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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.

Verification of the PERSENT Software

Ongoing commercial design activities require a thorough verification of the Argonne Reactor Computation codes be performed. DIF3D is central to this system and substantial work has been done to verify its accuracy on several identified commercial needs. This manuscript details the verification work done on PERSENT which relies upon the DIF3D code for its forward and adjoint flux solution. Previous work identified the PERSENT features required to be verified to support commercial design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying PERSENT’s ability to correctly calculate four key quantities: perturbation worth distributions, kinetics parameters, sensitivity coefficients, and cross section uncertainty quantification. This manuscript provides the verification tasks and their results with respect to these quantities needed for commercial design activities. For the perturbation worth distributions, hand calculations are deployed to verify the PERSENT calculated results. Similarly, hand calculation of the PERSENT computed kinetics parameters is also used to verify the PERSENT results. In both of these, the input to PERSENT is manipulated to ensure the hand calculation exactly matches the equations PERSENT is calculating. The sensitivity coefficients involve calculating the derivatives of a parameter (such as reactivity worth), with respect to the cross section data. Direct finite difference calculations with DIF3D are used to verify the PERSENT calculated results. For the uncertainty quantification, manufactured input to PERSENT is used to allow an exact hand calculation to reproduce the PERSENT calculated results. The work detailed in this report verified that significant issues were identified for earlier versions of PERSENT for sensitivity coefficients which were corrected in this work and thus version 12.1.0 of PERSENT must be used to reproduce all of the verified work in this report.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Demonstration of Probabilistic Sensitivity Analyses Tools on the Structural Response of a Representative Inflatable Space Structure

This work provides an initial step toward demonstrating a probabilistic numerical simulation capability to support trade studies and the development of a certification plan for inflatable space habitats. This study concentrates on interpreting the results from probabilistic analysis and numerical simulation tools to identify parameter sensitivities for a novel inflatable airlock concept, specifically the Non‐Axisymmetric Inflatable Pressure Structure (NAIPS) that was designed and tested under NASA's Minimalistic Advanced Softgoods Hatch (MASH) Program. A brief overview of the finite element model is provided along with the probabilistic sensitivity analysis approach. The sensitivity studies required a model that was numerically stable and efficient enough that hundreds of simulations could be completed in the allotted time. Therefore, the existing full model was simplified by: extracting a quarter symmetry section of the dome; focusing on a single inflation pressure; and replacing the non‐linear material stress‐strain curves with linear, isotropic materials defined by elastic moduli. Responses of interest include the sensitivity of various structural component loads to material properties, cord lengths, inflation pressure and friction. Multiple sensitivity studies were completed and three are reported here. The first study focused on utilizing wide input parameter ranges to provide an opportunity to assess numerical robustness. The next two studies narrowed the parameter ranges to enable focus on understanding uncertainty at a fixed operating condition. The completion of the sensitivity studies improved understanding of the interdependence of multiple inputs on the responses. In addition, numerical stability of the simulations over wide parameter ranges, shows the feasibility of incorporating uncertainty‐based methods in the design and certification of inflatable space habitats. With the experience and trust gained, it is anticipated that these same methods will be applied to nonlinear, orthotropic models in the future.

Lyle, Karen H.

A design method for minimizing sensitivity to plant parameter variations

A method is described for minimizing the sensitivity of multivariable systems to parameter variations. The variable parameters are considered as random variables and their effect is included in a quadratic performance index. The performance index is a weighted sum of the state and control covariances that stem from both the random system disturbances and the parameter uncertainties. The numerical solution of the problem is described and application of the method to several initially sensitive tracking systems is discussed. The sensitivity factor of reduction was typically 2 or 3 over a system based on random system noise only, and yet resulted in state RMS increases of only about a factor of two.

Hadass, Z.

