SINDA/FUINT For Advanced Design 에이블맥스㈜. Page 2 CAE ENGINEEREING TOTAL SOLUTION 목차 1.Introduction to Optimization 2.Automated

SINDA/FUINTFor

Advanced Design

에이블맥스㈜

Page 2CAE ENGINEEREING TOTAL SOLUTION http://www.ablemax.co.kr

목차

1. Introduction to Optimization2. Automated Determination of Worst Case Scenario3. Automating Model Calibration to Test Data4. Statistical Design: Reliability Engineering Module

Introduction To

Optimization

에이블맥스㈜


Purpose of this Class

The Solver is a high-level analysis module It is a way of tasking SINDA/FLUINT and/or Thermal Desktop It goes beyond the traditional “point design evaluation” mode of

steady-states and transients Optimize (minimize weight, maximize performance) Correlate (calibrate a model to test data) Fine the worst-case design scenario Estimate the reliability of a design Optimize the design for reliability

A related module, Reliability Engineering, is available for statistically evaluating the uncertainties in a design


What Kind of Problems can The Solver Solve?

Typical tasks:– What heater power and interface pad conductance will keep the

temperature of a component within its upper and lower limits during various design cases, while requiring minimal electrical power?

– What should the flow rate and coolant loop line diameter be such that a component is kept at 20°C, while keeping the peak pumping power less than 20W?

– Given three thermal balance tests and the transient changes in between, what are the best-estimate values for the bolted joint conductance, the thermal mass of the batteries, and the dissipation rate of the transformer?

The Solver ...– Aids in preliminary design sizing and selections– Allows a user to solve for input values given desired responses

■ Any parameter can become an output variable (an unknown)– Helps optimize existing point designs– Can be used to automatically correlate (calibrate) models to test data– Automates the search for worst-case scenarios: design case definition


Symbols & Registers: A Quick Review

Symbols are Thermal Desktop (TD) user variables Registers are SINDA/FLUINT (S/F) user variables Symbols and registers are independent by default. Otherwise:

– Symbols may be sent to S/F as initial values for registers– In the Dynamic Mode, S/F may send back register values as new symbol

values, and might command new calculations based on those changes


Symbols and Registers

TD Symbols S/F Registers

Properties,dimensions,trajectories,etc.

Set points,Dissipations,K-factorsetc.

COMMONTO BOTH

Sent as initial conditions(via Case Set Manager)

Optionally sent back indynamic mode(e.g., CALL TDSETREG)


The Solver in a Nutshell

SINDA/FLUINT autonomously changes one or more registers until some analysis objective, as defined by the user, is met– Registers are a “control panel” of “knobs” for centralized model changes– The Solver assumes control of one or more “knobs” on the control panel– Using the Dynamic Mode, the registers to be changed might also be TD

symbols, and updated TD calculations might be required Goal seeking

– Find an input value given a response (the “reverse problem”)– Example: find the conductivity such that T10 = 100.0 ... T→k, not k→T

Optimization– Minimize or maximize something subject to arbitrary constraints– Example: find the minimum heater power such that T10 > -20.0 at all times

Calibration to Test Data– Find the values of uncertainties that best fit available test data– Example: find the contact conductance by comparing with test data

Worst-Case Scenario Definition– Find the values of uncertainties/variations that generate the hot case, cold case ...


Symbols and Registers… and Design Variables




Sent as design variables(via Dynamic->Design tab)

Sent back indynamic mode(CALL TDSETDES)

DesignVariables


Optimization Terms

Objective– What is to be maximized, minimized, or meet some target value?

What distinguishes a good design from a better one? Design Variables

– What inputs can be changed as needed to achieve the objective?– Or, what are the unknowns that need to be determined?

Constraints– What are the limits on the design variables?– What criteria distinguish a viable design from a useless one?

