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Global Sensitivity Analyses for Test Planning with Black-Box Models for Mars Sample Return

This work describes sensitivity analyses performed on complex black-box models used to support experimental test planning under limited resources in the context of the Mars Sample Return program, which aims at bringing to Earth rock and atmospheric samples from Mars. We develop a systematic workflow that allows the analysts to simultaneously obtain quantitative insights on key drivers of uncertainty, on the direction of impact, and the presence of interactions. We apply novel optimal transport-based global sensitivity measures to tackle the multivariate nature of the output. On the modeling side, we apply multi-fidelity techniques that leverage low-fidelity models to speed up the calculations and make up for the limited amount of high-fidelity samples, while keeping these in the loop for accuracy guarantees. The sensitivity analysis reveals insights useful for the analysts to understand the model's behavior and identify the factors to focus on during testing in order to maximize the value of information extracted from them to ensure mission success when limited resources are available.

Giuseppe Cataldo↗

DOE OSTI2024

Core Design Optimization of the Westinghouse Lead Fast Reactor

Westinghouse is pursuing an advanced Nuclear Power Plant design based on Lead Fast Reactor (LFR) technology for global commercialization. To achieve an optimal combination of key attributes, such as safety, sustainability, and economic competitiveness, Westinghouse and ANL partnered in developing and applying a formalized core design optimization strategy. An LFR analysis workflow was developed to automate a suite of reactor physics, fuels performance, safety, and economics simulations on a selected LFR concept. The workflow streamlines analysis of a wide range of LFR designs with different dimensions and fuel types to assess their viability and economic performance, significantly reducing human processing time and risks of processing errors. The LFR optimization exercise was defined, resulting in selection of the design constraints (geometric, neutronics, thermo-mechanical, safety, thermal-hydraulics, and economics) and performance metrics researched (minimization of both the fuels LCOE and the first core inventory cost). A total of 14 varied design parameters were considered, including assembly dimensions, coolant temperature, and enrichment distribution throughout the core. The LFR analysis workflow was connected to DAKOTA for sensitivity and optimization analyses. Due to the extremely large size of the potential LFR optimization solution space relative to the computing time required to characterize one LFR solution, a multi-stage optimization approach was proposed to breakdown the problem into several stages with more reasonable sizes. This optimization approach enabled finding various viable core solutions with different cost tradeoffs that were considered by Westinghouse and justify selection of a smaller core with multi-batch 2-year cycle length.

Stauff, Nicolas E.↗

NASA NTRS1985

Tropical Ocean and Global Atmosphere (TOGA) heat exchange project: A summary report

A pilot data center to compute ocean atmosphere heat exchange over the tropical ocean is prposed at the Jet Propulsion Laboratory (JPL) in response to the scientific needs of the Tropical Ocean and Global Atmosphere (TOGA) Program. Optimal methods will be used to estimate sea surface temperature (SET), surface wind speed, and humidity from spaceborne observations. A monthly summary of these parameters will be used to compute ocean atmosphere latent heat exchanges. Monthly fields of surface heat flux over tropical oceans will be constructed using estimations of latent heat exchanges and short wave radiation from satellite data. Verification of all satellite data sets with in situ measurements at a few locations will be provided. The data center will be an experimental active archive where the quality and quantity of data required for TOGA flux computation are managed. The center is essential to facilitate the construction of composite data sets from global measurements taken from different sensors on various satellites. It will provide efficient utilization and easy access to the large volume of satellite data available for studies of ocean atmosphere energy exchanges.

