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Haftka, Raphael T.

Publications and source records attributed to Haftka, Raphael T..

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Testing Surrogate-Based Optimization with the Fortified Branin-Hoo Extended to Four Dimensions

Some popular functions used to test global optimization algorithms have multiple local optima, all with the same value, making them all global optima. It is easy to make them more challenging by fortifying them via adding a localized bump at the location of one of the optima. In previous work the authors illustrated this for the Branin-Hoo function and the popular differential evolution algorithm, showing that the fortified Branin-Hoo required an order of magnitude more function evaluations. This paper examines the effect of fortifying the Branin-Hoo function on surrogate- based optimization, which usually proceeds by adaptive sampling. Two algorithms are considered. The EGO algorithm, which is based on a Gaussian process (GP) and an algorithm based on radial basis functions (RBF). EGO is found to be more frugal in terms of the number of required function evaluations required to identify the correct basin, but it is expensive to run on a desktop, limiting the number of times the runs could be repeated to establish sound statistics on the number of required function evaluations. The RBF algorithm was cheaper to run, providing more sound statistics on performance. A four-dimensional version of the Branin-Hoo function was introduced in order to assess the effect of dimensionality. Furthermore, it was found that the difference between the ordinary function and the fortified one was much more pronounced for the four-dimensional function compared to the two dimensional one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Effect of curvature on extensional stiffness matrix of 2-D braided composite tubes

In the micromechanical analysis of braided composite tubes, the effects of curvature are often ignored. This approach is acceptable for thin-walled tubes with a large radius. However, in case of small diameter thick-walled tubes, such an approach may lead to inaccurate results. Therefore, it is of interest to determine when the curvature effects of tubular geometry become important in micromechanics. In this study, the extensional stiffness matrix of 2-D braided composite tubes was calculated using a curved unit-cell. The periodicity was imposed in circumferential and longitudinal directions of the tube. The extensional stiffness coefficients were calculated by simulating an internal pressure test, uniaxial tensile test, and torsion test. The obtained stiffness coefficients were compared to those obtained using a flat unit-cell. The results of curved unit-cell were different from that of flat unit-cell. The differences in stiffness coefficients, calculated using curved and flat unit cells were as high as 13%.

42 ENGINEERING↗
DOE OSTI2020

Accelerating high-strain continuum-scale brittle fracture simulations with machine learning

Failure in brittle materials under dynamic loading conditions is a result of the propagation and coalescence of microcracks. Simulating this discrete crack evolution at the continuum level is computationally expensive or, in some cases, intractable, resulting in the need to make broad assumptions or neglect key physics. In this work, we have developed an approach using machine learning that overcomes the current inability to represent meso-scale physics at the macro-scale. Our approach leverages damage and stress data from a computationally expensive high-fidelity model that explicitly resolves microcrack behavior to build an inexpensive machine learning emulator. Once trained, the machine learning emulator is used to predict the evolution of crack length statistics, which then informs a continuum-scale constitutive model. This results in a significant speed-up of the workflow by four orders of magnitude. Both the machine learning emulator and the continuum-scale model are validated against the high-fidelity model and experimental data, respectively, showing excellent agreement. There are two key findings. The first is that we can reduce the dimensionality of the problem, establishing that the machine learning emulator only needs the length of the longest crack and one of the maximum stress components to capture the necessary physics. Another compelling finding is that the emulator can be trained in one experimental setting and transferred successfully to predict behavior in a different setting.

36 MATERIALS SCIENCE↗
DOE OSTI2019

General-Surrogate Adaptive Sampling Using Interquartile Range for Design Space Exploration

Abstract A surrogate model is a common tool to approximate system response at untested points for design space exploration. Adaptive sampling has been studied for improving the accuracy of surrogates iteratively by introducing additional samples (simulations and experiments). New samples are often selected based on the estimated uncertainty in the design space. While some surrogates such as kriging have readily available uncertainty models for their predictions, other surrogates do not. Consequently, there have been studies of using the process of leaving-samples-out (LSO) used in cross-validation tools to estimate prediction uncertainty, such as the universal prediction distribution (UPD). In this paper, an adaptive sampling scheme for general surrogates is proposed based on LSO, similar to cross-validation and interquartile range (IQR). Multiple submodels are first developed from LSO. The uncertainty is then estimated from the IQR of these surrogates at a given point. New samples are added iteratively at the point with maximum IQR for design space exploration. The proposed scheme is illustrated using kriging, radial basis function, and neural network surrogates. The proposed scheme is evaluated using four algebraic test functions. Multiple sets of initial samples were produced to account for randomness. For these test functions, the proposed scheme was found to be more accurate and robust than kriging with its own uncertainty model. The proposed scheme was more accurate than the UPD for three out of the four test functions. For a fixed number of samples, the IQR-based adaptive sampling also proved to be more accurate than all-at-once sampling in most cases even when the estimated uncertainty was only mildly correlated with prediction errors.

