Surrogate Response Surface Research Articles

Estimation of plume distribution for carbon sequestration using parameter estimation with limited monitoring data

This study develops and evaluates an integrated methodology including parameter zonation, efficient global optimization, and multiple aquifer realizations that gives a useful forecast of the pressure distribution and the CO2 plume migration through a heterogeneous storage formation, over time, using only a few monitoring locations in a feasibly short amount of computing time, while dealing with data error. Geological characteristics of the example application are similar to a CO2 sequestration pilot test conducted in a fluvial‐deltaic geological setting. In the example, the CO2 injection problem is simulated with the TOUGH2 code, a numerical simulator for multiphase (gas and aqueous), multicomponent flow and transport. The inverse problem is difficult because the GCS optimization estimation problem has multiple local minima and the simulation is computationally expensive. The efficient surrogate response surface global optimization algorithm “Stochastic RBF” (stochastic radial basis function) is used to calibrate the model parameters. Results are averaged over three saline aquifer realizations. In the third numerical experiment using only pressure data, the CO2 plume could be determined with an average correlation coefficient compared to the actual plume of up to R2 = 0.916 (for current plume at t = 1.5 years) and average R2 = 0.80 (for forecasted plume estimated at t = 7.5 years years, using only the first 1.5 years of monitoring data). Adding gas saturation data improved the 6 year forecast somewhat (increasing average R2 = 0.85) but it was not significantly helpful in estimating the current plume. Both our inverse methodology and findings can be broadly applicable to GCS in heterogeneous sedimentary formations.

Comparison of optimization algorithms for parameter estimation of multi-phase flow models with application to geological carbon sequestration

Optimization of multi-phase transport models is important both for calibrating model parameters to observed data and for analyzing management options. We focus on examples of geological carbon sequestration (GCS) process-based multi-phase models. Realistic GCS models can be very computationally expensive not only due to the spatial distribution of the model but also because of the complex nonlinear multi-phase and multi-component transport equations to be solved. As a result we need to have optimization methods that get accurate answers with relatively few simulations. In this analysis we compare a variety of different types of optimization algorithms to understand the best type of algorithms to use for different types of problems. This includes an analysis of which characteristics of the problem are important in choice of algorithm. The goal of this paper is to evaluate which optimization algorithms are the most efficient in a given situation, taking into account shape of the optimization problem (e.g. uni- or multi-modal) and the number of simulations that can be done. The algorithms compared are the widely used derivative-based PEST optimization algorithm, the derivative-based iTOUGH2, the Kriging response surface algorithm EGO, the heuristics-based DDS (Dynamically Dimensioned Search), and the Radial Basis Function surrogate response surface based global optimization algorithms ‘GORBIT’ and ‘Stochastic RBF’. We calibrate a simple homogeneous model ‘3hom’ and two more realistic models ‘20layer’ and ‘6het’. The latter takes 2h per simulation. Using rigorous statistical tests, we show that while the derivative-based algorithms of PEST are efficient on the simple 3hom model, it does poorly in comparison to surrogate optimization methods Stochastic RBF and GORBIT on the more realistic models. We then identify the shapes of the optimization surface of the three models using enumerative simulations and discover that 3hom is smooth and unimodal and the more realistic models are rough and multi-modal. When the number of simulations is limited, surrogate response surfaces algorithms perform best on multi-modal, bumpy objective functions, which we expect to have for most realistic multi-phase flow models such as those for GCS.

Propagation of Uncertainties Using Improved Surrogate Models

We study the effect of various sources of error on the propagation of uncertain parameters and data through surrogate response surfaces approximating quantities of interest from stochastic differential equations. The main result centers on a novel approach for improving the pointwise accuracy of a surrogate with the use of an adjoint-based a posteriori estimate of its error. A general error analysis on propagated distribution functions for both forward and inverse problems is derived. To provide concrete examples focusing on the use of the improved surrogate, we consider standard polynomial spectral methods to approximate the surrogate. However, neither the definition of the improved surrogate nor the general error analysis for the computed distribution functions requires a specific surrogate formulation. Numerical results comparing pointwise errors in propagated distributions using a surrogate versus its improved counterpart demonstrate global decreases in both actual error and in error bounds for both f...