■ perhaps some complex function of the predicted performance Evaluation Procedure

– What analytic operations (steady states, transients, etc.) are required to evaluate a given design? What calculations are required to answer these questions:■ What is the value of the objective for a given set of design values?■ Did this design satisfy or violate the constraints? By how much?


Quick Verbal Example

Minimize the mass of a fin (extended surface) for a given root temperature and environment by varying its length and thickness, but don’t accept a fin efficiency of less than 80%.

Objective– the mass ( = length * thickness * width * density)

Design variables– two: the length and the thickness

Constraints– one: fin efficiency > 0.80 (a response calculated by SINDA/FLUINT

and/or Thermal Desktop) Evaluation Procedure

– given a length and a thickness ...■ calculate the current mass (the value of the objective)■ find the steady state, calculate the fin efficiency (the constraint)


Optimization Terms: Illustrated


Optimization Terms: Objective

The purpose of the analysis: that which is being maximized or minimized

■ The mass (to be minimized)■ The performance metric (to be maximized)■ The error between test data and predictions (to be minimized when

correlating)■ The difference between the desired (target) value of an input

parameter and the current value (to be minimized when goal seeking)■ The maximum/minimum temperature experienced (when seeking

hot/cold design cases) Examples:

■ Minimize the mass of a fin■ Objective: the current mass (of the design being evaluated)

■ Maximize the performance of the fin■ Objective: the fine efficiency of the current design

■ Minimize the number of cycles for a thermostatic heater■ Objective: the number of cycles required by the current design


Optimization Terms: Design Variables

The variables that can be changed to meet the objective■ These are the unknowns for which the Solver must estimate a value

Goal Seeking:The unknown value (a traditional input variable, for example)

Optimization:Anything that needs to be sized or selected

Calibration and Worst-case Definition:The unknown value (a traditional input variable, for example)

■ Contact conductance, bond line thickness, as-built insulation performance, optical properties, natural convection film coefficient, head loss coefficient

■ Environmental temperature, humidity, orbital beta angle, trajectory, angle of attack, altitude, etc.

■ Can be applied as a unit multiplying factor to retrofit a old model The objective might itself be a design variable!

■ Example: Fine the minimum length fin that is 80% efficient■ Or the objective might be a simple function of design variables(i.e., not

a function of predicted performance)


Optimization Terms: Constraints

Those criteria which distinguish a valid design from a useless one

■ Despite appearances, constraints are more similar to the objective than to design variables: like the objective, constraints help guide or restrict the solution

Side Constraints■ Fixed limits on the values of design variables

■ Example: the outer diameter cannot exceed 3cm Configuration Constraints

■ More complex (formula-based) limits on the values of design variables■ Example: the outer diameter must be at least 0.5cm greater than

the inner diameter Performance Constraints

■ Arbitrarily complex, user-defined limits, perhaps requiring an S/F and TD evaluation to measure the relative success or failure of a design

■ Example: the temperature of component must never exceed 100 degrees


Optimization Terms: Evaluation Procedure

The method by which the user tells the Solver how suitable a design is

At the start of evaluation procedure:■ The user is given a new set of design values: a point design■ This design will never violate fixed side constraints■ This design usually won’t violate configuration constraints, and if it does

it won’t by much, but the user must tolerate a certain degree of violation

■ This design will often violate performance constraints, since they are as yet unknown (they have not yet been evaluated)

By the end of the evaluation procedure■ The user must have provided a new value of OBJECT

■ Example: set OBJECT to the current fin efficiency■ The user must have similarly updated any constraint variables

■ Example: set the current value of a constrained temperature The procedure consists of whatever calculations are needed

to update the values of the objective and constraint functions “Calculations” can be made by S/F, TD, or user (logic, expressions)


Calling Hierarchy

Point Design Analysis (Traditional Usage):

– SINDA/FLUINT calls …■ OPERATIONS, which calls …

STEADY (for example)

With Solver:

– SINDA/FLUINT calls …■ OPERATIONS, which calls …

SOLVER, which calls …

» PROCEDURE, which calls …

STEADY (for example)

(Green denotes user choice)


A Quick Demo: Heated Bar

Aluminum bar, 1m long with 5cm x 5cm cross section, painted white (e=0.8), heated at one end (100W). Radiates to deep space. Initially at 100°C (uniform).

