NASA's In-Space Manufacturing Initiative: Initial Results from International Space Station Technology Demonstration and Future Plans
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Space Station↗
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NASA's In-Space Manufacturing Initiative: Initial Results from International Space Station Technology Demonstration and Future Plans
No abstract available
Prater, Tracie↗
NASA Earth Science Data Systems Evolution from Big Earth Data Initiative (BEDI) to Open-Source Science Initiative (OSSI)
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Jennifer Wei↗
Diabatic dynamic initialization
A generalized dynamical adjustment procedure was applied to a diabatic model to produce balanced initial conditions. Namely, backward adiabatic model integration is followed by forward diabatic model integration, with a high frequency (low pass) filter in the form of the Euler-backward time differencing scheme being applied throughout the whole integration. As a result of the application of such a diabatic dynamic initialization procedure within the Goddard Laboratory for Atmospheres (GLA) 4-D data assimilation system, the following properties of forecasts from initialized fields are achieved right from the beginning of the usual forecast integration: (1) the forecast tendencies (and fields) are free of any noise due to imbalance in initial conditions; (2) the shocks related to an initial imbalance between model physics and dynamics, and especially the substantial initial imbalance of precipitation and evaporation fields, or the initial spin-up effect, are practically removed. Diabatic dynamic initialization has been compared with implicit nonlinear normal mode initialization, and found to be superior in removing the initial spin-up effect, and also in improving the tropical structure. The diabatic dynamic initialization procedure was successfully tested for the GLA system with the use of all conventional data and the GLA satellite data retrievals. It allows a smooth data insertion without any shocks or imbalances, which is highly desirable for efficient functioning of 4-D data assimilation systems. The developed initialization procedure is computationally efficient and in principle easily applicable to different forecast models.
Fox-Rabinovitz, Michael S.↗
Relative Influence of Initial Surface and Atmospheric Conditions on Seasonal Water and Energy Balances
We constructed and analyzed wet and dry soil moisture composites for the mid-latitude GCIP region of the central US using long climate model simulations made with the NCAR CCM3 and reanalysis products from NCEP. Using the diagnostic composites as a guide, we have completed a series of predictability experiments in which we imposed soil water initial conditions in CCM3 for the GCIP region for June 1 from anomalously wet and dry years, with atmospheric initial conditions taken from June 1 of a year with 'near-normal' soil water, and initial soil water from the near-normal year and atmospheric initial conditions from the wet and dry years. Preliminary results indicate that the initial state of the atmosphere is more important than the initial state of soil water determining the subsequent late spring and summer evolution of sod water over the GCIP region. Surprisingly, neither the composites or the predictability experiments yielded a strong influence of soil moisture on the atmosphere. To explore this further, we have made runs with extreme dry soil moisture initial anomalies imposed over the GCIP region (the soil close to being completely dry). These runs did yield a very strong effect on the atmosphere that persisted for at least three months. We conclude that the magnitude of the initial soil moisture anomaly is crucial, at least in CCM3, and are currently investigating whether a threshold exists, below which little impact is seen. In a complementary study, we compared the impact of the initial condition of snow cover versus the initial atmospheric state over the western US (corresponding to the westward extension of the GAPP program follow-on to GCIP). In this case, the initial prescription of snow cover is far more important than the initial atmospheric state in determining the subsequent evolution of snow cover. We are currently working to understand the very different soil water and snow cover results.
Oglesby, Robert J.↗
The Influence of Soil Moisture, Coastline Curvature, and Land-Breeze Circulations on Sea-Breeze Initiated Precipitation
Idealized numerical simulations are performed with a coupled atmosphere/land-surface model to identify the roles of initial soil moisture, coastline curvature, and land breeze circulations on sea breeze initiated precipitation. Data collected on 27 July 1991 during the Convection and Precipitation Electrification Experiment (CAPE) in central Florida are used. The 3D Goddard Cumulus Ensemble (GCE) cloud resolving model is coupled with the Goddard Parameterization for Land-Atmosphere-Cloud Exchange (PLACE) land surface model, thus providing a tool to simulate more realistically land-surface/atmosphere interaction and convective initiation. Eight simulations are conducted with either straight or curved coast-lines, initially homogeneous soil moisture or initially variable soil moisture, and initially homogeneous horizontal winds or initially variable horizontal winds (land breezes). All model simulations capture the diurnal evolution and general distribution of sea-breeze initiated precipitation over central Florida. The distribution of initial soil moisture influences the timing, intensity and location of subsequent precipitation. Soil moisture acts as a moisture source for the atmosphere, increases the connectively available potential energy, and thus preferentially focuses heavy precipitation over existing wet soil. Strong soil moisture-induced mesoscale circulations are not evident in these simulations. Coastline curvature has a major impact on the timing and location of precipitation. Earlier low-level convergence occurs inland of convex coastlines, and subsequent precipitation occurs earlier in simulations with curved coastlines. The presence of initial land breezes alone has little impact on subsequent precipitation. however, simulations with both coastline curvature and initial land breezes produce significantly larger peak rain rates due to nonlinear interactions.
