<p class="MsoNormal" style="text-align: justify">This paper aims to fast and robustly estimate the fractional integrals and derivatives of positions from noisy accelerations for a class of fractional order vibration systems defined by the Caputo fractional derivative. The main idea is to convert the original issue into the estimation of the fractional integrals of accelerations and the ones of the unknown initial conditions, on the basis of the additive index law. Being proper integrals, the fractional integrals of accelerations can be estimated via a numerical method. Consequently, solving the original problem boils down to estimating the unknown initial values. To this end, the modulating functions method is adopted. By constructing appropriate modulating functions, the unknown initial values are exactly given in terms of algebraic integral formulas in different situations. Finally, two illustrations are presented to verify the correctness and robustness of the proposed estimators. Compared to our previous work, the main contributions of this article are highlighted as follows. 1) The considered&nbsp;model is described by the Caputo fractional derivative, while the Riemann-Liouville one was consider in our previous works. 2) The estimator designed in this work is suitable for not only the positions and velocities but also for the fractional integrals and derivatives of positions. 3) The fractional differentiation orders can be arbitrary real numbers, rather than the ones rational and commensurate.</p>

Modulating Functions Based Fast and Robust Estimation for a Class of Fractional Order Vibration Systems

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2021)

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