Normal question: How hot does the heated end get in 1000 seconds?


A Quick Demo: Heated Bar (Cont’d)

Possible Solver Questions: What power causes the hot end to reach 200°C in 1000 seconds?

Goal seeking, with the design variable power, and objective is the temperature reached at 1000 seconds (goal: 200°C).

Does not need the TD dynamic mode to solve since no geometric calculations are involved

Leaving power at 100W, what cross section (width, height) causes the same result (200°C hot end at 1000 seconds)? Goal seeking again (design variable is width=height), but this time

dynamic mode is needed What is the minimum mass bar that causes the hot end to reach

200°C (and no more) in 1000 seconds? True optimization: design variables are width, height, and length.

Objective is width*height*length (to be minimized) Constraint: final end temperature < 200°C

For a realistic answer, might add more constraints on shape, such as0.5 < width/height < 20.01 < width/length < 1


Heated Bar Goal Seeking(TD Demo)

Assuming height=width, what width causes the bar to reach 200°C in 1000 seconds?

Design variable: widthEvaluation procedure: transient simulationConstraints: noneObjective:

Method 1: Run transient for 1000 seconds.Objective=end temp., Goal=200

Method 2: Run transient until end reaches 200°C.Objective=end time, Goal=1000

Either way, the Solver changes widthuntil the Objective equals the Goal


Explaining Optimization: The Hill Climbing Analogy

The Solver is like a hill climber, trying to find the highest (or lowest) point on a hillside covered with fences and potentially rough terrain

OBJECTIVE■ A hill to be climbed to find the summit (if maximizing)

Design Variables■ The map coordinates the climber may follow■ If there are N design variables, the “design space” is N dimensional

Constraints■ Fences that may be encountered along the way; there may be many■ These often prevent the summit from being reached

Evaluation Procedure■ Altimeter: what is the current elevation?

The climber is nearly blind: it cannot see very far and must stop often and test the local shape of the hillside, and the shape of any fences it finds.


Hill Climbing, Illustrated


How the Solver Works

Finding a search direction■ Perturb each of the N design variables

■ Requires N evaluations of the objective and the constraints■ Find the shape of the local “terrain” by calculating the partial

derivatives of the objective and all active constraints to each design variable

■ If at an infeasible point, go towards the nearest feasible region■ Otherwise, initially head in the direction of steepest ascent

Searching■ Move linearly along the chosen search direction until:

■ Either a new constraint becomes active■ Or a local maximum (“ridge”) is found

■ Typically requires 3 to 10 more evaluations Perturb and fine a new search direction (varies by method

selected) New direction may be nearly tangential to a constraint, but is usually not

in the direction of steepest ascent even if no constraints are active


Summary so Far(for reference)

SOLVER is a high-level solution routine that may be called from OPERATIONS When called, SOLVER does the following:

Changes one or more design variables subject to limits and user constraints until OBJECT is as close as it can be to GOAL Design variables are a subset of registers Registers may also be TD symbols

To evaluate a particular design (e.g., a set of design values), Solver calls updates the model and then calls PROCEDURE

PROCEDURE: Arbitrary set of instructions, including BUILD/BUILDF statements and calls to solution

routines By the time PROCEDURE returns, the user is expected to provide fresh values of

OBJECT and any named constraint variables To pass design variables back to TD and update: CALL TDSETDES Then, to refresh the current case in TD before an S/F solution: CALL TDCASE After calculating OBJECT, send back to TD for display: CALL TDOBJ More detailed controls and communications are available: see TD manual

Anything that can go in OPERATIONS can go in PROCEDURE Usually OBJECT and constraint variables are updated at the end of PROCEDURE, but

they may be calculated initially, or cumulatively, or as part of an expression, etc.