Baker, David R.↗
Piezoelectrically Initiated Pyrotechnic Igniter
This innovation consists of a pyrotechnic initiator and piezoelectric initiation system. The device will be capable of being initiated mechanically; resisting initiation by EMF, RF, and EMI (electromagnetic field, radio frequency, and electromagnetic interference, respectively); and initiating in water environments and space environments. Current devices of this nature are initiated by the mechanical action of a firing pin against a primer. Primers historically are prone to failure. These failures are commonly known as misfires or hang-fires. In many cases, the primer shows the dent where the firing pin struck the primer, but the primer failed to fire. In devices such as "T" handles, which are commonly used to initiate the blowout of canopies, loss of function of the device may result in loss of crew. In devices such as flares or smoke generators, failure can result in failure to spot a downed pilot. The piezoelectrically initiated ignition system consists of a pyrotechnic device that plugs into a mechanical system (activator), which on activation, generates a high-voltage spark. The activator, when released, will strike a stack of electrically linked piezo crystals, generating a high-voltage, low-amperage current that is then conducted to the pyro-initiator. Within the initiator, an electrode releases a spark that passes through a pyrotechnic first-fire mixture, causing it to combust. The combustion of the first-fire initiates a primary pyrotechnic or explosive powder. If used in a "T" handle, the primary would ramp the speed of burn up to the speed of sound, generating a shock wave that would cause a high explosive to go "high order." In a flare or smoke generator, the secondary would produce the heat necessary to ignite the pyrotechnic mixture. The piezo activator subsystem is redundant in that a second stack of crystals would be struck at the same time with the same activation force, doubling the probability of a first strike spark generation. If the first activation fails to ignite, the device is capable of multiple attempts. Another unique aspect is in the design of the pyrotechnic device. There is an electrode that aids the generation of a directed spark and the use of a conductive matrix to support the first-fire material so that the spark will penetrate to the second electrode.
Quince, Asia↗
Bayesian estimation of crack initiation times from service data
Lockheed C-130 Hercules aircraft have during their service life been periodically inspected and growing cracks around rivet holes were recorded. This record has recently been used to determine the statistical distributions of crack initiation times and the distribution of initial crack sizes. When crack initiation times are calculated from such cracks, by backward extrapolation of the growth relation, the resulting distribution of crack initiation times will indicate a preponderance of short times to crack initiation. If however, such distributions are combined with the reliability of the inspection procedure, the statistical distribution of missed initiation times can be estimated. The method used is based on Bayes theorem which permits the calculation of the 'prior' distribution (initiation times before inspection) from a knowledge of the 'posterior' distribution (initiation times obtained from the inspection) and a 'likelihood function' (reliability of the inspection) procedure. The results indicate that during an early inspection a large percentage of initiation times will be missed and that the fraction of located initiation times increases during later inspections.