Engineering↗
DOE OSTI2019

Linear Regression Based Multi-fidelity Surrogate for Disturbance Amplification in Multi-phase Explosion

When simulations are very expensive and many are required, as for optimization or uncertainty quantification, a way to reduce cost is using surrogates. With multiple simulations to predict the quantity of interest, some being very expensive and accurate (high-fidelity simulations) and others cheaper but less accurate (low-fidelity simulations), it may be worthwhile to use multifidelity surrogates (MFSs). Moreover, if we can afford just a few high-fidelity simulations or experiments, MFS becomes necessary. Co-Kriging, which is probably the most popular MFS, replaces both low-fidelity and high-fidelity simulations by a single MFS. A recently proposed linear regression–based MFS (LR-MFS) offers the option to correct the LF simulations instead of correcting the LF surrogate in the MFS. When the low-fidelity simulation is cheap enough for use in an application, such as optimization, this may be an attractive option. Here, we explore the performance of LR-MFS using exact and surrogate-replaced low-fidelity simulations. The concern studied is a cylindrical dispersal of 100-μ m-diameter solid particles after detonation and the quantity of interest is a measure of the amplification of the departure from axisymmetry. We find very substantial accuracy improvements for this problem using the LR-MFS with exact low-fidelity simulations. Inspired by these results, we also compare the performance of co-Kriging to the use of Kriging to correct exact low-fidelity simulations and find a similar accuracy improvement when simulations are directly used. For this problem, further improvements in accuracy are achievable by taking advantage of inherent parametric symmetries. These findings may alert users of MFSs to the possible advantages of using exact low-fidelity simulations when this is affordable.

42 ENGINEERING↗
DOE OSTI2019

Early Time Evolution of Circumferential Perturbation of Initial Particle Volume Fraction in Explosive Cylindrical Multiphase Dispersion

When an annular bed of solid particles that surrounds a cylindrical high-energy explosive core gets radially dispersed after detonation, the expanding front of particles undergoes instabilities. One of the possible causes of the instabilities is an inhomogeneous initial distribution of particles. This study explores this possibility by introducing two-dimensional perturbations to the initial distribution of particles within the annular bed and quantifying the growth of these perturbations over time using two-dimensional simulations. The initial perturbations are in the form of superposition of up to three sinusoidal azimuthal modal variations in the initial particle volume fraction (PVF, ratio of particle to cell volume). These are observed to impact the particle distribution at later times through a channeling instability whose effects are: (i) to decrease the velocity in regions of larger particle volume (PV) and (ii) to facilitate circumferential particle migration into the slow moving high PV sectors. These departures from axisymmetry are quantified by introducing two metrics. The effect of varying the number of azimuthal modes contained in the initial PVF perturbation, along with their amplitudes, wavelengths, and relative phases is investigated. The proposed metrics do not vary substantially with the relative phases; however, there is a strong variation in the metrics due to changes in the wavenumber. Unimodal perturbations were found to amplify both metrics the most.

Engineering↗
DOE OSTI2019

A Kriging Surrogate Model for Computing Gas Mixture Equations of State

Accurate simulation of the complex flow following the detonation of an explosive material is a challenging problem. In these flows, the detonation products of the explosive must be treated as a real gas while the surrounding air is treated as an ideal gas. As the detonation process unfolds and the blast wave moves into the surrounding ambient air, the products of detonation expand outward and interact with the air creating a mixture region. In this region, both of the state equations for air and the products must be satisfied. One of the most accurate, yet computationally expensive, methods to handle this problem is an algorithm that iterates between the equations of state until both pressure and temperature reach an equilibrium inside of a computational cell. Since this mixture region moves and grows over time, this algorithm must be performed millions, or even billions, of times in a typical detonation simulation. As such, these calculations can account for a large percentage of the overall solution time. This work aims to use a kriging surrogate model to replace this process. The iterative method solves a nonlinear system of equations created from the gas mixture density, internal energy, and composition using a Broyden iterative solver to obtain an output pressure and temperature. Kriging is used to produce curve fits which interpolate selected pressures and temperatures from this solver from appropriate ranges of the mixture input quantities. Using a finite volume hydrocode, the performance of the model with respect to the iterative solver is demonstrated in the simulation of a pentaerythritol tetranitrate (PETN) charge detonation. The model's computational speed and accuracy are quantified as a function of the choice of sampling points in order to try optimize the combination as well as to show the benefits of this novel approach.

