44 research outputs found
Enhanced universal kriging for transformed input parameter spaces
With computational models becoming more expensive and complex, surrogate models have gained increasing attention in many scientific disciplines and are often necessary to conduct sensitivity studies, parameter optimization etc. In the scientific discipline of uncertainty quantification (UQ), model input quantities are often described by probability distributions. For the construction of surrogate models, space-filling designs are generated in the input space to define training points, and evaluations of the computational model at these points are then conducted. The physical parameter space is often transformed into an i.i.d. uniform input space in order to apply space-filling training procedures in a sensible way. Due to this transformation surrogate modeling techniques tend to suffer with regard to their prediction accuracy. Therefore, a new method is proposed in this paper where input parameter transformations are applied to basis functions for universal kriging. To speed up hyperparameter optimization for universal kriging, suitable expressions for efficient gradient-based optimization are developed. Several benchmark functions are investigated and the proposed method is compared with conventional methods
Enhanced Universal Kriging for Transformed Input Parameter Spaces
With computational models becoming more expensive and complex, surrogate
models have gained increasing attention in many scientific disciplines and are
often necessary to conduct sensitivity studies, parameter optimization etc. In
the scientific discipline of uncertainty quantification (UQ), model input
quantities are often described by probability distributions. For the
construction of surrogate models, space-filling designs are generated in the
input space to define training points, and evaluations of the computational
model at these points are then conducted. The physical parameter space is often
transformed into an i.i.d. uniform input space in order to apply space-filling
training procedures in a sensible way. Due to this transformation surrogate
modeling techniques tend to suffer with regard to their prediction accuracy.
Therefore, a new method is proposed in this paper where input parameter
transformations are applied to basis functions for universal kriging. To speed
up hyperparameter optimization for universal kriging, suitable expressions for
efficient gradient-based optimization are developed. Several benchmark
functions are investigated and the proposed method is compared with
conventional methods
Angle-of-Arrival based localization using polynomial chaos expansions
International audienceIn this paper, polynomial chaos expansions are applied to angle-of-arrival based localization. By using a polynomial chaos expansion on a least squares estimator, a new positioning method is designed. Simulation results show that the proposed method returns precise information about the statistical distribution of the position
Reliability analysis for data-driven noisy models using active learning
Reliability analysis aims at estimating the failure probability of an
engineering system. It often requires multiple runs of a limit-state function,
which usually relies on computationally intensive simulations. Traditionally,
these simulations have been considered deterministic, i.e., running them
multiple times for a given set of input parameters always produces the same
output. However, this assumption does not always hold, as many studies in the
literature report non-deterministic computational simulations (also known as
noisy models). In such cases, running the simulations multiple times with the
same input will result in different outputs. Similarly, data-driven models that
rely on real-world data may also be affected by noise. This characteristic
poses a challenge when performing reliability analysis, as many classical
methods, such as FORM and SORM, are tailored to deterministic models. To bridge
this gap, this paper provides a novel methodology to perform reliability
analysis on models contaminated by noise. In such cases, noise introduces
latent uncertainty into the reliability estimator, leading to an incorrect
estimation of the real underlying reliability index, even when using Monte
Carlo simulation. To overcome this challenge, we propose the use of denoising
regression-based surrogate models within an active learning reliability
analysis framework. Specifically, we combine Gaussian process regression with a
noise-aware learning function to efficiently estimate the probability of
failure of the underlying noise-free model. We showcase the effectiveness of
this methodology on standard benchmark functions and a finite element model of
a realistic structural frame
Development of reduced polynomial chaos-Kriging metamodel for uncertainty quantification of computational aerodynamics
2018 Summer.Includes bibliographical references.Computational fluid dynamics (CFD) simulations are a critical component of the design and development of aerodynamic bodies. However, as engineers attempt to capture more detailed physics, the computational cost of simulations increases. This limits the ability of engineers to use robust or multidisciplinary design methodologies for practical engineering applications because the computational model is too expensive to evaluate for uncertainty quantification studies and off-design performance analysis. Metamodels (surrogate models) are a closed-form mathematical solution fit to only a few simulation responses which can be used to remedy this situation by estimating off-design performance and stochastic responses of the CFD simulation for far less computational cost. The development of a reduced polynomial chaos-Kriging (RPC-K) metamodel is another step towards eliminating simulation gridlock by capturing the relevant physics of the problem in a cheap-to-evaluate metamodel using fewer CFD simulations. The RPC-K metamodel is superior to existing technologies because its model reduction methodology eliminates the design parameters which contribute little variance to the problem before fitting a high-fidelity metamodel to the remaining data. This metamodel can capture non-linear physics due to its inclusion of both the long-range trend information of a polynomial chaos expansion and local variations in the simulation data through Kriging. In this thesis, the RPC-K metamodel is developed, validated on a convection-diffusion-reaction problem, and applied to the NACA 4412 airfoil and aircraft engine nacelle problems. This research demonstrates the metamodel's effectiveness over existing polynomial chaos and Kriging metamodels for aerodynamics applications because of its ability to fit non-linear fluid flows with far fewer CFD simulations. This research will allow aerospace engineers to more effectively take advantage of detailed CFD simulations in the development of next-generation aerodynamic bodies through the use of the RPC-K metamodel to save computational cost
Accelerating hypersonic reentry simulations using deep learning-based hybridization (with guarantees)
In this paper, we are interested in the acceleration of numerical
simulations. We focus on a hypersonic planetary reentry problem whose
simulation involves coupling fluid dynamics and chemical reactions. Simulating
chemical reactions takes most of the computational time but, on the other hand,
cannot be avoided to obtain accurate predictions. We face a trade-off between
cost-efficiency and accuracy: the simulation code has to be sufficiently
efficient to be used in an operational context but accurate enough to predict
the phenomenon faithfully. To tackle this trade-off, we design a hybrid
simulation code coupling a traditional fluid dynamic solver with a neural
network approximating the chemical reactions. We rely on their power in terms
of accuracy and dimension reduction when applied in a big data context and on
their efficiency stemming from their matrix-vector structure to achieve
important acceleration factors ( to ). This paper aims
to explain how we design such cost-effective hybrid simulation codes in
practice. Above all, we describe methodologies to ensure accuracy guarantees,
allowing us to go beyond traditional surrogate modeling and to use these codes
as references.Comment: Under revie