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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1983

Statistical Analysis of a Debugging Model

Suppose that a system is undergoing a sequence of trials and design changes in an effort to find and eliminate design flaws in the system. Specifically, suppose that each trial is classified as an assignable cause failure (if the failure is due to one or more design flaws), an inherent failure (if the failure is not due to a design flaw), or a success. After each assignable cause failure, the design flaws that caused the failure are removed. In the case of statistically independent and identical design flaws, a probabilistic model is developed to describe this debugging process. Explicit expressions are obtained for the distributions of the important random variables and for the important measures of reliability. Statistical methods are developed for estimating the parameters of the model from accumulated test data.

Siegrist, K.↗
NASA NTRS1984

Advanced reliability method for fatigue analysis

When design factors are considered as random variables and the failure condition cannot be expressed by a closed form algebraic inequality, computations of risk (or probability of failure) may become extremely difficult or very inefficient. This study suggests using a simple and easily constructed second degree polynomial to approximate the complicated limit state in the neighborhood of the design point; a computer analysis relates the design variables at selected points. Then a fast probability integration technique (i.e., the Rackwitz-Fiessler algorithm) can be used to estimate risk. The capability of the proposed method is demonstrated in an example of a low cycle fatigue problem for which a computer analysis is required to perform local strain analysis to relate the design variables. A comparison of the performance of this method is made with a far more costly Monte Carlo solution. Agreement of the proposed method with Monte Carlo is considered to be good.

Wu, Y.-T.↗
NASA NTRS1984

Computing approximate random Delta v magnitude probability densities

This paper describes the development and use of an algorithm to compute approximate statistics of the magnitude of a single random trajectory correction maneuver (TCM) Delta v vector. The TCM Delta v vector is modeled as a three component Cartesian vector each of whose components is a random variable having a normal (Gaussian) distribution with zero mean and possibly unequal standard deviations. The algorithm uses these standard deviations as input to produce approximations to (1) the mean and standard deviation of the magnitude of Delta v, (2) points of the probability density function of the magnitude of Delta v, and (3) points of the cumulative and inverse cumulative distribution functions of Delta v. The approximates are based on Monte Carlo techniques developed in a previous paper by the author and extended here. The algorithm described is expected to be useful in both pre-flight planning and in-flight analysis of maneuver propellant requirements for space missions.

Chadwick, C.↗
NASA NTRS1984

Reliability considerations for the total strain range version of strainrange partitioning

A proposed total strainrange version of strainrange partitioning (SRP) to enhance the manner in which SRP is applied to life prediction is considered with emphasis on how advanced reliability technology can be applied to perform risk analysis and to derive safety check expressions. Uncertainties existing in the design factors associated with life prediction of a component which experiences the combined effects of creep and fatigue can be identified. Examples illustrate how reliability analyses of such a component can be performed when all design factors in the SRP model are random variables reflecting these uncertainties. The Rackwitz-Fiessler and Wu algorithms are used and estimates of the safety index and the probablity of failure are demonstrated for a SRP problem. Methods of analysis of creep-fatigue data with emphasis on procedures for producing synoptic statistics are presented. An attempt to demonstrate the importance of the contribution of the uncertainties associated with small sample sizes (fatique data) to risk estimates is discussed. The procedure for deriving a safety check expression for possible use in a design criteria document is presented.

Wirsching, P. H.↗
NASA NTRS1985

Probabilistic Finite Element Development

The probabilistic finite element computer program known as Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) is being developed for the analysis of critical structural components for reusable space propulsion systems. First year efforts involve the formulation of the probabilistic analysis strategy and the development of a probabilistic linear analysis code. The ultimate goal of the 3-year program is the development of a finite element code capable of performing nonlinear dynamic analysis of structures having stochastic material properties, geometry, and boundary conditions and subjected to random loading. Three levels of sophistication are envisioned for the stochastic description of the structural problem, namely: (1) homogeneous random variable for stiffness, mass, damping, and external loading; (2) stochastic characterization of variables at the element level, with specified interelement correlations; and (3) stochastic interpolation of variables within a finite element. Two alternative probabilistic analysis methods will be developed, allowing for all three levels of modeling sophistication.

