Probabilistic structural analysis methods for space propulsion system components

The development of a three-dimensional inelastic analysis methodology for the Space Shuttle main engine (SSME) structural components is described. The methodology is composed of: (1) composite load spectra, (2) probabilistic structural analysis methods, (3) the probabilistic finite element theory, and (4) probabilistic structural analysis. The progress in the development of generic probabilistic models for various individual loads which consist of a steady state load, a periodic load, a random load, and a spike, is discussed. The capabilities of the Numerical Evaluation of Stochastic Structures Under Stress finite element code designed for probabilistic structural analysis of the SSME are examined. Variation principles for formulation probabilistic finite elements and a structural analysis for evaluating the geometric and material properties tolerances on the structural response of turbopump blades are being designed.

In probabilistic structural analysis, the performance or response functions usually are implicitly defined and must be solved by numerical analysis methods such as finite element methods. In such cases, the most commonly used probabilistic analysis tool is the mean-based, second-moment method which provides only the first two statistical moments. This paper presents a generalized advanced mean value (AMV) method which is capable of establishing the distributions to provide additional information for reliability design. The method requires slightly more computations than the second-moment method but is highly efficient relative to the other alternative methods. In particular, the examples show that the AMV method can be used to solve problems involving non-monotonic functions that result in truncated distributions.

A probabilistic structural analysis method (PSAM) is described which makes an approximate calculation of the structural response of a system, including the associated probabilistic distributions, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The method employs the fast probability integration (FPI) algorithm of Wu and Wirsching. Typical solution strategies are illustrated by formulations for a representative critical component chosen from the Space Shuttle Main Engine (SSME) as part of a major NASA-sponsored program on PSAM. Typical results are presented to demonstrate the role of the methodology in engineering design and analysis.

Reliable and efficient vibroacoustic loads prediction is often critical in structural design, yet it remains a challenging task for many applications. Spacecraft structures are characterised by extensive use of composite materials, complex connections between components and various non-trivial geometrical features. Accurate treatment necessitates the construction of highly detailed numerical models, traditionally employing deterministic representations. Simultaneously, the broadband acoustic excitation due to the diffuse sound field experienced during launch requires modelling the fluid domain and solving the resulting elasto-acoustic interaction at = multiple frequencies. To alleviate the computational demand implications for large problem sizes, substructuring and reduction techniques for the structural domain are commonplace, component mode synthesis (CMS) being a framework widely adopted in the aerospace industry. Nevertheless, despite ongoing research, the topic still presents a range of difficulties when a universal, robust method of accounting for model uncertainties is sought. In this study, two CMS based approaches are proposed and evaluated. Firstly, the Craig-Bampton stochastic method (CBSM) is improved via a set of modifications enhancing its efficiency, and subsequently adapted for use in a vibroacoustic setting. Optimal perturbation levels and scope of validity of the technique are established against a probabilistic structural analysis (PSA) simulation for a spacecraft structure. Secondly, a novel stochastic finite element method (FEM) is presented. The underlying mathematical foundation is derived so that uncertainty can naturally be controlled at the subsystem level, in partitions of the corresponding condensed mass and stiffness matrices. This decomposition based approach ensures that realisations of the random matrices have key properties such as positive (semi)definiteness strictly preserved, guaranteeing complete robustness. The method is validated with a spacecraft test case, comparing its predictions against PSA, the improved CBSM and experimental data. A coupling scheme with a hierarchical matrix accelerated boundary element method is formulated, resulting in the construction of a complete stochastic vibroacoustic solver.

An efficient method for probabilistic finite element analysis with application to contact assessment of CANDU fuel channels

An effort has been ongoing to integrate manufacturing process simulations with probabilistic structural analyses in order to capture the important impacts of manufacturing uncertainties on component stress levels and life. A physics-based manufacturing process simulation code has been linked to the NESSUS structural analysis code to analyze annular deformation resistance welding manufacturing process. This paper describes the methodology developed to perform this integration, including an example. Although this effort is underway, particularly for fuller integration of a probabilistic analysis, the progress to date has been encouraging and a software interface that implements the methodology has been developed. The purpose of this paper is to report this development.

