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Evaluators : Dr. Suhail Ahmed

NESSUS presentation : Reliability 1

ReliabilityPresentation-1NESSUS

Introduction

Evaluators :Dr. Suhail Ahmed

Group 1 :Shivaji Grag

Rajat KapoorMradul Awasthi

Devesh Jain

RELIABILITY PRESENTATION : NESSUS 2

Significance of Reliability in Component DesignThe traditional design approach has been to adopt

safety factors to ensure that the risk of failure is sufficiently small, albeit not quantified due to uncertainties in loads, material properties, and geometries with random variables.

However, probabilistic analysis permits a more rigorous quantification of the various uncertainties, and ultimately will facilitate a more efficient design process.



NESSUS-BACKGROUNDNumerical Evaluation of Stochastic Structures Under Stress

The software was originally developed by a team led by Southwest Research Institute (SwRI) as part of the NASA project entitled ‘‘Probabilistic Structural Analysis Methods (PSAM) in 1984 for Select Space Propulsion Components’’ to perform probabilistic analysis of space shuttle main engine components.

SwRI continues to develop and apply NESSUS to a diverse range of problems including aerospace structures, automotive structures, biomechanics, gas turbine engines, geo mechanics, nuclear waste packaging, offshore structures, pipelines, etc.

NESSUS is a modular computer software program for performing probabilistic analysis of structural/mechanical components and systems.

NESSUS combines state-of-the-art probabilistic algorithms with general-purpose numerical analysis methods to compute the probabilistic response and reliability of engineered systems.

Variations in loading, material properties, geometry, boundary conditions, and initial conditions can be simulated.

Evaluators :

Dr. Suhail Ahmed

http://www.swri.org/4org/d18/mateng/matdev/biomech.htm


NESSUS-INTRODUCTIONNumerical Evaluation of Stochastic Structures Under Stress

• NESSUS can perform reliability analyses for multiple components and failure modes, and identify critical random variables and failure modes to support risk assessment.

• NESSUS allows the user to perform probabilistic analysis with analytical models, external computer programs such as commercial finite element codes, and general combinations of the two.

• The NESSUS graphical user interface (GUI) provides a capability for commercial or in-house developed codes to be easily integrated into the NESSUS framework.

• Eleven probabilistic algorithms are available in NESSUS including methods with major being :- Monte Carlo simulation First-Order Reliability Method Advanced Mean Value Method Adaptive Importance Sampling. Point Estimation Method



NESSUSNumerical Evaluation of Stochastic Structures Under Stress



NESSUS-OVERVIEWNumerical Evaluation of Stochastic Structures Under Stress

In NESSUS, component reliability analysis denotes the reliability of a component considering a single failure mode, where reliability is simply one minus the probability of failure, pf.

R = 1 – Pf

NESSUS can compute a single failure probability corresponding to a specific performance value(PDF), or multiple failure probabilities such that the complete cumulative distribution function (CDF) can be constructed.

The PDF provides the ability to predict values of a random variable, such as strength, with some associated probability. Another closely related model for a random variable is the cumulative distribution function, or CDF. Mathematically, the CDF is obtained by integrating the PDF. Thus, the CDF value corresponding to a particular value of strength represents the probability that the strength will be less than or equal to this value.

In other words, given the definition of a limit state, NESSUS computes the probability of failure and the statistical models of all input random variables.



Identification of Limit State Function NESSUS is based on the concept of a limit state that reflects the designer's definition of failure.

Some examples of failures include : (1). A stress or displacement exceeding some limiting value, (2).The natural vibrating frequency of a structure being too close to the operating frequency

of a mechanical component attached to the structure,(3). The number of cycles for a crack to grow to a critical length being less than that expected while in service.

In general, g will be more complex and will be given by g = g(X), where X are the input random variables.

In addition to the failure probability, NESSUS computes :-

Probabilistic Importance Factors, db/du, where b is inversely related to Pf and u are the input random variables transformed into standard normal space.

