Uncertainty Propagation of Missing Data Signals with the Interval Discrete Fourier Transform
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 9, Issue 3
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.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository online in accordance with funder data retention policies. The software for computing the interval DFT can be accessed in a single instance via GitHub at https://github.com/interval-fourier-transform/application-to-missing-data.
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© 2023 American Society of Civil Engineers.
History
Received: Dec 9, 2022
Accepted: Feb 9, 2023
Published online: Jun 16, 2023
Published in print: Sep 1, 2023
Discussion open until: Nov 16, 2023
ASCE Technical Topics:
- Algorithms
- Analysis (by type)
- Bodies of water (by type)
- Case studies
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Fluid mechanics
- Fourier analysis
- Hydrologic engineering
- Mathematics
- Methodology (by type)
- Motion (dynamics)
- Power spectral density
- Research methods (by type)
- Sea water
- Seas and oceans
- Solid mechanics
- Statistical analysis (by type)
- Uncertainty principles
- Water (by type)
- Water and water resources
- Water management
- Water waves
- Waves (fluid mechanics)
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