Design Space Scanning

Explore design space (range of possible design variable values) and/or find good starting point for Solver All utilities return best values found (per objective and

constraints) Each design variable must have both upper and lower limits for

these utilities DVSWEEP

Parametric sweep of a single design variable. DSCANFF

Full factorial scan of multiple design variables. Example: 4 design variables sampled 3 values each (low,

medium, high): 3*3*3*3=81 calls DSCANLH

Latin hypercube scan of multiple design variables: each design variable uniquely sampled NLOOPO times

Recommended prescan for Solver


Example Latin Hypercube

Two dimensional design space with sampling resolution of five In other words: two design variables A and B ranging from AL to AH, BL to

BH, and NLOOPO=5 Two possible samplings (DSCANLH chooses randomly each time it is

called)

Each parameter is therefore sampled NLOOPO times: it doesn’t cost much to try different values of a variable that doesn’t make much difference


Prescanning: Find a good starting point

Call DSCANLH before SOLVER in OPERATIONS

NLOOPO = 20 $ test each design variable at NLOOPO values CALL DSCANLH $ prescan! NLOOPO = 200 $ allow Solver more procedures to do its work CALL SOLVER $ optimize!

Helps avoid various problems, including poor initial conditions Almost mandatory for model calibration and worst-case scenario seeking Cost of prescan usually pays for itself in reduced Solver work

However … Requires each design variable to have both upper and lower limits Equality constraints or tightly limited constraints can yield no valid

solution Use OFFCST call to temporarily disable selected constraints during the prescan Or use temporary tolerancing on tight constraints during the prescan (see

manual)

Automated Determination of Worst Case Scenario

에이블맥스㈜


Automating Each Phase of the Design Process


Worst-case Design Scenarios

The first step in a design process is to identify the worst-case scenarios The design will be developed and tested against these scenarios:

their revision often forces a design change. For thermal: one “hot case” and one “cold case” as a minimum

Currently: Margins and uncertainties are stacked up Conditions that can’t possibly happen or co-exist (e.g., BOL

properties combined with EOL dissipations, or steady-state at the subsolar point or within a planetary shadow)

This is called the “Coffin Corner” approach It is often unclear what stack-up or combinations yield the

worst case, especially with articulating components and complex dissipation


The Problem

Despite the criticality of the results, cost of searching for the worst case scenarios can be prohibitive The number of cases grows geometrically Most older software does not facilitate repeated runs nor take

advantage of previous solutions In complex missions, the search must be repeated many times

during design development Approaches are informal (since no standards exist) and rarely

efficient. Common approaches: Full factorial (FF) search (all possible combinations of discretized

uncertainties) Monte Carlo (MC) search (hundreds to thousands of randomized

samples: a “shotgun” approach)


New Technology

Parametric Software and APIs (e.g., MS Excel) Repeated runs can be scripted and searches automated Special effort spent minimizing recalculation costs

Latin Hypercube (LH) Scan : SINDA/FLUINT DSCANLH Requires fewer samples than full factorial or Monte Carlo

NLP (Gradient-based Optimization) Search: SINDA/FLUINT Solver

Directly seeks the worst case with minimum evaluations Hybrid LH/NLP Method Future: Elimination of search-then-design; the elimination of

worst-case scenarios altogether


Demonstration Problem

Simple Sample Problem 3-axis stabilized LEO (300km) nadir-facing box 2-axis tracking solar panel on leading side (+X) 1-axis scanning (+/- 30o) paraboloid dish on trailing side (-X) 60W “payload” with 600W 10minute pulse on the +Z face SPV/CPV NiH “battery” on the –Z face, realistic

charge/discharge/trikcle-charge profiles vs. shadow +Y and –Y faces are fully utilized as radiators Thermal Desktop model available upon request

What is the hot case beta angle, dish position, and start time for the power pulse?


