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NASA NTRS2019

Deterministic Polishing of Replicating Grazing-Incidence Mandrels

In an effort to manufacture high-angular-resolution, grazing-incidence, x-ray optics, Marshall Space Flight Center (MSFC) is taking measures to improve its electroformed replicated optics. A key development is the use of computer-numerical control (CNC) polishing to deterministically improve the surface of electroless nickel mandrels used to replicate grazing- incidence optics. Metrology, control software and polishing parameters must function together seamlessly to reach the specifications required to replicate sub-arcsecond optics. Each change in polishing parameters effects the wear pattern of the polishing head. Using Richardson-Lucy deconvolution, the controller software fits the wear pattern to metrology data to calculate the changing feedrates across the mandrel. Here we present an overview of our process, and early results showing the effectiveness of deterministic polishing for replicated optics.

Davis, Jacqueline↗

NASA NTRS1972

An input adaptive, pursuit tracking model of the human opertor

Developed and evaluated is a simple model of the input adaptive behavior of the human operator (HO) in a pursuit tracking task in which the plant controlled consists of a pure gain. If it is assumed that the HO is approximately an optimal predictor using only position and velocity information, then there is a simple method of computing the values of the model parameters in terms of the autocorrelation function of the input signal. Experimental evidence indicates that the ability of the HO to use velocity information decreases with increasing signal velocity indicating that a biased estimator of the velocity weighting should be used. A suitable approximation is derived which has rapid convergence and low variance. The model thus derived is compared to actual subject transfer functions and is found to be in close agreement. In addition to tracking random processes the model can adapt to and track deterministic signals, such as sine waves, up to approximately the frequency at which human operators begin to track precognitively.

Ware, J. R.↗

NASA NTRS2018

Automated Impact Assessment: A New Approach to ISS Payload Operations Anomaly Response

The International Space Station (ISS) Payload Operations and Integration Center (POIC) is undergoing rapid growth as the space station program focuses on science and commercial activities. The ISS is expanding its onboard capabilities to support additional science activities. In parallel, the POIC is expanding the capabilities of our operations tools to support the higher pace of payload activities being executed each week. An effect of these changes is that anomaly resolution has become more challenging. In the event of a real-time system fault, operators are responsible for analyzing telemetry displays, anomaly monitoring tools, documentation, and system models in order to produce failure impacts and recovery strategies. This approach to operations relies on the operator to ingest, process, and analyze information from an array of deterministic sources to provide actionable data on impacted systems and activities. Changing the existing approach of anomaly response is necessary if the ISS community is to succeed in the age of science and commercialization of space. The creation of a tool that captures deterministic technical systems knowledge and integrates existing telemetry, documentation, and planning information will allow the burden of impact assessment to be automated, thereby allowing the operator to focus on non-deterministic tasks, such as recovering failed systems and restoring critical payload operations.

Hall, R. Mason↗

NASA NTRS1991

Markov reward processes

Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.

Smith, R. M.↗

NASA NTRS1992

Probabilistic design applications for the Space Transportation Main Engines

All of the current rocket engine designs are based on deterministic design analysis methods. The most recently designed engine, Space Shuttle Main Engines (SSME), was designed and developed using these techniques in the 1970's and 80's. The Space Transportation Main Engine (STME) design objective is to use a robust design methodology and to pro-actively assess and improve the design during the design process. The design approach is a combination of the traditional deterministic methodologies and recently developed probabilistic methodologies. The designer must use a more rigorous structural criteria, conduct pro-active reliability assessments (reliability allocations, failure modes and effects analysis, reliability growth studies, and design reliability assessment), use a damage tolerant design philosophy and perform probabilistic analyses. Rigorous application of this structured methodology will develop a better engine product.

