Details
| Original language | English |
|---|---|
| Article number | 04017020 |
| Number of pages | 10 |
| Journal | ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering |
| Volume | 3 |
| Issue number | 4 |
| Early online date | 22 Jul 2017 |
| Publication status | Published - Dec 2017 |
Abstract
In this paper, the challenge of quantifying the uncertainty in stochastic process spectral estimates based on realizations with missing data is addressed. Specifically, relying on relatively relaxed assumptions for the missing data and on a kriging modeling scheme, utilizing fundamental concepts from probability theory, and resorting to a Fourier-based representation of stationary stochastic processes, a closed-form expression for the probability density function (PDF) of the power spectrum value corresponding to a specific frequency is derived. Next, the approach is extended for also determining the PDF of spectral moments estimates. Clearly, this is of significant importance to various reliability assessment methodologies that rely on knowledge of the system response spectral moments for evaluating its survival probability. Further, utilizing a Cholesky decomposition for the PDF-related integrals kept the computational cost at a minimal level. Several numerical examples are included and compared against pertinent Monte Carlo simulations for demonstrating the validity of the approach.
Keywords
- Kriging, Missing data, Spectral estimation, Spectral moments, Survival probability, Uncertainty quantification
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. 3, No. 4, 04017020, 12.2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Uncertainty quantification of power spectrum and spectral moments estimates subject to missing data
AU - Zhang, Yuanjin
AU - Comerford, Liam
AU - Kougioumtzoglou, Ioannis A.
AU - Patelli, Edoardo
AU - Beer, Michael
N1 - Funding information: The first author is grateful for the financial support from the China Scholarship Council.
PY - 2017/12
Y1 - 2017/12
N2 - In this paper, the challenge of quantifying the uncertainty in stochastic process spectral estimates based on realizations with missing data is addressed. Specifically, relying on relatively relaxed assumptions for the missing data and on a kriging modeling scheme, utilizing fundamental concepts from probability theory, and resorting to a Fourier-based representation of stationary stochastic processes, a closed-form expression for the probability density function (PDF) of the power spectrum value corresponding to a specific frequency is derived. Next, the approach is extended for also determining the PDF of spectral moments estimates. Clearly, this is of significant importance to various reliability assessment methodologies that rely on knowledge of the system response spectral moments for evaluating its survival probability. Further, utilizing a Cholesky decomposition for the PDF-related integrals kept the computational cost at a minimal level. Several numerical examples are included and compared against pertinent Monte Carlo simulations for demonstrating the validity of the approach.
AB - In this paper, the challenge of quantifying the uncertainty in stochastic process spectral estimates based on realizations with missing data is addressed. Specifically, relying on relatively relaxed assumptions for the missing data and on a kriging modeling scheme, utilizing fundamental concepts from probability theory, and resorting to a Fourier-based representation of stationary stochastic processes, a closed-form expression for the probability density function (PDF) of the power spectrum value corresponding to a specific frequency is derived. Next, the approach is extended for also determining the PDF of spectral moments estimates. Clearly, this is of significant importance to various reliability assessment methodologies that rely on knowledge of the system response spectral moments for evaluating its survival probability. Further, utilizing a Cholesky decomposition for the PDF-related integrals kept the computational cost at a minimal level. Several numerical examples are included and compared against pertinent Monte Carlo simulations for demonstrating the validity of the approach.
KW - Kriging
KW - Missing data
KW - Spectral estimation
KW - Spectral moments
KW - Survival probability
KW - Uncertainty quantification
UR - http://www.scopus.com/inward/record.url?scp=85044482787&partnerID=8YFLogxK
U2 - 10.1061/AJRUA6.0000925
DO - 10.1061/AJRUA6.0000925
M3 - Article
AN - SCOPUS:85044482787
VL - 3
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 - 4
M1 - 04017020
ER -