Sample Problem Definition


Sample Problem Definition


Tools Used

Thermal Desktop/RadCAD for thermal/radiation model 15 orbit points, steady state plus 2 transient orbits per evaluation

for cyclic convergenceThermal Desktop “Dynamic Mode:” SINDA/FLUINT commands changes and recalculations as geometry/orbits change Per SINDA/FLUINT statistical analysis and optimization routines:

DSCANLH and SOLVER Total time to evaluate one case (all radiation and conduction

recalculations, steady/transient simulations): 45 seconds on a 2.2 GHz Pentium 4.


Full Factorial Scan (4x3x4=48 evaluations)

4 beta angles: 0, 30, 60, 90 3 scan angles: -30, 0, 30 4 pulse start times: 0, 1600, 3200, 4800 sec. from sobsolar

point


Latin Hypercube Explained

For N samples made, each parameter uniquely sampled 1/N times

For 2 variables A and B, if N=5:


Latin Hypercube Results

N=20 Samples (usually <20% of FF method) Example: b = 2.25, 6.75, 11.25, … 87.75

Found hotter temperatures in less evaluations: (note: this method is statistical: your mileage will vary slightly.)


Nonlinear Programming (optimization) Approach

Instead of “What is the best design” ask “What is the worst case?” Best design: vary A, B, C to minimize cost Worst case: what combination of A, B and C yield the maximum

temperature (hot case)?Good news: finds the worst point, not just nearby point

Bad news: sensitive to initial conditions Number of evaluations unknown (usually 20 to 100) Requires one search per component Might ‘stall’ at a local minimum

This isn’t serious for design optimization, but is more troublesome for test data calibration and acute for worst-case seeking


Using the Solver for Worst-case Seeking

Uncertainties Use design variables as environmental, mission uncertainties Easy to retrofit to a model as unit multiplying factors

Objective Maximize and/or minimize the design concern, for example:

Maximum temperature excursion Maximum heater power required Minimum battery power remaining

Evaluation Procedure Whatever solutions or series of solutions to stress design

The final set of such conditions is what is sought Can be just SINDA/FLUINT, or can include Thermal Desktop

calculations (e.g.: fine the worst-case beta angle)


Hybrid Method

Find good starting point with quick (say N=10) LH scan Finish off with NLP (Solver) Overcomes both initialization sensitivity of NLP and

discretization limitation of LH. The cost of LH “prescan” usually pays for itself in reduced NLP evaluations


Results Discussion: Sample Model

Results Battery peaked at intermediate beta angle: too low and the –Z

face doesn’t get much sun, too high and the battery isn’t used Payload peaked at fuller sun (high beta, but less than 90!) and

when pulse began near the subsolar point In retrospect:

Beta angle was the most important Pulse start time was of intermediate importance Scan angle for the dish was not important

FF and MC waste time resolving unimportant parameters. Discrete sampling like LH preserves the resolution of important parameters.


Battery’s Hot Case


Payload’s Hot Case


Conclusions

Existing statistical analysis and optimization tools can significantly reduce the cost (and improve the accuracy) of worst-case searches

Just like model calibration to test data, another nasty task has been automated

Automating Model Calibration to Test Data

에이블맥스㈜


Model Calibration to Test Data (aka “correlation”)

Thermal/fluid models are dominated by uncertainties■ Contact conductance■ Natural convection coefficients■ Surface optical properties■ Pressure losses in complex components■ As-built insulation performance

Calibration is critical■ Thermal/fluid models are often just intelligent extrapolations of known

test data to untestable conditions

Yet without the Solver, test data correlation is:■ Extremely time consuming■ Unstructured and informal

■ No procedures, methods, tools, or acceptance criteria■ Little mathematical basis for resulting “correlation”

■ Universally despised by analysts


Calibration as “Optimization?” Yes: Minimize Error

The Solver can find the best design…■ What dimensions, materials, etc. result in the least mass, the best

performance, etc.?

Or it can find the best model of a fixed design…■ What values of uncertainties result in the best fit to test data?

