Results for “Methods” — Page 57

NASA NTRSDate not supplied

The Two-Cavity Method for Characterizing Acoustical Materials—an Interlaboratory Study

This study focuses on understanding the sound absorption characteristics of porous acoustic materials, which are determined by two key parameters independent of material thickness: characteristic impedance and propagation constant. These parameters can be characterized by testing a porous sample concept in a normal incidence impedance tube using either the two-thickness or the two-cavity method. In the two-thickness method, two samples of varying thicknesses are required. In contrast, the two-cavity method requires testing one sample at two different air cavity depths behind the porous material. This method is particularly advantageous for materials that are costly or challenging to fabricate. This interlaboratory study evaluates the variability of characteristic properties determined using the two-cavity method. Porous acoustic materials were additively manufactured and tested in the Liner Technology Facility(LTF)at NASA Langley Research Center and the Mechanics, Acoustics and Dynamics Lab (MADLab) at Michigan Technological University. The characteristic properties derived from various cavity depth combinations were used to predict the surface impedance of the sample with a rigid backing. The prediction was then compared the measured impedance spectrum. It was also found that the combinations of cavity depths can significantly influence the accuracy of the deduced properties.

acoustic liners↗

NASA NTRSDate not supplied

A Wall-Distance Method for Turbulence Modeling

The distance from a grid point to the closest wall surface, wall distance, is a funda- mental quantity in turbulence modeling. Efficiency of wall-distance calculations has become more critical as the size of computational grids has significantly increased in recent years. This paper reports on an initial implementation of a new search-based wall-distance method that is suitable for general unstructured computational fluid dynamics (CFD) grids and tailored for requirements specific for turbulence modeling. The method represents a two-step approach to calculate the wall distance. In the first step, the wall distance is approximated for each grid point as the minimum distance from this point to a vertex of a triangular face at the wall. The point-to-vertex distance calculation is relatively inexpensive but may lead to a significant error in the wall-distance ap- proximation, especially for grid points near the wall. In the second step, for grid points located within a predefined distance ( threshold ) from the wall, the wall distance is computed as the minimum distance to wall faces. As a result, the wall distance is exact for all grid points within the threshold. This two-step approach reduces the computational cost yet achieves high and controllable accuracy in the evaluation of the wall distance. Algorithmic enhancements are presented to improve efficiency of wall-distance computations. Comprehensive assessment of the new method is reported for large-scale unstructured CFD grids generated for the Fifth AIAA CFD High-Lift Prediction Workshop. The performance of the new wall-distance method compares favorably with performance of two established methods implemented in high-performance CFD codes.

Wall Distance↗

NASA NTRSDate not supplied

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗

NASA NTRSDate not supplied

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗

NASA NTRSDate not supplied

Copula-based Method to Generate Consistent Surface Pressures Under Uncertainty

This paper establishes a method to create surface pressure databases that allow for uncertainty quantification. Aerodynamic databases are critical products for launch vehicles and other aeronautical systems, and surface pressure databases are one such database that constains large quantities of data. The focus of this work is the relationship between the integrated force and moment data base and the surface pressure database. In particular, the work attempts to provide a method that maintains consistency between these two databases when accounting for uncertainty. The integrated force and moment database and surface pressure databases are constructed from CFD data which is high-density but low-trust. However, the force and moment database will often also include data from high-trust but low-density sources such as from wind tunnel experiments. This means that the quantified uncertainty of the force and moment database is higher quality as it includes this high fidelity wind tunnel data. This motivates the idea to use the force and moment database uncertainty when constructing the surface pressure database uncertainty. The method utilizes the statistical idea of a copula in order to generate surface pressures that match with uncertain integrated force and moment distributions as well as being consistent with known CFD data. This statistical consistency is quantified by using the Maximum Mean Discrepancy two-sample test. The predictive error of the method is also approximated using leave-one-out error estimation and the good overall performance of the method is presented using probability boxes in a simulated uncertainty scenario.

