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All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes

The analysis and design of practical control systems requires that stochastic models be employed. Analysis and design tools have been developed, for example, for Markovian jump linear continuous and discrete-time systems, piecewise-deterministic processes (PDP's), and general stochastic hybrid systems (GSHS's). These model classes have been used in many applications, including fault tolerant control and networked control systems. This paper presents initial results on the analysis of a sampled-data PDP representation of a nonlinear sampled-data system with a jump linear controller. In particular, it is shown that the state of the sampled-data PDP satisfies the strong Markov property. In addition, a relation between the invariant measures of a sampled-data system driven by a stochastic process and its associated discrete-time representation are presented. As an application, when the plant is linear with no external input, a sufficient testable condition for the convergence in distribution to the invariant delta Dirac measure is given.

Herencia-Zapana, Heber↗
NASA NTRS1999

Quasi-Static Probabilistic Structural Analyses Process and Criteria

Current deterministic structural methods are easily applied to substructures and components, and analysts have built great design insights and confidence in them over the years. However, deterministic methods cannot support systems risk analyses, and it was recently reported that deterministic treatment of statistical data is inconsistent with error propagation laws that can result in unevenly conservative structural predictions. Assuming non-nal distributions and using statistical data formats throughout prevailing stress deterministic processes lead to a safety factor in statistical format, which integrated into the safety index, provides a safety factor and first order reliability relationship. The embedded safety factor in the safety index expression allows a historically based risk to be determined and verified over a variety of quasi-static metallic substructures consistent with the traditional safety factor methods and NASA Std. 5001 criteria.

Goldberg, B.↗
NASA NTRS1995

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Vanel, Florence O.↗
NASA NTRSDate not supplied

Proposed Reliability-Based Damage Tolerance Guidelines for Space Systems

Deterministic damage tolerance guidelines for highly reusable and efficiently designed launch systems can be challenging to meet and result in overly conservative assessments for tightly controlled manufacturing processes. Deterministic approaches may be unconservative when the structure is workmanship sensitive and there is a wide spread in fracture properties. Reliability-based damage tolerance assessments targeting a component reliability over the service life commensurate to mission risk posture is a promising alternative. Low production rates, short fleets, and lack of standards or guidance has slowed down widespread adoption of this method. Guidance for the robust application of reliability-based damage tolerance for space systems are proposed. These guidelines cover the treatment of uncertainty in damage tolerance analysis, the collection of data to develop probabilistic distributions, uncertainty propagation methods, and types of hardware.

Reliability-Based Damage Tolerance↗
NASA NTRS1981

Horizontal wind estimates deterministically derived from the STS-1 entry flight date--a comparison with available meteorology data

Two wind profiles were determined from STS-1 entry flight data based on preliminary best estimate trajectory (BET). The deterministic process used in deriving the atmospheric winds requires inertial estimates of the spacecraft angle-of-attack (alpha) and side-slip angle (beta) from the BET in conjunction with some air data system measurements of the actual angles. The current orbiter air data system (OADS) provides the necessary alpha information. Two beta profiles were adopted. The first profile assumed that the spacecraft would weathervane into any prevailing wind. The second assumed a conservative side-slip history computed from measured accelerations in the spacecraft body axes. It is shown that there are no major differences between the deterministic winds computed using both methods. Further, comparisons of these winds with raw measurements from Tehachapi, California, and preliminary winds obtained from the LaRC LAIRS file and the JSC/TRW descent BET are presented.

Kelly, G. M.↗
NASA NTRS1985

Protostars and planets - Overview from a planetary perspective

Today the simultaneous formation of a star and planetary system is understood to be natural and coupled consequences of the collapse of an interstellar cloud of molecular gas and dust. Ideas put forward to account for the existence of the solar system seem generally applicable to star formation throughout the universe. If this is indeed the case, then planetary systems should be present in large numbers throughout the universe. Even the gross structural features of the planetary system in the solar system seem largely to be the result of nearly deterministic processes, rather than the result of chance alone; many planetary systems throughout the universe may resemble this one. This chapter summarizes and examines some of the implications of ideas about the formation of stars and planetary systems.

Levy, E. H.↗
NASA NTRS1989

An introduction to chaotic and random time series analysis

The origin of chaotic behavior and the relation of chaos to randomness are explained. Two mathematical results are described: (1) a representation theorem guarantees the existence of a specific time-domain model for chaos and addresses the relation between chaotic, random, and strictly deterministic processes; (2) a theorem assures that information on the behavior of a physical system in its complete state space can be extracted from time-series data on a single observable. Focus is placed on an important connection between the dynamical state space and an observable time series. These two results lead to a practical deconvolution technique combining standard random process modeling methods with new embedded techniques.

