Details
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019 |
| Editors | Michael Beer, Enrico Zio |
| Place of Publication | Singapur |
| Pages | 2714-2718 |
| Number of pages | 5 |
| ISBN (electronic) | 9789811127243 |
| Publication status | Published - 2020 |
| Event | 29th European Safety and Reliability Conference, ESREL 2019 - Leibniz University Hannover, Hannover, Germany Duration: 22 Sept 2019 → 26 Sept 2019 |
Abstract
The distributions of ratios of random variables arise in many applied problems such as in structural dynamics working with frequency response functions (FRFs) and transmissibility functions (TFs). When analysing the distribution properties of ratio random variables through the definition of probability density functions (PDF), the problem is usually accompanied by multiple integrals. In this study, a unified solution is presented to efficiently calculate the PDF of a ratio random variable with its denominator and numerator specified by arbitrary distributions. With the use of probability density transformation principle, a unified expression can be derived for the ratio random variable by reducing the concerned problem into two-dimensional integrals. As a result, the PDFs of the ratio random variable can be efficiently computed by using effective numerical integration techniques. Finally, based on the vibration tests performed on the Alamosa Canyon Bridge, the proposed method is applied to the data to quantify the uncertainty of FRFs and TFs.
Keywords
- Frequency response function, Numerical integration, Probability density function, Ratio distribution, Structural dynamics, Transmissibility function
ASJC Scopus subject areas
- Engineering(all)
- Safety, Risk, Reliability and Quality
- Social Sciences(all)
- Safety Research
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Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019. ed. / Michael Beer; Enrico Zio. Singapur, 2020. p. 2714-2718.
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Probabilistic modelling for frequency response functions and transmissibility functions with complex ratio statistics
AU - Zhao, Meng-Yun
AU - Yan, Wang-Ji
AU - Ren, Wei-Xin
AU - Beer, Michael
N1 - Funding information: Dr. W.J. Yan was supported by the Marie Sklodowska-Curie individual Fellowships of the EU under Contract 741284 when visiting the University of Nottingham. The authors would thank Los Alamos National Laboratory for providing the data from the various vibration tests performed on the Alamosa Canyon Bridge to the public.
PY - 2020
Y1 - 2020
N2 - The distributions of ratios of random variables arise in many applied problems such as in structural dynamics working with frequency response functions (FRFs) and transmissibility functions (TFs). When analysing the distribution properties of ratio random variables through the definition of probability density functions (PDF), the problem is usually accompanied by multiple integrals. In this study, a unified solution is presented to efficiently calculate the PDF of a ratio random variable with its denominator and numerator specified by arbitrary distributions. With the use of probability density transformation principle, a unified expression can be derived for the ratio random variable by reducing the concerned problem into two-dimensional integrals. As a result, the PDFs of the ratio random variable can be efficiently computed by using effective numerical integration techniques. Finally, based on the vibration tests performed on the Alamosa Canyon Bridge, the proposed method is applied to the data to quantify the uncertainty of FRFs and TFs.
AB - The distributions of ratios of random variables arise in many applied problems such as in structural dynamics working with frequency response functions (FRFs) and transmissibility functions (TFs). When analysing the distribution properties of ratio random variables through the definition of probability density functions (PDF), the problem is usually accompanied by multiple integrals. In this study, a unified solution is presented to efficiently calculate the PDF of a ratio random variable with its denominator and numerator specified by arbitrary distributions. With the use of probability density transformation principle, a unified expression can be derived for the ratio random variable by reducing the concerned problem into two-dimensional integrals. As a result, the PDFs of the ratio random variable can be efficiently computed by using effective numerical integration techniques. Finally, based on the vibration tests performed on the Alamosa Canyon Bridge, the proposed method is applied to the data to quantify the uncertainty of FRFs and TFs.
KW - Frequency response function
KW - Numerical integration
KW - Probability density function
KW - Ratio distribution
KW - Structural dynamics
KW - Transmissibility function
UR - http://www.scopus.com/inward/record.url?scp=85089180141&partnerID=8YFLogxK
U2 - 10.3850/978-981-11-2724-3_0827-cd
DO - 10.3850/978-981-11-2724-3_0827-cd
M3 - Conference contribution
AN - SCOPUS:85089180141
SP - 2714
EP - 2718
BT - Proceedings of the 29th European Safety and Reliability Conference, ESREL 2019
A2 - Beer, Michael
A2 - Zio, Enrico
CY - Singapur
T2 - 29th European Safety and Reliability Conference, ESREL 2019
Y2 - 22 September 2019 through 26 September 2019
ER -