SLS↗

NASA NTRS2026

The Future of in-Situ Sequencing-Based Microbial Monitoring: Development of a Shelf-Stable Method for Artemis and Beyond

Microbial monitoring onboard the International Space Station (ISS) is essential for assessing the efficiency of the Environmental Control and Life Support Systems (ECLSS) and providing insight into potential risk to both crew and spacecraft. Historically, this monitoring required the need to culture organisms onboard, return these cultures to Earth, and then complete the identifications, a process that would take months. Over the past decade, and through numerous payloads, advances in molecular biology have enabled in-flight microbial identifications using nanopore sequencing. The swab-to-sequencer method resulting from these efforts was transitioned from research to operations for microbial monitoring under the Crew Health Care Systems (CHeCS) BioMole. Collectively, these accomplishments have propelled the swab-to-sequencer method to be selected as the Microbial Surface Monitor (MSM) for Gateway, as well as a payload on Artemis IV. However, the lack of cold stowage availability for Artemis requires modifications to the entire method due to the thermal instability of the reagents required for sample preparation. To achieve this, new development, optimization, and validations were undertaken. Key considerations included enzyme concentration, buffer compatibility, and equal or enhanced sensitivity and specificity. At each step, thorough side-by-side comparisons with the current ISS method were performed. The development of a robust shelf-stable method will ensure continued sequencing-based microbial monitoring for Artemis and beyond, providing data in near real-time, enhancing risk response time, and yielding clear insight into the microbiome of spacecraft.

Christian G Mena↗

NASA NTRS1964

Applications of the method of Monte Carlo to problems in thermal radiation

A summary of the work involving the Monte Carlo method in the solution of problems in thermal radiation transfer is presented, which indicates general methods previously used for solving problems in which radiation is coupled with other modes of energy transfer. Previous work involving radiation in absorbing-emitting media is included. An example is outlined to indicate the use of the Monte Carlo method in the design of a space radiator. Suggestions are given for solution of a complex case incorporating the effects of coupled conduction, convection and radiation, wavelength dependent and selective surfaces, nonisothermal conditions, and strongly directional or nondiffuse emitting and reflecting surfaces. A discussion is given of the factors that may affect convergence, running time, and accuracy of the Monte Carlo solutions and of the advantages and disadvantages of this approach for practical problems. Also discussed are the case of programming for complex problems and the probable machine time requirements of the method.

THERMAL RADIATION↗

NASA NTRS2004

A space radiation transport method development

Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from the preliminary design concepts to the final design. In particular, we will discuss the progress towards a full three-dimensional and computationally efficient deterministic code for which the current HZETRN evaluates the lowest-order asymptotic term. HZETRN is the first deterministic solution to the Boltzmann equation allowing field mapping within the International Space Station (ISS) in tens of minutes using standard finite element method (FEM) geometry common to engineering design practice enabling development of integrated multidisciplinary design optimization methods. A single ray trace in ISS FEM geometry requires 14 ms and severely limits application of Monte Carlo methods to such engineering models. A potential means of improving the Monte Carlo efficiency in coupling to spacecraft geometry is given in terms of re-configurable computing and could be utilized in the final design as verification of the deterministic method optimized design. Published by Elsevier Ltd on behalf of COSPAR.

NASA Center JSC↗

NASA NTRS2016

Similar Estimates of Temperature Impacts on Global Wheat Yield by Three Independent Methods

The potential impact of global temperature change on global crop yield has recently been assessed with different methods. Here we show that grid-based and point-based simulations and statistical regressions (from historic records), without deliberate adaptation or CO2 fertilization effects, produce similar estimates of temperature impact on wheat yields at global and national scales. With a 1 C global temperature increase, global wheat yield is projected to decline between 4.1% and 6.4%. Projected relative temperature impacts from different methods were similar for major wheat-producing countries China, India, USA and France, but less so for Russia. Point-based and grid-based simulations, and to some extent the statistical regressions, were consistent in projecting that warmer regions are likely to suffer more yield loss with increasing temperature than cooler regions. By forming a multi-method ensemble, it was possible to quantify 'method uncertainty' in addition to model uncertainty. This significantly improves confidence in estimates of climate impacts on global food security.

Climate impacts↗

NASA NTRS2017

On High-Order Upwind Methods for Advection

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom 𝐾 per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2𝐾−1, which is higher than the expected order of 𝐾.

