Incorporating System-level Probabilistic Reliability Into the Multi-disciplinary Component Design Process A status report A status report presented to

Incorporating System-level Probabilistic Incorporating System-level Probabilistic Reliability Into the Multi-disciplinary Reliability Into the Multi-disciplinary

Component Design ProcessComponent Design Process

A status reportA status report presented to

Dr. William E. Vesely Manager, Risk Assessment – Code Q, NASA Headquarters

by

N&R Engineering and Management Services, Inc.Parma Heights, Ohio 44130

NRengineering.com

Bill Strack, John Gyekenyesi, and Vinod Nagpal November, 2007

Many Relevant Software Tools Already ExistMany Relevant Software Tools Already ExistN&R Engineering

A user-friendly framework to integrate existing NASA and commercial codes into an overall reliability simulation that accounts for uncertainties and permits data sharing.

Discipline Example code

Constituent-level material properties models CEMCAN

Design modeling codes ANSYS

Finite element modeling structural analysis ANSYS, NESTEM

Manufacturing process models ProCAST

Life prediction methods NASAlife

Probabilistic reliability analysis (PRA) QRAS, SAPHIRE

However:

• These are independent codes that cannot communicate with each other.

• Most of these codes ignore uncertainties – they are deterministic simulations.

What is needed:

Bill Strack

While many of these codes are static, some are dynamic such as NASAlife that account for time varying mechanical and thermal loads, and material properties due to degradation.

Vision for Reliability AnalysesVision for Reliability Analyses

VVision:

Most future reliability analyses will account for uncertainties – both aleatory and epistemic.

Design processes will consider system reliability as a constraint at the component level.

GGoal:

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Develop a physics-based, multi-disciplinary future design tool (PRODAF) that enables this vision -- utilizing existing deterministic codes.

Bill Strack

It would be most useful if the uncertainty impacts were separated into 2 categories -- those caused by aleatory uncertainties and those caused by epistemic uncertainties. Doing so would provide decision makers the ability to allocate resources most effectively. E.g., if lack of information is the major cause of the response uncertainty (epistemic), then gather more data. But if aleotory uncertainties dominate (e.g. intrinsic phenomenon uncertainties), then funding the acquistition of more data won't help much to reduce uncertainty.

Review of PRODAF Development Status

NASA GRC Physics-based Probabilistic Reliability RoadmapNASA GRC Physics-based Probabilistic Reliability RoadmapN&R Engineering

Capability

Year2001 2003 2005 2007 2009

PRODAF

SUA Code AE

1999

PRODAF SBIR Phase I

NESTEM

Applications to real problems

- SBIR Phase II - Code Q

PRODAF: Probabilistic Design and Analysis Framework

Code Q funding

Other funding

Complementary funding sources

Bill Strack

The quest of this vision is summarized here in terms of the projects that have contributed to the overall progress. Some activities were Code-Q sponsored (green) while others were not (blue). An example of each of these projects is shown next.

Example SUA Problem: Probabilistic NASAlifeN&R Engineering

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Example Help Message

Develop a robust online help system to guide users -- select codes and inputs, detect input errors, suggest error recovery strategies.

Example: Provide guidance on how to select a distribution type for new users.

Bill Strack

Illustrating the proposed 2007 augmentation subtasks.

Example Architecture to Implement the PRODAF Vision

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Bill Strack

This is one representative PRODAF achitecture that illustrates the concept. We envision that PRODAF users will create whatever actual architectures they desire. In this example, the process starts with the definition of mission requirements and an initial set of design variable values (yellow). These are inputs to a CAE code such as ANSYS that yields a geometry model for each component of a system. The geometry models are input to physics-based component simulation codes (or empirical-based models if preferred) that produce a set of loads, weights, and performance values. Most of these codes are deterministic, but by interfacing them to a probabilistic tool such as SUA that does Monte-Carlo or FPI analyses, the physics-based output will be probabilistic in the form of CDF curves.This logic is repeated for subsequent design process steps (manufacturing, life prediction) so that eventually we obtain failure probability CDF curves that are fed into a PRA code such as QRAS or SAPHIRE. That is, an ensemble of physics-based component failure CDF's compose the input to a system-level probabilistic risk assessment code that calculates system reliability. The system reliability target value together with the calculated reliability and sensitivity results can be transferred down to the component level as a constraint in an iterative loop that yields component designs influenced by a system-level reliability target.

