Multi-Objective Design Exploration (MODE) Applied to a Regional Jet Design

Shigeru Obayashi Institute of Fluid Science

Tohoku University

Outline

n  Introduction n  Multi-Objective Design Exploration (MODE) n  MRJ structure modeling

n Objectives n Structure design of MRJ Horizontal Tail

n  Visualization of design space

n  Conclusion

MRJ: Mitsubishi Regional Jet

MODE Applications to MRJ

MODE as aircraft MDO has been proposed and applied to MRJ wing design (MHI-Tohoku-university collaboration) ■　Previous Applications •  Wing-body configuration MDO •  Wing-nacelle-pylon-body configuration MDO •  Winglet design MDO

MODE to Solve Multi-objective Optimization

Multi-objective  Genetic  Algorithm

Computational  Fluid  Dynamics

Design  Database

Design  Knowledge

Visualization  and  Data  Mining  

Multi-Objective  Design  Exploration  (MODE)

Step  1Multi-objectiveShape  Optimization

Step  2Knowledge  Mining

Data  mining:maps,  patterns,models,  rules

Reference vector for k-th unit Data vector

k-th unit High-dimensional Vector space

Map space

Self-Organizing Map (SOM)

" Visualization of design space " Neural network model proposed by Kohonen

n Unsupervised, competitive learning

" High-dimensional data　→　2D map " Qualitative description of data

http://www.brain.kyutech.ac.jp/~furukawa/index.html

SOM provides design visualization: Seeing is understanding (Essential design tool)

MRJ Structural Features

ü  Application of composite materials is about 12%

ü  Need to reduce structural weight of main components •  Aluminum wing box •  Composite horizontal tail box (present application) •  Composite vertical tail box •  etc…

Aluminum 83%

CFRP 9%

GFRP 3%

Titanium 3%

Steel 2%

•  Previous MODE applications - Aerodynamics : based on high-fidelity CFD model - Strength : based on low-fidelity structure model

•  Need to introduce high-fidelity structure model into MODE

Previous MDO modeling for MRJ

High-Fidelity CFD model

Low-Fidelity Structure model

Aircraft model for MRJ MDO

skin

stringer

skin-stringer equivalent plate

Actual aircraft design

Strength Criteria

Plate compressive and tensile stress (rough evaluation)

Various buckling modes for skin, stringer and spar etc.

Fidelity Gap

Structure of Horizontal Tail Wing Key Points for H-Tail Structural Design

ü  Various interactive criteria for buckling

•  Euler buckling, Stringer crippling

•  Skin bucking, Stiffened panel buckling

•  Spar web shear buckling

à Hard to determine optimum combination between rib pitch (A) & stringer pitch (B)

Skin Stringer

Spar Rib A

B

Conventional Approach for Rib-Str. Pitch Optimization

ü  Parameter study

à Limited search of design space with interactive buckling criteria

à Global optimum ? Local optimum ?

Rib P1 Str. P1

Rib P1 Str. P2

Rib P2 Str. P1

Rib P2 Str. P2

Weight Global Optimum ?

•  Introduce a high-fidelity structure model into MODE based on detailed buckling modes using realistic aircraft structure model

•  Apply the new MODE to MRJ Horizontal Tail

Objectives

Definition of Optimization Problem 1. Assumptions

•  Fixed H-Tail OML & box config.

•  Fixed design loads

•  Fixed stacking sequence

•  T-type stringer

à Fixed W & H à t = sizing parameter

•  Sizing criteria

à Euler & Skin buckling à Stringer crippling à Stiffened panel buckling à Spar web shear buckling

2. Objective

•  Minimize structural weight •  Minimize number of main structure parts (rib & stringer)

H

W

t

t

T-type Stringer

H-Tail OML (fixed)

Str. Pitch

Rib Pitch

H-tail box (fixed)

3. Design variables

•  Rib pitch (at regular intervals)

•  Str. pitch (at regular intervals)

4. Criteria

•  Str. thickness t > tmin (specified)

•  Strain margin > Specified margin

Flowchart of Present Approach

Define design space

Choose sample points

Strength evaluation

Construct surrogate model

Check the model and front

Extract design space

Design of experiment: Latin hypercube

Response surface model: Kriging model

Find non-dominated front of EIs Optimization: ARMOGA

Data mining: SOM

NASTRAN-based structural sizing

NASTRAN-based Structural Sizing

Design parameters

Automated FEM generation

Static analysis by NASTRAN

Structural sizing

OML (fixed)

Design Loads (fixed) Rib & Str. Pitch, Initial thicknesses

Internal stress, strain

New thicknesses, Weight

No

Yes

Converged thicknesses & weight

Converged ?

FEM update

OML: Outer Mold line FEM： Finite Element Model

NASTRAN Static Analysis

Horizontal Tail FEM

Number of stringers and ribs

Results - Optimum Solution

•  Kriging model was constructed based on 36 sample points

à Tradeoffs between two objective functions

à Improvements over the baseline design

Number of Structural Components

W eight

Initial points

1st update

2nd update

Baseline

Optimum  Direction20kg

10

Constructed Weight RSM Comparison of objective functions among the baseline and sample points

Results - Design Knowledge

•  SOMs were generated to extract design knowledge

Regular interval rib pitch (previous design concept)

Additional weight reduction by using larger outboard rib pitch than inboard

(new design concept)

Optimum pitch

à Optimum str. pitch can contribute to reduce both of the inboard & the outboard weights

Smaller pitch

à Smaller rib pitch is effective to reduce the inboard weight

Larger pitch

à Larger rib pitch is effective to reduce the outboard weight

Conclusion

MODE has been applied to the multi-objective structural design optimization for MRJ H-Tail n  Including detailed buckling evaluation n  Improved both of weight and number of main

structure parts compared with the baseline design

n  Provided a better design concept utilized for MRJ H-Tail structural design

Stay tuned for the first flight in 2013!