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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Progressive Response Surfaces

Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. Progressive response surfaces are ones that are built up progressively as global information is added from new sample points in the parameter space. As the response surfaces are globally upgraded based on new information, heuristic indications of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured fashion, or in an unstructured fashion. Whatever the approach, at least in early stages of sampling it is usually desirable to sample the entire parameter space uniformly. At later stages of sampling, depending on the nature of the quantity being resolved, it may be desirable to continue sampling uniformly over the entire parameter space (Progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in early stages of sampling (Adaptive response surfaces). Here we consider Progressive response surfaces where a balanced indication of global response over the parameter space is desired.We use a variant of Moving Least Squares to fit and interpolate structured and unstructured point sets over the parameter space. On a 2-D test problem we compare response surface accuracy for three incremental sampling methods: Progressive Lattice Sampling; Simple-Random Monte Carlo; and Halton Quasi-Monte-Carlo sequences. We are ultimately after a system for constructing efficiently upgradable response surface approximations with reliable error estimates.

Romero, V. J.↗
NASA NTRS1992

Tuning a fuzzy controller using quadratic response surfaces

Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

Schott, Brian↗
NASA NTRS2010

Estimation of Supersonic Stage Separation Aerodynamics of Winged-Body Launch Vehicles Using Response Surface Methods

Response surface methodology was used to estimate the longitudinal stage separation aerodynamic characteristics of a generic, bimese, winged multi-stage launch vehicle configuration at supersonic speeds in the NASA LaRC Unitary Plan Wind Tunnel. The Mach 3 staging was dominated by shock wave interactions between the orbiter and booster vehicles throughout the relative spatial locations of interest. The inference space was partitioned into several contiguous regions within which the separation aerodynamics were presumed to be well-behaved and estimable using central composite designs capable of fitting full second-order response functions. The underlying aerodynamic response surfaces of the booster vehicle in belly-to-belly proximity to the orbiter vehicle were estimated using piecewise-continuous lower-order polynomial functions. The quality of fit and prediction capabilities of the empirical models were assessed in detail, and the issue of subspace boundary discontinuities was addressed. Augmenting the central composite designs to full third-order using computer-generated D-optimality criteria was evaluated. The usefulness of central composite designs, the subspace sizing, and the practicality of fitting lower-order response functions over a partitioned inference space dominated by highly nonlinear and possibly discontinuous shock-induced aerodynamics are discussed.

Erickson, Gary E.↗
NASA NTRS1995

Application of response surface techniques to helicopter rotor blade optimization procedure

In multidisciplinary optimization problems, response surface techniques can be used to replace the complex analyses that define the objective function and/or constraints with simple functions, typically polynomials. In this work a response surface is applied to the design optimization of a helicopter rotor blade. In previous work, this problem has been formulated with a multilevel approach. Here, the response surface takes advantage of this decomposition and is used to replace the lower level, a structural optimization of the blade. Problems that were encountered and important considerations in applying the response surface are discussed. Preliminary results are also presented that illustrate the benefits of using the response surface.

Henderson, Joseph Lynn↗
NASA NTRS1998

Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle

The use of response surface models and kriging models are compared for approximating non-random, deterministic computer analyses. After discussing the traditional response surface approach for constructing polynomial models for approximation, kriging is presented as an alternative statistical-based approximation method for the design and analysis of computer experiments. Both approximation methods are applied to the multidisciplinary design and analysis of an aerospike nozzle which consists of a computational fluid dynamics model and a finite element analysis model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations. Four optimization problems are formulated and solved using both approximation models. While neither approximation technique consistently outperforms the other in this example, the kriging models using only a constant for the underlying global model and a Gaussian correlation function perform as well as the second order polynomial response surface models.