Comparison of Test and Finite Element Analysis for Two Full-Scale Helicopter Crash Tests

Finite element analyses have been performed for two full-scale crash tests of an MD-500 helicopter. The first crash test was conducted to evaluate the performance of a composite deployable energy absorber under combined flight loads. In the second crash test, the energy absorber was removed to establish the baseline loads. The use of an energy absorbing device reduced the impact acceleration levels by a factor of three. Accelerations and kinematic data collected from the crash tests were compared to analytical results. Details of the full-scale crash tests and development of the system-integrated finite element model are briefly described along with direct comparisons of acceleration magnitudes and durations for the first full-scale crash test. Because load levels were significantly different between tests, models developed for the purposes of predicting the overall system response with external energy absorbers were not adequate under more severe conditions seen in the second crash test. Relative error comparisons were inadequate to guide model calibration. A newly developed model calibration approach that includes uncertainty estimation, parameter sensitivity, impact shape orthogonality, and numerical optimization was used for the second full-scale crash test. The calibrated parameter set reduced 2-norm prediction error by 51% but did not improve impact shape orthogonality.

Annett, Martin S.

Neural Posterior Estimation for Scalable and Accurate Inverse Parameter Inference in Li-Ion Batteries

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter estimation via Bayesian calibration, diagnostics can account for the uncertainty due to model fitness, data noise, and the observability of any given parameter. However, Bayesian calibration in Li-ion batteries using electrochemical data is computationally intensive even when using a fast surrogate in place of physics-based models, requiring many thousands of model evaluations. A fully amortized alternative is neural posterior estimation (NPE). NPE shifts the computational burden from the parameter estimation step to data generation and model training, reducing the parameter estimation time from minutes to milliseconds, enabling real-time applications. The present work shows that NPE can infer parameters equally or more accurately than Bayesian calibration, even if it leads to higher voltage reconstruction errors. We also demonstrate that the higher computational costs for data generation are tractable even in high-dimensional cases (ranging from 6 to 27 estimated parameters). The NPE method also offers several interpretability advantages over Bayesian calibration, such as local parameter sensitivity to specific regions of the voltage curve. The NPE method is demonstrated using an experimental fast charge dataset, with parameter estimates validated against measurements of loss of lithium inventory and loss of active material. The implementation is made available in a companion repository (https://github.com/NatLabRockies/BatFIT).

25 ENERGY STORAGE

Automated Storm Tracking and the Lightning Jump Algorithm Using GOES-R Geostationary Lightning Mapper (GLM) Proxy Data

This study develops a fully automated lightning jump system encompassing objective storm tracking, Geostationary Lightning Mapper proxy data, and the lightning jump algorithm (LJA), which are important elements in the transition of the LJA concept from a research to an operational based algorithm. Storm cluster tracking is based on a product created from the combination of a radar parameter (vertically integrated liquid, VIL), and lightning information (flash rate density). Evaluations showed that the spatial scale of tracked features or storm clusters had a large impact on the lightning jump system performance, where increasing spatial scale size resulted in decreased dynamic range of the system's performance. This framework will also serve as a means to refine the LJA itself to enhance its operational applicability. Parameters within the system are isolated and the system's performance is evaluated with adjustments to parameter sensitivity. The system's performance is evaluated using the probability of detection (POD) and false alarm ratio (FAR) statistics. Of the algorithm parameters tested, sigma-level (metric of lightning jump strength) and flash rate threshold influenced the system's performance the most. Finally, verification methodologies are investigated. It is discovered that minor changes in verification methodology can dramatically impact the evaluation of the lightning jump system.

lightning jump

Association Between Vascular Density and Loss of Protective RAS During Early NPDR by Fractal Dimension