Ohara, Kevin↗

NASA NTRS2006

Spitzer Space Telescope Sequencing Operations Software, Strategies, and Lessons Learned

The Space Infrared Telescope Facility (SIRTF) was launched in August, 2003, and renamed to the Spitzer Space Telescope in 2004. Two years of observing the universe in the wavelength range from 3 to 180 microns has yielded enormous scientific discoveries. Since this magnificent observatory has a limited lifetime, maximizing science viewing efficiency (ie, maximizing time spent executing activities directly related to science observations) was the key operational objective. The strategy employed for maximizing science viewing efficiency was to optimize spacecraft flexibility, adaptability, and use of observation time. The selected approach involved implementation of a multi-engine sequencing architecture coupled with nondeterministic spacecraft and science execution times. This approach, though effective, added much complexity to uplink operations and sequence development. The Jet Propulsion Laboratory (JPL) manages Spitzer s operations. As part of the uplink process, Spitzer s Mission Sequence Team (MST) was tasked with processing observatory inputs from the Spitzer Science Center (SSC) into efficiently integrated, constraint-checked, and modeled review and command products which accommodated the complexity of non-deterministic spacecraft and science event executions without increasing operations costs. The MST developed processes, scripts, and participated in the adaptation of multi-mission core software to enable rapid processing of complex sequences. The MST was also tasked with developing a Downlink Keyword File (DKF) which could instruct Deep Space Network (DSN) stations on how and when to configure themselves to receive Spitzer science data. As MST and uplink operations developed, important lessons were learned that should be applied to future missions, especially those missions which employ command-intensive operations via a multi-engine sequence architecture.

missions operations↗

NASA NTRS1983

Measurements and predictions for nonevaporating sprays in a quiescent environment

Yule et al. (1982) have conducted a study of vaporizing sprays with the aid of laser techniques. The present investigation has the objective to supplement the measurements performed by Yule et al., by considering the limiting case of a spray in a stagnant environment. Mean and fluctuating velocities of the continuous phase are measured by means of laser Doppler anemometry (LDA) techniques, while Fraunhofer diffraction and slide impaction methods are employed to determine drop sizes. Liquid fluxes in the spray are found by making use of an isokinetic sampling probe. The obtained data are used as a basis for the evaluation of three models of the process, including a locally homogeneous flow (LHF) model, a deterministic separated flow (DSF) model, and a stochastic separated flow (SSF) model. It is found that the LHF and DSF models do not provide very satisfactory predictions for the test sprays, while the SSF model does provide reasonably good predictions of the observed structure.

Solomon, A. S. P.↗

NASA NTRS1992

Probabilistic evaluation of uncertainties and risks in aerospace components

This paper summarizes a methodology developed at NASA Lewis Research Center which computationally simulates the structural, material, and load uncertainties associated with Space Shuttle Main Engine (SSME) components. The methodology was applied to evaluate the scatter in static, buckling, dynamic, fatigue, and damage behavior of the SSME turbo pump blade. Also calculated are the probability densities of typical critical blade responses, such as effective stress, natural frequency, damage initiation, most probable damage path, etc. Risk assessments were performed for different failure modes, and the effect of material degradation on the fatigue and damage behaviors of a blade were calculated using a multi-factor interaction equation. Failure probabilities for different fatigue cycles were computed and the uncertainties associated with damage initiation and damage propagation due to different load cycle were quantified. Evaluations on the effects of mistuned blades on a rotor were made; uncertainties in the excitation frequency were found to significantly amplify the blade responses of a mistuned rotor. The effects of the number of blades on a rotor were studied. The autocorrelation function of displacements and the probability density function of the first passage time for deterministic and random barriers for structures subjected to random processes also were computed. A brief discussion was included on the future direction of probabilistic structural analysis.

Shah, A. R.↗

NASA NTRS1984

Predictions of spray combustion interactions

Mean and fluctuating phase velocities; mean particle mass flux; particle size; and mean gas-phase Reynolds stress, composition and temperature were measured in stationary, turbulent, axisymmetric, and flows which conform to the boundary layer approximations while having well-defined initial and boundary conditions in dilute particle-laden jets, nonevaporating sprays, and evaporating sprays injected into a still air environment. Three models of the processes, typical of current practice, were evaluated. The local homogeneous flow and deterministic separated flow models did not provide very satisfactory predictions over the present data base. In contrast, the stochastic separated flow model generally provided good predictions and appears to be an attractive approach for treating nonlinear interphase transport processes in turbulent flows containing particles (drops).

