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All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗
NASA NTRS1993

Boundary formulations for sensitivity analysis without matrix derivatives

A new hybrid approach to continuum structural shape sensitivity analysis employing boundary element analysis (BEA) is presented. The approach uses iterative reanalysis to obviate the need to factor perturbed matrices in the determination of surface displacement and traction sensitivities via a univariate perturbation/finite difference (UPFD) step. The UPFD approach makes it possible to immediately reuse existing subroutines for computation of BEA matrix coefficients in the design sensitivity analysis process. The reanalysis technique computes economical response of univariately perturbed models without factoring perturbed matrices. The approach provides substantial computational economy without the burden of a large-scale reprogramming effort.

Kane, J. H.↗
NASA NTRS1999

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics (CFD). The focus here is on those methods particularly well-suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid CFD algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid CFDs in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Newman, James C., III↗
NASA NTRS1998

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics. The focus here is on those methods particularly well- suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid computational fluid dynamics algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid computational fluid dynamics in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Newman, Perry A.↗
DOE OSTI2015

Second-order adjoint sensitivity analysis methodology (2ND-ASAM) for computing exactly and efficiently first- and second-order sensitivities in large-scale systems - 14356

This work presents the second-order adjoint sensitivity analysis methodology (2.-ASAM) for computing exactly and efficiently the second-order functional derivatives ('sensitivities') of system responses to the system's model parameters. For a physical system comprising N{sub α} parameters and N{sub r} responses, forward methods require a total of at least (N{sup 2}{sub α}/2+3N{sub α}/2) large-scale computations for obtaining all of the first- and second-order sensitivities, for all N{sub r} system responses. On the other hand, for one functional-type system response, the 2.-ASAM requires one large-scale computation using the first-level adjoint sensitivity system (1.-LASS) for obtaining all of the first-order sensitivities, followed by at most (2N{sub α}+1) large-scale computations using the second-level adjoint sensitivity systems (2.-LASS) for obtaining all of the second-order sensitivities. The second-order sensitivities contribute decisively to causing asymmetries in the response distribution, since they are the leading contributors to the third-order response correlations (skewness). They also cause the 'expected value of the response' to differ from the 'computed nominal value of the response'. The implementation of the 2.-ASAM requires very little additional effort beyond the construction of the adjoint sensitivity system needed for computing the first-order sensitivities. Only the sources on the right-sides of the diffusion (differential) operator needed to be modified; the left-side of the differential equations (and hence the 'solver' in large-scale practical applications) remain unchanged. The application of the 2.-ASAM is illustrated on a benchmark heat conduction/convection problem, which makes transparent the underlying mathematical derivations. For this illustrative problem, 4 'large-scale' adjoint computations suffice for computing exactly all of the 6 first- and 21 distinct second-order derivatives. The 2.-ASAM presented in this work should enable the hitherto very difficult, if not intractable, exact computation of all of the second-order response sensitivities for large-systems involving many parameters, which is expected to affect significantly other fields that need efficiently computed second-order response sensitivities, such as optimization, data assimilation/adjustment, model calibration, and predictive modeling. (author)

42 ENGINEERING↗
NASA NTRS1987

Design sensitivity analysis of nonlinear structural response

A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use.

Cardoso, J. B.↗
DOE OSTI2022

Preliminary Sensitivity Analysis for Sensors Impacts on Building Control Performance

This report describes the preliminary sensitivity analysis for sensor impacts on building control performance through the US Department of Energy’s Oak Ridge National Laboratory’s Flexible Research Platform (FRP-2) building. The rooftop unit system provides cooling and heating to the building. The main heating coil is a gas heating coil. Each zone is served by a variable air volume box with an electricity reheat coil. The rooftop unit and variable air volume box controls adopted the practical control sequences from ASHRAE Guideline 36-2018: High-Performance Sequences of Operation. For sensors, the incipient (time-changing) sensor errors, including bias sensor error and precision sensor error, are the inputs of interest. The outputs are energy consumption and thermal comfort (e.g., the predicted percentage of dissatisfied occupants). The large-scale simulation (3,600 cases) was conducted on a cloud platform by integrating sensor errors and ASHRAE Guideline 36 control sequences into an emulator based on the EnergyPlus simulation program with Python energy management system feature. The surrogate models were developed based on cloud simulation results. The uncertainty analysis showed that the sensor errors substantially affect building energy consumption and thermal comfort. The sensitivity analysis shows a ranking of sensor error impacts for each interested output item (e.g., cooling energy, reheat coil heating energy, predicted percentage of dissatisfied occupants). In FY 2022, sensor locations, types, and costs will be evaluated. The field test in Oak Ridge National Laboratory’s Flexible Research Platform building regarding sensor impacts will also be performed. Finally, a comparative analysis will be conducted based on the field test results and emulator results.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Uncertainty Quantification and Sensitivity Analysis of Non-Nuclear Advanced Controls Testbed Reactor Mockup

