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Scale Mixtures of Frechet Distributions as Asymptotic Approximations of Extreme Precipitation
This paper is a further development of the results of [20] where, based on the negative binomial model for the duration of wet periods measured in days [16], an asymptotic approximation was proposed for the distribution of the maximum daily precipitation volume within a wet period. This approximation has the form of a scale mixture of the Fr´echet distribution with the gamma mixing distribution and coincides with the distribution of a positive power of a random variable having the Snedecor–Fisher distribution. Here we extend this result to the mth extremes, m ∈ ℕ, and sample quantiles. The proof of this result is based on the representation of the negative binomial distribution as a mixed geometric (and hence, mixed Poisson) distribution [17] and limit theorems for extreme order statistics in samples with random sizes having mixed Poisson distributions [10]. Some analytic properties of the obtained limit distribution are described. In particular, it is demonstrated that under certain conditions the limit distribution of the maximum precipitation is mixed exponential and hence, is infinitely divisible. It is shown that under the same conditions this limit distribution can be represented as a scale mixture of stable or Weibull or Pareto or folded normal laws. The corresponding product representations for the limit random variable can be used for its computer simulation. The results of fitting this distribution to real data are presented illustrating high adequacy of the proposed model. It is also shown that the limit distribution of sample quantiles is the well-known Student distribution. Several methods are proposed for the estimation of the parameters of the asymptotic distributions. The obtained mixture representations for the limit laws and the corresponding asymptotic approximations provide better insight into the nature of mixed probability (“Bayesian”) models.
Compatible atmospheres for a space suit, Space Station, and Shuttle based on physiological principles
Fundamental physiological principles have been invoked to design compatible environments for a space suit, Space Station and the spacecraft used to transport the astronauts from earth. These principles include the long-term memory of tissues for a bubble-provoking decompression, the intermittent nature of blood flow in the tight connective tissue(s) responsible for the bends whose incidence in aviators has been shown to be related to bubble volume by the Weibull distribution. In the overall design an astronaut breathing a mixture of 30 percent O2 in N2 for 4-5 h in a spacecraft at 11.9 psia can transfer to a Space Station filled with the same mix at 8.7 psia and, after a further 4-5 h, go EVA at any time without any oxygen prebreathing at any stage. The probable incidence of decompression sickness has been estimated as less than 0.5 percent using the present suit operating at 4.3 psia but the risk could be reduced to zero if the suit pressure were increased to 6.5 psia.
Joint Modeling of Wind Speed and Wind Direction Through a Conditional Approach
Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. In this work, we develop a conditional approach to model these two variables, where the joint distribution is decomposed into the product of the marginal distribution of wind direction and the conditional distribution of wind speed given wind direction. To accommodate the circular nature of wind direction, a von Mises mixture model is used; the conditional wind speed distribution is modeled as a directional dependent Weibull distribution via a two-stage estimation procedure, consisting of a directional binned Weibull parameter estimation, followed by a harmonic regression to estimate the dependence of the Weibull parameters on wind direction. A Monte Carlo simulation study indicates that our method outperforms two other approaches in estimation efficiency: one that utilizes periodic spline quantile regression and another that generates data from the commonly used Abe-Ley distribution for cylindrical data. We illustrate our method by using the output from a regional climate model to investigate how the joint distribution of wind speed and direction may change under some future climate scenarios. Our method indicates significant changes in the variation of wind speed with respect to some directions.
Equibiaxial flexural strength determination of UO 2 using a ball-on-ring test
To increase nuclear fuel performance and reliability, their mechanical properties require an accurate and statistically relevant assessment. Biaxial flexural strength tests provide an alternative to bend bar techniques for assessing mechanical behavior; namely, the transverse rupture strength (TRS) of ceramic samples. Biaxial test samples require simple geometries and minimal surface preparation, reducing fabrication costs and handling hazards. This study investigated the TRS of polycrystalline UO 2 fuel forms at room temperature using a ball-on-ring test fixture. Here, pellets were fabricated from UO 2 powder using conventional powder processing and sintering techniques. The TRS and Weibull parameters were obtained through Weibull statistics on over 60 UO 2 samples tested under equibiaxial flexure. The larger sample size in this study enabled a more robust Weibull statistical analysis than alternative test methods, which may not capture the stochastic failure of typical ceramics. Furthermore, two different loading ball diameters were employed to assess the impact of contact damage on fracture strength. While Hertzian contact damage was observed with the smaller loading ball, the fracture strength remained unaffected. A fracture analysis of the tested UO 2 samples indicated a mixture of intergranular and transgranular fracture that transitions to transgranular fracture with increasing distance from the fracture origin. The characteristic strength of the combined data sets was determined to be 148 MPa, and the Weibull modulus was determined to be 9.1. The TRS values and Weibull parameters were close to values found in the literature for alternative testing techniques using samples with similar microstructure and density. The findings in this study validate the ball-on-ring method used to obtain the TRS of UO 2 with a sample geometry more representative of nuclear fuels. Additionally, experimental TRS results from this study can be implemented in modeling codes to predict fuel performance, which is critical to fuel burnup extension and advanced nuclear fuel technologies.
