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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Implementation of a multiblock sensitivity analysis method in numerical aerodynamic shape optimization

A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations. Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies. The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from the CFD discretized flow equations, recast in adjoint form, and solved using direct matrix inversion techniques. This investigation is performed to demonstrate an aerodynamic shape optimization technique on a multiblock domain and its applicability to complex geometries. The objectives are accomplished by shape optimizing two aerodynamic configurations. First, the shape optimization of a transonic airfoil is performed to investigate the behavior of the method in highly nonlinear flows and the effect of different grid blocking strategies on the procedure. Secondly, shape optimization of a two-element configuration in subsonic flow is completed. Cases are presented for this configuration to demonstrate the effect of simultaneously reshaping interfering elements. The aerodynamic shape optimization is shown to produce supercritical type airfoils in the transonic flow from an initially symmetric airfoil. Multiblocking effects the path of optimization while providing similar results at the conclusion. Simultaneous reshaping of elements is shown to be more effective than individual element reshaping due to the inclusion of mutual interference effects.

Lacasse, James M.↗
NASA NTRS1994

Aeroacoustic sensitivity analysis and optimal aeroacoustic design of turbomachinery blades

During the first year of the project, we have developed a theoretical analysis - and wrote a computer code based on this analysis - to compute the sensitivity of unsteady aerodynamic loads acting on airfoils in cascades due to small changes in airfoil geometry. The steady and unsteady flow though a cascade of airfoils is computed using the full potential equation. Once the nominal solutions have been computed, one computes the sensitivity. The analysis takes advantage of the fact that LU decomposition is used to compute the nominal steady and unsteady flow fields. If the LU factors are saved, then the computer time required to compute the sensitivity of both the steady and unsteady flows to changes in airfoil geometry is quite small. The results to date are quite encouraging, and may be summarized as follows: (1) The sensitivity procedure has been validated by comparing the results obtained by 'finite difference' techniques, that is, computing the flow using the nominal flow solver for two slightly different airfoils and differencing the results. The 'analytic' solution computed using the method developed under this grant and the finite difference results are found to be in almost perfect agreement. (2) The present sensitivity analysis is computationally much more efficient than finite difference techniques. We found that using a 129 by 33 node computational grid, the present sensitivity analysis can compute the steady flow sensitivity about ten times more efficiently that the finite difference approach. For the unsteady flow problem, the present sensitivity analysis is about two and one-half times as fast as the finite difference approach. We expect that the relative efficiencies will be even larger for the finer grids which will be used to compute high frequency aeroacoustic solutions. Computational results show that the sensitivity analysis is valid for small to moderate sized design perturbations. (3) We found that the sensitivity analysis provided important insight into how airfoils should be modified to improve their aeroelastic stability. Using this insight, we redesigned an aeroelastically unstable cascade to produce a stable cascade.

Hall, Kenneth C.↗
NASA NTRS1987

Sensitivity Analysis in Engineering

The symposium proceedings presented focused primarily on sensitivity analysis of structural response. However, the first session, entitled, General and Multidisciplinary Sensitivity, focused on areas such as physics, chemistry, controls, and aerodynamics. The other four sessions were concerned with the sensitivity of structural systems modeled by finite elements. Session 2 dealt with Static Sensitivity Analysis and Applications; Session 3 with Eigenproblem Sensitivity Methods; Session 4 with Transient Sensitivity Analysis; and Session 5 with Shape Sensitivity Analysis.