Heller, R. A.↗
Hypervelocity Impact Initiation of Explosive Transfer Lines
The Gemini, Apollo and Space Shuttle spacecraft utilized explosive transfer lines (ETL) in a number of applications. In each case the ETL was located behind substantial structure and the risk of impact initiation by micrometeoroids and orbital debris was negligible. A current NASA program is considering an ETL to synchronize the actuation of pyrobolts to release 12 capture latches in a contingency. The space constraints require placing the ETL 50 mm below the 1 mm thick 2024-T72 Whipple shield. The proximity of the ETL to the thin shield prompted analysts at NASA to perform a scoping analysis with a finite-difference hydrocode to calculate impact parameters that would initiate the ETL. The results suggest testing is required and a 12 shot test program with surplused Shuttle ETL is scheduled for February 2012 at the NASA White Sands Test Facility. Explosive initiation models are essential to the analysis and one exists in the CTH library for HNS I, but not the HNS II used in the Shuttle 2.5 gr/ft rigid shielded mild detonating cord (SMDC). HNS II is less sensitive than HNS I so it is anticipated that these results using the HNS I model are conservative. Until the hypervelocity impact test results are available, the only check on the analysis was comparison with the Shuttle qualification test result that a 22 long bullet would not initiate the SMDC. This result was reproduced by the hydrocode simulation. Simulations of the direct impact of a 7 km/s aluminum ball, impacting at 0 degree angle of incidence, onto the SMDC resulted in a 1.5 mm diameter ball initiating the SMDC and 1.0 mm ball failing to initiate it. Where one 1.0 mm ball could not initiate the SMDC, a cluster of six 1.0 mm diameter aluminum balls striking simultaneously could. Thus the impact parameters that will result in initiating SMDC located behind a Whipple shield will depend on how well the shield fragments the projectile and spreads the fragments. An end-to-end simulation of the impact of an aluminum ball onto a Whipple shield covering SMDC is problematic due to the hydrocode fracture models. Regardless, two simulations were performed resulting in a 5 mm ball initiating the SMDC and a 4 mm ball failing to initiate the SMDC.
Bjorkman, Michael D.↗
Flight demonstration of laser diode initiated ordnance
A program has been initiated by NASA Headquarters to validate laser initiated ordnance in flight applications. The primary program goal is to bring together a team of government and industry members to develop a laser initiated ordnance system having the test and analysis pedigree to be flown on launch vehicles. The culmination of this effort was a flight of the Pegasus launch vehicle which had two fin rockets initiated by this laser system. In addition, a laser initiated ordnance squib was fired into a pressure bomb during thrusting flight. The complete ordnance system comprising a laser diode firing unit, fiber optic cable assembly, laser initiated detonator, and laser initiated squib was designed and built by The Ensign Bickford Company. The hardware was tested to the requirements of the Pegasus launch vehicle and integrated into the vehicle by The Ensign Bickford Company and the Orbital Sciences Corporation. Discussions include initial program concept, contract implementation, team member responsibilities, analysis results, vehicle integration, safing architecture, ordnance interfaces, mission timeline and telemetry data. A complete system description, summary of the analyses, the qualification test results, and the results of flight are included.
Boucher, Craig J.↗
Planar Strain-Rate-Free Diffusion Flames: Initiation, Properties, and Extinction
An effectively strain-rate-free diffusion flame constitutes the most vigorous laminar combustion of initially unmixed reactive gases. Such a diffusion flame is characterized by a relatively long residence time and by a relatively large characteristic length scale. If such a flame were also planar, providing high symmetry, it would be particularly suitable for experimental and theoretical investigations of key combustion phenomena, such as multicomponent diffusion, chemical kinetics, and soot inception, growth, and oxidation. Unfortunately, a planar strain-rate-free diffusion flame is highly disrupted in earth-gravity (e.g., in a counterflow-diffusion-flame apparatus) because of the very rapid onset (approx. 100 ms) of gravity-induced instability. Accordingly, a specially dedicated apparatus was designed, fabricated, and initially checked out for the examination of a planar strain-rate-free diffusion flame in microgravity. Such a diffusion flame may be formed within a hollowed-out squat container (initially configured as 25 cm x 25 cm x 9 cm), with isothermal, noncatalytic, impervious walls. At test initiation, a thin metallic sheet (approx. 1 mm in thickness) that separates the internal volume into two equal portions, each of dimensions 25 cm x 25 cm x 4.5 cm, is withdrawn, by uniform translation (approx. 50 cm/s) in its own plane, through a tightly fitting slit in one side wall. Thereupon, diluted fuel vapor (initially confined to one half-volume of the container) gains access to diluted oxygen (initially with the same pressure, density, and temperature as the fuel, but initially confined to the other half-volume). After a brief delay (approx. 10 ms), to permit limited but sufficient-for-flammability diffusional interpenetration of fuel vapor and oxidizer, burning is initiated by discharge of a line igniter, located along that side wall from which the trailing edge of the separator withdraws. The ignition spawns a triple-flame propagation across the 25 cm x 25 cm centerplane. When a diffusion flame is emplaced in the centerplane, any subsequent travel, and change in temperature, of that planar diffusion flame may be tracked, along with the effectively spatially uniform but temporally evolving pressure within the container. Eventually, nearly complete depletion of the stoichiometrically deficient reactant, along with heat loss to the container surfaces, effects extinction. These data afford an opportunity to check theoretical models of diffusion and chemical kinetics under conditions ranging from intense burning to flame out, or, alternatively, to evolve simple empirical representations of these phenomena. Thus, the project sought to utilize microgravity testing to elucidate commonly encountered phenomenology, arising in the commonly-encountered mode of combustion (whether related to heating, manufacturing, boiling, and propulsion, or to uncontrolled, free-burning fire in structures and wildland vegetation), of those commonly utilized fuels usually categorized as gaseous fuels (such as hydrogen, natural gas, and propane, which are gaseous under atmospheric conditions).
