The CO2 Project (Design with Constraint Solving) Laurent ZIMMER DASSAULT AVIATION Research and Future Business Division [email protected]

The CO2 Project(Design with Constraint Solving)

Laurent ZIMMER

DASSAULT AVIATION

Research and Future Business Division

[email protected]

2

FJCP WORKSHOP25-27/10/94

• A National Research Project– Labelled by a network for Software Development of

the French Ministry of Research

Context

– Granted by the French Ministry of Economy, Finance and Industry

3


• 6 partners

– 2 Industrial

– 2 Informatics Labs

– 2 Engineering Labs

Context

4


Purpose

• To develop in parallel– A (mainly) interval constraint-based software

dedicated to engineering design called CE :• Modelling• Solving

– A relating design methodology:• inverted and integrated design• constraint formulation

5


Basic Principle

Concept

Calculus Calculus

Sol2

Model

Sol 1 Sol N...Solution

Requirements

Req.

DV

PV

PV

DV+PV

Point to Point design Set-based design (Toyota)

Classical Design Process I.I. Design Process

6


Methodology

To test the approach through many case studies:

• Academic case studies– preliminary aircraft vehicle design

• Industrial case studies– mechanical design problem– design of an Air Conditioning System (ACS)

7


Software Development

• Every 6 months Release• Initial version of the tool:

– Hull consistency with decomposition (HC3)– Interval arithmetic directly implemented with the

floating point arithmetic instructions of the C++ compiler (outer rounding)

– infinite numbers are not processed

First Case-Study

Global Unmanned Aircraft Preliminary Design

9


Problem Description

• Requirements resulting from mission profile:– Range, cruise speed, cruise altitude, volume of

payload ..

• Constraint Model:– 51 variables,35 equations and 26 inequalities,– 5 Geometrical Design Variables :

• Body diameter, Wing span, Wing root chord• Wing thickness/chord ratio, Wing aspect ratio

10


PossibleDesigns

TL

Swl

arrow

delta

trapezoidalTiCRaT = T / L

wing thickness/chord ratio

Swl

wing leading sweep angle

11


Some tests

• T1: Dimensioning (VC -> VP)– to fix the geometrical variables– Range = f(MachNo)

• T2: Reverse Computing– MachNo = f(Range)

• T3:Parametric Study– Range=f(Swl)

12


T1

AspRat Bdepth Croot Span TiCRat MachNo Range

[0 , ns] [0 , ns] [0 , ns] [0 , ns] [0 , ns] [0 , ns] [0 ,ns]

2 0.5 4 [3.99 ,6.03] [0.166 , 79330.79] [0 , 2.1673990604568] [0, ns]

2 0.5 4 4 [0.482 , 55055.147] [0 , 0.8469449298259] [0 , ns]

2 0.5 4 4 0.483 [0 , 0.8467896833306] [0 , ns]

2 0.5 4 4 0.483 0.7 3496.159

H = 5000

13


T2

H = 5000, Range = 3496


2 0.5 4 4 0.483 [0 , ns] 3496

2 0.5 4 4 0.483 [0.346 , 0.847] 3496


2 0.5 4 4 0.483 0.69987131 3496


2 0.5 4 4 0.483 0.82245094 3496

14


T3

H Bdepth Croot Swl TiCRat MachNo Range

[0 , ns] [0 , ns] [0 , ns] [0 , ns] [0 , ns] [0 , ns] [0 ,ns]

10000 0.5 4 42 0.1 0.7 3879.405

10000 0.5 4 43 0.1 0.7 3873.318

10000 0.5…

4…

44…

0.1…

0.7…

3866.85…

1000 0.5 4 52 0.1 0.7 3796.78

10000 0.5 4 53 0.1 0.7 XXXXXX

15


Results

• T1 is OK

• T2 is OK but not very efficient

• T3 is OK however parametric study is to automate

16


reverse calculus vs direct parametric study

Range against MachNo

34903492349434963498350035023504350635083510351235143516351835203522352435263528353035323534

0.69 0.71 0.73 0.75 0.77 0.79 0.81 0.83

MachNo

Ran

ge

17


Revised version

• A correct Interval Arithmetic Library implemented on a robust floating point library(Gaol F. Goualard 2000)

• A new propagation architecture implementing up-to-date consistency algorithms(L. Granvilliers & M. Christie)

• Some specialised solving strategies– parametric studies– optimisation (min, iterative approximating S. Preswitch 99)

Second Case-Study

Pressure Device Design

19


PurposePurpose

Stiffened Plate

Stiffener Plate

Pressure2,5 Bar

Design of a Pressure device

20


Design problem of a stiffened plateDesign problem of a stiffened plate

Design challenge • Increasing the mechanical resistance without decreasing the cost of

the resulting product

Design variables • Thickness of the plate

• Type of stiffeners,

• Type of material,

• number of longitudinal and lateral stiffeners

ny

nx

type de raidisseur

h

21


Constraint Formulation

Not only analytical functions !