Adelman, Howard M.↗
NASA NTRS2016

Sensitivity Analysis of the Integrated Medical Model for ISS Programs

Sensitivity analysis estimates the relative contribution of the uncertainty in input values to the uncertainty of model outputs. Partial Rank Correlation Coefficient (PRCC) and Standardized Rank Regression Coefficient (SRRC) are methods of conducting sensitivity analysis on nonlinear simulation models like the Integrated Medical Model (IMM). The PRCC method estimates the sensitivity using partial correlation of the ranks of the generated input values to each generated output value. The partial part is so named because adjustments are made for the linear effects of all the other input values in the calculation of correlation between a particular input and each output. In SRRC, standardized regression-based coefficients measure the sensitivity of each input, adjusted for all the other inputs, on each output. Because the relative ranking of each of the inputs and outputs is used, as opposed to the values themselves, both methods accommodate the nonlinear relationship of the underlying model. As part of the IMM v4.0 validation study, simulations are available that predict 33 person-missions on ISS and 111 person-missions on STS. These simulated data predictions feed the sensitivity analysis procedures. The inputs to the sensitivity procedures include the number occurrences of each of the one hundred IMM medical conditions generated over the simulations and the associated IMM outputs: total quality time lost (QTL), number of evacuations (EVAC), and number of loss of crew lives (LOCL). The IMM team will report the results of using PRCC and SRRC on IMM v4.0 predictions of the ISS and STS missions created as part of the external validation study. Tornado plots will assist in the visualization of the condition-related input sensitivities to each of the main outcomes. The outcomes of this sensitivity analysis will drive review focus by identifying conditions where changes in uncertainty could drive changes in overall model output uncertainty. These efforts are an integral part of the overall verification, validation, and credibility review of IMM v4.0.

medical equipment↗
NASA NTRS1984

New Uses for Sensitivity Analysis: How Different Movement Tasks Effect Limb Model Parameter Sensitivity

Original results for a newly developed eight-order nonlinear limb antagonistic muscle model of elbow flexion and extension are presented. A wider variety of sensitivity analysis techniques are used and a systematic protocol is established that shows how the different methods can be used efficiently to complement one another for maximum insight into model sensitivity. It is explicitly shown how the sensitivity of output behaviors to model parameters is a function of the controller input sequence, i.e., of the movement task. When the task is changed (for instance, from an input sequence that results in the usual fast movement task to a slower movement that may also involve external loading, etc.) the set of parameters with high sensitivity will in general also change. Such task-specific use of sensitivity analysis techniques identifies the set of parameters most important for a given task, and even suggests task-specific model reduction possibilities.

Winters, J. M.↗
NASA NTRS1988

Recent developments in structural sensitivity analysis

Recent developments are reviewed in two major areas of structural sensitivity analysis: sensitivity of static and transient response; and sensitivity of vibration and buckling eigenproblems. Recent developments from the standpoint of computational cost, accuracy, and ease of implementation are presented. In the area of static response, current interest is focused on sensitivity to shape variation and sensitivity of nonlinear response. Two general approaches are used for computing sensitivities: differentiation of the continuum equations followed by discretization, and the reverse approach of discretization followed by differentiation. It is shown that the choice of methods has important accuracy and implementation implications. In the area of eigenproblem sensitivity, there is a great deal of interest and significant progress in sensitivity of problems with repeated eigenvalues. In addition to reviewing recent contributions in this area, the paper raises the issue of differentiability and continuity associated with the occurrence of repeated eigenvalues.

Haftka, Raphael T.↗
NASA NTRS1989

On equivalence of discrete-discrete and continuum-discrete design sensitivity analysis

Developments in design sensitivity analysis (DSA) method have been made using two fundamentally different approaches as shown. In the first approach, a discretized structural finite element model is used to carry out DSA. There are three different methods in the discrete DSA approach: finite difference, semi-analytical, and analytical methods. The finite difference method is a popular one due to its simplicity, but a serious shortcoming of the method is the uncertainty in the choice of a perturbation step size of design variables. In the semi-analytical method, the derivatives of stiffness matrix is computed by finite differences, whereas in the analytical method, the derivatives are obtained analytically. For the shape design variable, computation of analytical derivative of stiffness matrix is quite costly. Because of this, the semi-analytical method is a popular choice in discrete shape DSA approach. However, recently, Barthelemy and Haftka presented that the semi-analytical method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. They found that accuracy problems occur even for a simple cantilever beam. In the second approach, a continuum model of the structure is used to carry out DSA.

