Multi-level, multi-variate, non-stationary, random field modeling of engineering systems

Engineering systems can often be represented considering models at multiple levels. Such levels can be defined by state variables (i.e., variables that describe the properties of the objective) or other quantities of interest (e.g., probability of failure) for the components in a system. For an engineering system, different properties within each level are typically inhomogeneous in space and cross-correlated, while properties of different levels are physically dependent on each other. In addition, system properties usually vary in time due to effects of external environmental conditions. Current analysis techniques cannot model the spatially inhomogeneous, intra-level correlated, inter-level dependent, and temporally varying system properties. This dissertation proposes multi-level, multi-variate, non-stationary, random field formulations for the modeling of system properties. To consider the inhomogeneous spatial variability, this study proposes a regressor-based random field formulation using an improved latent space approach (ILSA). To considers the intra-level correlation, this study improves the random field formulation by incorporating non-stationary cross-correlation in the modeling. To capture the inter-dependency, this study proposes a multi-level and multi-variate random field formulation for system modeling. To capture the temporal evolution, this study uses a state-dependent model that enables the updating of multi-level random fields in time. To calibrate a multi-level random field model, we need data of both response variables and regressors measured at the same locations in different levels. However, data of different variables are usually measured independently at inconsistent locations (i.e., data at some locations and levels are missing). This study proposes a new formulation for the calibration of multi-level random field when data at different levels are either partially or completely missing. The proposed formulation considers the spatial correlation and inter-level dependency in the missing data prediction and multi-level model calibration. Predictive distributions are estimated for the objectives from the lowest to the highest level to capture the uncertainty propagation. Finally, this dissertation implements the proposed formulations in solving two real-world problems. The first example develops a two-level model for climate-dependent storm surge. Specifically, Level 1 predicts the probability of different locations being flooded, and Level 2 estimates the storm surge height given one location is flooded using random fields. The second example implements the multi-level formulation in the modeling of material load-displacement behaviors such as stress-strain responses. The example uses the multi-level random field to capture the inter-dependency between different material behaviors and the auto-correlation in the load-displacement curve development. In both examples, the dissertation presents in detail how to build the multi-level models, and how to calibrate and validate such models based on data of different quantities of interest.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Xu, Hao

Contributors dc:contributor

• Gardoni, Paolo
• Valocchi, Albert J.
• Li, Bo
• Jia, Gaofeng
• Cusatis, Gianluca

• Multi-level modeling
• Random field
• System reliability
• Missing data
• Bayesian updating

Statement dc:rights

• Copyright 2020 Hao Xu

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/108126

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/108126