User has complete control over:■ The uncertainties to vary

■ By how much, in what order (if not simultaneous)■ The comparison procedure

■ A single steady state run■ A single transient run (end-point or cumulative comparison)■ A complex series of runs or test cases

■ The determination of a best fit■ Least squares, minimized maximum error, etc.


Using the Solver for Model Calibration

Correlation Parameters■ Use design variables as correlation parameters■ Choose the degree of uncertainty in each, apply as limits■ Easy to retrofit to a model as unit multiplying factors

Objective■ Minimize the difference between test and predictions■ Least squares or RMS: minimize the square root of the mean of squared

differences■ MINIMAX: minimize the maximum deviation

Comparison Procedure■ Whatever solutions or series of solutions to produce comparison■ Comparison can be singular (At the end of the solution), or cumulative

(accrued during the solution), weighted based on relative importance of comparison points, etc.

■ Can be just SINDA/FLUINT, or can include Thermal Desktop calculations (e.g.: find the best-fit emissivity)


Quick Verbal Example

Consider a fin (extended surface) heated at the root with a specified room air temperature, cooled by a fan

■ Root temperatures are known at three different base heater settings

What single convection coefficient best explains all test data points? Objective

■ Minimize the least square error between measured and predicted root temperatures:

OBJECT = SQRT ( ( Tm,1 – Tp,1)2 + (Tm,2 – Tp,2)2 + (Tm,3-Tp,3)2 )

“Design Variables” (aka Correlation Parameters)■ One: the convection coefficient “HCONV”

Constraints■ None (other than maybe lower and upper limits on HCONV)

Evaluation Procedures■ Given a current value of HCONV:

■ Run three steady-state at each of the three power levels to predict root temperature

■ After each steady-state, sum the squared error in OBJECT (see above)■ After all three solutions are completed, take the square root of OBJECT


Correlation Support Routines

Correlation involves handling and comparing a lot of data COMPARE

■ Compare two arrays (one test data, one predictions)■ Generate a report, or return values for the Solver

PREPLIST■ Prepare a COMPARE array given a list of node/lump/path IDs

PREPDAT1■ Prepare a COMPARE test data array from interpolations of singlet or

bivariate arrays

PREPDAT2■ Prepare a COMPARE test data array from tabular data (such as might

come from Excel or an electronic data logger)


TD Demo:Find the Properties of a Rod Given Axial Temperature Profile

A 1m long, 1cm diameter rod of unknown conductivity and surface emissivity is used to suspend a 40K LH2 tank from a 300K chamber wall

The radiation environment can be considered an effective “sink temperature” but its value is unknown

Test data is taken for the temperature profile along the rod■ Miraculously, these points correspond to the node locations when the resolution is 20

and edge nodes are used:

What is the rod conductivity, surface emissivity, and effective chamber radiation temperature that corresponds to (best explains) the above temperatures?


TD Demo:Using MINIMAX

Define “errmax” on Symbol Manager







Statistical Design: Reliability Engineering

Module

에이블맥스㈜


Reliability Engineering: Introduction

Treat uncertainties and unknowns statistically, not deterministically.

What is the resulting reliability?


Symbols and Registers… and Random Variables




Sent as design variables(via Dynamic->Design tab)

Sent back indynamic mode(CALL TDSETRAN)

RandomVariables


Using Reliability Engineering

Identify which registers are to be used as random variables These are the uncertainties in dimensions, environment, properties, etc. Define the way in which each random variable varies: its distribution

function Uniform: upper and lower bound only Normal (Gaussian): mean and standard deviation (or coef. of variation) Array: table of probability vs. value (truncated Gaussian, triangular “Witch’s Hat,”

Weibull, Chi-square, log normal, test data, etc.) Optionally, provide a list of arbitrarily complex reliability constraints

(responses and the limits on those responses that define failure: failure limits is perhaps a better term) Example: “The design fails if this temperature exceeds 100°C. Will it

happen?”Paraphrasing: “What are the chances that this temperature will exceed 100°C?”

