Uncertainty modelling in power spectrum estimation of environmental processes with applications in high rise building performance evaluation
Final Report Abstract
Since the quantification of uncertainties that occur in real measured data have extreme effects on the simulation results, the quantification of these is of utmost importance. An incorrect assessment of these uncertainties can, in the worst case, lead to simulation results that are within an acceptable range, although the actual system behaviour would be catastrophic. Therefore, every effort must be made to adequately quantify these uncertainties and determine their impact on system behaviour. Within the course of this project, various methods were developed to quantify these uncertainties and to take them into account in the simulation and its results. The developed methods are thus able to project the uncertainties onto the results and thus determine safe and critical ranges of the system behaviour. The more robust estimation of power spectra using the median and the weighted median provide an alternative, especially in the case of spectral outliers, to estimate a reliable spectrum. The classification approach, on the other hand, is particularly helpful when using highly variant data sets to classify groups and thus refine the simulation results. Critical system behaviour can thus be detected much easier while the results of the standard approach would in most of the cases lie an acceptable range. The main part of this project, the development of two relaxed power spectra, resulted in the following methods: First, a relaxed power spectrum, which is based on a probabilistic approach and can be derived especially when a large amount of date records is available, as only then reliable statistics be derived a probabilistic approach. And on the other hand, a relaxed power spectrum, which is based on imprecise probabilities and can be derived especially when the number of available data is low. With a small number, deriving reliable statistics is not possible, which is why an interval approach without probabilistic estimation is used here. Based on the probabilistic and imprecise approach, the two relaxed power spectra are particularly able to determine critical system behaviour in specific ranges with a certain degree of reliability. In addition to the methods proposed in the project, the interval Fourier transform was developed, which considers the signals to be transformed as intervals and projects them through the DFT. This allows the uncertainty of a single signal in the frequency domain to be determined and to obtain an upper and lower bound of the power spectrum. Overall, the developments from this project contribute significantly to the quantification of uncertainties in stochastic processes. The simulation of buildings and structures can thus be carried out in more detail, taking these uncertainties into account, and critical system behaviour can thus be better identified. In addition, it is possible to assess the reliability of structures with certain probability, depending on the uncertainty of the input data.
Publications
- (2018): Synchronized Load Quantification from Multiple Data Records for Analysing High-rise Buildings. 7th Asia Conference on Earthquake Engineering, Bangkok, Thailand
Behrendt, M.; Punurai, W.; Beer, M.
(See online at https://doi.org/10.15488/4957) - (2019): Development of a Relaxed Stationary Power Spectrum using Imprecise Probabilities with Application to High-rise Buildings., IEEE Symposium Series on Computational Intelligence (SSCI)
Behrendt, M., Comerford, L., Beer, M.
(See online at https://doi.org/10.1109/SSCI44817.2019.9002899) - (2019): Relaxed Stationary Power Spectrum Model Using Imprecise Probabilities, COMPDYN Proceedings, 1, pp. 592-599
Behrendt, M., Comerford, L., Beer, M.
(See online at https://doi.org/10.7712/120119.6941.19045) - (2019): Stochastic Processes Identification from Data Ensembles via Power Spectrum Classification., 13th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP13)
Behrendt, M.; Comerford, L.; Beer, M.
(See online at https://doi.org/10.22725/ICASP13.407) - (2020): Copula-Based Quantification of Probabilistic Dependence Configurations of Material Parameters in Damage Constitutive Modeling of Concrete, Journal of Structural Engineering, 146(9), Article 04020194
Tao, J.J.; Chen, J.B.; Ren, X.D.
(See online at https://doi.org/10.1061/(ASCE)ST.1943-541X.0002729) - (2020): Parameter Investigation of Relaxed Uncertain Power Spectra for Stochastic Dynamic Systems, Proceedings of the XI International Conference on Structural Dynamics (EURODYN 2020), Athens, Greece
Behrendt, M.; Bittner, M.; Comerford, L.; Broggi, M.; Beer, M.
(See online at https://doi.org/10.47964/1120.9311.18861) - (2020): Reduction of random variables in the Stochastic Harmonic Function representation via spectrum-relative dependent random frequencies, Mechanical Systems and Signal Processing, 141, Article 106718
Chen, J.B.; Comerford, L.; Peng, Y.B; Beer, M.; Li, J.
(See online at https://doi.org/10.1016/j.ymssp.2020.106718) - (2021): Forward interval propagation through the discrete Fourier transform, The 9th international workshop on Reliable Engineering Computing
De Angelis, M.; Behrendt, M.; Comerford, L.; Zhang, Y.; Beer, M.
(See online at https://doi.org/10.48550/arXiv.2012.09778) - (2022): Relaxed power spectrum estimation from multiple data records utilising subjective probabilities, Mechanical Systems and Signal Processing, 165, Article 108346
Behrendt, M.; Bittner, M.; Comerford, L.; Beer, M.; Chen, J.B.
(See online at https://doi.org/10.1016/j.ymssp.2021.108346)