Nagtegaal, J.↗
NASA NTRS1982

Computer program for prediction of capture maneuver probability for an on-off reaction controlled upper stage

A FORTRAN coded computer program which computes the capture transient of a launch vehicle upper stage at the ignition and/or separation event is presented. It is for a single degree-of-freedom on-off reaction jet attitude control system. The Monte Carlo method is used to determine the statistical value of key parameters at the outcome of the event. Aerodynamic and booster induced disturbances, vehicle and control system characteristics, and initial conditions are treated as random variables. By appropriate selection of input data pitch, yaw and roll axes can be analyzed. Transient response of a single deterministic case can be computed. The program is currently set up on a CDC CYBER 175 computer system but is compatible with ANSI FORTRAN computer language. This routine has been used over the past fifteen (15) years for the SCOUT Launch Vehicle and has been run on RECOMP III, IBM 7090, IBM 360/370, CDC6600 and CDC CYBER 175 computers with little modification.

Knauber, R. N.↗
NASA NTRS1985

Exponential order statistic models of software reliability growth

Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

Miller, D. R.↗
NASA NTRS1984

Multiobjective optimization in structural design with uncertain parameters and stochastic processes

The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

Rao, S. S.↗
NASA NTRS1980

Solid-propellant rocket motor internal ballistics performance variation analysis, phase 5

The results of research aimed at improving the predictability of internal ballistics performance of solid-propellant rocket motors (SRM's) including thrust imbalance between two SRM's firing in parallel are presented. Static test data from the first six Space Shuttle SRM's is analyzed using a computer program previously developed for this purpose. The program permits intentional minor design biases affecting the imbalance between any two SMR's to be removed. Results for the last four of the six SRM's, with only the propellant bulk temperature as a non-random variable, are generally within limits predicted by theory. Extended studies of internal ballistic performance of single SRM's are presented based on an earlier developed mathematical model which includes an assessment of grain deformation. The erosive burning rate law used in the model is upgraded and made more general. Excellent results are obtained in predictions of the performances of five different SRM's of quite different sizes and configurations. These SRM's all employ PBAN type propellants with ammonium perchlorate oxidizer and 16 to 20% aluminum except one which uses carboxyl terminated butadiene binder. The only non-calculated parameters in the burning rate equations that are changed for the different SRM's are the zero crossflow velocity burning rate coefficients and exponents. The results, in general, confirm the importance of grain deformation. The improved internal ballistic model makes practical development of an effective computer program for application of an optimization technique to SRM design which is also demonstrated. The program uses a pattern search technique to minimize the difference between a desired thrust-time trace and one calculated based on the internal ballistic model.

Sforzini, R. H.↗
NASA NTRS1986

Optimal partitioning of random programs across two processors

The optimal partitioning of random distributed programs is discussed. It is concluded that the optimal partitioning of a homogeneous random program over a homogeneous distributed system either assigns all modules to a single processor, or distributes the modules as evenly as possible among all processors. The analysis rests heavily on the approximation which equates the expected maximum of a set of independent random variables with the set's maximum expectation. The results are strengthened by providing an approximation-free proof of this result for two processors under general conditions on the module execution time distribution. It is also shown that use of this approximation causes two of the previous central results to be false.

Nicol, D. M.↗
NASA NTRS1986

Exponential order statistic models of software reliability growth

Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

Miller, D. R.↗
NASA NTRS1986

Software reliability modeling and analysis

A discrete and, as approximation to it, a continuous model for the software reliability growth process are examined. The discrete model is based on independent multinomial trials and concerns itself with the joint distribution of the first occurrence time of its underlying events (bugs). The continuous model is based on the order statistics of N independent nonidentically distributed exponential random variables. It is shown that the spacings between bugs are not necessarily independent or exponentially (geometrically) distributed. However, there is a statistical rationale for viewing them so conditionally. Some identifiability problems are pointed out and resolved. In particular, it appears that the number of bugs in a program is not identifiable. Estimated upper bounds and confidence bounds for the residual program eror content are given based on the spacings of the first k bugs removed.

Scholz, F.-W.↗
NASA NTRS1985

Advanced reliability methods for structural evaluation

Fast probability integration (FPI) methods, which can yield approximate solutions to such general structural reliability problems as the computation of the probabilities of complicated functions of random variables, are known to require one-tenth the computer time of Monte Carlo methods for a probability level of 0.001; lower probabilities yield even more dramatic differences. A strategy is presented in which a computer routine is run k times with selected perturbed values of the variables to obtain k solutions for a response variable Y. An approximating polynomial is fit to the k 'data' sets, and FPI methods are employed for this explicit form.

Wirsching, P. H.↗
NASA NTRS1987

Statistical analysis of the 70 meter antenna surface distortions

Statistical analysis of surface distortions of the 70 meter NASA/JPL antenna, located at Goldstone, was performed. The purpose of this analysis is to verify whether deviations due to gravity loading can be treated as quasi-random variables with normal distribution. Histograms of the RF pathlength error distribution for several antenna elevation positions were generated. The results indicate that the deviations from the ideal antenna surface are not normally distributed. The observed density distribution for all antenna elevation angles is taller and narrower than the normal density, which results in large positive values of kurtosis and a significant amount of skewness. The skewness of the distribution changes from positive to negative as the antenna elevation changes from zenith to horizon.

