multidisciplinary design optimization for an all-electric geo … · 2019. 9. 5. · aets comprises...

Multidisciplinary Design Optimization for

an All-electric GEO Satellite

Beijing Institute of Technology

School of Aerospace Engineering

Renhe Shi

2016.10.25

The 1st APSCO & ISSI-BJ Space Science School

Outline

Introduction

AETS MDO problem definition

Multidisciplinary modeling for AETS

Surrogate assisted design optimization

Summary

Introduction Since the dawn of the space era, the satellites in geosynchronous orbit have gained

great interests because of the merits in communications, earth observation, navigation,

etc. State-of-the-art GEO satellites are capable of using electric thrusters to

perform all propulsive tasks like orbit-raising and station-keeping. Compared with

conventional GEO satellites using the all-chemical or hybrid propulsion systems, all-

electric GEO satellite can save considerable amount of propellant owing to the

superior efficiency of electric propulsion (EP) system, which results in significant

reduction of the launch cost and additional payloads.

BSS-702SP of Boeing

0

0.05

0.1

0.15

0.2

0.25

All-Chemical Hybrid All-Electric

Payload Ratio of different propulsion model

Introduction

Although all-electric GEO satellites consume much less propellant than the competitive

chemical ones, it requires extremely long transfer time due to the low thrust produced

by electric thrusters. Not only does this delay the deployment of GEO satellites, but

also result in serious radiation damage of devices like solar arrays caused by the

prolonged transfer time within the Van Allen belts. It requires that the design of

geosynchronous transfer orbit, station-keeping strategy, power, attitude control,

propulsion, and structure subsystems, etc. should be considered simultaneously.

Hence, the designers must make tradeoffs among different subsystems (disciplines) of

an all-electric satellite. Multidisciplinary design optimization (MDO) is therefore

preferred to deal with the satellite system design problems. MDO was originally

proposed by Sobieski , which was defined as “a methodology for the design of

complex engineering systems and subsystems that coherently exploits the synergy

of mutually interacting phenomena” by NASA’s Langley Research Center.

Introduction

A surrogate assisted MDO framework is utilized to handle the all-electric GEO

satellite multidisciplinary design optimization problem.

Construct/Refine Surrogate

Optimization Results

Convergence?

Surrogate assisted Optimization

Orbit

Disciplinary Modeling and Validation

Optimal Design

Design Variables

MDO Problem Definiation

Objective Constraints

… … … Optimizer Disciplines

Output

Validation

Y

N

Analysis Models

… … …

Structure

Power

Multidisciplinary Design Analysis Process

Geosynchron

ous transfer1GEO station

keeping2

Solar power3

Structure4

Analysis Models Computer Simulations

Invoke

Response

Global Optimization (GA/PSO…)

Global/Sequential Bias

Sampling in Design Space

Input

Outline

Introduction




Summary


The studied all-electric telecommunication satellite (AETS) is a kind of GEO

communication satellite. AETS comprises payload module, service module, solar arrays,

and payloads. AETS uses four ion thrusters mounted on the bottom of the satellite

to execute geosynchronous transfer and GEO station keeping maneuvers. The ion

thrusters can provide a maximum thrust of 200mN with 4.5kW power and 4000s

specific impulse.

Studied all-electric telecommunication satellite

Top Plate

CC South Plate

CC East Plate

CC North Plate

CC West PlateCentral

Cylinder

CC Clipboard

Middle Plate

SC East Plate

SC West Plate

Joint Ring

SC South Plate

SC North Plate

Bottom Plate

SC Clipboard

CC: Communication Cabin SC: Service Cabin

Fuel Tank

X

Y

Z


In view of the typical characteristics of all-electric GEO satellite, we mainly choose the

geosynchronous transfer, GEO station-keeping, solar power, and structure as the

modeled disciplines for AETS MDO problem. The coupling relationship for the MDO

problem is organized in design structure matrix (DSM).

