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At least 217 records · Page 12

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.↗

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.↗

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.↗

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.↗

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.↗

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.↗

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↗

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.↗

Creep life prediction based on stochastic model of microstructurally short crack growth

A nondimensional model of microstructurally short crack growth in creep is developed based on a detailed observation of the creep fracture process of 304 stainless steel. In order to deal with the scatter of small crack growth rate data caused by microstructural inhomogeneity, a random variable technique is used in the model. A cumulative probability of the crack length at an arbitary time, G(bar a, bar t), and that of the time when a crack reaches an arbitary length, F(bar t, bar a), are obtained numerically by means of a Monte Carlo method. G(bar a, bar t), and F(bar t, bar a) are the probabilities for a single crack. However, multiple cracks generally initiate on the surface of a smooth specimen from the early stage of creep life to the final stage. TAking into account the multiple crack initiations, the actual crack length distribution observed on the surface of a specimen is predicted by the combination of probabilities for a single crack. The prediction shows a fairly good agreement with the experimental result for creep of 304 stainless steel at 923 K. The probability of creep life is obtained from an assumption that creep fracture takes place when the longest crack reaches a critical length. The observed and predicted scatter of the life is fairly small for the specimens tested.

Kitamura, Takayuki↗

Making statistical inferences about software reliability

Failure times of software undergoing random debugging can be modeled as order statistics of independent but nonidentically distributed exponential random variables. Using this model inferences can be made about current reliability and, if debugging continues, future reliability. This model also shows the difficulty inherent in statistical verification of very highly reliable software such as that used by digital avionics in commercial aircraft.

Miller, Douglas R.↗

Modelling of SAR polarisation phase difference from trees

The data for polarization phase difference Delta Phi between the HH- and VV-polarized backscattered waves from tree-covered fields were obtained with an airborne synthetic aperture radar at 1.225 GHz. The mean values over tree-covered fields were derived from the images of the phase difference and were examined as a function of incident beam angle from 15 to 55 deg. A theoretical model for simulating these data, based on the electromagnetic wave scatterings from the tree trunk and its branches, both of which are assumed as very long dielectric cylinders was developed. The radius and direction of a tree branch are taken as random variables and are chosen by a Monte Carlo method to encounter the incident waves in producing the scattering events. The Monte Carlo simulated results are in good agreement with the observations within experimental uncertainty.

Mo, Tsan↗

Making statistical inferences about software reliability

Failure times of software undergoing random debugging can be modelled as order statistics of independent but nonidentically distributed exponential random variables. Using this model inferences can be made about current reliability and, if debugging continues, future reliability. This model also shows the difficulty inherent in statistical verification of very highly reliable software such as that used by digital avionics in commercial aircraft.

Miller, Douglas R.↗

NESSUS (Numerical Evaluation of Stochastic Structures Under Stress)/EXPERT: Bridging the gap between artificial intelligence and FORTRAN

The development of a probabilistic structural analysis methodology (PSAM) is described. In the near-term, the methodology will be applied to designing critical components of the next generation space shuttle main engine. In the long-term, PSAM will be applied very broadly, providing designers with a new technology for more effective design of structures whose character and performance are significantly affected by random variables. The software under development to implement the ideas developed in PSAM resembles, in many ways, conventional deterministic structural analysis code. However, several additional capabilities regarding the probabilistic analysis makes the input data requirements and the resulting output even more complex. As a result, an intelligent front- and back-end to the code is being developed to assist the design engineer in providing the input data in a correct and appropriate manner. The type of knowledge that this entails is, in general, heuristically-based, allowing the fairly well-understood technology of production rules to apply with little difficulty. However, the PSAM code, called NESSUS, is written in FORTRAN-77 and runs on a DEC VAX. Thus, the associated expert system, called NESSUS/EXPERT, must run on a DEC VAX as well, and integrate effectively and efficiently with the existing FORTRAN code. This paper discusses the process undergone to select a suitable tool, identify an appropriate division between the functions that should be performed in FORTRAN and those that should be performed by production rules, and how integration of the conventional and AI technologies was achieved.

Fink, Pamela K.↗

Probabilistic structural analysis methods and applications

An advanced algorithm for simulating the probabilistic distribution of structural responses due to statistical uncertainties in loads, geometry, material properties, and boundary conditions is reported. The method effectively combines an advanced algorithm for calculating probability levels for multivariate problems (fast probability integration) together with a general-purpose finite-element code for stress, vibration, and buckling analysis. Application is made to a space propulsion system turbine blade for which the geometry and material properties are treated as random variables.

Cruse, T. A.↗

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, David M.↗

Creep life prediction based on stochastic model of microstructurally short crack growth

A nondimensional model of microstructurally short crack growth in creep is developed based on a detailed observation of the creep fracture process of 304 stainless steel. In order to deal with the scatter of small crack growth rate data caused by microstructural inhomogeneity, a random variable technique is used in the model. A cumulative probability of the crack length at an arbitrary time, G(bar a, bar t), and that of the time when a crack reaches an arbitrary length, F(bar t, bar a), are obtained numerically by means of a Monte Carlo method. G(bar a, bar t), and F(bar t, bar a) are the probabilities for a single crack. However, multiple cracks generally initiate on the surface of a smooth specimen from the early stage of creep life to the final stage. Taking into account the multiple crack initiations, the actual crack length distribution observed on the surface of a specimen is predicted by the combination of probabilities for a single crack. The prediction shows a fairly good agreement with the experimental result for creep of 304 stainless steel at 923 K. The probability of creep life is obtained from an assumption that creep fracture takes place when the longest crack reaches a critical length. The observed and predicted scatter of the life is fairly small for the specimens tested.

Kitamura, Takayuki↗

Screening actuator locations for static shape control

Correction of shape distortion due to zero-mean normally distributed errors in structural sizes which are random variables is examined. A bound on the maximum improvement in the expected value of the root-mean-square shape error is obtained. The shape correction associated with the optimal actuators is also characterized. An actuator effectiveness index is developed and shown to be helpful in screening actuator locations in the structure. The results are specialized to a simple form for truss structures composed of nominally identical members. The bound and effectiveness index are tested on a 55-m radiometer antenna truss structure. It is found that previously obtained results for optimum actuators had a performance close to the bound obtained here. Furthermore, the actuators associated with the optimum design are shown to have high effectiveness indices. Since only a small fraction of truss elements tend to have high effectiveness indices, the proposed screening procedure can greatly reduce the number of truss members that need to be considered as actuator sites.

Haftka, Raphael T.↗

Probabilistic analysis of bladed turbine disks and the effect of mistuning

Probabilistic assessment of the maximum blade response on a mistuned rotor disk is performed using the computer code NESSUS. The uncertainties in natural frequency, excitation frequency, amplitude of excitation and damping are included to obtain the cumulative distribution function (CDF) of blade responses. Advanced mean value first order analysis is used to compute CDF. The sensitivities of different random variables are identified. Effect of the number of blades on a rotor on mistuning is evaluated. It is shown that the uncertainties associated with the forcing function parameters have significant effect on the response distribution of the bladed rotor.

Shah, A. R.↗