Purpose: Our hypothesis predicts that blood vessels within the retina increase in density during early-stage nonproliferative diabetic retinopathy (NPDR), based on previous results of a small retrospective study. For the current prospective study, the remodeling of arteries and veins during progression of early NPDR is assessed by a repertoire of parameters that includes the fractal dimension (D(sub f) ). In complex structures such as branching vascular trees, D(sub f) is a sensitive measure of space-filing capacity. The renin-angiotensin system (RAS) is implicated in DR pathogenesis and the function of circulating angiogenic cells (CACs), a critical bone marrow-derived population instrumental in vascular repair. Methods: Arterial and venous branching patterns were extracted from images of 6 normal controls and 3 early NPDR subjects (2 moderate, 1 mild) acquired by Heidelberg Spectralis (Registered Trademark) OCT following fluorescein angiography (FA). The vascular branching patterns were analyzed by NASAs VESsel GENeration Analysis (VESGEN) software, in which skeletonized representations were generated automatically to yield D(sub f) by the box-counting method. For binary 2D images, D(sub f) varies between limiting Euclidean dimensions of 1 and 2. Peripheral blood of diabetics and controls was collected for CD34+ CAC isolation. The gene expression of RAS in CACs was assessed by qPCR for Mas receptor to Ang-(1-7). The vasoreparative function of the CACs was measured by migration ability toward CXCL12 (SDF-1). Results: By D(sub f), venous and arterial densities were 1.370 +/- 0.006 and 1.329 +/- 0.016 for early NPDR, compared to 1.318 +/- 0.012 and 1.320 +/- 0.036 for control. The space filling capacity in early NPDR measured by D(sub f), a sensitive parameter, therefore demonstrated a pronounced increase for veins, but not for arteries. Mas receptor mRNA in CACs was increased in diabetics without DR but reduced with onset of NPDR, indicating possible loss of compensation of protective RAS during early DR. Migratory dysfunction of CD34+ cells was further associated with DR. Conclusions: As assessed by the fractal dimension in our preliminary study, the space-filling capacity of veins, but not arteries, was greater in early NPDR than in control. Larger patient populations will be examined as we complete our ongoing longitudinal study. Results further suggest the protective RAS axis within diabetic CACs is lost early in DR and is associated with increased vascular remodeling as evidenced by VESGEN analysis.

vascular

Additive Manufacturing Process Development DOE for NASA HR-1 using Laser Blown Powder Directed Energy Deposition

NASA HR-1 is a Fe-Ni-Cr alloy that is used for high pressure hydrogen applications such as rocket engines, energy, and oil and gas. This investigation was focused on conducting a design of experiment program aimed at mapping the parameter process window for NASA HR-1 using the laser blown powder directed energy deposition (LP-DED) process. A two phased design of experiments (DOE), the first phase of the experiment was focused on optimizing single bead tracks while the second phase of the experiment was focused on optimizing bead overlap hatching in a multi pass bead build up. During the first phase of the deposition parameters, namely laser power, travel speed, and powder feed rate were varied. A down selection from the single bead parameter set was made and hatching experiments were conducted that focused on the overlap distance. In this paper the approach for conducting the DOE and results are discussed. The results focused on measurement of bead geometry, the as-built microstructural evolution, and porosity within the samples. The team at MSFC saw a variety of results across the process map created during the first phase of experimentation and were able to down select a parameter that created an optimal bead shape with a minimal amount of build porosity. It was determined that laser power and robot travel speed were the most sensitive parameters. The results from this investigation will inform future laser powder directed energy deposition parameter developments.

Parker Shake

Efficient Updating of Model Parameters Using Modal Coordinates

Model correlation methods based on iterative modification of physical model parameters have been used with frequent success. The cost and time to perform these methods is driven mostly by the need to recompute normal modes and parameter sensitivities from the full finite element model after each adjustment.

modal

The effects of stimulated star formation on the evolution of the galaxy. III - The chemical evolution of nonlinear systems

The evolution of models for star formation in galaxies with disk and halo components is discussed. Two phases for the halo (gas and stars) and three for the disk (including clouds) are used in these calculations. The star-formation history is followed using nonlinear phase-coupling models which completely determine the populations of the phases as a function of time. It is shown that for a wide range of parameters, including the effects of both spontaneous and stimulated star formation and mass exchange between the spatial components of the system, the observed chemical history of the galaxy can easily be obtained. The most sensitive parameter in the detailed metallicity and star-formation history for the system is the rate of return of gas to the diffuse phase upon stellar death.

