Marco Behrendt, Insitute for Risk and Reliability, Leibniz Universität Hannover, Germany
Uncertainty modelling in power spectrum estimation of environmental processes (2022)
Supervisor: Prof. Dr.-Ing. Michael Beer
Keywords: Stochastic dynamics, Power spectral density estimation, Stochastic processes, Random vibrations, Uncertainty quantification, Imprecise probabilities
For efficient reliability analysis of buildings and structures, robust load models are required in stochastic dynamics, estimated from environmental processes such as earthquakes or wind loads. The power spectral density (PSD) function is a widely used tool to identify frequency components and corresponding amplitudes of environmental processes. The real data sets used for this purpose are often subject to uncertainties, and the PSD estimation process can introduce further uncertainties. To address these issues, alternative loading models using probabilistic and non-deterministic approaches are proposed to efficiently account for uncertainties and model the loadings accordingly. (1) Reliable statistical information can be extracted from multiple data records to create a PSD function model with epistemic uncertainties. (2) If only a limited amount of data is available, an interval-based approach is proposed, determining upper and lower bounds without relying on any distribution within these bounds. (3) Grouping similar data using the Bhattacharyya distance and k-means algorithm can generate multiple load models, leading to more accurate simulation results. (4) A method is presented to efficiently transform interval uncertainty in time signals into the frequency domain by the so-called interval discrete Fourier transform. These novel load model representations effectively quantify epistemic uncertainties in real data records and the PSD estimation process.
More information on Marco's work:
Personal webpage: github.io
References:
- Behrendt, M.; de Angelis, M.; Beer, M. (2023): Uncertainty Propagation of Missing Data Signals with the Interval Discrete Fourier Transform, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, Volume 9, Issue 3, doi.org/10.1061/AJRUA6.RUENG-1048
- Behrendt, M.; Faes, M.G.R.; Valdebenito, M.A.; Beer, M. (2023): Estimation of an imprecise power spectral density function with optimised bounds from scarce data for epistemic uncertainty quantification, Mechanical Systems and Signal Processing, 189, Article 110072, doi.org/10.1016/j.ymssp.2022.110072
- Behrendt, M.; Kitahara, M.; Kitahara, T.; Comerford, L.; Beer, M. (2022): Data-driven reliability assessment of dynamic structures based on power spectrum classification, Engineering Structures, 268, 114648, doi.org/10.1016/j.engstruct.2022.114648
- Behrendt, M.; de Angelis, M.; Comerford, L.A.; Zhang, Y.J.; Beer, M. (2022): Projecting interval uncertainty through the discrete Fourier transform: an application to time signals with poor precision, Mechanical Systems and Signal Processing, Volume 172, 1 June 2022, 108920, doi.org/10.1016/j.ymssp.2022.108920
- Behrendt, M.; Bittner, M.; Comerford, L.; Beer, M.; Chen, J.B. (2022): Relaxed power spectrum estimation from multiple data records utilising subjective probabilities, Mechanical Systems and Signal Processing, 165, Article 108346, doi.org/10.1016/j.ymssp.2021.108346