The research presented in this report describes our progress in applying stochastic methods and uncertainty quantification, parametric study, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated with Griffin, with the goal of developing a reduced order (surrogate) model which can be rapidly sampled while perturbing multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums, which are controlled by a hybrid proportional, integral and derivative (PID) controller, actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time and $\beta$ from a transient Griffin simulation executed with the improved quasi-static method to provide the kinetic parameters) as inputs to functions which control the CD rotation angle. Using a number of stochastic method approaches, we developed a dual purpose training-surrogate model of the NTP system using polynomial regression. The trained model can be rapidly sampled while simultaneously perturbing various input parameters of the model, such as coefficients on the PID control, or temperature (directly affect the neutron cross section). The surrogate model delivers accurate results orders-of-magnitude faster (minutes, not days) than the base model. Once the base model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs and their effect on the output. For example, coefficients used in the PID control system may vary due to some physical interference, or there may be uncertainty in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters and operational boundaries can be determined. The goal of this work is to support development of an advanced control system to operate CDs in a functioning NTP system.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Global Sensitivity Analysis of Large Distribution System with PVs using Deep Gaussian Process

Global sensitivity analysis (GSA) of the voltage to uncertain power injection variations plays an important role for appropriate Volt-VAR optimization. This paper proposes a data-driven GSA method for large-scale distribution systems with a large number of uncertain sources. Specifically, the deep Gaussian process is used to identify the mapping relationship between uncertain power injections and voltages. This allows us to resort to the analysis of variance framework to calculate the Sobol indices for GSA. Unlike the existing polynomial chaos expansion and Gaussian process-based approaches, our proposed method has much better scalability. Test results on the EPRI 1747-node K1 circuit with a different number and different probability distributions of uncertain sources demonstrate that the proposed method can achieve accurate GSA under various conditions.

14 SOLAR ENERGY↗
NASA NTRS1988

Sensitivity analysis and multidisciplinary optimization for aircraft design: Recent advances and results

Optimization by decomposition, complex system sensitivity analysis, and a rapid growth of disciplinary sensitivity analysis are some of the recent developments that hold promise of a quantum jump in the support engineers receive from computers in the quantitative aspects of design. Review of the salient points of these techniques is given and illustrated by examples from aircraft design as a process that combines the best of human intellect and computer power to manipulate data.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1988

Sensitivity analysis and multidisciplinary optimization for aircraft design - Recent advances and results

Optimization by decomposition, complex system sensitivity analysis, and a rapid growth of disciplinary sensitivity analysis are some of the recent developments that hold promise of a quantum jump in the support engineers receive from computers in the quantitative aspects of design. Review of the salient points of these techniques is given and illustrated by examples from aircraft design as a process that combines the best of human intellect and computer power to manipulate data.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1994

Automatic differentiation for design sensitivity analysis of structural systems using multiple processors

An automatic differentiation tool (ADIFOR) is incorporated into a finite element based structural analysis program for shape and non-shape design sensitivity analysis of structural systems. The entire analysis and sensitivity procedures are parallelized and vectorized for high performance computation. Small scale examples to verify the accuracy of the proposed program and a medium scale example to demonstrate the parallel vector performance on multiple CRAY C90 processors are included.