Probabilistic Sensitivity Factors, db/dФ, where Φ is the parameters of the input random variables, e.g., mean value and standard deviation.

Evaluators :

Dr. Suhail Ahmed


NESSUS-COMPONENT v/s SYSTEM RELIABILITYNumerical Evaluation of Stochastic Structures Under Stress

Component Reliability Analysis :-Single component with single mode of failure. Traditional reliability analysis involves computing the probability of stress, S, exceeding strength, R, Pr[R ≤ S] or Pr[g ≤ 0], where g = R - S is referred to as the limit state function.

System Reliability Analysis :- Most engineering structures can fail in more than one way. System reliability considers the possible failure of multiple components of a system, or multiple failure modes of a component or combination of both.

In NESSUS, system reliability problems are formulated and solved using a Probabilistic Fault Tree Analysis (PFTA) method. A fault tree is constructed in NESSUS by connecting ‘‘bottom events’’ with ‘‘AND’’ and ‘‘OR’’ gates where each bottom event models a separate failure event.



Deterministic v/s Probabilistic Approach• A key output from NESSUS is a CDF of the performance measure associated with a

particular mode of failure. In a design scenario, the CDF can be used in conjunction with a target reliability to obtain the required level of performance.

• A major advantage over the deterministic approach to design is that in contrast to the simple "go-no go" evaluation produced by a traditional analytical approach, probabilistic analysis provides a means of assessing the probability that stress might exceed a certain critical value, and, therefore, a means of predicting the risk of failure.

• Another key output from NESSUS is the relative importance of the input random variables to the performance measure under consideration. The probabilistic sensitivity factors (PSF) identify to the designer which features of a design lead to risk and give some indication as to how to minimize this risk. Thus, using the PSFs, the designer can effectively allocate resources to optimize the structure to provide maximum reliability at minimum cost.

• Conversely, the sensitivity factors also expose which variables are relatively unimportant in reliability, information important in establishing design and manufacturing controls for maximum cost effectiveness as well as structural reliability.



RELIABILITY MODELLING The steps needed to solve a reliability problem in

NESSUS include: (1) develop the functional relationships that define the

model, (2) define the random variable inputs, (3) define the numerical models needed in the

functional relationship, (4) perform parameter variation studies to check and understand the deterministic behavior of the model, (5) perform the probabilistic analysis, (6) visualize the results.Evaluators :

Dr. Suhail Ahmed

RELIABILITY PRESENTATION : NESSUS 11Evaluators : Dr. Suhail Ahmed

PROBLEM IDENTIFICATION Problem statement definition

The problem statement window in NESSUS is where the functional relationships are entered todefine the model.


Random Variable Input Probabilistic Database

PDF & CDF)plotting capability inNESSUS provides a quick visual inspection of the random variables.


In NESSUS, system reliability problems are formulated and solved using a Probabilistic Fault Tree Analysis method. A fault tree is constructed in NESSUS by connecting ‘‘bottom events’’ with ‘‘AND’’ and ‘‘OR’’ gates where each event models a separate failure event.

FAULT TREE ANALYSIS


RESPONSE MODEL DEFINITION

APPLICATION TYPE interfaced codes or a user-defined code. This capability allows users to link developed codes with NESSUSModel type include analytical, regression, numerical, and predefined

NESSUS allows random variables to be defined from the probabilistic database


RESPONSE MODEL DEFINITIONDETERMINISTIC & PROBABILISTIC VARIATION ANALYSIS


RESULT VISUALIZATION


Importance of Design Optimization Method• In addition to quantifying the system reliability,

NESSUS also computes probabilistic sensitivities of the system probability of failure with respect to the each random variables mean value and

standard deviation. • These results provide a ranking based on the

relative contribution of each variable to the total probability of failure.

• The sensitivities are also useful in design optimization, test planning and resource allocation.



Sensitivity analysis

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