Liu, W. T.↗

NASA NTRS2002

Designing a Unique Single Point Cross Over Method

The idea behind genetic algorithms is to extract optimization strategies nature uses successfully - known as Darwinian Evolution - and transform them for application in mathematical optimization theory to find the global optimum in a defined phase space. One could imagine a population of individual 'explorers' sent into the optimization phase-space. Each explorer is defined by its genes, what means, its position inside the phase-space is coded in his genes. Every explorer has the duty to find a value of the quality of his position in the phase space. (Consider the phase-space being a number of variables in some technological process, the value of quality of any position in the phase space - in other words: any set of the variables - can be expressed by the yield of the desired chemical product.) Then the struggle of 'life' begins. The three fundamental principles are selection, mating/crossover, and mutation. Only explorers (= genes) sitting on the best places will reproduce and create a new population. This is performed in the second step (mating/crossover). The 'hope' behind this part of the algorithm is, that 'good' sections of two parents will be recombined to yet better fitting children. In fact, many of the created children will not be successful (as in biological evolution), but a few children will indeed fulfill this hope. These good sections are named in some publications as building blocks. Now there appears a problem. Repeating these steps, no new area would be explored. The two former steps would only exploit the already known regions in the phase space, which could lead to premature convergence of the algorithm with the consequence of missing the global optimum by exploiting some local optimum. The third step, mutation, ensures the necessary accidental effects. One can imagine the new population being mixed up a little bit to bring some new information into this set of genes. Whereas in biology a gene is described as a macro-molecule with four different bases to code the genetic information, a gene in genetic algorithms is usually defined as a bitstring (a sequence of b 1's and 0's).

Wilson, Richard Phillip↗

NASA NTRS2019

Optimization of a Remote Sensing Energy Balance Method over Different Canopy Applied at Global Scale

Parameterization methods which calculate turbulent heat and water fluxes with thermal remote sensing data were evaluated in the revised remote sensing surface energy balance system (SEBS) model (Chen et al., 2013). The model calculates sensible heat (H) based on the Monin-Obukhov similarity theory (MOST) and determines latent heat (LE) as the residual of energy balance. We examined the uncertainties of H and LE in the SEBS model due to five key parameters at the local station point scale. Observations at 27 flux towers located in seven land cover types (needle-leaf forest, broad leaf forest, shrub, savanna, grassland, cropland, and sparsely vegetated land) and an artificial intelligence particle swarm optimization (PSO) algorithm was combined to calibrate the five parameters (leaf drag coefficient, leaf heat transfer coefficients, roughness length for soil, and two parameters for ground heat calculation) in the SEBS model. The root-mean-square error at the site scale was reduced by 9 W/sq.m for H, and 92 W/sq.m for LE, and their correlation coefficients were increased by 0.07 (H) and 0.11 (LE) after using the calibrated parameters. The updated model validation was further conducted globally for the remotely sensed evapotranspiration (ET) calculations. Overestimation of SEBS global ET was significantly improved by using the optimized values of the parameters. The results suggested PSO was able to consistently locate the global optimum of the SEBS model, and appears to be capable of solving the ET model optimization problem.

Chen, Xuelong↗

NASA NTRS1987

DYCAST: A finite element program for the crash analysis of structures

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

Pifko, A. B.↗

NASA NTRS1991

InP/Ga0.47In0.53As monolithic, two-junction, three-terminal tandem solar cells

The work presented has focussed on increasing the efficiency of InP-based solar cells through the development of a high-performance InP/Ga(0.47)In(0.53)As two-junction, three-terminal monolithic tandem cell. Such a tandem is particularly suited to space applications where a radiation-hard top cell (i.e., InP) is required. Furthermore, the InP/Ga(0.47)In(0.53)As materials system is lattice matched and offers a top cell/bottom cell bandgap differential (0.60 eV at 300 K) suitable for high tandem cell efficiencies under AMO illumination. A three-terminal configuration was chosen since it allows for independent power collection from each subcell in the monolithic stack, thus minimizing the adverse impact of radiation damage on the overall tandem efficiency. Realistic computer modeling calculations predict an efficiency boost of 7 to 11 percent from the Ga(0.47)In(0.53)As bottom cell under AMO illumination (25 C) for concentration ratios in the 1 to 1000 range. Thus, practical AMO efficiencies of 25 to 32 percent appear possible with the InP/Ga(0.47)In(0.53)As tandem cell. Prototype n/p/n InP/Ga(0.47)In(0.53)As monolithic tandem cells were fabricated and tested successfully. Using an aperture to define the illuminated areas, efficiency measurements performed on a non-optimized device under standard global illumination conditions (25 C) with no antireflection coating (ARC) give 12.2 percent for the InP top cell and 3.2 percent for the Ga(0.47)In(0.53)As bottom cell, yielding an overall tandem efficiency of 15.4 percent. With an ARC, the tandem efficiency could reach approximately 22 percent global and approximately 20 percent AMO. Additional details regarding the performance of individual InP and Ga(0.47)In(0.53)As component cells, fabrication and operation of complete tandem cells and methods for improving the tandem cell performance, are also discussed.

