Theory of time-varying spectral analysis and complex Wishart matrix processes
Distributional results pertaining to complex Wishart processes and time varying spectral estimators on null hypothesis of stationary Gaussian time series
Dubman, M. R.↗
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Results for “wishart”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Wishart variate generators
Subroutine WSHRT for generating matrix of variances and covariances of Wishart distribution
Smith, W. B.↗
Characterizations of linear sufficient statistics
A surjective bounded linear operator T from a Banach space X to a Banach space Y must be a sufficient statistic for a dominated family of probability measures defined on the Borel sets of X. These results were applied, so that they characterize linear sufficient statistics for families of the exponential type, including as special cases the Wishart and multivariate normal distributions. The latter result was used to establish precisely which procedures for sampling from a normal population had the property that the sample mean was a sufficient statistic.
Peters, B. C., Jr.↗
Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics
In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes.
Elrod, Chris↗
Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis
There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.
Uncertainty quantification↗
What’s Next in Regional (Air) Mobility? Finding the next possible big ideas in selected problems
This presentation summarizes studies ongoing under the "What's Next in Regional (Air) Mobility" umbrella within the Intercenter Systems Analysis Team. It includes a look at the Regional Air Mobility (RAM) market potential, simulation of a RAM passenger network to gather statistics, and scrutinizes airport energy needs to support RAM operations. It also references a companion presentation provided by the DOT Volpe Center presented by Jacob Wishart related to RAM market and demand estimates.
Advanced Air Mobility↗
Supersonic jet control via point disturbances inside the nozzle
Experiments on supersonic jet control via point disturbances inside the nozzle were conducted using a pressure-matched converging-diverging nozzle with an exit diameter of 3.11 cm and an exit Mach number of 2.1. The disturbance generators are situated on the supersonic nozzle wall between the throat and the jet exit plane; the resulting fluid-mechanical disturbances are observed at the intersection of the disturbance cone and the jet lip. It is demonstrated that a single disturbance generator leads to a polygonal jet appearance, while two symmetric disturbances lead to a symmetric rectangular jet shape and two nonsymmetric disturbances lead to a star-like appearance. Significant cusps are formed in all cases.
Wishart, D. P.↗
Aeronautics and Air Transportation System Related Life Cycle Costs
Explore the source record for details and available documents.
Jacob Wishart↗
Multi-Vehicle (m:N) Operations in the NAS - NASA's Research Plans
The Advanced Air Mobility movement is occurring across the world with goals of enabling, affordable, efficient, accessible, and safe air transportation at a much larger scale than today’s operations, largely enabled by electrification and automation. Transformative and disruptive innovations are emerging that will support an ecosystem designed to transport goods and people to locations not traditionally served by air transportation. To realize the full vision of AAM, technology will be needed to allow a few operators to operate many vehicles (m:N). The benefits of m:N operations are described, along with the current state-of-the-art, barriers, need, and NASA’s plans to address some of the barriers, including a Multi-Vehicle (m:N) Working Group with goals of producing a community-developed operational approval roadmap for various domains.
multi-vehicle↗
Update on Subsonic Single Aft Engine (SUSAN) Electrofan Trade Space Exploration
NASA is conducting an ongoing trade study analysis of the SUSAN Electrofan aircraft concept, which utilizes 20-MW-class electrified aircraft propulsion to enable propulsive, aerodynamic, and control benefits while retaining the range, speed, and size of typical narrow-body regional aircraft. The study is constrained by the ground rules of operating within the current airport and airspace infrastructure. This ongoing study seeks to find a configuration and combination of technologies that yield significant fuel burn and emissions benefits. Another key goal is to reduce cost per passenger mile. Currently, the study is focused on a configuration that utilizes jet A or sustainable aviation fuels, however, we plan to consider other fuel alternatives in the future. This paper describes the progress in defining the architecture of the aircraft, engine, power system, control system, and initial understandings of the sensitivity of the potential configurations to technology assumptions based on key performance parameters. Additionally, progress towards definition and refinement of driving operational, economic, infrastructure, certification, and technical requirements is discussed.