Shore, Steven N.

Development and Calibration of a System-Integrated Rotorcraft Finite Element Model for Impact Scenarios

Two full-scale crash tests of an MD-500 helicopter were conducted in 2009 and 2010 at NASA Langley's Landing and Impact Research Facility in support of NASA s Subsonic Rotary Wing Crashworthiness Project. The first crash test was conducted to evaluate the performance of an externally mounted composite deployable energy absorber (DEA) under combined impact conditions. In the second crash test, the energy absorber was removed to establish baseline loads that are regarded as severe but survivable. The presence of this energy absorbing device reduced the peak impact acceleration levels by a factor of three. Accelerations and kinematic data collected from the crash tests were compared to a system-integrated finite element model of the test article developed in parallel with the test program. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests were conducted to evaluate the impact performances of various components and subsystems, including new crush tubes and the DEA blocks. Parameters defined for the system-integrated finite element model were determined from these tests. Results from 19 accelerometers placed throughout the airframe were compared to finite element model responses. The model developed for the purposes of predicting acceleration responses from the first crash test was inadequate when evaluating more severe conditions seen in the second crash test. A newly developed model calibration approach that includes uncertainty estimation, parameter sensitivity, impact shape orthogonality, and numerical optimization was used to calibrate model results for the full-scale crash test without the DEA. This combination of heuristic and quantitative methods identified modeling deficiencies, evaluated parameter importance, and proposed required model changes. The multidimensional calibration techniques presented here are particularly effective in identifying model adequacy. Acceleration results for the calibrated model were compared to test results and the original model results. There was a noticeable improvement in the pilot and copilot region, a slight improvement in the occupant model response, and an over-stiffening effect in the passenger region. One lesson learned was that this approach should be adopted early on, in combination with the building-block approaches that are customarily used, for model development and pretest predictions. Complete crash simulations with validated finite element models can be used to satisfy crash certification requirements, potentially reducing overall development costs.

Annett, Martin S.

Calibration of Airframe and Occupant Models for Two Full-Scale Rotorcraft Crash Tests

Two full-scale crash tests of an MD-500 helicopter were conducted in 2009 and 2010 at NASA Langley's Landing and Impact Research Facility in support of NASA s Subsonic Rotary Wing Crashworthiness Project. The first crash test was conducted to evaluate the performance of an externally mounted composite deployable energy absorber under combined impact conditions. In the second crash test, the energy absorber was removed to establish baseline loads that are regarded as severe but survivable. Accelerations and kinematic data collected from the crash tests were compared to a system integrated finite element model of the test article. Results from 19 accelerometers placed throughout the airframe were compared to finite element model responses. The model developed for the purposes of predicting acceleration responses from the first crash test was inadequate when evaluating more severe conditions seen in the second crash test. A newly developed model calibration approach that includes uncertainty estimation, parameter sensitivity, impact shape orthogonality, and numerical optimization was used to calibrate model results for the second full-scale crash test. This combination of heuristic and quantitative methods was used to identify modeling deficiencies, evaluate parameter importance, and propose required model changes. It is shown that the multi-dimensional calibration techniques presented here are particularly effective in identifying model adequacy. Acceleration results for the calibrated model were compared to test results and the original model results. There was a noticeable improvement in the pilot and co-pilot region, a slight improvement in the occupant model response, and an over-stiffening effect in the passenger region. This approach should be adopted early on, in combination with the building-block approaches that are customarily used, for model development and test planning guidance. Complete crash simulations with validated finite element models can be used to satisfy crash certification requirements, thereby reducing overall development costs.

Annett, Martin S.

