Uncertainty modelling in power spectrum estimation of environmental processes with applications in high rise building performance evaluation

Abstract

The overall aim of the project is to provide a general framework of algorithms for producing non-stationary spectral stochastic load models that utilize process record ensemble statistics to account for inherent uncertainties that exist in real data sets. Although the resulting models will be highly general, and hence widely applicable across different engineering fields, they will be considered in this project primarily in the context of super high-rise building dynamics problems. Specifically, the problem of extreme earthquake and wind loading, to which super high-rise buildings are particularly vulnerable, will be investigated.

Nowadays, owing to the development of cheaper, and more reliable data acquisition systems, vast amounts of environmental load process data are becoming accessible. As such data becomes more ever more numerous, in many cases, when estimating power spectra, the need for assuming spectral models and fitting them to the data becomes unnecessary. This realization is further supported by the fact that many established spectral model assumptions, for various scientific fields are highly outdated.

Particularly in the field of environmental stochastic load modelling, where this project is concentrated, when estimating any spectral model from multiple source records, the common ergodic assumption that each record, if it existed in the limit, conforms to the same power spectrum is highly improbable. Therefore, there is a need for a stochastic load representation framework that accounts for epistemic model uncertainties by encompassing inherent statistical differences that exist across real data sets. Only recently has it become possible that such uncertainties may be reliably quantified, due to the increasing size and availability of source data.

The initial project focus will be to define improved, robust estimation techniques for traditional spectral model determination by following a general treatment of record ensemble characteristics. This will yield immediate results that are directly applicable in scenarios where power spectra are estimated from process record ensembles. Following this, avenues for quantifying the uncertainty in the spectral model will be explored, ultimately resulting in more realistic process representation methods. Once formulated, a probability density evolution method will be employed for utilizing the new models in the context of induced wind and earthquake loading of high-rise buildings. This final proof-of-concept stage will validate the research, directly demonstrating its practicality in addressing real-world problems.

Throughout the project, every attempt will be made to account for data sets that may be unevenly sampled, presenting difficulty for the majority of standard spectrum estimation methods. Although data sampling problems are not the primary focus of this work, developing methodologies that are robust in this setting will extend the value of the research and further justify its practicality.

Keywords

stochastic dynamics; spectral stochastic analysis; dynamic load representation; power spectra; epistemic uncertainties

Project Partner

Prof. Jianbing Chen, Tongji University