Vinod K. Nagpal

Calculating Confidence Bounds for Reliability Index to Quantify Effect of Distribution Parameter Uncertainty

Probabilistic methods for risk and reliability assessment require knowledge of statistical variation of design parameters. Often the parameters themselves are uncertain. In such cases it is important to quantify the effect of parameter uncertainty on the reliability calculations. Since parameter uncertainty is a reducible uncertainty, the use of confidence interval bounds to quantify the uncertainty in the reliability predictions is preferred. Obtaining confidence bounds for reliability requires characterizing the uncertainty of distribution parameters of the uncertain variables, and calculating confidence intervals for reliability index based on parameter uncertainty. In this paper, we present different options for calculating confidence intervals for reliability when the distributions of the distribution parameters of the uncertain variables are specified. This accuracy, computational cost and limitations of the different methods presented to calculate lower confidence bound of reliability index ( β ) are discussed. The methods are applied to calculating lower confidence bound of reliability index for a simple beam example.

Probabilistic Design and Analysis for System-Level Application

This paper focuses on the computation of system reliability and its application to probabilistic design. While success has been reported with methods for individual components and failure modes, integrating them to estimate overall system-level reliability faces several hurdles, such as integration across multiple levels and multiple physics. Computational effort is a major challenge, especially when evaluating reliability over time and considering progressive damage and interactions among multiple failure mechanisms. This paper discusses techniques to overcome some of these challenges, considering trade-offs between accuracy and efficiency.

Probabilistic structural analysis of ultra efficient engine technology ceramic matrix composite combustor liners

A probabilistic structural analysis of NASAs ultra efficient engine technology (UEET) ceramic matrix composite (CMC) combustor liners has been completed using the NESTEM Code. The purpose was to identify the maximum stress locations and perform a probabilistic structural analysis at these locations on the inner and outer liners for given thermal loadings to determine the probability of failure at these locations. The probabilistic structural analysis included quantifying the influence of uncertainties in material stiffness properties and the coefficient of thermal expansion. Results of the analysis indicate that the circumferential component of stress was the most severe stress component and that the inner liner was more likely to fail than the outer liner. Tests of the combustor liners by general electric aerospace engines (GEAE) qualitatively support the results of this analysis.

Incorporating Distribution Parameter Uncertainty in Reliability Calculation

Probabilistic methods for risk and reliability assessment require knowledge of statistical variation of design parameters. Often the parameters themselves are uncertain. In such cases it is important to understand how parameter uncertainties will affect the reliability measures, probability of failure or reliability index calculations. This article presents the different methods that have been developed to calculate sensitivities of reliability index (beta) or probability of failure (Pf) to the distribution parameters. Different point and interval estimates for reliability measures in the presence of parameter uncertainty are discussed.

A Software Tool Subjecting Component Designs to System-Level Reliability Constraints

A software tool entitled PRODAF (Probabilistic Design and Analysis Framework) is described that demonstrates a practical, multidisciplinary, design-for-reliability methodology for aerospace systems. PRODAF allows system-level reliability constraints to impact component-level designs. The method interfaces user-selected, physics-based deterministic modeling codes with a Fast Probability Integration code to obtain high-fidelity probabilistic component failure rate data. The computed component failure rates are input into a system-level probabilistic risk assessment code such as QRAS or SAPHIRE. A feedback loop from the risk assessment tool to the analysis/design tools enables the system-level reliability constraint to affect the component design. Accuracy measures of the probability calculations (confidence intervals) are provided to account for uncertainties in the uncertainty parameters. Design variable optimization is accelerated through the use of adaptive response surface modeling. On-screen results are presented graphically in terms of CDF/PDF plots and sensitivity charts. The software tool is currently in development.

Potential application of FORM and SORM for PRA

The focus of this paper is two-fold: 1) a discussion of a process by which a probabilistic risk assessments (PRA) system model is used to direct a multi-disciplinary development project. 2) Under this framework, a potential technique for the application of the First-Order Reliability Method (FORM) and Second-Order Reliability Method (SORM) to provide probabilistic failure data for PRA of structural systems. Technique 2) is an elaboration of the analysis techniques described in chapter 14 of [1]. Specifically, the technique relies on the concept of the limit state function in conjunction with varying levels of model fidelity, sound engineering judgment, and expert opinion. This methodology is complementary to the Response Surface Method presented in [2] and is best utilized during the conceptual or preliminary stages of a design project. This technique is beneficial when reliability data is not readily available and/or one is constrained by aggressive development schedules. As the design matures, the events in the system event tree can be systematically re-defined by a process that uses the results of refined physics-based models.

Development of Probabilistic Structural Analysis Integrated With Manufacturing Processes

An effort has been initiated 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. Two physics-based manufacturing process models (one for powdered metal forging and the other for annular deformation resistance welding) have been linked to the NESSUS structural analysis code. This paper describes the methodology developed to perform this integration including several examples. Although this effort is still underway, particularly for full 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 preliminary development.

NESTEM: A Computational Tool to Perform Probabilistic Structural Analysis of Components Subjected to Uncertain Mechanical and Thermal Loading

This paper presents an overview of a newly developed code, NESTEM that analyzes structural components subjected to varying thermal and mechanical loads. This program is an enhanced version of NESSUS and has all the capabilities of NESSUS. In addition, it allows one to perform heat transfer analysis. The basic heat transfer variables can be included as random variables along with the mechanical random variables to quantify risk using probabilistic methods and to perform sensitivity analysis.The analysis capabilities of NESTEM have been demonstrated by analyzing a cylindrical combustor liner. This analysis includes evaluating stresses and their variations at critical points on the liner using material properties, pressure loading and basic heat transfer variables as the random variables. The heat transfer variables are convection temperatures, film coefficients, radiation temperatures, emissivity, absorptivity and conductivity. Cumulative distribution functions and sensitivity factors, for stress responses, for mechanical and thermal random variables are calculated. These results can be used to quickly identify the most critical design variables, in order to optimize the design, to make it cost effective.Copyright