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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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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.
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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A Hurst exponent estimator based on autoregressive power spectrum estimation with order selection.

Yen-Ching Chang1, Li-Chun Lai, Liang-Hwa Chen

  • 1Department of Medical Informatics, Chung Shan Medical University and Department of Medical Imaging, Chung Shan Medical University Hospital, Taichung, 40201, Taiwan, ROC.

Bio-Medical Materials and Engineering
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Summary

Estimating the Hurst exponent for discrete-time fractional Gaussian noise (DFGN) is improved by using autoregressive (AR) models with selected orders. This approach enhances accuracy compared to methods ignoring AR model order selection.

Keywords:
Fractional Brownian motionHurst exponentautoregressivefractional Gaussian noiseorder selection

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Area of Science:

  • Signal processing
  • Time series analysis
  • Statistical modeling

Background:

  • Discrete-time fractional Gaussian noise (DFGN) is a regular process.
  • DFGN can be modeled as an infinite-order autoregressive (AR) process per Wold and Kolmogorov theorems.
  • Existing Hurst exponent estimators based on AR power spectrum estimation often neglect AR model order selection.

Purpose of the Study:

  • To improve the accuracy of Hurst exponent estimation for DFGN.
  • To investigate the impact of AR model order selection on Hurst exponent estimation accuracy.

Main Methods:

  • Applied six common autoregressive (AR) model order selection methods.
  • Utilized selected AR model orders for Hurst exponent estimation.
  • Compared the performance of selected AR methods against a standard AR method without order selection.

Main Results:

  • The application of AR model order selection methods significantly enhanced the accuracy of Hurst exponent estimation.
  • All six tested AR order selection methods outperformed the original AR method that did not consider order selection.
  • The proposed methods demonstrate improved precision in characterizing DFGN properties.

Conclusions:

  • Autoregressive model order selection is crucial for accurate Hurst exponent estimation in discrete-time fractional Gaussian noise.
  • The investigated AR order selection techniques provide a more reliable approach for analyzing DFGN.
  • This study offers practical improvements for time series analysis involving fractional Gaussian noise.