Like:• Cost models• Use of components of the shelf• A global physical model of the behaviour of

the plate

22


Cost models(*******************************************************************)(* Définition du process de fabrication *)(*******************************************************************)

(* Temps de Découpe de la tôle *)h<=8E-3 -> T1=1/2;h>8E-3 -> T1=(1/2)*(L1+L2);T1>0;

(* Cassure des raidisseurs *)hauteur<=1E-2 -> T2=ny*(nx+1)/20;hauteur>1E-2 -> T2=ny*(nx+1)/10;T2>0;

Need of a trigger mechanismto express

Experience or Business rules

23


Components of the shelf

IPE80 à IPE600 Carrés22 à carrés200

Catalogue of stiffeners

Catalogue of materials

Steel, Iron, Iron cast, Titanium ..

24


Catalogues

25


Global Physical Model

Finite Elements Model

26


Global Physical Model

LearningCasebase

Approximation by a set of analytical functions

27


Feedback

• The case study has been processed• The processing of non analytical knowledge is

not easy :– Finite Elements models– Interpolation tables– existing programs– ..

It is a real bottleneck for ICP

And Nowwe are working on

an industrial case study

An Aircraft Air Conditioning System Design

29


Half closed motorised Air conditioning cycle

soute avion iquepressurisée

T M oteur C

a irdynam ique

giffard

vanne by-pass

pré-refro id isseuréchangeur princ ipa l

dess icant

Turbo-réacteur

vanne d 'arrê t

vanne d 'arrê t g iffard

vanne de régulation

pressurisationcarburant

30


Close/Half-Close Cycle Design

Pre-coolingHeat Exchanger

Turbo

reactor

Atmosphere Cabin

Atmosphere

Main Heat Exchanger

Turbine

Compressor

motor

switch on

31


Schéma d’architecture global du SCASchéma d’architecture global du SCA

T7 entre –40 °C et 71 °CSection d’ entrée

Ai

Ouvert

Fermé

32


Variability in the Design Problem

Possible free parameters:• Motor Power• Ram Air section• Heat exchangers characteristics

Design is hard

33


Cross-Flow Heat Exchangers

Lx

MAIN AIR

RAM AIR

Lz

Ly

34


Dimensioning Heat Exchangers

Lx, Ly, Lz

Type of Exchange Surfacesdifferent typesdifferent properties (5)

Type of ExchangersCross-Flow, Multi-pass ...

35


equations

u s ec t i o n

1 - 3

1

113r3r

4r

PT

T an

P

raq̂maq

λ 1,1.0λ

u s e u r 4 , 5

1²

2

11 MT a1rT 1

12

1²

MPη ad1 rP

6

11

11

11

1

21

11

ˆ

ˆˆ²ˆ1ˆ

ˆˆ

ˆˆ1

ˆ

ˆ2²ˆ1ˆ

2

ˆ²ˆ

m

em

c

c KA

AfK

G

11

21

PP

PP

7

r

merr

r

m

cr

rr

r

rrcr

r KA

AfK

G

21

21

11

2

31

21

ˆ

ˆˆ²ˆ1ˆ

ˆˆ

ˆˆ1

ˆ

ˆ2²ˆ1ˆ

2

ˆ²ˆ

2 r2 r

3 r2 r

PP

PPr é -r e f r o i d i s s e u r

8 , 91

21

1

12 r ε

TT

ε

εT

11

2 r1 r2 T

λ

T

λ

TT

1 0

32

32

22

3

42

32

ˆ

ˆˆ²ˆ1ˆ

ˆˆ

ˆˆ1

ˆ

ˆ2²ˆ1ˆ

2

ˆ²ˆ

m

em

c

c KA

AfK

G

33

43

PP

PP

1 1

r

merr

r

m

cr

rr

r

rrcr

r KA

AfK

G

12

12

22

1

22

12

ˆ

ˆˆ²ˆ1ˆ

ˆˆ

ˆˆ1

ˆ

ˆ2²ˆ1ˆ

2

ˆ²ˆ

1 r1 r

2 r1 r

PP

PP

n g e u rc i p a l

1 2 , 1 32

43

2

21r ε

TT

ε

εT

1

30

2 r

0

1 r4 T

-1λ

T

τ-1λ

TT

36


State Space ConfigurationState Space Configuration

Critères Point 1COP 2,71

Mma (kg) non définiMra (kg) 101,00

M soute (kg) 67,40


Mma (kg) non définiMra (kg) 29,43

M soute (kg) 57,10


Mma (kg) 781,55Mra (kg) 135,39

Msoute (kg) 96,86


Mma (kg) 276,12Mra (kg) 186,45

M soute (kg) 42,33

Altitude

Temps

3000 m

16500 m

7500 m

6000 m

M=0.6

M=0.3

M=0.6

M=0.65

37


Partial results

• We are able to dimension the ACS in a given configuration

• if we enlarge the search space:– type of exchange surfaces– type of exchangers– number of configurations

then we address a problem currently out of scope

38


Conclusion

A lot of research effort remain to do if we want to fully address the field of Design

Interesting themes :– Hard mixed integer and real non linear problems– Large search spaces of numerical underconstraint

problems– Decision Support

39


Decision Support Model of soft flexible interval constraints

• Easy and relevant engineer ’s preferences expression

• Automatic generation of Pareto Frontier

ADCdefconXii

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Documents

The CO2 Project (Design with Constraint Solving) Laurent ZIMMER DASSAULT AVIATION Research and Future Business Division [email protected]