Advanced probabilistic methods for quantifying the effects of various uncertainties in structural response

The effects of actual variations, also called uncertainties, in geometry and material properties on the structural response of a space shuttle main engine turbopump blade are evaluated. A normal distribution was assumed to represent the uncertainties statistically. Uncertainties were assumed to be totally random, partially correlated, and fully correlated. The magnitude of these uncertainties were represented in terms of mean and variance. Blade responses, recorded in terms of displacements, natural frequencies, and maximum stress, was evaluated and plotted in the form of probabilistic distributions under combined uncertainties. These distributions provide an estimate of the range of magnitudes of the response and probability of occurrence of a given response. Most importantly, these distributions provide the information needed to estimate quantitatively the risk in a structural design

Statefinder diagnostic for modified Chaplygin gas cosmology in f(R,T) gravity with particle creation

In this paper, we have studied flat Friedmann--Lema\^{\i}tre--Robertson--Walker (FLRW) model with modified Chaplygin gas (MCG) having equation of state p_{m}=A\rho -% \frac{B}{\rho ^{\gamma }}, where $0\leq A\leq 1$, $0\leq \gamma \leq 1$ and $B$ is any positive constant in }${\footnotesize f(R,T)}${\footnotesize \ gravity with particle creation. We have considered a simple parametrization of the Hubble parameter $H$ in order to solve the field equations and discussed the time evolution of different cosmological parameters for some obtained models showing unique behavior of scale factor. We have also discussed the statefinder diagnostic pair $\{r,s\}$ that characterizes the evolution of obtained models and explore their stability. The physical consequences of the models and their kinematic behaviors have also been scrutinized here in some detail.Comment: 21 pages, 23 figures. arXiv admin note: text overlap with arXiv:1603.02573 by other author

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

PROCESSOR ARCHITECTURES FOR FAST COMPUTATION OF MULTI-DIMENSIONAL UNITARY TRANSFORMS.

This work presents the development of new algorithms and special purpose sequential processor architectures for the computation of a class of one-, two- and multi-dimensional unitary transforms. In particular, a technique is presented to factorize the transformation matrices of a class of multi-dimensional unitary transforms, having separable kernels, into products of sparse matrices. These sparse matrices consist of Kronecker products of factors of the one-dimensional transformation matrix. Such factorizations result in fast algorithms for the computation of a variety of multi-dimensional unitary transforms including Fourier, Walsh-Hadamard and generalized Walsh transforms. It is shown that the u-dimensional Fourier and generalized Walsh transforms can be implemented with a u-dimensional radix-r butterfly operation requiring considerably fewer complex multiplications than the conventional implementation using a one-dimensional radix-r butterfly operation. Residue number principles and techniques are applied to develop novel special purpose sequential processor architectures for the computation of one-dimensional discrete Fourier and Walsh-Hadamard transforms and convolutions in real-time. The residue number system (RNS) based implementations yield a significant improvement in processing speed over the conventional realizations using the binary number system. As an illustration of the factorization techniques developed in this work, novel sequential architectures of RNS-based fast Fourier, Walsh-Hadamard and generalized Walsh transform processors for real-time processing of two-dimensional signals are presented. These sequential processor architectures are capable of processing large bandwidth (\u3e 5 M.Hz) input sequences. The application of the proposed FFT processors for the real-time computation of two-dimensional convolutions is also investigated. A special memory structure to support two-dimensional convolution operations is presented and it is shown that the two-dimensional FFT processor architecture proposed in this work requires less hardware than the conventional implementations. The FFT algorithms and processor architectures are verified by computer simulation.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1981 .N246. Source: Dissertation Abstracts International, Volume: 42-08, Section: B, page: 3366. Thesis (Ph.D.)--University of Windsor (Canada), 1981

Probabilistic structural analysis to quantify uncertainties associated with turbopump blades

A probabilistic study of turbopump blades has been in progress at NASA Lewis Research Center for over the last two years. The objectives of this study are to evaluate the effects of uncertainties in geometry and material properties on the structural response of the turbopump blades to evaluate the tolerance limits on the design. A methodology based on probabilistic approach was developed to quantify the effects of the random uncertainties. The results indicate that only the variations in geometry have significant effects

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

Quantifying uncertainties in the structural response of SSME blades

To quantify the uncertainties associated with the geometry and material properties of a Space Shuttle Main Engine (SSME) turbopump blade, a computer code known as STAEBL was used. A finite element model of the blade used 80 triangular shell elements with 55 nodes and five degrees of freedom per node. The whole study was simulated on the computer and no real experiments were conducted. The structural response has been evaluated in terms of three variables which are natural frequencies, root (maximum) stress, and blade tip displacements. The results of the study indicate that only the geometric uncertainties have significant effects on the response. Uncertainties in material properties have insignificant effects

Distributed Multi-Robot Algorithms for the TERMES 3D Collective Construction System

The research goal of collective construction is to develop systems in which large numbers of autonomous robots build large-scale structures according to desired specifications. We present algorithms for TERMES, a multi-robot construction system inspired by the building activities of termites. The system takes as input a high-level representation of a desired structure, and provides rules for an arbitrary number of simple climbing robots to build that structure, using passive solid building blocks under conditions of gravity. These rules are decentralized, rely on local information and implicit coordination, and provably guarantee correct completion of the target structure. Robots build staircases of blocks (potentially removable as temporary scaffolds) that they can climb to build structures much larger than themselves.Engineering and Applied Science