These are cheap. Add lots of them, or use postprocessing for hindsight. Provide an arbitrarily complex evaluation procedure

Use any solution within SINDA/FLUINT to calculate how well any one design instance behaves relative to the reliability constraints

Reliability estimation routines perturb the random variables to determine the chances of each reliability constraint being violated


Using Reliability Engineering, Cont’d

Three different methods are available to predict reliability: SAMPLE: Monte Carlo sampling. (Typical: 1000 evaluations)

Simple random perturbations. Slow but powerful. DSAMPLE: Descriptive sampling. (Typical: 100 evaluations)

Breaks distributions into NLOOPR equal chunks. Much faster than SAMPLE, but was NLOOPR enough?

RELEST: Gradient method. (Typical: 5 to 10 evaluations) Makes a few assumptions: not applicable in all cases. Much faster than DSAMPLE, but were approximations OK?

Routine SAMPLE DSAMPLE RELEST

Method Monte Carlo Sampling Descriptive Sampling Gradient Method

Speed Slow Intermediate Fast

Convergence Detected? Yes No No

Fixed Execution Cost? No Yes Yes

Finds Overall Reliability?

Yes Yes No

Cumulative? Yes Somewhat No

Applicability? Unlimited Unlimited Limited. Assumes: - Gaussian random variables - Continuous and linear responses - Fixed failure limits


Data Flow for All Three Methods

Evaluation Procedure (user provided)

SAMPLE,Given these values of design variables,perform SINDA/FLUINT analysesor other calculations to determine: - the values of any constraints (if any)

New values of random variables

current values of reliability constraints

DSAMPLE,RELEST

Reliability Calc.(RELEST only)

Done

Convergence?(SAMPLE only)


Example Latin Hypercubes (DSAMPLE method)

Two dimensional variational space with sampling resolution of five In other words: two random variables A and B ranging from AL to AH, BL to

BH, and NLOOPR=5 Two possible samplings (DSAMPLE chooses randomly each time it is

called)

Each parameter is therefore sampled NLOOPR times: it doesn’t cost much to try different values of a variable that doesn’t make much difference


A Quick Demo: Heated Bar (TD Demo)

Aluminum bar 1m long 5cm x 5cm cross section Painted white (e=0.8)

Radiates to deep space

Heated at one end (100W)

Normal Question: How hot does the heated end get at steady state? Nominal steady hot end

temperature is about 115°C


Example Statistical Problem (TD Demo)

What if some properties or boundary conditions weren’t known exactly?

Uncertainties: Width(=height): 5cm ± 0.1cm (= 1s,

normal distribution) Emissivity: Any value between 0.75 and

0.85 equally Power: 100W ± 5W (= 1s, normal

distribution)

New Question: What are the chances the hot end will be less than 100°C?

0.75

pro

babili

ty

5cm

pro

babili

ty

0.1cm

100W

pro

babili

ty

5W

0.85


Example Problem, ResultsRANTAB (mostly useful to echo inputs)

NUMBER OF RANDOM VARIABLES = 3 NUMBER OF REL. CONSTRAINTS = 3 RELPROCEDURE CALLS (LOOPCR) = 0 VS. MAXIMUM (NLOOPR) = 100 OVERALL RELIABILITY TALLY = -1.00000 (UNAVAIL.) TOTAL CUMULATIVE CALLS = 0 NSEED = 94740687, AERRR = 1.000000E-05, RERRR = 1.000000E-03, LAST ROUTINE: NONE

RANDOM VARIABLE TABULATION

NAME TYPE MEAN STD DEV COEF VAR LOWER LIM 1% 50% 99% UPPER LIM

WIDTH NORMAL 5.00000E-02 1.00000E-03 2.00000E-02 -1.00000E+30 4.76737E-02 5.00000E-02 5.23263E-02 1.00000E+30 EMISS UNIFORM 0.80000 2.88675E-02 3.60844E-02 0.75000 0.75100 0.80000 0.84900 0.85000 POWER NORMAL 100.00 5.0000 5.00000E-02 -1.00000E+30 88.368 100.00 111.63 1.00000E+30