The traditional decision-making process during early design stages deals with deterministically evaluating the design candidates in accordance with concrete objectives by assuming optimal or nominal design performance values for the candidates. However, this may increase subjectivity in the decision process since the design knowledge during early design is usually imprecise and incomplete, and mostly needs to be iteratively updated throughout product design development. To diminish the subjectivity, the knowledge of the design requirements can be precisely and accurately represented by means of probabilistic constraints that describe the uncertainties in the design requirements; therefore, in this work, a systematic design framework supported by reliability analysis is developed in such a way that it is able to provide an effective connection among the early design steps especially both at system level and component level. Thus, the probability of failures of the design candidates and their sub-solutions are investigated, based on design constraints with Gaussian distributions, or lower and upper bounds, by utilizing Monte Carlo method. To illustrate the potential applicability and efficacy of the proposed framework, a two-finger gripper design problem is considered. The results clearly demonstrate that the proposed framework is effective to achieve reliable design solutions that have uncertain quantitative characteristics to be used further in probabilistic structural analysis during the next design stages such as embodiment and detail design stages.

All engineering design problems can be characterized by the underlying assumptions around which the problem is formulated. The effect of these assumptions - including everything from general assumptions defining an operating environment to detailed assumptions regarding material properties - is variability in system performance, and resulting deviations from expected performance. Assumptions are made to eliminate uncertainties that would prevent the quantification of design performance. Probabilistic methods have been developed in recent decades to convert such deterministic problem formulations into probabilistic formulations to model and assess the effects of these known uncertainties and thus relax restrictive assumptions. Until very recently, however, the computational expense of probabilistic analysis of a single design has made its application impractical for all but very simplistic design problems. Consequently, probabilistic optimization has been considered prohibitively expensive, particularly for complex multidisciplinary systems. Today a number of enabling technologies are available to support probabilistic design analysis and optimization for complex engineering design problems, including: flexible software frameworks that allow integration and automation of a complex multidisciplinary process; probabilistic analysis and optimization tools that allow uncertainty to be modeled and performance variation to be measured and reduced; large scale parallel processing capabilities leading to greatly increased efficiency; and advanced surrogate modeling capabilities to replace complex nonlinear analyses with computationally efficient approximation models. Along with steady increases in computing power, the combination of these enabling technologies can facilitate effective probabilistic analysis and optimization for complex design problems. In this paper we focus primarily on two of these enabling technologies. We present a comprehensive probabilistic design optimization formulation, a six sigma based approach that incorporates variability within all elements of the formulation - input design variable bound formulation, output constraint formulation, and robust objective formulation. We discuss the applicability of kriging, one surrogate modeling approach that supports the approximation of complex nonlinear analyses, for facilitating probabilistic multidisciplinary design optimization. These enabling technologies, as implemented within the commercial software framework provided by iSIGHT, including capability to facilitate parallel processing, are demonstrated for a multidisciplinary conceptual ship design problem.

Probabilistic fatigue analysis of all-ceramic crowns based on the finite element method

This chapter introduces the basic definitions and methods of probability and statistical analysis, which are the foundation for all work reliability and fire risk analysis, and other topics of this section. With increased availability of sizeable quantities of reliable data on a whole range of topics related to fire protection engineering, it is essential that the analysis of this data be based on sound mathematical principles from probability and statistical theory. The chapter is divided into two main sections: probability theory, and statistics.

An electrical power system is typically operated at least cost given some technical and reliability constraints. To that end, many utilities use deterministic methods such as n−1 criterion in order to ensure reliability. This method though being used worldwide and for a really long time can be expensive as contingencies occur rarely. In order to evaluate power systems, it must be noted that contingencies are stochastic in nature. Since reliability of supply and economic cost must be balanced, probabilistic analysis seems to be one of the tools which can be applied. In the case of generator dispatch, the most recognized probability tool is the Capacity Outage Probability Table (COPT). However, the synthesis of the COPT using the Recursive Method as proposed by Billinton and Allan can be cumbersome. This paper presents an integration of probabilistic and deterministic methods for outage analysis. It shows an alternative method to develop the COPT using a pseudo-deterministic method combined with a Monte Carlo method. Thus, making the process of developing a COPT simpler and can reduce computation time.