aircraft concept↗
Update on Subsonic Single Aft Engine (SUSAN) Electrofan Trade Space Exploration
NASA is conducting an ongoing trade study analysis of the SUSAN Electrofan aircraft concept, which utilizes 20-MW-class electrified aircraft propulsion to enable propulsive, aerodynamic, and control benefits while retaining the range, speed, and size of typical narrow-body regional aircraft. The study is constrained by the ground rules of operating within the current airport and airspace infrastructure. This ongoing study seeks to find a configuration and combination of technologies that yield significant fuel burn and emissions benefits. Another key goal is to reduce cost per passenger mile. Currently, the study is focused on a configuration that utilizes jet A or sustainable aviation fuels, however, we plan to consider other fuel alternatives in the future. This presentation describes the progress in defining the architecture of the aircraft, engine, power system, control system, and initial understandings of the sensitivity of the potential configurations to technology assumptions based on key performance parameters. Additionally, progress towards definition and refinement of driving operational, economic, infrastructure, certification, and technical requirements is discussed.
Ralph H. Jansen↗
Regional Air Mobility Market Demand Study
Research objective to identify and measure potential demand for regional air mobility (RAM), in addition to providing emission profiles of competing transportation modes.
Jacob Wishart↗
SUSAN Single Aisle Market Analysis
SUSAN uses a 20MW class Electrified Aircraft Propulsion system to enable advanced Propulsion Airframe Integration (PAI) in transport category aircraft. Alternative fuels will be used to reduce the amount of emissions per energy used. By combining these features there is the potential to reduce aircraft emissions by 50% per passenger/mile while retaining the size, speed, and range of large regional jets. Problem: Aircraft emissions need to be reduced by at least a factor of two, with a goal of zero emissions. Constraint: Must use existing airport infrastructure, be flight certifiable, and be more cost effective Solution To Be Developed: Hybrid Electric Large Aircraft Specific Concept To Be Developed: SUSAN Electrofan
Jacob Wishart↗
Market Analysis of the Subsonic Single Aft Engine (SUSAN) Transport Aircraft Concept
This paper presents a detailed market analysis of the U.S. domestic aviation market in support of the NASA subsonic single aft engine (SUSAN) regional aircraft concept. The current scoping of the SUSAN concept is intended to compete in the medium to large (160-180 seats) narrow body market, with range capabilities of up to 2,500 nautical miles, and expected fuel burn reduction up to 40% relative to conventional 2 engine aircraft. Recent historical trends suggest growth in aviation passenger demand will continue to be met by the narrow body fleet of aircraft; however, a comprehensive review is required to understand how these current fleet trends could evolve in the future. Moreover, estimating and forecasting the potential market size is the critical first step when developing a new aircraft concept to determine commercial viability. To assist in the trade space exploration of the SUSAN concept, a generalized traffic and fleet forecast of the U.S. aviation market is conducted. Using publicly available aviation data from the U.S. Bureau of Transportation Statistics and passenger demand forecasts from FAA, a multinomial logit model is estimated to predict the composition of the future fleet by aircraft size. These fleet forecasts are then used as inputs for a fleet evolution model to provide required operational forecasts at the aircraft specific level. Forecast scenarios with and without the SUSAN concept are compared, and a breakeven analysis is performed to evaluate the commercial viability of the SUSAN aircraft from an operating cost perspective. Results from the multinomial logit fleet forecast indicate the narrow body size category of 150+ seats dominating the market, comprising 87% of the future revenue passenger miles market share in 2050 (up from 60% in 2019). Forecast scenarios with the SUSAN concept see a maximum cumulative decline in fuel cost of 20% by 2050, while a breakeven analysis shows competitive advantage of the SUSAN aircraft, due to expected fuel burn reduction, at moderate levels of increased maintenance and capital costs.
