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Stochastic approximation theory to obtain algorithms for recovery of functions, using noisy measurements taken at randomly selected points
The study reported here explored the development and utility of a spline representation of the sample quantile function of a continuous probability distribution in providing a functional description of a random sample and a method of generating random variables. With a spline representation, the random samples are generated by transforming a sample of uniform random variables to the interval of interest. This is useful, for example, in simulation studies in which a random sample represents the only known information about the distribution. The spline formulation considered here consists of a linear combination of cubic basis splines (B-splines) fit in a least squares sense to the sample quantile function using equally spaced knots. The following discussion is presented in five parts. The first section highlights major results realized from the study. The second section further details the results obtained. The methodology used is described in the third section, followed by a brief discussion of previous research on quantile functions. Finally, the results of the study are evaluated.
OBJECTIVE: To evaluate a new system, ISAID (Internet-based Semi-automated Indexing of Documents), and to generate textbook indexes that are more detailed and more useful to readers. DESIGN: Pilot evaluation: simple, nonrandomized trial comparing ISAID with manual indexing methods. Methods evaluation: randomized, cross-over trial comparing three versions of ISAID and usability survey. PARTICIPANTS: Pilot evaluation: two physicians. Methods evaluation: twelve physicians, each of whom used three different versions of the system for a total of 36 indexing sessions. MEASUREMENTS: Total index term tuples generated per document per minute (TPM), with and without adjustment for concordance with other subjects; inter-indexer consistency; ratings of the usability of the ISAID indexing system. RESULTS: Compared with manual methods, ISAID decreased indexing times greatly. Using three versions of ISAID, inter-indexer consistency ranged from 15% to 65% with a mean of 41%, 31%, and 40% for each of three documents. Subjects using the full version of ISAID were faster (average TPM: 5.6) and had higher rates of concordant index generation. There were substantial learning effects, despite our use of a training/run-in phase. Subjects using the full version of ISAID were much faster by the third indexing session (average TPM: 9.1). There was a statistically significant increase in three-subject concordant indexing rate using the full version of ISAID during the second indexing session (p < 0.05). SUMMARY: Users of the ISAID indexing system create complex, precise, and accurate indexing for full-text documents much faster than users of manual methods. Furthermore, the natural language processing methods that ISAID uses to suggest indexes contributes substantially to increased indexing speed and accuracy.
Low-density carbon fiber preforms, used as thermal protection systems (TPS) materials for planetary entry systems, have permeable, highly porous microstructures consisting of interlaced fibers. Internal gas transport in TPS is important in modeling the penetration of hot boundary-layer gases and the in-depth transport of pyrolysis and ablation products. The gas effective diffusion coefficient of a porous material must be known before the gas transport can be modeled in material response solvers; however, there are very little available data for rigid fibrous insulators used in heritage TPS.The tortuosity factor, which reflects the efficiency of the percolation paths, can be computed from the effective diffusion coefficient of a gas inside a porous material and is based on the micro-structure of the material. It is well known, that the tortuosity factor is a strong function of the Knudsen number. Due to the small characteristic scales of porous media used in TPS applications (typical pore size of the order of 50 micron), the transport of gases can occur in the rarefied and transitional regimes, at Knudsen numbers above 1. A proper way to model the gas dynamics at these conditions consists in solving the Boltzmann equation using particle-based methods that account for movement and collisions of atoms and molecules.In this work we adopt, for the first time, the Direct Simulation Monte Carlo (DSMC) method to compute the tortuosity factor of fibrous media in the rarefied regime. To enable realistic simulations of the actual transport of gases in the porous medium, digitized computational grids are obtained from X-ray micro-tomography imaging of real TPS materials. The SPARTA DSMC solver is used for simulations. Effective diffusion coefficients and tortuosity factors are obtained by computing the mean-square displacement of diffusing particles.We first apply the method to compute the tortuosity factors as a function of the Knudsen number for computationally designed materials such as random cylindrical fibers and packed bed of spheres with prescribed porosity. Results are compared to literature values obtained using random walk methods in the rarefied and transitional regime and a finite-volume method for the continuum regime. We then compute tortuosity factors for a real carbon fiber material with a transverse isotropic structure (FiberForm), quantifying differences between through-thickness and in-plain tortuosities at various Knudsen regimes.
Aerospace structures and spacecraft are a complex assemblage of structural components that are subjected to a variety of complex, cyclic, and transient loading conditions. Significant modeling uncertainties are present in these structures, in addition to the inherent randomness of material properties and loads. To properly account for these uncertainties in evaluating and assessing the reliability of these components and structures, probabilistic structural mechanics (PSM) procedures must be used. Much research has focused on basic theory development and the development of approximate analytic solution methods in random vibrations and structural reliability. Practical application of PSM methods was hampered by their computationally intense nature. Solution of PSM problems requires repeated analyses of structures that are often large, and exhibit nonlinear and/or dynamic response behavior. These methods are all inherently parallel and ideally suited to implementation on parallel processing computers. New hardware architectures and innovative control software and solution methodologies are needed to make solution of large scale PSM problems practical.