Reactor safety and risk are dominated by the potential and major contribution for human error in the design, operation, control, management, regulation and maintenance of the plant, and hence to all accidents. Given the possibility of accidents and errors, now we need to determine the outcome (error) probability, or the chance of failure. Conventionally, reliability engineering is associated with the failure rate of components, or systems, or mechanisms, not of human beings in and interacting with a technological system. The probability of failure requires a prior knowledge of the total number of outcomes, which for any predictive purposes we do not know or have. Analysis of failure rates due to human error and the rate of learning allow a new determination of the dynamic human error rate in technological systems, consistent with and derived from the available world data. The basis for the analysis is the “learning hypothesis” that humans learn from experience, and consequently the accumulated experience defines the failure rate. A new “best” equation has been derived for the human error, outcome or failure rate, which allows for calculation and prediction of the probability of human error. We also provide comparisons to the empirical Weibull parameter fitting used in and by conventional reliability engineering and probabilistic safety analysis methods. These new analyses show that arbitrary Weibull fitting parameters and typical empirical hazard function techniques cannot be used to predict the dynamics of human errors and outcomes in the presence of learning. Comparisons of these new insights show agreement with human error data from the world’s commercial airlines, the two shuttle failures, and from nuclear plant operator actions and transient control behavior observed in transients in both plants and simulators. The results demonstrate that the human error probability (HEP) is dynamic, and that it may be predicted using the learning hypothesis and the minimum failure rate, and can be utilized for probabilistic risk analysis purposes.

The geotechnical properties of municipal solid waste (MSW) in landfills vary considerably depending on the composition, time, and the rate of waste density. This variability in geotechnical properties leads to many uncertainties in the analysis of landfill slope stability. This study, using probabilistic methods investigates the slope stability and the probability of failure of a Kahrizak landfill under the conditions of spatial variability of physical and geotechnical properties of MSW. To achieve this goal, the random field theory has been used with a finite difference numerical method in the framework of the Monte Carlo simulation. MSW’s shear strength parameters such as cohesion and friction angle as well as the unit weight of layers are considered as random variables. An extensive literature review was conducted to address the probable variation of above-mentioned parameters in Kahrizak landfill. The results of several different laboratory researches on MSW samples collected from Kahrizak landfill were also employed in the modelings. Output results are presented in the form of probability distributions of the factor of safety as well as the probability of failure corresponding to these distributions. Moreover, the effect of various parameters such as coefficient of variation and correlation distance of input parameters on these output results has been investigated. The results show that considering the spatial variability in probabilistic methods would help to determine the various mechanisms affecting the performance and the probability of failure of the landfill slope. In addition, the output of such probabilistic analyses can be used as guidance for engineers to design safe and reliable landfill.

Derivation of site-specific remediation goals by incorporating the bioaccessibility of polycyclic aromatic hydrocarbons with the probabilistic analysis method

A computational methodology is described to probabilistically simulate the stress concentration factors (SCF's) in composite laminates. This new approach consists of coupling probabilistic composite mechanics with probabilistic finite element structural analysis. The composite mechanics is used to probabilistically describe all the uncertainties inherent in composite material properties, whereas the finite element is used to probabilistically describe the uncertainties associated with methods to experimentally evaluate SCF's, such as loads, geometry, and supports. The effectiveness of the methodology is demonstrated by using is to simulate the SCF's in three different composite laminates. Simulated results match experimental data for probability density and for cumulative distribution functions. The sensitivity factors indicate that the SCF's are influenced by local stiffness variables, by load eccentricities, and by initial stress fields.