Simpson, Timothy W.↗
NASA NTRS1998

Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

Simpson, Timothy W.↗
NASA NTRS1993

Effect of design selection on response surface performance

The mathematical formulation of the engineering optimization problem is given. Evaluation of the objective function and constraint equations can be very expensive in a computational sense. Thus, it is desirable to use as few evaluations as possible in obtaining its solution. In solving the equation, one approach is to develop approximations to the objective function and/or restraint equations and then to solve the equation using the approximations in place of the original functions. These approximations are referred to as response surfaces. The desirability of using response surfaces depends upon the number of functional evaluations required to build the response surfaces compared to the number required in the direct solution of the equation without approximations. The present study is concerned with evaluating the performance of response surfaces so that a decision can be made as to their effectiveness in optimization applications. In particular, this study focuses on how the quality of approximations is effected by design selection. Polynomial approximations and neural net approximations are considered.

Carpenter, William C.↗
NASA NTRS2010

Advanced Response Surface Modeling of Ares I Roll Control Jet Aerodynamic Interactions

The Ares I rocket uses roll control jets. These jets have aerodynamic implications as they impinge on the surface and protuberances of the vehicle. The jet interaction on the body can cause an amplification or a reduction of the rolling moment produced by the jet itself, either increasing the jet effectiveness or creating an adverse effect. A design of experiments test was planned and carried out using computation fluid dynamics, and a subsequent response surface analysis ensued on the available data to characterize the jet interaction across the ascent portion of the Ares I flight envelope. Four response surface schemes were compared including a single response surface covering the entire design space, separate sector responses that did not overlap, continuously overlapping surfaces, and recursive weighted response surfaces. These surfaces were evaluated on traditional statistical metrics as well as visual inspection. Validation of the recursive weighted response surface was performed using additionally available data at off-design point locations.

Favaregh, Noah M.↗
NASA NTRS2001

Response Surface Modeling Using Multivariate Orthogonal Functions

A nonlinear modeling technique was used to characterize response surfaces for non-dimensional longitudinal aerodynamic force and moment coefficients, based on wind tunnel data from a commercial jet transport model. Data were collected using two experimental procedures - one based on modem design of experiments (MDOE), and one using a classical one factor at a time (OFAT) approach. The nonlinear modeling technique used multivariate orthogonal functions generated from the independent variable data as modeling functions in a least squares context to characterize the response surfaces. Model terms were selected automatically using a prediction error metric. Prediction error bounds computed from the modeling data alone were found to be- a good measure of actual prediction error for prediction points within the inference space. Root-mean-square model fit error and prediction error were less than 4 percent of the mean response value in all cases. Efficacy and prediction performance of the response surface models identified from both MDOE and OFAT experiments were investigated.

Morelli, Eugene A.↗
DOE OSTI2021

An Iterative Response-Surface-Based Approach for Chance-Constrained AC Optimal Power Flow Considering Dependent Uncertainty

A modern power system is characterized by a stochastic variation of the loads and an increasing penetration of renewable energy generation, which results in large uncertainties in its states. These uncertainties bring formidable challenges to the power system planning and operation process. To address these challenges, we propose a cost-effective, iterative response-surface-based approach for the chance-constrained AC optimal power-flow problem that aims to ensure the secure operation of the power systems considering dependent uncertainties. Starting from a stochastic-sampling-based framework, we first utilize the copula theory to simulate the dependence among multivariate uncertain inputs. Then, to reduce the prohibitive computational time required in the traditional Monte-Carlo method, we propose, instead of using the original complicated power-system model, to rely on a polynomial-chaos-based response surface. This response surface allows us to efficiently evaluate the time-consuming power-system model at arbitrary distributed sampled values with a negligible computational cost. This further enables us to efficiently conduct an online stochastic testing for the system states that not only screens out the statistical active constraints, but also assists in a better design of the tightened bounds without using any Gaussian or symmetric assumption. Finally, an iterative procedure is executed to fine-tune the optimal solution that better satisfies a predefined probability. The simulations conducted in multiple test systems demonstrate the excellent performance of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2011

Autonomous Aerobraking: Thermal Analysis and Response Surface Development

A high-fidelity thermal model of the Mars Reconnaissance Orbiter was developed for use in an autonomous aerobraking simulation study. Response surface equations were derived from the high-fidelity thermal model and integrated into the autonomous aerobraking simulation software. The high-fidelity thermal model was developed using the Thermal Desktop software and used in all phases of the analysis. The use of Thermal Desktop exclusively, represented a change from previously developed aerobraking thermal analysis methodologies. Comparisons were made between the Thermal Desktop solutions and those developed for the previous aerobraking thermal analyses performed on the Mars Reconnaissance Orbiter during aerobraking operations. A variable sensitivity screening study was performed to reduce the number of variables carried in the response surface equations. Thermal analysis and response surface equation development were performed for autonomous aerobraking missions at Mars and Venus.