Wanlaas, M. W.↗

NASA NTRS1990

Optimization of aircraft configurations in a multidisciplinary environment

A decomposition and multidisciplinary optimization methodology for aircraft design is presented, based on multilevel optimization and use of global sensitivity equations to account for interdisciplinary effects. A brief study of a hypersonic cruise vehicle is developed to illustrate methodology. The vehicle is sized for minimum take-off gross weight considering aerodynamics, structures, and mission performance.

Logan, Trent R.↗

NASA NTRS1993

Global water cycle

This research is the MSFC component of a joint MSFC/Pennsylvania State University Eos Interdisciplinary Investigation on the global water cycle extension across the earth sciences. The primary long-term objective of this investigation is to determine the scope and interactions of the global water cycle with all components of the Earth system and to understand how it stimulates and regulates change on both global and regional scales. Significant accomplishments in the past year are presented and include the following: (1) water vapor variability; (2) multi-phase water analysis; (3) global modeling; and (4) optimal precipitation and stream flow analysis and hydrologic processes.

Robertson, Franklin↗

NASA NTRS1992

Multivariable frequency domain identification via 2-norm minimization

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

Bayard, David S.↗

NASA NTRS1998

Parallel Directionally Split Solver Based on Reformulation of Pipelined Thomas Algorithm

In this research an efficient parallel algorithm for 3-D directionally split problems is developed. The proposed algorithm is based on a reformulated version of the pipelined Thomas algorithm that starts the backward step computations immediately after the completion of the forward step computations for the first portion of lines This algorithm has data available for other computational tasks while processors are idle from the Thomas algorithm. The proposed 3-D directionally split solver is based on the static scheduling of processors where local and non-local, data-dependent and data-independent computations are scheduled while processors are idle. A theoretical model of parallelization efficiency is used to define optimal parameters of the algorithm, to show an asymptotic parallelization penalty and to obtain an optimal cover of a global domain with subdomains. It is shown by computational experiments and by the theoretical model that the proposed algorithm reduces the parallelization penalty about two times over the basic algorithm for the range of the number of processors (subdomains) considered and the number of grid nodes per subdomain.

Povitsky, A.↗

NASA NTRS2005

Reliability-Based Control Design for Uncertain Systems

This paper presents a robust control design methodology for systems with probabilistic parametric uncertainty. Control design is carried out by solving a reliability-based multi-objective optimization problem where the probability of violating design requirements is minimized. Simultaneously, failure domains are optimally enlarged to enable global improvements in the closed-loop performance. To enable an efficient numerical implementation, a hybrid approach for estimating reliability metrics is developed. This approach, which integrates deterministic sampling and asymptotic approximations, greatly reduces the numerical burden associated with complex probabilistic computations without compromising the accuracy of the results. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.

Crespo, Luis G.↗

NASA NTRS2016

In-Flight Pitot-Static Calibration

A GPS-based pitot-static calibration system uses global output-error optimization. High data rate measurements of static and total pressure, ambient air conditions, and GPS-based ground speed measurements are used to compute pitot-static pressure errors over a range of airspeed. System identification methods rapidly compute optimal pressure error models with defined confidence intervals.

Foster, John V.↗

NASA NTRS2021

Optimizing GRACE/GRACE-FO Data and A priori Hydrological Knowledge for Improved Global Terrestial Water Storage Component Estimates

The comprehensive information of global terrestrial water storage (TWS) components (soil moisture, groundwater, snow, surface water) is essential for effective assessment of water resource availability, climate variation, and disaster mitigation measures. Observational data provided by the Gravity Recovery And Climate Experiment (GRACE) and GRACE Follow-On satellite missions offer global TWS variation (ΔTWS) in terms of an integrated water column. However, GRACE spatial resolution is relatively coarse (i.e., 3°), and the vertically integrated value cannot be separated into ΔTWS components directly. This study demonstrates the feasibility to estimate ΔTWS components at any desired spatial-vertical resolution by effectively maintaining the native resolution of the employed hydrological knowledge. It utilizes a least-squares with constraints (LSC) approach to rigorously incorporate GRACE and GRACE-FO data and a priori hydrological knowledge, with the aim to improve global ΔTWS components’ accuracy and spatial resolution. The 3°×3° GRACE mascon derived ΔTWS data is disaggregated into the 0.5°×0.5° anomalous soil moisture storage (ΔSMS), groundwater storage (ΔGWS), snow water equivalent (ΔSWE), and surface water storage (ΔSWS) based on the covariance information obtained from the Community Atmosphere Biosphere Land Exchange (CABLE) and the PCRaster Global Water Balance (PCR-GLOBWB) models. Evaluation with different ground measurements and satellite products between 2002 and 2019 exhibits significantly improved accuracy in all individual ΔTWS components. This improvement is of particular note in ΔGWS and ΔSWS, where the LSC approach increases the globally averaged correlation values by approximately 0.13 and 0.05, respectively. Reliable prior knowledge leads to a more accurate ΔTWS component estimate, and the use of ensemble-mean knowledge yields the best result.