Jacob M. Wishart↗
Subsonic Single Aft Engine Narrowbody (SUSAN) Freighter Concept and Market Analysis
The dedicated air cargo and freight market has the potential to be a critical early pathway for emerging technologies in low to zero emission propulsion. This study analyzes the cargo aviation market to understand current market trends and future market viability of a mid-sized all-electric or hybrid-electric concept aircraft. While cargo aviation’s overall emissions footprint is small relative to commercial passenger aviation, it remains an important and challenging transportation sector to decarbonize. Past research has focused on small, less than 19-seat electrified aircraft propulsion concepts that could serve both passenger and air cargo markets This study extends the electrified market space into larger aircraft classes, considering if a purpose-built large hybrid electric turboprop freighter can compete in the market currently served primarily by conversion narrowbody freighters. Specifically, this paper focuses on the mid-sized cargo market with payload ranges of 40,000-50,000lbs, and an all-electric range potential up to 750 miles. The concept aircraft is based on a 4-engine turboprop configuration, with mounted wing battery packs and an aft cargo door to allow for standardized palletization. The market analysis indicates broad market coverage with 73% of the existing mid-sized cargo network within the range of 750 miles. A breakeven analysis of operating and capital costs shows potential for market competition, however, additional energy and acquisition cost savings from the concept aircraft are needed. Evidence from the breakeven analysis also points to higher rates of aircraft utilization being a critical path to lowering costs and increasing cost effectiveness.
Jacob M. Wishart↗
Hybrid Electric Turboprop Commercial Freighter (HETCOF) Market Study
The dedicated air cargo and freight market has the potential to be a critical early pathway for emerging technologies in low to zero emission propulsion. This study analyzes the cargo aviation market to understand current market trends and future market viability of a mid-sized all-electric or hybrid-electric concept aircraft. While cargo aviation’s overall emissions footprint is small relative to commercial passenger aviation, it remains an important and challenging transportation sector to decarbonize. Past research has focused on small, less than 19-seat electrified aircraft propulsion concepts that could serve both passenger and air cargo markets. This study extends the electrified market space into larger aircraft classes, considering if a purpose-built large hybrid electric turboprop freighter can compete in the market currently served primarily by conversion narrowbody freighters. Specifically, this paper focuses on the mid-sized cargo market with payload ranges of 40,000-50,000lbs, and an all-electric range potential up to 750 miles. The concept aircraft is based on a 4-engine turboprop configuration, with wing mounted battery packs and an aft cargo door to allow for standardized palletization. The market analysis indicates broad market coverage with 73% of the existing mid-sized cargo network within the range of 750 miles. A breakeven analysis of operating and capital costs shows potential for market competition; however, this would require additional energy and acquisition cost savings from the concept aircraft. Evidence from the breakeven analysis also points to higher rates of aircraft utilization being a critical path to lowering costs and increasing cost effectiveness.
Hybrid Electric↗
Hybrid Electric Turboprop Commercial Freighter Opportunity
As the era of electric and hybrid electric aviation is dawning, we have the opportunity to reduce cost, energy use, and emissions of air transportation. In this paper, the case is made for the potential efficiency benefits that can be gained with hybrid electric propulsion. Initial economic, mission profile, and propulsion system concepts for a large turboprop aircraft we designate as the Hybrid Electric Turboprop Commercial Freighter (HETCOF) are presented. Market analysis shows HETCOF has the potential to serve a large market share, but the cost requirements for a new purpose built are challenging relative to the repurposed narrow body aircraft currently operating in the market. Comparing HETCOF to a genericized large turboprop freighter the payload capacity is reduced by 40% for the TRL 5+ configuration but is equivalent to the baseline for the TRL 1-2 configuration. All HETCOF configurations result in increased efficiency and subsequent block fuel, block energy, and block emissions reductions. An integrated power/thermal/and energy storage system is presented and analyzed using key performance parameters to estimate weights and losses at three technology readiness levels. Analysis shows that for a concept like this to have economic and energy benefits, many TRL 1-2 level technologies would be needed. Relevant ARPA-E programs and NASA technologies being developed to enable the benefit are also described. The most significant result of this paper is that the HETCOF concept can close with reduced fuel burn, energy use, and emissions while retaining some or all of the cargo capability of the baseline aircraft across TRL level assumptions, which enables this platform to be used for near term introduction with increasing benefits as technology matures.
Ralph H Jansen↗