Nguyen, Duc T.↗
DOE OSTI2012

Sensitivity analysis of coupled criticality calculations

Perturbation theory based sensitivity analysis is a vital part of todays' nuclear reactor design. This paper presents an extension of standard techniques to examine coupled criticality problems with mutual feedback between neutronics and an augmenting system (for example thermal-hydraulics). The proposed procedure uses a neutronic and an augmenting adjoint function to efficiently calculate the first order change in responses of interest due to variations of the parameters describing the coupled problem. The effect of the perturbations is considered in two different ways in our study: either a change is allowed in the power level while maintaining criticality (power perturbation) or a change is allowed in the eigenvalue while the power is constrained (eigenvalue perturbation). The calculated response can be the change in the power level, the reactivity worth of the perturbation, or the change in any functional of the flux, the augmenting dependent variables and the input parameters. To obtain power- and criticality-constrained sensitivities power- and k-reset procedures can be applied yielding identical results. Both the theoretical background and an application to a one dimensional slab problem are presented, along with an iterative procedure to compute the necessary adjoint functions using the neutronics and the augmenting codes separately, thus eliminating the need of developing new programs to solve the coupled adjoint problem. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2012

Sensitivity Analysis of FEAST-Metal Fuel Performance Code: Initial Results

This memo documents the completion of the LANL milestone, M3FT-12LA0202041, describing methodologies and initial results using FEAST-Metal. The FEAST-Metal code calculations for this work are being conducted at LANL in support of on-going activities related to sensitivity analysis of fuel performance codes. The objective is to identify important macroscopic parameters of interest to modeling and simulation of metallic fuel performance. This report summarizes our preliminary results for the sensitivity analysis using 6 calibration datasets for metallic fuel developed at ANL for EBR-II experiments. Sensitivity ranking methodology was deployed to narrow down the selected parameters for the current study. There are approximately 84 calibration parameters in the FEAST-Metal code, of which 32 were ultimately used in Phase II of this study. Preliminary results of this sensitivity analysis led to the following ranking of FEAST models for future calibration and improvements: fuel conductivity, fission gas transport/release, fuel creep, and precipitation kinetics. More validation data is needed to validate calibrated parameter distributions for future uncertainty quantification studies with FEAST-Metal. Results of this study also served to point out some code deficiencies and possible errors, and these are being investigated in order to determine root causes and to improve upon the existing code models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1988

A semianalytical technique for sensitivity analysis of unsteady aerodynamic computations

A semianalytical approach is developed for the sensitivity analysis of linear unsteady aerodynamic loads. The semianalytical approach is easier to implement than the analytical approach. It is also computationally less expensive than the finite difference approach when used with panel methods, which require a large number of panels. The semianalytical approach is applied to an isolated airfoil in a 2-D flow and rotating propfan blades in 3-D flow. Sensitivity coefficients with respect to non-shape-dependent variables are shown for some cases. It is expected that the semianalytical approach will be useful in aeroelastic design procedures particularly when mistuning is present, and that it is potentially useful for shape sensitivity analysis of linear unsteady aerodynamics.

Murthy, Durbha V.↗
DOE OSTI2025

Uncertainty and Sensitivity Analysis Methods and Applications in the GDSA Framework (FY2025)

The Spent Fuel and Waste Science and Technology Campaign (SFWST) of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE) is conducting research and development on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). Two priorities for SFWST are design concept development and disposal system modeling. These priorities are directly addressed in the Geologic Disposal Safety Assessment (GDSA) control account, which is charged with developing a geologic repository system modeling and analysis capability, and the associated software, GDSA Framework, for evaluating disposal system performance for nuclear waste in geologic media. This report describes specific activities in the Fiscal Year (FY) 2025 associated with the GDSA Uncertainty and Sensitivity Analysis Methods work package. This report fulfills the GDSA Uncertainty and Sensitivity Analysis Methods work package (SF-25SN01030407) level 3 milestone, Uncertainty and Sensitivity Analysis Methods and Applications in GDSA Framework (FY2025) (M3SF-25SN010304072). This work was closely coordinated with the other Sandia National Laboratory GDSA work packages: the GDSA Framework Development work package (SF-25SN01030408), the GDSA Repository Systems Analysis work package (SF-25SN01030409), and the GDSA PFLOTRAN Development work package (SF-25SN01030410). This report builds on developments reported in previous GDSA Framework milestones, particularly M3SF-24SN010304072.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