GRACE↗

NASA NTRS1998

Initial Results of an MDO Method Evaluation Study

The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of re- producible experiments. In the first phase of the study, three MDO methods were implemented in the SIGHT: framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, other formulations, optimality conditions, and sensitivity of solutions to various perturbations. Optimization algorithms are used to solve a particular MDO formulation. It is then appropriate to speak of local convergence rates and of global convergence properties of an optimization algorithm applied to a specific formulation. An analogous distinction exists in the field of partial differential equations. On the one hand, equations are analyzed in terms of regularity, well-posedness, and the existence and unique- ness of solutions. On the other, one considers numerous algorithms for solving differential equations. The area of MDO methods studies MDO formulations combined with optimization algorithms, although at times the distinction is blurred. It is important to

Alexandrov, Natalia M.↗

NASA NTRS2017

Automation of POST Cases via External Optimizer and "Artificial p2" Calculation

During early conceptual design of complex systems, speed and accuracy are often at odds with one another. While many characteristics of the design are fluctuating rapidly during this phase there is nonetheless a need to acquire accurate data from which to down-select designs as these decisions will have a large impact upon program life-cycle cost. Therefore enabling the conceptual designer to produce accurate data in a timely manner is tantamount to program viability. For conceptual design of launch vehicles, trajectory analysis and optimization is a large hurdle. Tools such as the industry standard Program to Optimize Simulated Trajectories (POST) have traditionally required an expert in the loop for setting up inputs, running the program, and analyzing the output. The solution space for trajectory analysis is in general non-linear and multi-modal requiring an experienced analyst to weed out sub-optimal designs in pursuit of the global optimum. While an experienced analyst presented with a vehicle similar to one which they have already worked on can likely produce optimal performance figures in a timely manner, as soon as the "experienced" or "similar" adjectives are invalid the process can become lengthy. In addition, an experienced analyst working on a similar vehicle may go into the analysis with preconceived ideas about what the vehicle's trajectory should look like which can result in sub-optimal performance being recorded. Thus, in any case but the ideal either time or accuracy can be sacrificed. In the authors' previous work a tool called multiPOST was created which captures the heuristics of a human analyst over the process of executing trajectory analysis with POST. However without the instincts of a human in the loop, this method relied upon Monte Carlo simulation to find successful trajectories. Overall the method has mixed results, and in the context of optimizing multiple vehicles it is inefficient in comparison to the method presented POST's internal optimizer functions like any other gradient-based optimizer. It has a specified variable to optimize whose value is represented as optval, a set of dependent constraints to meet with associated forms and tolerances whose value is represented as p2, and a set of independent variables known as the u-vector to modify in pursuit of optimality. Each of these quantities are calculated or manipulated at a certain phase within the trajectory. The optimizer is further constrained by the requirement that the input u-vector must result in a trajectory which proceeds through each of the prescribed events in the input file. For example, if the input u-vector causes the vehicle to crash before it can achieve the orbital parameters required for a parking orbit, then the run will fail without engaging the optimizer, and a p2 value of exactly zero is returned. This poses a problem, as this "non-connecting" region of the u-vector space is far larger than the "connecting" region which returns a non-zero value of p2 and can be worked on by the internal optimizer. Finding this connecting region and more specifically the global optimum within this region has traditionally required the use of an expert analyst.

Dees, Patrick D.↗

NASA NTRS1986

A methodology for designing robust multivariable nonlinear control systems

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Grunberg, D. B.↗

NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine and compared to earlier methods. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