high-order methods↗

NASA NTRSDate not supplied

Explicit Discontinuous Galerkin Methods for Conservation Laws

The two explicit DG methods in this study are based on a ‘predictor-corrector’ formulation, the first introduced by Lörcher, Gassner, and Munz (2007, 2008) called space–time expansion discontinuous Galerkin or STE-DG scheme, and the second, introduced independently by the author (Huynh 2006, 2013) called the upwind moment scheme. The predictor step of the two methods is essentially identical using a Cauchy-Kovalevsky (CK) procedure, which involves no interaction of the data among neighboring cells. The corrector step also shares the same space-time integration formulation and is where interaction of the data among neighboring cells takes place; the difference, however, is in how the resulting space-time volume integral is estimated. As a consequence of the different estimates, for the case of advection in one spatial dimension (1D), the moment scheme has a CFL (Courant-Friedrichs-Lewy) condition of 1 for all p and is accurate to order 2p+1, i.e., it possesses the super accuracy property, whereas the STE-DG method has a more restrictive CFL condition and is accurate to the expected order of p+1. For 1D advection, compared with the CFL conditions of 1/(2p+1) of standard RK-DG (Runge-Kutta) scheme where space and time discretization are of the same order, the moment scheme allows a significantly larger time step size. It also turns out that the scheme yields a result identical to Van Leer’s scheme III (1977), which amounts to shifting the data a distance of advection corresponding to the time step and projecting the result onto the space of polynomial solutions. Contrary to Van Leer’s approach, however, the space-time ‘predictor-corrector’ formulation facilitates extensions to the case of systems of equations. Concerning 2D extensions, in the case of advection, when the flow is along the diagonal direction, the CFL conditions for the moment schemes become restrictive as will be shown by Fourier (Von Neumann) stability and accuracy analyses. Since the moment scheme employs the right Radau points as collocation points in time, the method is closely related to the implicit Radau IIA scheme, which is stable for any time step size. The role of Radau IIA in relieving stability restriction for these explicit DG schemes remains to be explored

Discontinuous Galerkin↗

NASA NTRSDate not supplied

Applying Formal Methods to Safety-Critical Systems

How do you know a proof is correct? Traditionally, mathematical proofs are socially verified – at least one human, following a set of implicit rules of natural language and logic, determines if the proof is believable. If the proof becomes overly tedious and/or is essential to some safety- or mission-critical application, it becomes necessary to determine the soundness to a higher standard. 'Formal methods' refer to mathematically rigorous techniques and tools that enable specification, design, and verification of hardware and software systems. The specification used in formal methods are statements in a mathematical logic while the formal verifications are deductions in that logic. Formal methods can be difficult or time/resource intensive, but offer a higher level of assurance than standard verification through testing or handwritten proofs. This talk will introduce formal methods, motivated by applications of interest to NASA, including uncrewed aircraft operations in the national airspace, urban air environments, and wildfire areas. The audience will be given a crash course in mechanically verified proofs in the Prototype Verification System (PVS), an interactive theorem prover.

Formal Methods↗

NASA NTRSDate not supplied

Acoustic Emission Methods for the Health Evaluation of Integrated Pressure Components

At the request of the Pressure Systems Senior Discipline Expert, to overcome the access and detectable flaw size limitations of other nondestructive evaluation (NDE) methods for integrated components, a technique akin to seismology was advanced to perceive the earliest signs of cracking in titanium components before they escalate into serious issues. In this project we achieved a landmark in Acoustic Emission (AE) testing with the first NASA Probability of Detection (POD) study. This is an important first step to the certification of the AE method for flight components and was based on the testing of notched panels. By working closely with industry allies and employing approved methods from the boiler and pressure vessel sector, we not only met but surpassed all POD benchmarks with our test and acceptance criteria. In experiments involving solution heat-treated and aged 6Al-4V-Ti alloy tested with broadband sensors, we recorded a 96% success rate, with zero false positives reported. Our research shows that in some cases, AE testing can locate smaller cracks than other NDE methods. An industry tool for scaling results to full pressure vessels is highlighted. However, before applying our findings to NASA components, tests to validate the transfer functions are advised.

acoustic↗

NASA NTRSDate not supplied

Multicriterion Design Methods for Aerospace Systems

An efficient method is presented for multi-criterion preliminary design and demonstrated for a tetrahedral truss platform. The present method requires minimal analysis effort and permits rapid estimation of optimized truss behavior for preliminary design. A 14-m-diameter, 3-ring truss platform represents a candidate reflector support structure for space-based science spacecraft. The truss members are divided into 9 groups by truss ring and position. Design variables are the cross-sectional area of all members in a group, and are either 1, 3 or 5 times the minimum member area. Non-structural mass represents the node and joint hardware used to assemble the truss structure. Taguchi methods are used to efficiently identify key points in the set of Pareto-optimal truss designs. Key points identified using Taguchi methods are the maximum frequency, minimum mass, and maximum frequency-to-mass ratio truss designs. Low-order polynomial curve fits through these points are used to approximate the behavior of the full set of Pareto-optimal designs. The resulting Pareto-optimal design curve is used to predict frequency and mass for optimized trusses. Performance improvements are plotted in frequency-mass (criterion) space and compared to results for uniform trusses. Application of constraints to frequency and mass and sensitivity to constraint variation are demonstrated.