Fendell, Francis↗
Use of MODIS Land and Sea Surface Temperatures to Initialize Mesoscale Models
As computer power continues to increase, mesoscale models are initialized at all hours of the day and continue to be run at higher and higher spatial resolutions. As a result, initializing land surface temperature can be problematic. The majority of research-based models are initialized at 00 and 12 UTC when upper air observations and reanalysis fields are available. The landsea surface temperatures are then set equal to the two-meter air temperature produced by the preprocessor analysis system. This particular procedure might be valid in the early morning hours just prior to sunrise, but it becomes less valid during the remainder of the diurnal cycle. Operational models, such as the Rapid Update Cycle run at the National Centers for Environmental Prediction (NCEP), are initialized every hour on a daily basis. This presents a unique challenge to the initial specification of the land temperature, especially during the first several hours of the solar heating cycle when land and overlying air temperatures are far from being the same. Another issue that needs to be addressed is the spatial variability of land surface temperature. By early next year, the NCEP operational Eta model will be employed at 8 km resolution. Methods to accurately specify the initial land surface temperature at such high resolution need to be explored. This paper presents the results of using data from the NASA Moderate Imaging Sensor aboard the TERRA Satellite to initialize land and sea surface temperatures within the Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) 5'th generation Mesoscale Model (MM5). We have simulated a northern Gulf Coast sea breeze case to demonstrate the utility of using the MODIS data to initialize both the land and sea surface temperature fields. Model grid configurations of 12-, 4-, and l-km are employed.
Arnold, James E.↗
Alternative Approaches to Land Initialization for Seasonal Precipitation and Temperature Forecasts
The seasonal prediction system of the NASA Global Modeling and Assimilation Office is used to generate ensembles of summer forecasts utilizing realistic soil moisture initialization. To derive the realistic land states, we drive offline the system's land model with realistic meteorological forcing over the period 1979-1993 (in cooperation with the Global Land Data Assimilation System project at GSFC) and then extract the state variables' values on the chosen forecast start dates. A parallel series of forecast ensembles is performed with a random (though climatologically consistent) set of land initial conditions; by comparing the two sets of ensembles, we can isolate the impact of land initialization on forecast skill from that of the imposed SSTs. The base initialization experiment is supplemented with several forecast ensembles that use alternative initialization techniques. One ensemble addresses the impact of minimizing climate drift in the system through the scaling of the initial conditions, and another is designed to isolate the importance of the precipitation signal from that of all other signals in the antecedent offline forcing. A third ensemble includes a more realistic initialization of the atmosphere along with the land initialization. The impact of each variation on forecast skill is quantified.