Engineering↗
NASA NTRS2013

Quantifying Effects of Voids in Woven Ceramic Matrix Composites

Randomness in woven ceramic matrix composite architecture has been found to cause large variability in stiffness and strength. The inherent voids are an aspect of the architecture that may cause a significant portion of the variability. A study is undertaken to investigate the effects of many voids of random sizes and distributions. Response surface approximations were formulated based on void parameters such as area and length fractions to provide an estimate of the effective stiffness. Obtaining quantitative relationships between the properties of the voids and their effects on stiffness of ceramic matrix composites are of ultimate interest, but the exploratory study presented here starts by first modeling the effects of voids on an isotropic material. Several cases with varying void parameters were modeled which resulted in a large amount of variability of the transverse stiffness and out-of-plane shear stiffness. An investigation into a physical explanation for the stiffness degradation led to the observation that the voids need to be treated as an entity that reduces load bearing capabilities in a space larger than what the void directly occupies through a corrected length fraction or area fraction. This provides explanation as to why void volume fraction is not the only important factor to consider when computing loss of stiffness.

Goldsmith, Marlana B.↗
NASA NTRS2013

Effects of Microstructural Variability on Thermo-Mechanical Properties of a Woven Ceramic Matrix Composite

The objectives of this paper include identifying important architectural parameters that describe the SiC/SiC five-harness satin weave composite and characterizing the statistical distributions and correlations of those parameters from photomicrographs of various cross sections. In addition, realistic artificial cross sections of a 2D representative volume element (RVE) are generated reflecting the variability found in the photomicrographs, which are used to determine the effects of architectural variability on the thermo-mechanical properties. Lastly, preliminary information is obtained on the sensitivity of thermo-mechanical properties to architectural variations. Finite element analysis is used in combination with a response surface and it is shown that the present method is effective in determining the effects of architectural variability on thermo-mechanical properties.

Goldsmith, Marlana B.↗
NASA NTRS2007

Improving the Hydrodynamic Performance of Diffuser Vanes via Shape Optimization

The performance of a diffuser in a pump stage depends on its configuration and placement within the stage. The influence of vane shape on the hydrodynamic performance of a diffuser has been studied. The goal of this effort has been to improve the performance of a pump stage by optimizing the shape of the diffuser vanes. The shape of the vanes was defined using Bezier curves and circular arcs. Surrogate model based tools were used to identify regions of the vane that have a strong influence on its performance. Optimization of the vane shape, in the absence of manufacturing, and stress constraints, led to a nearly nine percent reduction in the total pressure losses compared to the baseline design by reducing the extent of the base separation.

Goel, Tushar↗
NASA NTRS2005

Surrogate-based Analysis and Optimization

A major challenge to the successful full-scale development of modem aerospace systems is to address competing objectives such as improved performance, reduced costs, and enhanced safety. Accurate, high-fidelity models are typically time consuming and computationally expensive. Furthermore, informed decisions should be made with an understanding of the impact (global sensitivity) of the design variables on the different objectives. In this context, the so-called surrogate-based approach for analysis and optimization can play a very valuable role. The surrogates are constructed using data drawn from high-fidelity models, and provide fast approximations of the objectives and constraints at new design points, thereby making sensitivity and optimization studies feasible. This paper provides a comprehensive discussion of the fundamental issues that arise in surrogate-based analysis and optimization (SBAO), highlighting concepts, methods, techniques, as well as practical implications. The issues addressed include the selection of the loss function and regularization criteria for constructing the surrogates, design of experiments, surrogate selection and construction, sensitivity analysis, convergence, and optimization. The multi-objective optimal design of a liquid rocket injector is presented to highlight the state of the art and to help guide future efforts.

Queipo, Nestor V.↗