taguchi methods↗

NASA NTRS2024

A Method of Compliance for Achieving Target Collision Risk in UTM Operations

This work proposes a method of compliance to ensure that the collision risks among small unmanned aircraft systems meet the target level of safety. This method presents what is needed for a strategic conflict detection service to achieve the target level of safety when conflict between operational intents are not permitted in nominal situations. A volume-based collision risk model is first developed to calculate the UA-to-UA collision risk given any two operational intent volumes. With this collision risk model, a test strategy is then proposed to assess if a strategic conflict detection service can reduce the collision risk and meet the target level of safety. The method also specifies operational data that are required to be collected to verify if requirements on conformance are being met. Additionally, two new requirements are identified and proposed by this method beyond the current standard for strategic conflict detection. In the sensitivity analysis, three main factors contributing to the collision risk are investigated. The analysis shows that buffers should be considered in a strategic conflict detection service when deconflicting operational intents. The results also reveal that the selection of test cases plays an important role in evaluating the strategic conflict detection service, and they should be representative and sufficiently complex in evaluation tests.

Collision Risk↗

NASA NTRSDate not supplied

A Method of Compliance for Achieving Target Collision Risk in UTM Operations

This work proposes a method of compliance to ensure that the collision risks among small unmanned aircraft systems meet the target level of safety. This method presents what is needed for a strategic conflict detection service to achieve the target level of safety when conflict between operational intents are not permitted in nominal situations. A volume-based collision risk model is first developed to calculate the UA-to-UA collision risk given any two operational intent volumes. With this collision risk model, a test strategy is then proposed to assess if a strategic conflict detection service can reduce the collision risk and meet the target level of safety. The method also specifies operational data that are required to be collected to verify if requirements on conformance are being met. Additionally, two new requirements are identified and proposed by this method beyond the current standard for strategic conflict detection. In the sensitivity analysis, three main factors contributing to the collision risk are investigated. The analysis shows that buffers should be considered in a strategic conflict detection service when deconflicting operational intents. The results also reveal that the selection of test cases plays an important role in evaluating the strategic conflict detection service, and they should be representative and sufficiently complex in evaluation tests.

UTM, Method of Compliance, collision risk↗

NASA NTRSDate not supplied

A Method of Compliance for Achieving Target Collision Risk in UTM Operations

This work proposes a method of compliance to ensure that the collision risks among small unmanned aircraft systems meet the target level of safety. This method presents what is needed for a strategic conflict detection service to achieve the target level of safety when conflict between operational intents are not permitted in nominal situations. A volume-based collision risk model is first developed to calculate the UA-to-UA collision risk given any two operational intent volumes. With this collision risk model, a test strategy is then proposed to assess if a strategic conflict detection service can reduce the collision risk and meet the target level of safety. The method also specifies operational data that are required to be collected to verify if requirements on conformance are being met. Additionally, two new requirements are identified and proposed by this method beyond the current standard for strategic conflict detection. In the sensitivity analysis, three main factors contributing to the collision risk are investigated. The analysis shows that buffers should be considered in a strategic conflict detection service when deconflicting operational intents. The results also reveal that the selection of test cases plays an important role in evaluating the strategic conflict detection service, and they should be representative and sufficiently complex in evaluation tests.

UTM↗

NASA NTRS2024

Survey of Methods for Assessing Safety Compliance of sUAS BVLOS Operations

To ensure the safety of small Unmanned Aircraft System (sUAS) Beyond Line of Sight (BVLOS) operations in the National Airspace System (NAS), the FAA offers a guideline on how sUAS operators can demonstrate compliance with FAA rules, including regulations, advisory circulars, policy statements, and acceptable means of compliance (AMOC), using a formal and top-down approach. According to FAA Advisory Circular 23.2010-1, the AMOC refers to “one method, but not the only method, to show compliance with a regulatory requirement.” It is common for regulations to include a performance and safety standard rather than a detailed design or operation requirement, which allows for flexibility in fulfilling the regulatory requirements while still achieving a predetermined level of safety. This technical report explores existing frameworks for sUAS BVLOS safety analysis. It begins by discussing how sUAS BVLOS operations can be strategically deconflicted and then discusses their hazards. The next step is to establish safety assessment methods commonly used by the aviation industry and the FAA, illustrate how these methods can be applied to several safety-critical air traffic systems, and list collision models that the FAA and industry use. This investigation documents the processes for assessing safety risks in sUAS BVLOS operations and will allow sUAS BVLOS operations to be assessed for safety compliance more efficiently.

sUAS BVLOS Operations↗