Kiedron, K.↗
NASA NTRS1987

The NESSUS finite element code

The objective of this development is to provide a new analysis tool which integrates the structural modeling versatility of a modern finite element code with the latest advances in the area of probabilistic modeling and structural reliability. Version 2.0 of the NESSUS finite element code was released last February, and is currently being exercised on a set of problems which are representative of typical Space Shuttle Main Engine (SSME) applications. NESSUS 2.0 allows linear elastostatic and eigenvalue analysis of structures with uncertain geometry, material properties and boundary conditions, which are subjected to a random mechanical and thermal loading environment. The NESSUS finite element code is a key component in a broader software system consisting of five major modules. NESSUS/EXPERT is an expert system under development at Southwest Research Institute, with the objective of centralizing all component-specific knowledge useful for conducting probabilistic analysis of typical Space Shuttle Main Engine (SSME) components. NESSUS/FEM contains the finite element code used for the structural analysis and parameter sensitivity evaluation of these components. The task of parametrizing a finite element mesh in terms of the random variables present is facilitated with the use of the probabilistic data preprocessor in NESSUS/PRE. An external database file is used for managing the bulk of the data generated by NESSUS/FEM.

Dias, J. B.↗
NASA NTRS1987

NESSUS/expert and NESSUS/FPI in the Probabilistic Structural Analysis Methods (PSAM) program

The Numerical Evaluation of Stochastic Structures under Stress (NESSUS) is the primary computer code being developed in the NASA Probabilistic Structural Analysis Methods (PSAM) project. It consists of four modules NESSUS/EXPERT, NESSUS/FPI, NESSUS/PRE and NESSUS/FEM. This presentation concentrates on EXPERT and FPI. To provide an effective interface between NESSUS and the user, an expert system module called NESSUS/EXPERT is being developed. That system uses the CLIPS artificial intelligence code developed to NASA-JSC. The code is compatible with FORTRAN, the standard language for codes in PSAM. The user interacts with the CLIPS inference engine, which is linked to the knowledge database. The perturbation database generated by NESSUS/FEM and managed in EXPERT is used to develop the so-called response or performance model in the random variables. Two independent probabilistic methods are available in PSAM for the computation of the probabilistic structural response. These are the Fast Probability Integration (FPI) method and Monte Carlo simulation. FPI is classified as an advanced reliability method and has been developed over the past ten years by researchers addressing the reliability of civil engineering structures. Monte Carlo is a well-established technique for computing probabilities by conducting a number of deterministic analyses with specified input distributional information.

Burnside, O. H.↗
NASA NTRS1987

Probabilistic SSME blades structural response under random pulse loading

The purpose is to develop models of random impacts on a Space Shuttle Main Engine (SSME) turbopump blade and to predict the probabilistic structural response of the blade to these impacts. The random loading is caused by the impact of debris. The probabilistic structural response is characterized by distribution functions for stress and displacements as functions of the loading parameters which determine the random pulse model. These parameters include pulse arrival, amplitude, and location. The analysis can be extended to predict level crossing rates. This requires knowledge of the joint distribution of the response and its derivative. The model of random impacts chosen allows the pulse arrivals, pulse amplitudes, and pulse locations to be random. Specifically, the pulse arrivals are assumed to be governed by a Poisson process, which is characterized by a mean arrival rate. The pulse intensity is modelled as a normally distributed random variable with a zero mean chosen independently at each arrival. The standard deviation of the distribution is a measure of pulse intensity. Several different models were used for the pulse locations. For example, three points near the blade tip were chosen at which pulses were allowed to arrive with equal probability. Again, the locations were chosen independently at each arrival. The structural response was analyzed both by direct Monte Carlo simulation and by a semi-analytical method.

Shiao, Michael↗
NASA NTRS1987

A probabilistic Hu-Washizu variational principle

A Probabilistic Hu-Washizu Variational Principle (PHWVP) for the Probabilistic Finite Element Method (PFEM) is presented. This formulation is developed for both linear and nonlinear elasticity. The PHWVP allows incorporation of the probabilistic distributions for the constitutive law, compatibility condition, equilibrium, domain and boundary conditions into the PFEM. Thus, a complete probabilistic analysis can be performed where all aspects of the problem are treated as random variables and/or fields. The Hu-Washizu variational formulation is available in many conventional finite element codes thereby enabling the straightforward inclusion of the probabilistic features into present codes.

Liu, W. K.↗