Liapunov method used to obtain sufficient conditions for buckling stability of long cylindrical shells with random imperfections
A method is developed for predicting the probability of stress-corrosion fracture of structures under random loadings. The formulation is based on the cumulative damage hypothesis and the experimentally determined stress-corrosion characteristics. Under both stationary and nonstationary random loadings, the mean value and the variance of the cumulative damage are obtained. The probability of stress-corrosion fracture is then evaluated using the principle of maximum entropy. It is shown that, under stationary random loadings, the standard deviation of the cumulative damage increases in proportion to the square root of time, while the coefficient of variation (dispersion) decreases in inversed proportion to the square root of time. Numerical examples are worked out to illustrate the general results.
Thermal conductivity and tensile properties (elastic modulus, proportional limit strength, inplane tensile strength, and strain to failure) of a SiC/SiC composite were experimentally determined at 816 and 1204 C. Tests were performed at room temperature on the same material to obtain interlaminar shear and tensile strength. For each thermal and mechanical property 24 tests were conducted to capture the variation. A random sampling method was used to quantify the variability exhibited by the mean values of the thermal and mechanical properties. The minimum number of tests required to characterize the mean value of each thermal or mechanical property for the composite was determined by varying the group size of the random sample.
Despite high mortality rates, elder self-neglect is characterized by refusal of medical and social interventions. To date there have been no tested clinical interventions in elders who self-neglect. Previous research from the TEAM Institute has shown significantly low vitamin D levels in this population. This study aimed to determine the feasibility of a clinical intervention. Replacement of vitamin D was chosen because of its ease of administration and favorable safety profile. Methods: A randomized clinical trial using directly observed therapy of vitamin D was conducted using 50 elders, >65 years of age, with Adult Protective Services (APS) validated self-neglect. A staggered intervention with waiting controls was used to maximize statistical power. One-third (n=17) of the group was administered 50,000 IU vitamin D2 (ergocalciferol) monthly and the remainder (n=33) were administered 400 IU monthly. Serum 25-OH vitamin D was assessed at baseline and 5-months. Results: 69% agreed to participate in the study and of those n=40 (80%) remained at 5-months. At baseline, 12% (n=7) were deficient in vitamin D (<30nmol/L) and approximately 38% (n=22) had inadequate vitamin D levels (<50nmol/L). The baseline 25-OH vitamin D level was 59 nmol/L +25 (mean SD), and increased significantly to 72nmol/L +21 nmol/L at 5-months. Conclusion: These data are the first to provide evidence that clinical interventions are feasible in elders who self-neglect. The increase in vitamin D levels confirmed that the study personnel were able to successfully intervene community-dwelling elders with self-neglect. This study sets the precedent for future intervention and prevention studies
The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.
The 'cleanroom' software development process is a technical and organizational approach to developing software with certifiable reliability. Key ideas behind the process are well structured software specifications, randomized testing methods and the introduction of statistical controls; but the main point is to deny entry for defects during the development of software. This latter point suggests the use of the term 'cleanroom' in analogy to the defect prevention controls used in the manufacturing of high technology hardware. In the 'cleanroom', the entire software development process is embedded within a formal statistical design, in contrast to executing selected tests and appealing to the randomness of operational settings for drawing statistical inferences. Instead, random testing is introduced as a part of the statistical design itself so that when development and testing are completed, statistical inferences are made about the operation of the system.
A novel method for implementing aerodynamic data dispersion analysis is herein introduced. A general mathematical approach combined with physical modeling tailored to the aerodynamic quantity of interest enables the generation of more realistically relevant dispersed data and, in turn, more reasonable flight simulation results. The method simultaneously allows for the aerodynamic quantities and their derivatives to be dispersed given a set of non-arbitrary constraints, which stresses the controls model in more ways than with the traditional bias up or down of the nominal data within the uncertainty bounds. The adoption and implementation of this new method within the NASA Ares I Crew Launch Vehicle Project has resulted in significant increases in predicted roll control authority, and lowered the induced risks for flight test operations. One direct impact on launch vehicles is a reduced size for auxiliary control systems, and the possibility of an increased payload. This technique has the potential of being applied to problems in multiple areas where nominal data together with uncertainties are used to produce simulations using Monte Carlo type random sampling methods. It is recommended that a tailored physics-based dispersion model be delivered with any aerodynamic product that includes nominal data and uncertainties, in order to make flight simulations more realistic and allow for leaner spacecraft designs.
A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.
Maximum sample excursions of Kiefer-Wolfowitz stochastic approximation processes
Generalized random walk method presented as master equation in nonequilibrium statistical mechanics
Linear transformation method for random data vector reduction by matrix algebra
Random variable method of analyzing propulsion system performance and stage inert weight of two stage rocket vehicles
The report provides a status report and description of THE ALOHA SYSTEM research project at the University of Hawaii. THE ALOHA SYSTEM involves the analysis and construction of advanced methods of random access communications in large computer-communication systems. The existing ALOHA SYSTEM computer-communication network uses two 24,000 baud channels in the UHF band. The system employs message switching techniques similar to those of the ARPANET, in conjunction with a novel form of random access radio channel multiplexing. By means of these techniques the system has the capacity to accommodate several hundred active users of alphanumeric consoles on the two channels available. Each of these users can transmit and receive at a peak data rate of 24,000 baud although the average data rate of the users must of course be considerably less.