Dec, John A.↗
NASA NTRS2000

Neural Network and Response Surface Methodology for Rocket Engine Component Optimization

The goal of this work is to compare the performance of response surface methodology (RSM) and two types of neural networks (NN) to aid preliminary design of two rocket engine components. A data set of 45 training points and 20 test points obtained from a semi-empirical model based on three design variables is used for a shear coaxial injector element. Data for supersonic turbine design is based on six design variables, 76 training, data and 18 test data obtained from simplified aerodynamic analysis. Several RS and NN are first constructed using the training data. The test data are then employed to select the best RS or NN. Quadratic and cubic response surfaces. radial basis neural network (RBNN) and back-propagation neural network (BPNN) are compared. Two-layered RBNN are generated using two different training algorithms, namely solverbe and solverb. A two layered BPNN is generated with Tan-Sigmoid transfer function. Various issues related to the training of the neural networks are addressed including number of neurons, error goals, spread constants and the accuracy of different models in representing the design space. A search for the optimum design is carried out using a standard gradient-based optimization algorithm over the response surfaces represented by the polynomials and trained neural networks. Usually a cubic polynominal performs better than the quadratic polynomial but exceptions have been noticed. Among the NN choices, the RBNN designed using solverb yields more consistent performance for both engine components considered. The training of RBNN is easier as it requires linear regression. This coupled with the consistency in performance promise the possibility of it being used as an optimization strategy for engineering design problems.

Vaidyanathan, Rajkumar↗
NASA NTRS2003

Method for Constructing Composite Response Surfaces by Combining Neural Networks with other Interpolation or Estimation Techniques

A method and system for design optimization that incorporates the advantages of both traditional response surface methodology (RSM) and neural networks is disclosed. The present invention employs a unique strategy called parameter-based partitioning of the given design space. In the design procedure, a sequence of composite response surfaces based on both neural networks and polynomial fits is used to traverse the design space to identify an optimal solution. The composite response surface has both the power of neural networks and the economy of low-order polynomials (in terms of the number of simulations needed and the network training requirements). The present invention handles design problems with many more parameters than would be possible using neural networks alone and permits a designer to rapidly perform a variety of trade-off studies before arriving at the final design.

Rai, Man Mohan↗
NASA NTRS1998

Response Surface Model Building and Multidisciplinary Optimization Using D-Optimal Designs

This paper discusses response surface methods for approximation model building and multidisciplinary design optimization. The response surface methods discussed are central composite designs, Bayesian methods and D-optimal designs. An over-determined D-optimal design is applied to a configuration design and optimization study of a wing-body, launch vehicle. Results suggest that over determined D-optimal designs may provide an efficient approach for approximation model building and for multidisciplinary design optimization.

Unal, Resit↗
NASA NTRS2008

Estimation of Supersonic Stage Separation Aerodynamics of Winged-Body Launch Vehicles Using Response Surface Methods

A collection of statistical and mathematical techniques referred to as response surface methodology was used to estimate the longitudinal stage separation aerodynamic characteristics of a generic, bimese, winged multi-stage launch vehicle configuration using data obtained on small-scale models at supersonic speeds in the NASA Langley Research Center Unitary Plan Wind Tunnel. The simulated Mach 3 staging was dominated by multiple shock wave interactions between the orbiter and booster vehicles throughout the relative spatial locations of interest. This motivated a partitioning of the overall inference space into several contiguous regions within which the separation aerodynamics were presumed to be well-behaved and estimable using cuboidal and spherical central composite designs capable of fitting full second-order response functions. The primary goal was to approximate the underlying overall aerodynamic response surfaces of the booster vehicle in belly-to-belly proximity to the orbiter vehicle using relatively simple, lower-order polynomial functions that were piecewise-continuous across the full independent variable ranges of interest. The quality of fit and prediction capabilities of the empirical models were assessed in detail, and the issue of subspace boundary discontinuities was addressed. The potential benefits of augmenting the central composite designs to full third order using computer-generated D-optimality criteria were also evaluated. The usefulness of central composite designs, the subspace sizing, and the practicality of fitting low-order response functions over a partitioned inference space dominated by highly nonlinear and possibly discontinuous shock-induced aerodynamics are discussed.