Choi, Kyung K.↗
NASA NTRS1996

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗
DOE OSTI2024

Development of Decay Heat Sensitivity Analysis Capability in SCALE/ORIGEN

In this work, a decay heat sensitivity analysis capability was developed and implemented in the ORIGEN code of the SCALE nuclear modeling and simulation suite. This capability introduces improved numerical integration schemes, which overcome the challenges associated with accurately modeling the behavior of adjoint nuclide amounts during coarse time steps for both nuclide amount and decay heat sensitivity calculations. This capability significantly improves the accuracy of calculations without compromising computational efficiency compared to the existing method. Extensive verification was conducted for various benchmark problems, including a 238 Pu decay and an irradiation problem involving 135 Xe, evaluated with both coarse and fine time grids. The results show excellent agreement with reference direct perturbation solutions, reaffirming the computational accuracy of the newly proposed numerical integration methods. Furthermore, sensitivity analyses were performed for fission product inventories ( 147 Sm, 150 Sm, 155 Gd) in pressurized water reactor UO 2 and MOX fuel assemblies. These analyses demonstrated that the ORIGEN sensitivity analysis capability can capture detailed sensitivity coefficients and underlying physics in real applications. Additionally, a decay heat sensitivity analysis for high-assay low-enriched uranium fuel, including various initial 235 U enrichment and burnup points, highlights the extended capabilities of SCALE/ORIGEN in comprehensively assessing the factors influencing total decay heat. These advancements in ORIGEN offer valuable insights for reactor analysis, fuel design, and safety assessments, especially in the context of advanced nuclear fuel development and design changes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1992

FOCUS - An experimental environment for fault sensitivity analysis

FOCUS, a simulation environment for conducting fault-sensitivity analysis of chip-level designs, is described. The environment can be used to evaluate alternative design tactics at an early design stage. A range of user specified faults is automatically injected at runtime, and their propagation to the chip I/O pins is measured through the gate and higher levels. A number of techniques for fault-sensitivity analysis are proposed and implemented in the FOCUS environment. These include transient impact assessment on latch, pin and functional errors, external pin error distribution due to in-chip transients, charge-level sensitivity analysis, and error propagation models to depict the dynamic behavior of latch errors. A case study of the impact of transient faults on a microprocessor-based jet-engine controller is used to identify the critical fault propagation paths, the module most sensitive to fault propagation, and the module with the highest potential for causing external errors.

Choi, Gwan S.↗
NASA NTRSDate not supplied

Sensitivity Analysis of the Human Research Program’s Impact 1.0 Model

Sensitivity analysis estimates the relative contribution of the uncertainty in input values to the uncertainty of model outputs. Partial Rank Correlation Coefficient (PRCC) and Leave One Out (LOO) are methods of conducting sensitivity analysis on non-linear simulation models like the IMPACT Model. The PRCC method estimates the sensitivity using partial correlation of the ranks of the generated input values to each generated output value. The “partial” part is due to the adjustments made for the linear effects of all the other input values in the calculation of correlation between a particular input and each output. LOO removes a medical condition from test suite and calculates the change in the outcome. This is used to identify the influence of the condition input in the model The inputs to the sensitivity procedures include the number of occurrences of each of the one hundred plus IMPACT medical conditions generated over the simulations, and the IMPACT outputs from the MEDPRAT mathematical model. The outputs total task time lost (TTL), number of return to definitive care (RTDC), and number of loss of crew lives (LOCL). The IMPACT team will report the results of using PRCC and LOO on IMPACT 1.0. Tornado plots will assist in the visualization of the condition-related input sensitivities to each of the main outcomes. The outcomes of this sensitivity analysis will drive review focus by identifying conditions where changes in uncertainty, and input values could drive changes in overall model output uncertainty. These efforts are an integral part of the overall verification, validation, and credibility review of IMPACT 1.0.

Sensitivity Anaylsis↗
NASA NTRS2000

LSENS, The NASA Lewis Kinetics and Sensitivity Analysis Code

A general chemical kinetics and sensitivity analysis code for complex, homogeneous, gas-phase reactions is described. The main features of the code, LSENS (the NASA Lewis kinetics and sensitivity analysis code), are its flexibility, efficiency and convenience in treating many different chemical reaction models. The models include: static system; steady, one-dimensional, inviscid flow; incident-shock initiated reaction in a shock tube; and a perfectly stirred reactor. In addition, equilibrium computations can be performed for several assigned states. An implicit numerical integration method (LSODE, the Livermore Solver for Ordinary Differential Equations), which works efficiently for the extremes of very fast and very slow reactions, is used to solve the "stiff" ordinary differential equation systems that arise in chemical kinetics. For static reactions, the code uses the decoupled direct method to calculate sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of dependent variables and/or the rate coefficient parameters. Solution methods for the equilibrium and post-shock conditions and for perfectly stirred reactor problems are either adapted from or based on the procedures built into the NASA code CEA (Chemical Equilibrium and Applications).