RCSTTAB (main output routine)

NUMBER OF RANDOM VARIABLES = 3 NUMBER OF REL. CONSTRAINTS = 3 RELPROCEDURE CALLS (LOOPCR) = 100 VS. MAXIMUM (NLOOPR) = 100 OVERALL RELIABILITY TALLY = 0.03000 ( 3.000%) TOTAL CUMULATIVE CALLS = 10 NSEED = 94740687, AERRR = 1.000000E-05, RERRR = 1.000000E-03, LAST ROUTINE: DSAMPLE

RELIABILITY CONSTRAINT TABULATION

NO. NAME MEAN STD DEV COEF VAR LOWER LIM REL: TALLY REL: NORM UPPER LIM REL: TALLY REL: NORM

1 UNNAMED 114.80 8.2696 7.20329E-02 130.00 0.96000 0.96695 2 UNNAMED 114.80 8.2696 7.20329E-02 115.00 0.51000 0.50953 3 UNNAMED 114.80 8.2696 7.20329E-02 100.00 3.00000E-02 3.67271E-02

3% chance by tally

3.7% chance by fit to Gaussian curve


Example Problem, Histograms (EZXY Demo)

■ EZXY also allows the results to be queried in hindsight


Reliability Engineering for Users of the Solver

Like the Solver, it is an Advanced Design Module

High-level design solutions beyond steady state and transient

Many parallels to the Solver even re-uses a few of the control parameters like NERVUS easier to learn and use

Can be used instead of the Solver Can be used with the Solver: Reliability-based Optimization


Similarities Between the Solver and Reliability Engr.


Nesting Reliability Engineering within the Solver (Advanced)


High-level Operations:Robust Design (Advanced)

Reliability engineering plus optimization: design for reliability What is the best design that is at least 99% reliable? What tolerances are acceptable? Avoid both under-design (risk) and over-design (cost)

Example: Reinterpreting the intent of MIL-STD 1540d Traditional approach: Keep the junction temperature under 125°C

(qualification) Apply 10°C margin (acceptance) plus 11°C (analysis/environ.

uncertainty) Stack up worst case dimensions, properties, environments, and then

hope might use the Solver to help find the worst cases, then again to synthesize

such a design applying 21°C margin as an optimization constraint might use Reliability Engineering to evaluate such a design

Robust Design approach to the same problem Apply 10°C margin (acceptance) as a reliability constraint (failure limit) Convert the 11°C into uncertainties in as-built properties, orbit, etc. Maximize performance, minimize weight using the Solver Use the reliability allocated to the thermal subsystem as an

optimization constraint


Robust Design, Illustrated

감 사 합 니 다 .CAE TOTAL SOLUTION 에이블맥스 ( 주 )

Page 75CAE TOTAL SOLUTION www.ablemax.co.kr

A Quick Demo: Heated Bar

Aluminum bar, 1m long with 5cm x 5cm cross section, painted white (e=0.8), heated at one end (100W). Radiates to deep space. Initially at 100°C (uniform).

Normal question: How hot does the heated end get in 1000 seconds?

Page 76CAE TOTAL SOLUTION www.ablemax.co.kr

A Quick Demo: Heated Bar – Goal Seeking

What power causes the hot end to reach 200°C in 1000 seconds? Goal seeking, with the design variable power, and objective is the

temperature reached at 1000 seconds (goal: 200°C). Does not need the TD dynamic mode to solve since no geometric

calculations are involved

Documents

SINDA/FUINT For Advanced Design 에이블맥스㈜. Page 2 CAE ENGINEEREING TOTAL SOLUTION 목차 1.Introduction to Optimization 2.Automated