Main PRODAF User Interface

Bill Strack

This is the main PRODAF user interface. It is composed of a library of available simulation codes in the lefthand pane and a "Design Process Manager" pane on the righthand side. Users can grab codes from the library and add them to the design process diagram. That is, the user configures the design process in the right pane by arranging a sequence of code invocations. Codes may be added or deleted from the library, or rearranged into logical groups under a heading.Codes may be invoked either from the library or from the design process manager, and in most cases either deterministically or probabilistically. Links connect codes and are intended to enable data transfer. However, such data transfer capability usually involves the creation of a specific interface that must be constructed by the user although some will be provided as defaults such as the QRAS Interface illustrated.

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PRODAF Design Space Options

1. Execute the design process for a single design point

2. Perform a parametric design space exploration

3. Optimize a set of design variables – deterministically

4. Optimize a set of design variables – probabilistically

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Example MDO Problem

Turbine engine performance code - fan pressure ratio - compressor pressure ratio

Airplane performance, weight, economics code - wing loading - wing aspect ratio - wing LE sweep angle

Data interface

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PRODAF Optimization Manager

Generalized Reliability Analysis Procedure

Convergence to MPP?

Limit State Approximation Adaptive Response Surface

FORM, SORM, Monte Carlo based on Response Surface

Failure Probability

Initial Focus Region(Centered at Mean Values)

No

Focus Region Update

Minimum Distance in Focus Region Sequential Quadratic Programming

Adaptive Importance Sampling

Design of ExperimentsOptimal Symmetric Latin Hypercube

No

FORM, SORM, MCresults close enough?

Yes

Yes

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Bill Strack

This is the general outline of the response surface procedure. It is a global-local iterative procedure aimed at efficiently modeling the response surface by employing an Optimal Symmetric Latin Hypercube to select points for the DOE, and a sequence of local regions (called focus regions here) to search for the most probable point, MPP. This technique has been successfully used in an automotive application, but needs to be implemented in generic software.

OSLH Design: Example

(a) 9X2 Random LH Design

0

0.125

0.25

0.375

0.5

0.625

0.75

0.875

1

0 0.1250.250.3750.50.6250.750.875 1X1

X2

(b) 9X2 Symmetric LH Design

0

0.125

0.25

0.375

0.5

0.625

0.75

0.875

1

0 0.130.250.38 0.5 0.630.750.88 1X1

X2

(c) 9X2 OSLH Design

0

0.125

0.25

0.375

0.5

0.625

0.75

0.875

1

0 0.130.250.38 0.5 0.630.750.88 1X1

X2

9x2 Latin Hypercube Designs

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Iteration history of searching for the MPPfor x1^3+x2^3-18=0 using quadratic local approximation

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0

X1'

X2

'

Limit StateTrust region 1Trust region 2Trust region 3Trust region 4Approx1Approx2Approx3Approx4Iteration history

MPP Search : Numerical ExampleN&R Engineering

X1’

X2’

Limit state

Focus region 1

Focus region 2

Focus region 3

Focus region 4

Bill Strack

This is a simple illustration of the MPP search technique. It uses an analytic response function and a sequence of "focus regions."

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PRODAF FY2007 Tasks

Provide confidence bounds that account for uncertainties in the uncertainty parameters.

Surrogate adaptive response surface approach for optimization using a 2-phase global/local MPP search method to handle non-linear, implicit limit state functions.

Facilitate physics-based progressive failure modeling of complex systems.

Provide a mechanism for distributed computing capability.

Bill Strack

These are recently initiated tasks. The adaptive response surface approach is useful is situations where the number of uncertainties is relatively large (e.g., more than 8) and the response function evaluation is computationally intense. An approximate response function (i.e., response surface) is a tractable technique provided it is reasonably accurate and does not require too many function evaluations of its own. The distributed computing subtask will free users from having to install all codes on their local computer. Codes and data files may reside anywhere on a network including the Internet.

Component Mean failure probability

Shaft 0.000000001

Disk 0.03511

Fan blade 0.00143

System (shaft, disk, 24 fan blades) 0.06818

Application of PRODAF to Shaft/Disk/24-Blade System 1800 RPM, Tshaft = Tdisk = 600 °F, Tblade = 400-700 °F, Time = 50,000 sec.

