Uncertainty propagation of missing data signals with the interval discrete Fourier transform

Behrendt, Marco and de Angelis, Marco and Beer, Michael (2023) Uncertainty propagation of missing data signals with the interval discrete Fourier transform. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 9 (3). 04023022. ISSN 2376-7642 (https://doi.org/10.1061/AJRUA6.RUENG-1048)

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Abstract

The interval discrete Fourier transform (DFT) algorithm can propagate signals carrying interval uncertainty. By addressing the repeated variables problem, the interval DFT algorithm provides exact theoretical bounds on the Fourier amplitude and estimates of the power spectral density (PSD) function while running in polynomial time. Thus, the algorithm can be used to assess the worst-case scenario in terms of maximum or minimum power, and provide insights into the amplitude spectrum bands of the transformed signal. To propagate signals with missing data, an upper and lower value for the missing data present in the signal must be assumed, such that the uncertainty in the spectrum bands can also be interpreted as an indicator of the quality of the reconstructed signal. For missing data reconstruction, there are a number of techniques available that can be used to obtain reliable bounds in the time domain, such as Kriging regressors and interval predictor models. Alternative heuristic strategies based on variable—as opposed to fixed—bounds can also be explored. This work aims to investigate the sensitivity of the algorithm against interval uncertainty in the time signal. The investigation is conducted in different case studies using signals of different lengths generated from the Kanai-Tajimi PSD function, representing earthquakes, and the Joint North Sea Wave Observation Project (JONSWAP) PSD function, representing sea waves as a narrowband PSD model.

ORCID iDs

Behrendt, Marco, de Angelis, Marco ORCID logoORCID: https://orcid.org/0000-0001-8851-023X and Beer, Michael;
  • Item type:Article
    ID code:86135
    Dates:
    Date
    Event
    16 June 2023
    Published
    9 February 2023
    Accepted
    Notes:Copyright © 2023 American Society of Civil Engineers. This material may be downloaded for personal use only. Any other use requires prior permission of the American Society of Civil Engineers. This material may be found at https://doi.org/10.1061/AJRUA6.RUENG-1048
    Subjects:Technology > Engineering (General). Civil engineering (General)
    Department:Faculty of Engineering > Civil and Environmental Engineering
    Depositing user: Pure Administrator
    Date deposited:13 Jul 2023 08:55
    Last modified:11 Nov 2024 13:59
    URI:https://strathprints.strath.ac.uk/id/eprint/86135
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