Coefficient estimation of a beam structure governing equation based on sparse measurements

LI Zhipeng, HE Yi, YAN Zhitao

Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (23) : 312-320.

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PDF(3105 KB)
Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (23) : 312-320.

Coefficient estimation of a beam structure governing equation based on sparse measurements

  • LI Zhipeng, HE Yi, YAN Zhitao
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Abstract

The governing differential equations of beams have many engineering applications. This study proposes a method to identify the coefficients of the governing equation from sparsely measured displacement responses. First, the full-field displacement is reconstructed by the compressive sensing theory. The reconstructed displacement field is then fitted by B-spline surface basis functions, and the derived control points are further used to calculate other responses, which are derivatives of displacement. The genetic algorithm is finally utilized to seek the coefficients of the governing equation by substituting the fitted responses into the equation. The proposed method is both numerically and experimentally validated, together with a parametric study to evaluate its performance under various conditions. The salient advantages of the proposed method are that it requires only few sensors for measurement and the derivatives are calculated in a robust and easy way.

Key words

Full-filed response / compressive sensing / B-spline basis functions / beam / governing differential equations

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LI Zhipeng, HE Yi, YAN Zhitao. Coefficient estimation of a beam structure governing equation based on sparse measurements[J]. Journal of Vibration and Shock, 2024, 43(23): 312-320

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