Establishment of a center of excellence for applied mathematical and statistical research
The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.
High Temperature Mechanical Characterization of Ceramic Matrix Composites
A high temperature mechanical characterization laboratory has been assembled at NASA Lewis Research Center. One contribution of this work is to test ceramic matrix composite specimens in tension in environmental extremes. Two high temperature tensile testing systems were assembled. The systems were assembled based on the performance and experience of other laboratories and meeting projected service conditions for the materials in question. The systems use frames with an electric actuator and a center screw. A PC based data acquisition and analysis system is used to collect and analyze the data. Mechanical extensometers are used to measure specimen strain. Thermocouples, placed near the specimen, are used to measure the specimen gage section temperature. The system for testing in air has a resistance element furnace with molybdenum disilicide elements and pneumatic grips with water cooling attached to hydraulic alignment devices. The system for testing in an inert gas has a graphite resistance element furnace in a chamber with rigidly mounted, water cooled, hydraulically actuated grips. Unidirectional SiC fiber reinforced reaction bonded Si3N4 and triaxially woven, two dimensional, SiC fiber reinforced enhanced SiC composites were tested in unidirectional tension. Theories for predicting the Young's modulus, modulus near the ultimate strength, first matrix cracking stress, and ultimate strength were applied and evaluated for suitability in predicting the mechanical behavior of SiC/RBSN and enhanced SiC/SiC composites. The SiC/RBSN composite exhibited pseudo tough behavior (increased area under the stress/strain curve) from 22 C to 1500 C. The rule of mixtures provides a good estimate of the Young's modulus of the SiC/RBSN composite using the constituent properties from room temperature to 1440 C for short term static tensile tests in air or nitrogen. The rule of mixtures significantly overestimates the secondary modulus near the ultimate strength. The ACK theory provides the best approximation of the first matrix cracking stress when residual stresses are ignored. The theory of Cao and Thouless, based on Weibull statistics, gave the best prediction for the composite ultimate strength. The enhanced SiC/SiC composite exhibited nonlinear stress/strain behavior from 24 C to 1370 C in air with increased ultimate strain when compared to monolithic SiC. The theory of Yang and Chou with the assumption of a frictional fiber/matrix interface provided the best estimate of the Young's modulus. The theory of Cao and Thouless gave the best estimate for the ultimate strength.
Accelerated Stress Testing on Multichannel Drivers—Updated Test Results
This report is the second in a series of studies about accelerated stress testing (AST) of drivers used for SSL luminaires. Two-stage drivers intended for use in downlights, troffers and street lights were selected to undergo exposure to an AST environment consisting of 75°C and 75% relative humidity (7575). The 7575 AST environment was chosen for this study because a previous study demonstrated that 38% of a sample population of 6-inch downlights failed in less than 2,500 hours in these conditions. A mixture of single-channel (i.e., one output current channel designed for use with one LED primary) and multichannel (i.e., separate output current channels designed for use with multiple for LED primaries) two-stage drivers were exposed to the 7575 environment. This report provides updated AST test results for only the multichannel driver products. The multichannel driver population consisted of three products (with two-stage architecture) and a total of five samples. In addition to AST results, the product life distribution (Weibull analysis) of two-stage driver Hammer Test samples is reported.
High Temperature Mechanical Characterization and Analysis of Al2O3 /Al2O3 Composition
Sixteen ply unidirectional zirconia coated single crystal Al2O3 fiber reinforced polycrystalline Al2O3 was tested in uniaxial tension at temperatures to 1400 C in air. Fiber volume fractions ranged from 26 to 31%. The matrix has primarily open porosity of approximately 40%. Theories for predicting the Young's modulus, first matrix cracking stress, and ultimate strength were applied and evaluated for suitability in predicting the mechanical behavior of Al2O3/Al2O3 composites. The composite exhibited pseudo tough behavior (increased area under the stress/strain curve relative to monolithic alumina) from 22 to 1400 C. The rule-of-mixtures provides a good estimate of the Young's modulus of the composite using the constituent properties from room temperature to approximately 1200 C for short term static tensile tests in air. The ACK theory provides the best approximation of the first matrix cracking stress while accounting for residual stresses at room temperature. Difficulties in determining the fiber/matrix interfacial shear stress at high temperatures prevented the accurate prediction of the first matrix cracking stress above room temperature. The theory of Cao and Thouless, based on Weibull statistics, gave the best prediction for the composite ultimate tensile strength.