Radhakrishnan, K.↗
NASA NTRS2001

LISA Telescope Sensitivity Analysis

The results of a LISA telescope sensitivity analysis will be presented, The emphasis will be on the outgoing beam of the Dall-Kirkham' telescope and its far field phase patterns. The computed sensitivity analysis will include motions of the secondary with respect to the primary, changes in shape of the primary and secondary, effect of aberrations of the input laser beam and the effect the telescope thin film coatings on polarization. An end-to-end optical model will also be discussed.

Waluschka, Eugene↗
NASA NTRS1987

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Yao, Tse-Min↗
NASA NTRS1986

Design sensitivity analysis using EAL. Part 2: Shape design parameters

A numerical implementation of shape design sensitivity analysis of built-up structures is presented, using the versatility and convenience of an existing finite element structural analysis code and its data base management system. This report is a continuation of a previous report on conventional design parameters. The finite element code used in the implementation presented is the Engineering Analysis Language (EAL), which is based on a hybrid analysis method. It has been shown that shape design sensitivity computations can be carried out using the database management system of EAL, without writing a separate program and a separate data base. The material derivative concept of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to derive shape design sensitivity information of structural performances. A domain method of shape design sensitivity analysis and a design component method are used. Displacement and stress functionals are considered as performance criteria.

Dopker, B.↗
NASA NTRS1974

The application of sensitivity analysis to models of large scale physiological systems

A survey of the literature of sensitivity analysis as it applies to biological systems is reported as well as a brief development of sensitivity theory. A simple population model and a more complex thermoregulatory model illustrate the investigatory techniques and interpretation of parameter sensitivity analysis. The role of sensitivity analysis in validating and verifying models, and in identifying relative parameter influence in estimating errors in model behavior due to uncertainty in input data is presented. This analysis is valuable to the simulationist and the experimentalist in allocating resources for data collection. A method for reducing highly complex, nonlinear models to simple linear algebraic models that could be useful for making rapid, first order calculations of system behavior is presented.

Leonard, J. I.↗
NASA NTRS1987

Application of a sensitivity analysis technique to high-order digital flight control systems

A sensitivity analysis technique for multiloop flight control systems is studied. This technique uses the scaled singular values of the return difference matrix as a measure of the relative stability of a control system. It then uses the gradients of these singular values with respect to system and controller parameters to judge sensitivity. The sensitivity analysis technique is first reviewed; then it is extended to include digital systems, through the derivation of singular-value gradient equations. Gradients with respect to parameters which do not appear explicitly as control-system matrix elements are also derived, so that high-order systems can be studied. A complete review of the integrated technique is given by way of a simple example: the inverted pendulum problem. The technique is then demonstrated on the X-29 control laws. Results show linear models of real systems can be analyzed by this sensitivity technique, if it is applied with care. A computer program called SVA was written to accomplish the singular-value sensitivity analysis techniques. Thus computational methods and considerations form an integral part of many of the discussions. A user's guide to the program is included. The SVA is a fully public domain program, running on the NASA/Dryden Elxsi computer.

Paduano, James D.↗
NASA NTRS2016

Uncertainty and Sensitivity Analysis of Afterbody Radiative Heating Predictions for Earth Entry

The objective of this work was to perform sensitivity analysis and uncertainty quantification for afterbody radiative heating predictions of Stardust capsule during Earth entry at peak afterbody radiation conditions. The radiation environment in the afterbody region poses significant challenges for accurate uncertainty quantification and sensitivity analysis due to the complexity of the flow physics, computational cost, and large number of un-certain variables. In this study, first a sparse collocation non-intrusive polynomial chaos approach along with global non-linear sensitivity analysis was used to identify the most significant uncertain variables and reduce the dimensions of the stochastic problem. Then, a total order stochastic expansion was constructed over only the important parameters for an efficient and accurate estimate of the uncertainty in radiation. Based on previous work, 388 uncertain parameters were considered in the radiation model, which came from the thermodynamics, flow field chemistry, and radiation modeling. The sensitivity analysis showed that only four of these variables contributed significantly to afterbody radiation uncertainty, accounting for almost 95% of the uncertainty. These included the electronic- impact excitation rate for N between level 2 and level 5 and rates of three chemical reactions in uencing N, N(+), O, and O(+) number densities in the flow field.

West, Thomas K., IV↗