System failure probability

CDF

Bill Strack

This is an example of using PRODAF to perform a reliability calculation of a 3-component system composed of a shaft, a disk, and a set of 24 blades. Each component's failure probability was determined using a physics-based code (NESTEM) and the reuslts were fed to QRAS via the QRAS Interface code. The QRAS Interface code modifies the QRAS binary database that holds the reliability information. (As a standalone code, QRAS does not have an option to import externally-generated probability data directly.)

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Current PRODAF Development Tasks

PRODAF Development Task SBIR II Code Q Status

Task 1 – Develop confidence intervals with uncertain uncertainties 75%

Task 2 – Develop rapid adaptive response surface methodology 100%

Task 3 – Develop progressive failure modeling of complex systems 60%

Task 4 – Develop executive code (GUI, distributed computing, help) 80%

Task 5 – Provide automatic code/data interfacing during design process 100%

Task 6 – Interface process-based cost modules such as P-BEAT 2%

Task 7 – Validate code and usefulness with commercial customer (GE) 2%

Task 8 – Provide example applications to relevant NASA problems 25%

Task 9 – Author comprehensive methodology/theory and users manual 55%

Task 10 – Develop robust reliability-based design space optimization 85%

Task 11 – Provide robust online user help system 60%

Task 12 – Establish a code and data management system 90%

SBIR II: “Physics-based Probabilistic Design Tool with System-Level Reliability ConstraintPhysics-based Probabilistic Design Tool with System-Level Reliability Constraint ””

Code Q:Code Q: ““Physics-based Multi-disciplinary PRA Physics-based Multi-disciplinary PRA DDesign esign SSystem for ystem for RReliabilityeliability””

Bill Strack

SBIR II (not Code Q) and DSR (Code Q) tasks are currently underway in a complementary manner. The augmentation tasks are proposed for FY2007 in order to strengthen the capabilities of the PRODAF tool.PRODAF is intended to be a flexible framework that enables users to integrate physics-based codes into the design process including a system-level reliability constraint.

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PRODAF Milestones and Deliverables as Defined in Original Proposal

Methodologies

Software

Deliverables

FY07 FY08

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

1

Methodology Milestones Software Milestones .

1. Response surface methodology and coding complete

2. System-level progressive failure methodology complete

3. Confidence interval methodology complete

4. Code interfaces, cost module, 1st example problem complete

5. Robust design space optimization methodology complete

Deliverables (in addition to quarterly/annual progress reports)

A PRODAF software version 1.0 (includes confidence intervals and response surface features)

B PRODAF software version 2.0 (includes all methodologies/features)

C Final Theoretical Report and Users Manual

3

4

2

B C

4

6. Code/database management system

7. Online help system completed

8. Distributed computing implemented

9. External evaluation/validation complete

10. Ares application examples completed

7

5

1 2 3

A

56 8 9 10

Dr. Satchi VenkataramanSan Diego State University

Dr. Sankaran MahadevanVanderbilt University

PRODAF Project Organization

Confidence interval methodology Optimization with uncertainty

Response surface methodology

System-level progressive failure

Robust design space optimization

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N&R Project Manager

NASA COTRs

Software development

On-line help system

Distributed computing

Mr. William StrackN&R Engineering

Dr. Shantaram S. Pai & Ed Zampino

Dr. John Z. GyekenyesiN&R Engineering

Software testingGeneral Electric

Dr. Vinod K. NagpalN&R Engineering

Life prediction methodology Manufacturing processes Example applications

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FY07 PRODAF Code Q Funding

Proposed Tasks FY07

Validate code and usefulness with commercial customer (GE) 77K

Provide example applications to relevant NASA problems 21

Develop robust reliability-based design space optimization 55

Provide robust online user help system, theory, users manuals 57

Establish a code and data management system 43

Total $253K

Contractual effort: $253K

Funding actually provided in FY07: $110K

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Proposed FY08 PRODAF Code Q Funding

Proposed Tasks FY08

Validate code and usefulness with commercial customer (GE) 90K

Provide example applications to relevant NASA problems 140

Add cost estimating modules to PRODAF 60

Provide theory and users manuals 30

Total $320K

Contractual effort: $320K

PRODAF will provide engineers with user-friendly tools to conduct a broad spectrum of probabilistic reliability analyses using existing deterministic modeling codes. It will provide a practical reliability-based design framework that captures the impact of uncertainties.