Shuen, J. S.↗

NASA NTRS1989

Land surface hydrology parameterization for atmospheric general circulation models including subgrid scale spatial variability

Parameterizations are developed for the representation of subgrid hydrologic processes in atmospheric general circulation models. Reasonable a priori probability density functions of the spatial variability of soil moisture and of precipitation are introduced. These are used in conjunction with the deterministic equations describing basic soil moisture physics to derive expressions for the hydrologic processes that include subgrid scale variation in parameters. The major model sensitivities to soil type and to climatic forcing are explored.

Entekhabi, D.↗

NASA NTRS1992

Combustion noise and combustion instabilities in propulsion systems

This paper is concerned with some aspects of non-linear behavior of unsteady motions in combustion chambers. The emphasis is on conditions under which organized oscillations having discrete frequencies may exist in the presence of random motions. In order to treat the two types of motions together, and particularly to investigate coupling between noise and combustion instabilities, the unsteady field is represented as a synthesis of acoustic modes having time-varying amplitudes. Each of the amplitudes are written as the sum of two parts, one associated with the random field and the remainder representing the organized oscillations. After spatial averaging, the general problem is reduced to solution of a set of second-order ordinary differential equations whose structure depends on the sorts of nonlinear processes accounted for. This formulation accommodates any physical process; in particular, terms are included to represent noise sources, although only limited modeling is discussed. Our results suggest that random sources of noise have only small effects on combustion instabilities and seem not to be a cause of unstable motions. However, the coupling between the two sorts of unsteady motions may be important as an essential process in a proposed scheme for noise control. It is now a familiar observation that many nonlinear deterministic systems are capable of exhibiting apparently random motions called 'chaos.' This is a particularly interesting possibility for systems which also executed non-deterministic random motions. In combustion chambers, a nonlinear deterministic system (acoustical motions) exists in the presence of noise produced by flow separation, turbulent motions, and energy released by combustion processes. The last part of the paper is directed to the matter of discovering whether or not chaotic motions exist in combustion systems. Analysis has not progressed sufficiently far to answer the question. We report here recent results of processing data taken in one combustor to determine the dimensions of any attractors in the motions. No evidence has been found for chaos in the strict sense, but the method seems to be an important means of investigating the nonlinear behavior of combustion systems.

F. E. C. Culick↗

NASA NTRS1993

An in-depth probabilistic study of external tank attach ring

This report deals with conducting a probabilistic study of the external tank attach ring (ETA) used as an interface between the external tank attach struts and the solid rocket booster. The ideas were to use probabilistic distributions for material, geometric, and load properties; to calculate probabilistic margins of safety; and then to compare results against the deterministic factors of safety that were used in the actual design process. The report describes how this was done and discusses some of the road blocks and data problems that were encountered during the study and provides some conclusions. A further refinement of this study is being considered for future work which would make more direct use of finite element analysis data coupled with Monte Carlo simulation. The basic conclusion herein indicates that the probabilistic margins of safety for the cases analyzed (by use of existing data) appear to support deterministic results and actually indicate higher reliabilities.

Pizzano, Frank↗

NASA NTRS1990

Small-scale transition in a plane mixing layer

An experimental study was conducted to investigate the generation process of random small-scale turbulence in an originally laminar mixing layer. The evolutions of the two types of deterministic structures, the spanwise and streamwise vortices, were first clarified in order to determine their roles in the transition process. A scaling rule for the streamwise distance from the trailing edge of the splitter plate to the vortex merging position was found for various velocity ratios. After this stremwise lengthscale was determined, it became clear that the spanwise wavelength of the streamwise vortices doubled after the merging of the spanwise structures which nominally doubled streamwise wavelengths. The most interesting finding was that the random small-scale eddies were produced by the interactions between the merging spanwise structures and the streamwise vortices.

Huang, Lein-Saing↗

NASA NTRS1986

Mechanisms of crustal deformation in the western US

The deformation processes in the western United States were studied, considering both deterministic models and random or statistical models. The role of the intracrustal delamination and mechanisms of crustal thinning were also examined. The application of fractal techniques to understand how the crust is deforming was studied in complex regions. Work continued on the development of a fractal based model for deformation in the western United States. Fractal studies were also extended to the study of topography and the geoid.

