, and finance, where equations may be too complex for traditional algebraic methods to handle. The method relies on an iterative process that refines an initial estimate using the function’s derivative to approach the true solution progressively.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

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Related Experiment Videos

Dynamic fuzzy neural networks-a novel approach to function approximation.

S Wu1, M J Er

  • 1Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|February 5, 2008
PubMed
Summary

This study introduces dynamic fuzzy neural networks (D-FNN) for Takagi-Sugeno-Kang (TSK) systems. The novel algorithm dynamically adjusts neurons for faster learning and improved performance in RBF networks.

Related Experiment Videos

Area of Science:

  • Artificial Intelligence
  • Computational Neuroscience
  • Machine Learning

Background:

  • Takagi-Sugeno-Kang (TSK) fuzzy systems are widely used for modeling complex systems.
  • Radial basis function (RBF) neural networks offer powerful function approximation capabilities.
  • Existing learning algorithms for fuzzy neural networks can be computationally intensive and may result in complex structures.

Purpose of the Study:

  • To propose a novel architecture for dynamic fuzzy neural networks (D-FNN) implementing TSK fuzzy systems.
  • To introduce a new learning algorithm for D-FNN that enables dynamic neuron recruitment and deletion.
  • To achieve a more compact structure and higher performance compared to existing methods.

Main Methods:

  • Developed a D-FNN architecture based on extended RBF neural networks.
  • Implemented a hierarchical, on-line, self-organizing learning algorithm.
  • Dynamically recruited or deleted neurons based on their significance to system performance.

Main Results:

  • The proposed D-FNN architecture effectively implements TSK fuzzy systems.
  • The novel learning algorithm demonstrated fast learning speeds.
  • Simulation studies confirmed that the approach yields a more compact structure with higher performance.

Conclusions:

  • The proposed D-FNN architecture and learning algorithm offer a significant advancement in fuzzy system implementation.
  • Dynamic neuron management leads to improved efficiency and performance.
  • This approach provides a competitive alternative to existing learning algorithms for fuzzy neural networks.