The Role of Uncertainty Quantification in Model Verification and Validation. Part 4 NESSUS Overview

Transcription

1 The Role of Uncertainty Quantification in Model Verification and Validation Part 4 NESSUS Overview 1

2 NESSUS Overview Short Course on Probabilistic Analysis and Uncertainty Quantification Southwest Research Institute San Antonio, Texas

3 NESSUS NESSUS is a modular computer software system 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. Uncertainty in loading, material properties, geometry, boundary conditions and initial conditions can be simulated. Many deterministic modeling tools can be used such as finite element, boundary element, hydrocodes, and user-defined Fortran subroutines. NESSUS offers and wide range of capabilities, a graphical user interface, and is verified using hundreds of test problems. NESSUS was initially developed by SwRI for NASA 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, geomechanics, nuclear waste packaging, offshore structures, pipelines, and rotordynamics. To accomplish this, the codes have been interfaced with many well-known third-party and commercial deterministic analysis programs.

4 NESSUS 9.7 Probabilistic Analysis Software Inputs -Java-based graphical user interface -Free format keyword interface -18 probability density functions -Correlated random variables Outputs -Cumulative distribution function -Prob. of failure given performance -Performance given prob. of failure -Probabilistic sensitivity factors -Confidence Bounds -Empirical CDF and histogram Results Visualization -XY, bar, pie charts -Comparison of multiple solutions Deterministic Analysis -Parameter variation analysis -Design of Experiments (DOE) Probabilistic Analysis Methods -First-order reliability method (FORM) -Second-order reliability method (SORM) -Fast probability integration (FPI) -Advanced mean value (AMV+) -Response surface method (RSM) -Monte Carlo simulation (MC) -Importance sampling (ISAM) -Latin hypercube simulation (LHS) -Adaptive importance sampling (AIS) -Hybrid method (AMV+/AIS2) -Probabilistic fault-tree (PFTA) -Efficient global reliability analysis (EGRA) -Importance sampling at MPP (ISMPP) -Gaussian process RSM (GPRSM) -Global sensitivities Copyright 2014, Southwest Research Institute. All Rights Reserved Further Information 210/ Applications -Component/system reliability -Reliability-based optimization -Reliability test planning -Inspection scheduling -Design certification -Risk-based cost analysis -MVFO probability contouring -Model Validation Performance Functions -Analytical (direct) -Numerical (FEM, CFD, other) -Dynamically linked libraries -Gaussian process models Interfaces -ABAQUS/Standard/Explicit -MSC.NASTRAN -ANSYS -NASA/GRC-FEM -DYNA/PARADYN -LS-DYNA -MADYMO -NASA analysis modules -NASGRO -User-defined -MATLAB -CTH -WCN Other -Automated restart -Batch processing -Distributed processing support Hardware -Windows -Linux -Mac OS X

5 Getting Started Log into your nanohub account Open the workspace tool Open an xterm In the xterm use p nessus Download the svn repository svn checkout uq4mm Or update the svn repository svn update NESSUS.sh (this launches the NESSUS software)

6 Getting Started Starting a session create a new analysis file load an existing analysis file The file menu can also be used

7 Problem Outline Outline guides the user through the problem setup Verification of input Problem Definition performance function random variables Deterministic analysis Parameter Variations Design of Experiments Probabilistic Analysis Results Visualization

8 Project Information Problem title Multi-line description (currently text only)

9 Problem Statement Central part of the user interface Syntax highlighting blue functions green variables brown intrinsics black - numbers red - error Each line represents a separate evaluation Variables are assigned constant values, analytical expressions, model responses, or random variables Variable and function names are limited to 8 characters

10 Problem Statement Sequential models are evaluated from the bottom up The top equation is the performance measure Standard Fortran syntax is used for equations Addition: + Subtraction: - Multiplication: * Division: / Exponents: ** (a = a**b)

11 Problem Statement Supported intrinsic functions: sqrt, exp, log, log10, sin, cos, tan, cotan, atan, asin, acos, sinh, cosh, tanh, abs, int Right mouse click in problem statement window for a list of intrinsic functions The argument for trigonometric intrinsics use radians

12 Problem Statement Things to remember when defining the problem statement Equations are evaluated from the bottom up Variable and function names are limited to 8 characters Press the "Apply" button to apply changes

13 Edit Random Variables Random variables can be defined in the Problem Statement or the Edit Random Variables sections.

14 Edit Random Variables Variables are defined by moments or natural parameters

15 Define Correlations Correlation coefficients are defined between variables that are not statistically independent Linear correlation

16 Problem Definition Defining the problem statement and variables completes the problem definition for analytical functions. Deterministic Analysis Mean run: no other definitions required Parameter Variation: define perturbed values of variables Probabilistic Analysis Define analysis type and method at a minimum

17 Deterministic Analysis Use the deterministic analysis option to: Verify problem definition Explore model sensitivities via parameter variation studies Mange multiple model runs Set up and run design of experiments (DOE)

18 Deterministic Analysis Table interface manages deterministic runs Each row is a run, each column a variable Values specified in standard normal or original units Mean value run Edit, import, save runs Blank cells: Mean value is used for that input

19 Example

20 Deterministic Analysis Visualize Results Standard Deviations Variable Values

21 Probabilistic Analysis The main strength of the NESSUS program

22 Set Confidence Bounds Confidence bounds are used to put an upper and lower bound on the probability of failure based on uncertainty in the mean and standard deviation of a random variable.

23 Set Analysis Type Compute the performance value given the probability (inverse reliability problem) Compute the probability given the performance. Used for reliability analysis (P[g<0]) NESSUS selects points to cover the CDF between +- 5 standard deviations Global sensitivity analysis

24 Specify Analysis Data Specify performance levels or probability levels Not required by Full CDF Analysis

25 Set Analysis Method NESSUS has 17 probabilistic methods Some methods require additional input but defaults are provided Methods may have advanced settings to for the user to have additional control of the algorithm Some methods only supported for certain analysis types

26 Perform Analysis Only the final performance variable in the problem statement can be used for probabilistic analysis

27 Visualize Results XY plots of CDF and sensitivity factors Bar charts of probabilistic sensitivities Table of CDF results

28 DEFINING A RESPONSE SURFACE MODEL IN NESSUS

29 Problem Statement Use function notation to define problem statement Function name is user-defined (max 8 characters) Additional equations can be added either before or after the response surface

30 Random Variables Assign distributions to the random variables

31 Define Response Model: Model Type

32 Polynomial Regression Models 3 choices for polynomial regression NESSUS provides 4 options for the regression model type Polynomial regression models may be defined using either data or coefficients Uninitialized regression training data

33 Gaussian Process Options NESSUS provides 2 options for defining Gaussian Process model: User-provided training data Previously saved GP model