Turcotte, Donald L.↗

NASA NTRS2011

Probabilistic Risk Assessment Procedures Guide for NASA Managers and Practitioners (Second Edition)

Probabilistic Risk Assessment (PRA) is a comprehensive, structured, and logical analysis method aimed at identifying and assessing risks in complex technological systems for the purpose of cost-effectively improving their safety and performance. NASA's objective is to better understand and effectively manage risk, and thus more effectively ensure mission and programmatic success, and to achieve and maintain high safety standards at NASA. NASA intends to use risk assessment in its programs and projects to support optimal management decision making for the improvement of safety and program performance. In addition to using quantitative/probabilistic risk assessment to improve safety and enhance the safety decision process, NASA has incorporated quantitative risk assessment into its system safety assessment process, which until now has relied primarily on a qualitative representation of risk. Also, NASA has recently adopted the Risk-Informed Decision Making (RIDM) process [1-1] as a valuable addition to supplement existing deterministic and experience-based engineering methods and tools. Over the years, NASA has been a leader in most of the technologies it has employed in its programs. One would think that PRA should be no exception. In fact, it would be natural for NASA to be a leader in PRA because, as a technology pioneer, NASA uses risk assessment and management implicitly or explicitly on a daily basis. NASA has probabilistic safety requirements (thresholds and goals) for crew transportation system missions to the International Space Station (ISS) [1-2]. NASA intends to have probabilistic requirements for any new human spaceflight transportation system acquisition. Methods to perform risk and reliability assessment in the early 1960s originated in U.S. aerospace and missile programs. Fault tree analysis (FTA) is an example. It would have been a reasonable extrapolation to expect that NASA would also become the world leader in the application of PRA. That was, however, not to happen. Early in the Apollo program, estimates of the probability for a successful roundtrip human mission to the moon yielded disappointingly low (and suspect) values and NASA became discouraged from further performing quantitative risk analyses until some two decades later when the methods were more refined, rigorous, and repeatable. Instead, NASA decided to rely primarily on the Hazard Analysis (HA) and Failure Modes and Effects Analysis (FMEA) methods for system safety assessment.

Stamatelatos,Michael↗

NASA NTRSDate not supplied

Sampling Functions from Gaussian Processes and Structured Covariance Gaussian Networks

When learning aerodynamic models from data, it is critical to incorporate estimates of model uncertainty. This motivates the design of probabilistic aerodynamic databases which can be sampled to generate physically and statistically plausible aerodynamic models. In this talk we discuss how to sample deterministic functions from two different kinds of probabilistic models and demonstrate their use. First, Gaussian Process Regressors (GPRs) are a widely used probabilistic kernel-based model which can be thought of as Gaussian distributions over functions. GPRs are generally trained by maximizing the marginal likelihood of seeing the training data over the kernel parameter space. Sample functions are easily generated by drawing points from the Gaussian distribution at desired input points. However, when the points are not known ahead of time, the classical sampling approach is not possible since successive function samples will generate different function realizations. We present an approach for sampling consistent function evaluations from a GPR over multiple samples. Second, we describe a neural network architecture which learns a conditional Gaussian distribution by maximizing the marginal likelihood at each point in the input space. We then discuss and compare several options for generating sample functions which match this distribution. Finally, we demonstrate the use of these probabilistic aerodynamic models in an atmospheric reentry simulation.

Gaussian process regression↗

NASA NTRS2008

Simulation of Stochastic Processes by Coupled ODE-PDE

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

Zak, Michail↗

NASA NTRS1997

Inherent Conservatism in Deterministic Quasi-Static Structural Analysis

The cause of the long-suspected excessive conservatism in the prevailing structural deterministic safety factor has been identified as an inherent violation of the error propagation laws when reducing statistical data to deterministic values and then combining them algebraically through successive structural computational processes. These errors are restricted to the applied stress computations, and because mean and variations of the tolerance limit format are added, the errors are positive, serially cumulative, and excessively conservative. Reliability methods circumvent these errors and provide more efficient and uniform safe structures. The document is a tutorial on the deficiencies and nature of the current safety factor and of its improvement and transition to absolute reliability.

Verderaime, V.↗