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Error analysis and new dual-cosine window for estimating the sensor frequency response function from the step

Shuang-Long Yang1, Li-Ping Liang1, Hou-De Liu2

  • 1School of Electrical and Automation Engineering, Hefei University of Technology, Hefei 230009, People's Republic of China.

The Review of Scientific Instruments
|April 2, 2018
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Summary

A new dual-cosine window reduces sensor frequency response function (FRF) estimation errors by improving transient error suppression. This method offers a practical alternative to traditional techniques for accurate FRF estimation.

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Area of Science:

  • Mechanical Engineering
  • Signal Processing
  • System Identification

Background:

  • Traditional window-based spectral estimation methods for sensor frequency response function (FRF) estimation suffer from interpolation and transient errors.
  • The Hanning window, commonly used, has limitations in minimizing these errors, particularly transient errors.

Purpose of the Study:

  • To develop a novel windowing method to reduce estimation errors in FRF.
  • To improve the accuracy and efficiency of FRF estimation from step response data.

Main Methods:

  • Derived non-parameter error models for interpolation and transient errors.
  • Analyzed window effects on these errors.
  • Constructed a new dual-cosine window with specific discrete Fourier transform bins.
  • Validated the method using a wind tunnel strain gauge balance model and actual data.

Main Results:

  • The new dual-cosine window offers equivalent interpolation error suppression to the Hanning window.
  • It significantly improves transient error suppression, reducing the asymptotic property from O(N^-2) to O(N^-4).
  • The method demonstrated superior performance over Hanning, Gans, and LPM methods in simulations and real-world applications, with reduced computation and data requirements.

Conclusions:

  • The new dual-cosine window is an effective and practical method for FRF estimation.
  • It provides enhanced accuracy and efficiency, especially for high-order, small-damping, non-minimum phase systems.
  • The method shows significant advantages in computation simplicity, time consumption, and data requirements.