Crack opening calculation in phase-field modeling of fluid-filled fracture: A robust and efficient strain-based method

The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry poses a significant challenge in calculating the crack opening (aperture) of phase-field fracture, which governs the fracture permeability and hence the overall hydromechanical behavior. Although several approaches have been devised to compute the crack opening of phase-field fracture, they require a sophisticated algorithm for post-processing the phase-field values or an additional parameter sensitive to the element size and alignment. Here, we develop a novel method for calculating the crack opening of fluid-filled phase-field fracture, which enables one to obtain the crack opening without additional algorithms or parameters. Here we transform the displacement-jump-based kinematics of a fracture into a continuous strain-based version, insert it into a force balance equation on the fracture, and apply the phase-field approximation. Through this procedure, we obtain a simple equation for the crack opening which can be calculated with quantities at individual material points. We verify the proposed method with analytical and numerical solutions obtained based on discrete representations of fractures, demonstrating its capability to calculate the crack opening regardless of the element size or alignment.

58 GEOSCIENCES

Evaluation and Improvement of Liquid Propellant Rocket Chugging Analysis Techniques. Part 1: A One-Dimensional Analysis of Low Frequency Combustion Instability in the Fuel Preburner of the Space Shuttle Main Engine

Low frequency combustion instability, known as chugging, is consistently experienced during shutdown in the fuel and oxidizer preburners of the Space Shuttle Main Engines. Such problems always occur during the helium purge of the residual oxidizer from the preburner manifolds during the shutdown sequence. Possible causes and triggering mechanisms are analyzed and details in modeling the fuel preburner chug are presented. A linearized chugging model, based on the foundation of previous models, capable of predicting the chug occurrence is discussed and the predicted results are presented and compared to experimental work performed by NASA. Sensitivity parameters such as chamber pressure, fuel and oxidizer temperatures, and the effective bulk modulus of the liquid oxidizer are considered in analyzing the fuel preburner chug. The computer program CHUGTEST is utilized to generate the stability boundary for each sensitivity study and the region for stable operation is identified.

Lim, Kair Chuan

A Method Based on Radiative Cooling for Detecting Structural Changes in Undercooled Metallic Liquids

We introduce a structure-sensitive parameter for undercooled melts which can be measured in containerless processing experiments. We have established that the ratio, R(T), of hemispherical total emissivity epsilon(sub T)(T) to constant-pressure specific heat c(sub p)(T) can serve as an indicator which is sensitive to any changes in short range atomic order in undercooled metallic melts. R(T) (triple bonds) epsilon(sub T)(T)/c(sub p)(T) values for nickel, zirconium, and silicon have been obtained using the high temperature electrostatic levitator while the levitated melts were undergoing purely radiative cooling into the deeply undercooled region. R(T) plots for undercooled liquid nickel and zirconium indicate no significant change in short-range structure from their melting temperatures to 15% undercooling. In contrast, liquid silicon shows marked short-range structural changes beginning above its melting temperature and extending throughout the undercooled region. The short-range structure of liquid silicon is related to the highly-directional covalent bonding which characterizes its solid form. The nickel and zirconium data show that epsilon(sub T) varies linearly with T, in support of metal emissivity theories.

Rulison, Aaron J.

Methodology Report of Cost Benefit Analysis of Space Based Solar Power

Space-based solar power (SBSP) is the concept of gathering power in space and transmitting it wirelessly to users on Earth or elsewhere in space. SBSP has seen renewed interest from governments, businesses, and universities for reasons including persistent operations in space, achieving carbon neutrality targets, and more. Several major government agencies in Europe, Asia, and the Americas have renewed their SBSP investigations, and hundreds of millions of dollars have been donated to universities to advance the technical state of the art. Given the renewed interest, this study will identify and update some key system parameters to current performance levels. This paper presents the methodology and approach to identify the fiscal and environmental costs and benefits of SBSP when compared to other sustainable and grid-scale energy sources. From these divergent angles the models evaluate fiscal and environmental impacts, identify the state of the most sensitive parameters of the designs, and seek to provide context to leadership on the relative value of pursuing SBSP related technologies.

Space-based solar power