Details
| Original language | English |
|---|---|
| Article number | 04023022 |
| Journal | ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering |
| Volume | 9 |
| Issue number | 3 |
| Early online date | 16 Jun 2023 |
| Publication status | Published - 1 Sept 2023 |
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.
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Building and Construction
- Engineering(all)
- Safety, Risk, Reliability and Quality
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In: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, Vol. 9, No. 3, 04023022, 01.09.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Uncertainty Propagation of Missing Data Signals with the Interval Discrete Fourier Transform
AU - Behrendt, Marco
AU - De Angelis, Marco
AU - Beer, Michael
PY - 2023/9/1
Y1 - 2023/9/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85163399235&partnerID=8YFLogxK
U2 - 10.1061/AJRUA6.RUENG-1048
DO - 10.1061/AJRUA6.RUENG-1048
M3 - Article
AN - SCOPUS:85163399235
VL - 9
JO - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
JF - ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
SN - 2376-7642
IS - 3
M1 - 04023022
ER -