Koster, Randal↗
Radar Differential Phase Signatures of Ice Orientation for the Prediction of Lightning Initiation and Cessation
The majority of lightning-related casualties typically occur during thunderstorm initiation (e.g., first flash) or dissipation (e.g., last flash). The physics of electrification and lightning production during thunderstorm initiation is fairly well understood. As such, the literature includes a number of studies presenting various radar techniques (using reflectivity and, if available, other dual-polarimetric parameters) for the anticipation of initial electrification and first lightning flash. These radar techniques have shown considerable skill at forecasting first flash. On the other hand, electrical processes and lightning production during thunderstorm dissipation are not nearly as well understood and few, if any, successful techniques have been developed to anticipate the last flash and subsequent cessation of lightning. One promising approach involves the use of dual-polarimetric radar variables to infer the presence of oriented ice crystals in lightning producing storms. In the absence of strong vertical electric fields, ice crystals fall with their largest (semi-major) axis in the horizontal associated with gravitational and aerodynamic forces. In thunderstorms, strong vertical electric fields (100-200 kV m(sup -1)) have been shown to orient small (less than 2 mm) ice crystals such that their semi-major axis is vertical (or nearly vertical). After a lightning flash, the electric field is typically relaxed and prior radar research suggests that ice crystals rapidly resume their preferred horizontal orientation. In active thunderstorms, the vertical electric field quickly recovers and the ice crystals repeat this cycle of orientation for each nearby flash. This change in ice crystal orientation from primarily horizontal to vertical during the development of strong vertical electric fields prior to a lightning flash forms the physical basis for anticipating lightning initiation and, potentially, cessation. Research has shown that radar reflectivity (Z) and other co-polar back-scattering radar measurements like differential reflectivity (Z(sub dr)) typically measured by operational dual-polarimetric radars are not sensitive to these changes in ice crystal orientation. However, prior research has demonstrated that oriented ice crystals cause significant propagation effects that can be routinely measured by most dual-polarimetric radars from X-band (3 cm) to S-band (10 cm) wavelengths using the differential propagation phase shift (often just called differential phase, phi(sub dp)) or its range derivative, the specific differential phase (K(sub dp)). Advantages of the differential phase include independence from absolute or relative power calibration, attenuation, differential attenuation and relative insensitivity to ground clutter and partial beam occultation effects (as long as the signal remains above noise). In research mode, these sorts of techniques have been used to anticipate initial cloud electrification, lightning initiation, and cessation. In this study, we develop a simplified model of ice crystal size, shape, orientation, dielectric, and associated radar scattering and propagation effects in order to simulate various idealized scenarios of ice crystals responding to a hypothetical electric field and their dual-polarimetric radar signatures leading up to lightning initiation and particularly cessation. The sensitivity of the K(sub dp) ice orientation signature to various ice properties and radar wavelength will be explored. Since K(sub dp) is proportional to frequency in the Rayleigh- Gans scattering regime, the ice orientation signatures should be more obvious at higher (lower) frequencies (wavelengths). As a result, simulations at radar wavelengths from 10 cm down to 1 cm (Ka-band) will be conducted. Resonance effects will be considered using the T-matrix method. Since most K(sub dp) Vbased observations have been shown at S-band, we will present ice orientation signatures from C-band (UAH/NASA ARMOR) and X-bd (UAH MAX) dual-polarimetric radars located in Northern Alabama. Issues related to optimal radar scanning for the detection of oriented ice will be discussed. Preliminary suggestions on how these differential phase signatures of oriented ice could contribute to lightning initiation and cessation algorithms will be presented.
Carey, L.D.↗
Weather Research and Forecasting Model Sensitivity Comparisons for Warm Season Convective Initiation
Mesoscale weather conditions can significantly affect the space launch and landing operations at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS). During the summer months, land-sea interactions that occur across KSC and CCAFS lead to the formation of a sea breeze, which can then spawn deep convection. These convective processes often last 60 minutes or less and pose a significant challenge to the forecasters at the National Weather Service (NWS) Spaceflight Meteorology Group (SMG). The main challenge is that a "GO" forecast for thunderstorms and precipitation is required at the 90 minute deorbit decision for End Of Mission (EOM) and at the 30 minute Return To Launch Site (RTLS) decision at the Shuttle Landing Facility. Convective initiation, timing, and mode also present a forecast challenge for the NWS in Melbourne, FL (MLB). The NWS MLB issues such tactical forecast information as Terminal Aerodrome Forecasts (TAFs), Spot Forecasts for fire weather and hazardous materials incident support, and severe/hazardous weather Watches, Warnings, and Advisories. Lastly, these forecasting challenges can also affect the 45th Weather Squadron (45 WS), which provides comprehensive weather forecasts for shuttle launch, as well as ground operations, at KSC and CCAFS. The need for accurate mesoscale model forecasts to aid in their decision making is crucial. Both the SMG and the MLB are currently implementing the Weather Research and Forecasting Environmental