Scargle, Jeffrey D.↗
NASA NTRS2011

Pre-Finishing of SiC for Optical Applications

13 Manufacturing & Prototyping A method is based on two unique processing steps that are both based on deterministic machining processes using a single-point diamond turning (SPDT) machine. In the first step, a high-MRR (material removal rate) process is used to machine the part within several microns of the final geometry. In the second step, a low-MRR process is used to machine the part to near optical quality using a novel ductile regime machining (DRM) process. DRM is a deterministic machining process associated with conditions under high hydrostatic pressures and very small depths of cut. Under such conditions, using high negative-rake angle cutting tools, the high-pressure region near the tool corresponds to a plastic zone, where even a brittle material will behave in a ductile manner. In the high-MRR processing step, the objective is to remove material with a sufficiently high rate such that the process is economical, without inducing large-scale subsurface damage. A laser-assisted machining approach was evaluated whereby a CO2 laser was focused in advance of the cutting tool. While CVD (chemical vapor deposition) SiC was successfully machined with this approach, the cutting forces were substantially higher than cuts at room temperature under the same machining conditions. During the experiments, the expansion of the part and the tool due to the heating was carefully accounted for. The higher cutting forces are most likely due to a small reduction in the shear strength of the material compared with a larger increase in friction forces due to the thermal softening effect. The key advantage is that the hybrid machine approach has the potential to achieve optical quality without the need for a separate optical finishing step. Also, this method is scalable, so one can easily progress from machining 50-mm-diameter samples to the 250-mm-diameter mirror that NASA desires.

Rozzi, Jay↗
NASA NTRS2004

Propulsion Airframe Aeroacoustics Technology Evaluation and Selection Using a Multi-Attribute Decision Making Process and Non-Deterministic Design

The Systems Analysis Branch at NASA Langley Research Center has investigated revolutionary Propulsion Airframe Aeroacoustics (PAA) technologies and configurations for a Blended-Wing-Body (BWB) type aircraft as part of its research for NASA s Quiet Aircraft Technology (QAT) Project. Within the context of the long-term NASA goal of reducing the perceived aircraft noise level by a factor of 4 relative to 1997 state of the art, major configuration changes in the propulsion airframe integration system were explored with noise as a primary design consideration. An initial down-select and assessment of candidate PAA technologies for the BWB was performed using a Multi-Attribute Decision Making (MADM) process consisting of organized brainstorming and decision-making tools. The assessments focused on what effect the PAA technologies had on both the overall noise level of the BWB and what effect they had on other major design considerations such as weight, performance and cost. A probabilistic systems analysis of the PAA configurations that presented the best noise reductions with the least negative impact on the system was then performed. Detailed results from the MADM study and the probabilistic systems analysis will be published in the near future.

Burg, Cecile M.↗
NASA NTRS1967

Study of random process theory aids digital data processing

Study of techniques for all random process technology, including stationary, nonstationary, and Gaussian bivariate, aids digital data processing. It presents material on digital filtering, correlation function, optimal spectral smoothing, deterministic data processing, and nonstationary spectrum and correlation analyses.

Bordner, G. W.↗
NASA NTRSDate not supplied

A Practical Approach to Uncertainty Quantification Using Probability Boxes

To date, while the use of CFD for aerospace vehicle design and development is prevalent, the documentation of uncertainties associated with the simulations are rare. Instead, the current state-of-the-art relies heavily on the experience of the CFD practitioner to estimate the uncertainty associated with their simulations through simple sensitivity studies or subject matter expertise. This practice will have to be replaced with a formal uncertainty quantification (UQ) process if CFD is to play an expanded role in the research and engineering design community, test and evaluation community, and ultimately certification for flight. Accounting for uncertainties in a formal manner is a tedious process. Moreover, the typical CFD practitioner is not likely to be familiar with formal UQ methods. These factors have prevented the adoption of UQ methods in the engineering design and development cycle. This presentation will outline a credible approach to UQ using Probability Boxes that is straightforward to apply, and can readily be automated using existing UQ tool sets such as the DAKOTA packaged developed at Sandia. The added expense incurred when moving away from a deterministic CFD process to a stochastic one that captures uncertainties to enable risk-informed decision making will be discussed, as well as effective ways to reduce the computational costs.

Uncertainty Quantification↗
NASA NTRS1984

High spectral resolution remote sensing of the land

Spectral remote sensing has been practiced on a large scale since the launch of Landsat 1 in 1972. The limited information contained in this spectrally undersampled data set has led to the development of sophisticated statistical-inferential methods for data analysis. The results are usually limited by the availability of ground truth information. Recent technological developments have made it feasible to create narrow-band, contiguous, spectral image data sets that make possible the identification of surface cover materials based on the complete reflectance spectrum for each picture element. This capability will revolutionize the use of remote sensing data and require new deterministic image processing techniques to extract the full information content from the data. Sensors, based on the concept of imaging spectrometry and the new technology of area array infrared detectors, have been constructed and are candidates for Shuttle and space platform flights.