Producibility of fibrous refractory composite insulation, FRCI 40-20
Fibrous Refractory Composite Insulation (FRCI) is a NASA-developed, second generation, reusable heat-shield material that comprises a mixture of aluminoborosilicate fibers, silica fibers, and silicon carbide. Under NASA contract, a program was conducted to demonstrate the capability for manufacturing FRCI 40-20 billets. A detailed fabrication procedure was written and validated by testing specimens from the first two billets. The material conformed to NASA requirements for density, tensile strength, modulus of rupture, thermal expansion, cristobalite content, and uniformity. Twenty-four billets were prepared to provide 20 deliverable articles. Production billets were checked for density, modulus of rupture, cristobalite content, and uniformity. Billet density ranged from 309.48 to 332.22 kg/cu m (19.32 to 20.74 lb/cu ft) and modulus of rupture from 4690 to 10,140 kPa (680 to 1470 psi). Cristobalite content was less than 1 percent. A Weibull analysis of modulus-of-rupture data indicated a 1.5 percent probability for failure below the specified strength of 4480 kPa (650 psi).
Reliability comparisons between additively manufactured and conventional SiC–Si ceramic composites
Abstract An additively manufactured reaction‐bonded silicon carbide ceramic composite is fabricated using a bimodal powder feedstock and the binder‐jetting printing technique. On fabricating, the ceramic is investigated to report its composition, mechanical, and thermal properties at room temperature and high temperatures (up to 750). The ceramic has a density of 2.76 g/cc, and shows a hardness of 21.74 GPa, and a flexure strength of 207.5 MPa at room temperature. The mechanical property of flexure strength is used to estimate its failure probability under applied stress, using a Weibull distribution. The mechanical properties and failure probabilities are compared with those of conventionally fabricated reaction‐bonded silicon carbide ceramics reported in the literature. These ceramics were fabricated using methods such as slip‐casting, compacting, and tape‐casting. The comparison is used to elucidate the advantages and areas of improvement of the present additive manufacturing technique for reaction‐bonded ceramics.
Evaluation Of Risk And Possible Mitigation Schemes For Previously Unidentified Hazards
This report presents the results of arc track testing conducted to determine if such a transfer of power to un-energized wires is possible and/or likely during an arcing event, and to evaluate an array of protection schemes that may significantly reduce the possibility of such a transfer. The results of these experiments may be useful for determining the level of protection necessary to guard against spurious voltage and current being applied to safety critical circuits. It was not the purpose of these experiments to determine the probability of the initiation of an arc track event only if an initiation did occur could it cause the undesired event: an inadvertent thruster firing. The primary wire insulation used in the Orbiter is aromatic polyimide, or Kapton , a construction known to arc track under certain conditions [3]. Previous Boeing testing has shown that arc tracks can initiate in aromatic polyimide insulated 28 volts direct current (VDC) power circuits using more realistic techniques such as chafing with an aluminum blade (simulating the corner of an avionics box or lip of a wire tray), or vibration of an aluminum plate against a wire bundle [4]. Therefore, an arc initiation technique was chosen that provided a reliable and consistent technique of starting the arc and not a realistic simulation of a scenario on the vehicle. Once an arc is initiated, the current, power and propagation characteristics of the arc depend on the power source, wire gauge and insulation type, circuit protection and series resistance rather than type of initiation. The initiation method employed for these tests was applying an oil and graphite mixture to the ends of a powered twisted pair wire. The flight configuration of the heater circuits, the fuel/oxider (or ox) wire, and the RCS jet solenoid were modeled in the test configuration so that the behavior of these components during an arcing event could be studied. To determine if coil activation would occur with various protection wire schemes, 145 tests were conducted using various fuel/ox wire alternatives (shielded and unshielded) and/or different combinations of polytetrafuloroethylene (PTFE), Mystik tape and convoluted wraps to prevent unwanted coil activation. Test results were evaluated along with other pertinent data and information to develop a mitigation strategy for an inadvertent RCS firing. The SSP evaluated civilian aircraft wiring failures to search for aging trends in assessing the wire-short hazard. Appendix 2 applies Weibull statistical methods to the same data with a similar purpose.