Response Surface Method for Material Uncertainty Quantification of Infrastructures

Abstract

Recently, probabilistic simulations became an inseparable part of risk analysis. Managers and stakeholders prefer to make their decision knowing the existing uncertainties in the system. Nonlinear dynamic analysis and design of infrastructures are affected by two main uncertainty sources, i.e., epistemic and aleatory. In the present paper, the epistemic uncertainty is addressed in the context of material randomness. An old ultra-high arch dam is selected as a vehicle for numerical analyses. Four material properties are selected as random variables in the coupled dam-reservoir-foundation system, i.e., concrete elasticity, mass density, compressive (and tensile) strength, and the rock modulus of elasticity. The efficient Box-Behnken experimental design is adopted to minimize the required simulations. A response surface metamodel is developed for the system based on different outputs, i.e., displacement and damage index. The polynomial-based response surface model is subsequently validated with a large number of simulations based on Latin Hypercube sampling. Results confirm the high accuracy of proposed technique in material uncertainty quantification.

Validation and Improvement of a Bicycle Crank Arm Based in Numerical Simulation and Uncertainty Quantification

“…To reduce the number of simulations necessary to assess the uncertainty of a finite element model, it is commonly accepted to use metamodels constructed from the results of the several simulations generated with the variation of the input parameters [14][15][16]24]. These surrogate models provide a computationally efficient analysis.…”

“…To reduce the number of simulations required to quantify the uncertainty of the complex computational model, a subrogate model can be used [15]. This subrogate model known as the metamodel represents the behavior of a zone of interest in the computational model and allows to identify the principal variables of influence of the system [16]. The metamodels are used to understanding the physical system analyzed, predicting its response.…”

On the Dynamic Capacity of Concrete Dams

“…So far, the ETA was applied for a gravity dam with deterministic material properties. However, it is well accepted that there are different levels of uncertainties in quantifying the material properties especially for large deteriorated concrete structures [78,79]. This implies that finite element models should be analyzed multiple times, each one with different combinations of the material properties to properly account for all the potential combinations.…”

“…However, the first step is to develop an efficient number of random finite element models. In general, there are two broad approaches to achieve this goal: (1) using one of the Monte Carlo family models such as Latin hypercube sampling (LHS) [80] or (2) using one of many design of experiment (DOE) methods [79]. In this paper, the DOE technique was adopted to develop a series of capacity functions, each one based on a specific material combination.…”

An advanced pseudo excitation method and application in analyzing stochastic wind-induced response of slender bridge tower

“…In such case, direct Monte Carlo approach may be unacceptable in the stochastic analysis since the finite element dynamic analysis must be required in every sample. The present research, therefore, adopts response surface method (RSM; Faravelli, 1989; Hariri-Ardebili et al, 2018; Zhao et al, 2016; Zheng and Das, 2000). Through approximating the implicit response function by a basic and explicit polynomial, the RSM provides an efficient and versatile way to apply numerical methods suitable for the explicitly expressed function taken into analysis with the implicit form (Huh and Haldar, 2001).…”