Goetz, A. F. H.↗
NASA NTRS1994

An experiment in hurricane track prediction using parallel computing methods

The barotropic model is used to explore the advantages of parallel processing in deterministic forecasting. We apply this model to the track forecasting of hurricane Elena (1985). In this particular application, solutions to systems of elliptic equations are the essence of the computational mechanics. One set of equations is associated with the decomposition of the wind into irrotational and nondivergent components - this determines the initial nondivergent state. Another set is associated with recovery of the streamfunction from the forecasted vorticity. We demonstrate that direct parallel methods based on accelerated block cyclic reduction (BCR) significantly reduce the computational time required to solve the elliptic equations germane to this decomposition and forecast problem. A 72-h track prediction was made using incremental time steps of 16 min on a network of 3000 grid points nominally separated by 100 km. The prediction took 30 sec on the 8-processor Alliant FX/8 computer. This was a speed-up of 3.7 when compared to the one-processor version. The 72-h prediction of Elena's track was made as the storm moved toward Florida's west coast. Approximately 200 km west of Tampa Bay, Elena executed a dramatic recurvature that ultimately changed its course toward the northwest. Although the barotropic track forecast was unable to capture the hurricane's tight cycloidal looping maneuver, the subsequent northwesterly movement was accurately forecasted as was the location and timing of landfall near Mobile Bay.

Song, Chang G.↗
NASA NTRS2001

Investigating Uncertainty in Predicting Carbon Dynamics in North American Biomes: Putting Support-Effect Bias in Perspective

A fundamental strategy in NASA's Earth Observing System's (EOS) monitoring of vegetation and its contribution to the global carbon cycle is to rely on deterministic, process-based ecosystem models to make predictions of carbon flux over large regions. These models are parameterized (that is, the input variables are derived) using remotely sensed images such as those from the Moderate Resolution Imaging Spectroradiometer (MODIS), ground measurements and interpolated maps. Since early applications of these models, investigators have noted that results depend partly on the spatial support of the input variables. In general, the larger the support of the input data, the greater the chance that the effects of important components of the ecosystem will be averaged out. A review of previous work shows that using large supports can cause either positive or negative bias in carbon flux predictions. To put the magnitude and direction of these biases in perspective, we must quantify the range of uncertainty on our best measurements of carbon-related variables made on equivalent areas. In other words, support-effect bias should be placed in the context of prediction uncertainty from other sources. If the range of uncertainty at the smallest support is less than the support-effect bias, more research emphasis should probably be placed on support sizes that are intermediate between those of field measurements and MODIS. If the uncertainty range at the smallest support is larger than the support-effect bias, the accuracy of MODIS-based predictions will be difficult to quantify and more emphasis should be placed on field-scale characterization and sampling. This talk will describe methods to address these issues using a field measurement campaign in North America and "upscaling" using geostatistical estimation and simulation.

Dungan, Jennifer L.↗
NASA NTRS2014

Integrated Arrival and Departure Schedule Optimization Under Uncertainty

In terminal airspace, integrating arrivals and departures with shared waypoints provides the potential of improving operational efficiency by allowing direct routes when possible. Incorporating stochastic evaluation as a post-analysis process of deterministic optimization, and imposing a safety buffer in deterministic optimization, are two ways to learn and alleviate the impact of uncertainty and to avoid unexpected outcomes. This work presents a third and direct way to take uncertainty into consideration during the optimization. The impact of uncertainty was incorporated into cost evaluations when searching for the optimal solutions. The controller intervention count was computed using a heuristic model and served as another stochastic cost besides total delay. Costs under uncertainty were evaluated using Monte Carlo simulations. The Pareto fronts that contain a set of solutions were identified and the trade-off between delays and controller intervention count was shown. Solutions that shared similar delays but had different intervention counts were investigated. The results showed that optimization under uncertainty could identify compromise solutions on Pareto fonts, which is better than deterministic optimization with extra safety buffers. It helps decision-makers reduce controller intervention while achieving low delays.

stochastic optimization↗
NASA NTRSDate not supplied

A System to Provide Deterministic Flight Software Operation and Maximize Multicore Processing Performance: The Safe and Precise Landing – Integrated Capabilities Evolution (SPLICE) Datapath

A method and design are described for a system that processes multiple data streams, utilizing a multicore asymmetric processing architecture, that eliminates data interrupts to the application processors. The design supports a deterministic environment for flight software in NASA’s Safe and Precise Landing – Integrated Capabilities Evolution (SPLICE) project. The SPLICE project develops sensor, algorithm, and compute technologies for Precision Landing and Hazard Avoidance (PL&HA) capabilities. The compute technology for SPLICE is the Descent and Landing Computer (DLC). The DLC hosts several SPLICE algorithms with high computational resource requirements that must be executed in a real-time and deterministic manner. The software runs on a custom Single Board Computer (SBC), with a Xilinx Ultrascale+ Multiprocessor System-on-a-Chip (MPSoC). Input data for the flight software is from a variety of sensors, unique with respect to data rate and packet size. A data path between the SPLICE sensors and algorithms is designed to efficiently deliver this data to the flight software using the MPSoC asymmetric processing cores and Field Programmable Gate Array (FPGA) fabric. This is implemented in a manner that isolates the application processors running the flight software from interrupts associated with the input data. By leveraging real-time processors on the MPSoC, and a structure with the appropriate interfaces in the shared memory on the SBC, the flight software can use the full set of application processors. The available utilization for each processor in this set is also maximized for the SPLICE applications, providing a sufficiently deterministic execution environment without the cost and overhead of a real-time operating system.

heterogeneous processing system↗