Erickson, Gary E.↗
DOE OSTI2020

Multi-objective optimization of peel and shear strengths in ultrasonic metal welding using machine learning-based response surface methodology

Ultrasonic metal welding (UMW) is a solid-state joining technique with varied industrial applications. Despite of its numerous advantages, UMW has a relative narrow operating window and is sensitive to variations in process conditions. As such, it is imperative to quantitatively characterize the influence of welding parameters on the resulting joint quality. The quantification model can be subsequently used to optimize the parameters. Conventional response surface methodology (RSM) usually employs linear or polynomial models, which may not be able to capture the intricate, nonlinear input-output relationships in UMW. Furthermore, some UMW applications call for simultaneous optimization of multiple quality indices such as peel strength, shear strength, electrical conductivity, and thermal conductivity. To address these challenges, this paper develops a machine learning (ML)-based RSM to model the input-output relationships in UMW and jointly optimize two quality indices, namely, peel and shear strengths. The performance of various ML methods including spline regression, Gaussian process regression (GPR), support vector regression (SVR), and conventional polynomial regression models with different orders is compared. A case study using experimental data shows that GPR with radial basis function (RBF) kernel and SVR with RBF kernel achieve the best prediction accuracy. The obtained response surface models are then used to optimize a compound joint strength indicator that is defined as the average of normalized shear and peel strengths. In addition, the case study reveals different patterns in the response surfaces of shear and peel strengths, which has not been systematically studied in the literature. While developed for the UMW application, the method can be extended to other manufacturing processes.

42 ENGINEERING↗
NASA NTRS2005

Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

Response construction methods using Moving Least Squares (MLS), Kriging and Radial Basis Functions (RBF) are compared with the Global Least Squares (GLS) method in three numerical examples for derivative generation capability. Also, a new Interpolating Moving Least Squares (IMLS) method adopted from the meshless method is presented. It is found that the response surface construction methods using the Kriging and RBF interpolation yields more accurate results compared with MLS and GLS methods. Several computational aspects of the response surface construction methods also discussed.

Krishnamurthy, Thiagarajan↗
DOE OSTI2025

An Assessment of the Error Due to Computing Waste Isolation Pilot Plant Porosity Using the Porosity Response Surface Approach

The Waste Isolation Pilot Plant Performance Assessment (WIPP PA) must predict the likelihood that radionuclides will escape into the biosphere via mechanisms that depend on geohydraulic flow. Ideally, one would predict the geohydraulic flow using coupled geohydraulic and geomechanical simulations, but such coupled simulations are not computationally tractable. Instead, Sandia has historically used a look-up table of porosities for a given fluid pressure and time, called the porosity response surface, but this approach can introduce porosity errors because it largely ignores the porosity’s dependence on the past fluid pressure history. This report discusses efforts to quantify these porosity errors for both the legacy and new porosity response surfaces. Six hundred different fluid pressure histories were fed through the legacy/new geomechanical model and the legacy/new porosity response surface to generate six hundred porosity error histories. The error associated with the legacy porosity surface was substantial, while the error associated with the new porosity surface was typically small, except when fluid pressures exceeded the lithostatic pressure at the repository. In response to the errors at high pressures, a preliminary study of the WIPP PA’s sensitivity to these porosity errors was conducted. The study found that reducing the porosity errors at high pressures negligibly affected predictions of radionuclide releases. Finally, an initial machine-learned model for porosity was developed. This ML model significantly reduced the porosity error at high pressures, but sizable errors remained, so more development is necessary before coupling an ML model to the geohydraulic model.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