Modeling System (WRF EMS) software into their operations. The WRF EMS software allows users to employ both dynamical cores - the Advanced Research WRF (ARW) and the Non-hydrostatic Mesoscale Model (NMM). There are also data assimilation analysis packages available for the initialization of the WRF model- the Local Analysis and Prediction System (LAPS) and the Advanced Regional Prediction System (ARPS) Data Analysis System (ADAS). Having a series of initialization options and WRF cores, as well as many options within each core, provides SMG and NWS MLB with a lot of flexibility. It also creates challenges, such as determining which configuration options are best to address specific forecast concerns. The goal of this project is to assess the different configurations available and to determine which configuration will best predict warm season convective initiation in East-Central Florida. Four different combinations of WRF initializations will be run (ADAS-ARW, ADAS-NMM, LAPS-ARW, and LAPS-NMM) at a 4-km resolution over the Florida peninsula and adjacent coastal waters. Five candidate convective initiation days using three different flow regimes over East-Central Florida will be examined, as well as two null cases (non-convection days). Each model run will be integrated 12 hours with three runs per day, at 0900, 1200, and 1500 UTe. ADAS analyses will be generated every 30 minutes using Level II Weather Surveillance Radar-1988 Doppler (WSR-88D) data from all Florida radars to verify the convection forecast. These analyses will be run on the same domain as the four model configurations. To quantify model performance, model output will be subjectively compared to the ADAS analyses of convection to determine forecast accuracy. In addition, a subjective comparison of the performance of the ARW using a high-resolution local grid with 2-way nesting, I-way nesting, and no nesting will be made for select convective initiation cases. The inner grid will cover the East-Central Florida region at a resolution of 1.33 km. The authors will summarize the relative skill of the various WRF configurations and how each configuration behaves relative to the others, as well as determine the best model configuration for predicting warm season convective initiation over East-Central Florida.
Watson, Leela R.↗
initMIP-Antarctica: an Ice Sheet Model Initialization Experiment of ISMIP6
Ice sheet numerical modeling is an important tool to estimate the dynamic contribution of the Antarctic ice sheet to sea level rise over the coming centuries. The influence of initial conditions on ice sheet model simulations, however, is still unclear. To better understand this influence, an initial state intercomparison exercise (initMIP) has been developed to compare, evaluate, and improve initialization procedures and estimate their impact on century-scale simulations. initMIP is the first set of experiments of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6), which is the primary Coupled Model Intercomparison Project Phase 6 (CMIP6) activity focusing on the Greenland and Antarctic ice sheets. Following initMIP-Greenland, initMIP-Antarctica has been designed to explore uncertainties associated with model initialization and spin-up and to evaluate the impact of changes in external forcings. Starting from the state of the Antarctic ice sheet at the end of the initialization procedure, three forward experiments are each run for 100 years: a control run, a run with a surface mass balance anomaly, and a run with a basal melting anomaly beneath floating ice. This study presents the results of initMIP-Antarctica from 25 simulations performed by 16 international modeling groups. The submitted results use different initial conditions and initialization methods, as well as ice flow model parameters and reference external forcings. We find a good agreement among model responses to the surface mass balance anomaly but large variations in responses to the basal melting anomaly. These variations can be attributed to differences in the extent of ice shelves and their upstream tributaries, the numerical treatment of grounding line, and the initial ocean conditions applied, suggesting that ongoing efforts to better represent ice shelves in continental-scale models should continue.
ice sheet model↗
Flight inspection data and crack initiation times
Lockheed C-130 service-flight inspection data is reduced by means of fracture mechanics and statistical analysis into a form from which the probability of time to crack initiation and the distribution of initial flaw sizes for various locations on the aircraft can be determined. Crack sizes are normalized by extrapolating a growing crack backwards from its first recorded size to .03 inches (crack initiation size) yielding the time to crack initiation. In a similar fashion, the crack is grown backwards to a time equal to zero to yield an initial flaw size. In order to perform the discussed computations, crack growth constants were computed for each individual location and were analyzed statistically. Statistical distributions were fitted to times to crack initiation and to initial flaw sizes in order to describe their expected behavior. Weibull and Johnson distributions have been found to fit the data reasonably well but for a better fit convolution integrals of Poisson load distributions and Weibull strength distributions are needed.
Johnson, W. S.↗
Methods of sequential estimation for determining initial data in numerical weather prediction
Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear differential equations, in which initial values are known incompletely and inaccurately. Observational data available at the initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic dynamic systems provides a natural approach to such problems. For linear stochastic dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method, for linear models, the optimal combined data assimilation-initialization method is a modified version of the KB filter.
Cohn, S. E.↗