Computational Reduction for Parametrized PDEs: Strategies and Applications

In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of the reduced basis method, focusing on greedy algorithms for the construction of the reduced spaces. An alternative family of reduction techniques based on surrogate response surface models is briefly recalled too. Then, a simple example dealing with inviscid flows is presented, showing the reliability of the reduced basis method and a comparison between this technique and some surrogate models.

A method for selecting surrogate models in crashworthiness optimization

Surrogate model or response surface based design optimization has been widely adopted as a common process in automotive industry, as large-scale, high fidelity models are often required. However, most surrogate models are built by using a limited number of design points without considering data uncertainty. In addition, the selection of surrogate model in the literature is often arbitrary. This paper presents a Bayesian metric to complement root mean square error for selecting the best surrogate model among several candidates in a library under data uncertainty. A strategy for automatically selecting the best surrogate model and determining a reasonable sample size was proposed for design optimization of large-scale complex problems. Lastly, a vehicle example with full-frontal and offset-frontal impacts was presented to demonstrate the proposed methodology.

Air Vehicle Enviroment in C++: A Computational Design Environment for Conceptual Innovations

Aerospacetechnologyplannersintheairforceresearchlaboratoryareactivelydeveloping processes that produce a priority order for corporate investments. Technology assessment is one such process. Aerospace technology can be evaluated in the context of computationally intensive designs of innovative vehicle concepts. Computational design optimization traces technology performance metrics to system level design objectives and constraints. The air vehicle environment in C++ will support this process in the form of a pilot code currently underdevelopment.DesigninnovatorswillbenefitfromairvehicleenvironmentinC++atone of three levels. These three levels benefit a) the end user through interactive operations and file input/output, b) the object-oriented programmer through a compiled library of properly documented and inheritable objects, and c) the air vehicle environment in C++ developer who wishes to enhance air vehicle environment in C++ capability with modifications to the source code. The pilot environment described here focuses on parent‐child relationships, automated dependency management, geometry, meshing, analysis, and eventually gradientbased optimization. All together, the overall capability leads to design variant management that will populate a database for either surrogate (response surface) modeling or high-level Pareto optimization. The proposed test case targets a suite of high-altitude-long-endurance aeroelastic concepts with geometric nonlinearity and follower forces.

Optimization of draw-in for an automotive sheet metal part: An evaluation using surrogate models and response surfaces

In the present paper, an optimization of the draw-in of an automotive sheet metal part has been carried out using response surface methodology (RSM) and space mapping technique. The optimization adjusts the draw bead restraining force in the model such that the draw-in in the FE-model corresponds to the draw-in in the physical process. The conclusion of this study is that space mapping is a very effective and accurate method to use when calibrating the draw-in of a sheet metal process. In order to establish draw bead geometry from the draw bead restraining force a 2D-model was utilized. The draw bead geometry found showed good agreement with the physical draw bead geometry.

Using surrogate models and response surfaces in structural optimization ? with application to crashworthiness design and sheet metal forming

The aim of this paper is to determine if the Space Mapping technique using surrogate models together with response surfaces is useful in the optimization of crashworthiness and sheet metal forming. In addition, the efficiency of optimization using Space Mapping will be compared to traditional structural optimization using the Response Surface Methodology (RSM). Five examples are used to study the algorithm: one optimization of an analytic function and four structural optimization problems. All examples are constrained optimization problems. In all examples, the algorithm converged to an improved design with all constraints fulfilled, even when a conventional RSM optimization failed to converge. For the crashworthiness design problems, the total computing time for convergence was reduced by 53% using Space Mapping compared to conventional RSM. For the sheet metal forming problems the total computing time was reduced by 63%. The conclusions are that optimization using Space Mapping and surrogate models can be used for optimization in crashworthiness design and sheet metal forming applications with a significant reduction in computing time.

Uncertainty analysis of decomposing polyurethane foam

Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation’s nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. The response variable was chosen as the steady-state decomposition front velocity. Four different analyses are presented, including (1) an analytical mean value (MV) analysis, (2) a linear surrogate response surface (LIN) using a constrained latin hypercube sampling (LHS) technique, (3) a quadratic surrogate response surface (QUAD) using LHS, and (4) a direct LHS (DLHS) analysis using the full grid and time step resolved finite element model. To minimize the numerical noise, 50 μm elements and approximately 1 ms time steps were required to obtain stable uncertainty results. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model.