SummaryN&R Engineering

Backup Charts

Multiple runs

FortranC/C++Excel spreadsheet

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The Systems Uncertainty Analysis (SUA) Tool

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PRODAF Code Database Manager

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PRODAF Probabilistic Manager

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PRODAF Uncertainty Definition Dialog

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Uncertainty in Statistical Parameters

• Parameters estimated from data with measurement errors– Random and bias errors

• Parameters estimated from limited number of samples – Scenario 1: Actual test data available –small sample size O(10)– Scenario 2: Population distribution and sample size known– Scenario 3: Population distribution known, sample size unknown– Scenario 4: Population distribution unknown, sample size known– Scenario 5: Population distribution and sample size unknown

• Parameters specified by experts (no test data) – Scenario 6: Bounds specified but distribution is not– Scenario 7: Bounds specified with most likely value

Bill Strack

Calculating confidence intervals can be challenging when there is uncertainty in the uncertainty parameters. Various situations are anticipated as listed here, and different approaches are to be considered in dealing with each of these scenarios.

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““Physics-based Multi-disciplinary PRA Design System for ReliabilityPhysics-based Multi-disciplinary PRA Design System for Reliability”” Tasks

Enable automatic code/data interfacing during the design process

Integrate cost module into PRODAF (e.g., NAFCOM) including optimum sparing strategy

Develop NASA-relevant application example

Comprehensive theory and users manuals

Option A Option B

Adv. Development $cx1 $cy1

DDT&E cx2 cy2

Production cx3 cy3

Launch cx4 cy4

LLC $cx $cy

CEV-SM

Bill Strack

These are example subtasks within the Code-Q sponsored task initiated in the spring of 2006.

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Acronyms

CALCE Center for Advanced Life Cycle Engineering’s code to estimate failure probability of printed circuit cards

CEMCAN Ceramic Matrix Composites Analyzer

NASAlife NASA life prediction code

NESTEM Hybrid of NESSUS and CSTEM codes

PRODAF Probabilistic Design and Analysis Framework code

QRAS Quantitative Risk Assessment System (PRA code)

SAPHIRE Systems Analysis Programs for Hands-on Integrated Reliability (PRA code)

SUA Systems Uncertainty Analysis code

Example Probabilistic Analysis Using SUA

SSME Fuel Turbopump Temperature

Critical Space Shuttle reliability component is the SSME high-pressure fuel turbopumps

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Fuel turbopump temperature Probabilistic sensitivity factors

SSME system model

Power Output of the ISS EPS Probabilistic Sensitivities

ISS EPS Uncertainties

Probabilistic Analysis of ISS Electrical Power System (EPS)N&R Engineering

Application of Probabilistic Methods to Honeywell Blade MistuningN&R Engineering

DoD SBIR

QRAS

NESTEM or CALCE

Fetch probabilistic data

Process data to get Pfail

Call Delphi code to modify QRAS DB

Display results to user

Create Delphi input file

Phase I C++ interface code

No provision in QRAS to import component data – uses multiple Paradox binary relational database tables to store internally generated input data.

files

Fetch probabilistic data

Process data to get Pfail

Display results to user

Phase II C++ interface code

Modify QRAS DB

QRAS

NESTEM or CALCE

files

PRODAF NESTEM to QRAS InterfaceN&R Engineering

Example QRAS Interface using NESTEM and CALCEN&R Engineering

Example Architecture for Physics-based Probabilistic Probabilistic Design with System-Level Reliability ConstraintDesign with System-Level Reliability Constraint

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PRODAF

SUA

Code Q

Manufacturing Process Simulation InterfaceN&R Engineering

Development of Probabilistic Structural Analysis Integrated with Deformation Resistance Annular Welding Simulation: Dr. Anantanarayanan, Delphi Energy & Chassis Systems

Residual stress for SS316

ProbDRAW pre-processor

- Import IGES files to DEFORM files

- Convert cdb ANSYS files to DEFORM files

- Setup and run DEFORM

- Integrate with NESTEM

- Integrate with other mfg. simulation codes

Completed

Unfunded

DEFORM Simulation

Underway

Bill Strack

One manufacturing process simulation code has been addressed so far. It is DEFORM which models the deformation resistence annular welding process.This code may be invoked by the pre-processor code ProbDRAW. ProbDRAW converts mainstream geometry files (e.g., IGES or ANSYS cdb files) into DEFORM formatted input files. Integration with NESTEM (currently underway) permits a probabilistic simulation of this manufacturing process using the deterministic DEFORM code.

Documents

Incorporating System-level Probabilistic Reliability Into the Multi-disciplinary Component Design Process A status report A status report presented to