Geosynchron

ous transfer1

GEO station

keeping2

Solar power3

Structure4

y12 y13

y23

y42

y24

y34

y14

x1 p1 x2 p2 x3 p3 x4 p4

y1 y2 y3 y4

y41

satellite 1 2 3 4min ( ), [ , , , ]

( , , ) 0, 1,2,3,4.

( , , ) 0, 1,2,3,4

T

i i i ij

i i i ij

M f

D is t

C i

X X x x x x

x y y

x y y

Design Structure Matrix of the MDO problem


Design variable Symbol Unit Range Initial

design

Optimal

design

Thrust angle in the first GTO stage α ° [0,60°] 0 29.79

The T position of thruster dT mm [500,1180] 1180 503.28

The N position of thruster dN mm [800,1050] 1050 962.40

Solar array area Asa m2 [100,120] 110 117.49

Core thickness of service cabin

SN\EW plates SH mm [17,25] 20 17.6

Core thickness of communication

cabin SN\EW plates CH mm [17,25] 20 17.1

Core thickness of central cylinder TBH mm [17,25] 20 22.4

Ply thickness of service cabin

SN\EW plates SP mm [2.8e-4,5.2e-4] 4e-4 3.8e-4

Ply thickness of communication

cabin SN\EW plates CP mm [2.8e-4,5.2e-4] 4e-4 3.3e-4

Ply thickness of bearing cylinder TBP mm [7e-5,1.3e-4] 1e-4 7.8e-5

Design Variables of the MDO problem


Constraint Symbol Unit Range Initial

design

Optimal

design

Total orbit transfer time tf Day ≤180 166.11 130.10

EWSK accuracy max ° ≤0.05 0.035 0.027

NSSK accuracy maxi ° ≤0.05 0.036 0.036

Beginning-of-life power PBOL kW ≥22.90 21.41 22.90

Ending-of-life power PEOL kW ≥16.30 19.86 21.20

First order rotational modal round X fX Hz ≥12 13.48 12.25

First order rotational modal round Y fY Hz ≥12 13.39 12.16

First order translational modal round Z fZ Hz ≥25 25.55 26.17

Constraints of the MDO problem

Outline

Introduction

Surrogate assisted MDO framework



Summary


A two-stage electric propulsion transfer is utilized to determine the geosynchronous

transfer orbit (GTO) to accomplish low continuous thrust GEO insertion of the satellite.

Geosynchronous transfer discipline modeling

POe

Os

QH

T

R N

OsU

VH

2

2

2 2

2 2

2

2

d 2( sin (1 cos ))

d 1

d 1( sin (cos cos ))

d

d cos

d 1

d sin

d 1 sin

d 1 d( cos (1 )sin ) cos

d d

d 1( (cos 2 ) (1 )sin )

d

R T

R T

N

N

R T

R T

aF e f F e f

t n e

e eF f F f E

t na

i r uF

t na e

r uF

t na e i

e rF f F f i

t nae p t

M e r rn F f e F f

t nae p p

A

P

Q

H

A

U

V

W

-2

0

2 x 104

-2 -1 0 1 2 3 4

x 104

-5000

0

5000

X

Y

Z

-20

24

x 104

-20

24

x 104

-5000

0

5000

XY

Z

In the first stage, the eccentricity is reduced to

0.

In the second stage, the semi-major axis is increased

to 42166km and the inclination is reduced to 0°.


The GEO position-keeping discipline models the north/south station keeping (NSSK)

and east/west station keeping (EWSK) maneuvers implemented by EP system to

determine the thruster installation configuration. A completed EP position keeping

period lasts for two weeks with seven short periods of two days.

GEO station-keeping discipline modeling

Thrust1,2 Work

Equatorial

Plane

Orbital Plane

Y

X

Z

1# 2#

4#3#

Thruster3,4 Work

lomg

3

2

sin 2 cos

cos 2 sin

cos

sin

T

s

R

s

R Tx

s s

R Ty

s s

Nx

s

Ny

s

D Va

V

V

V Ve l l

V V

V Ve l l

V V

Vi l

V

Vi l

V

Thruster1

Os(MC)T

N

R

NThruster2

Thruster3 Thruster4

Thruster2(1)

Thruster4(3)

Os(MC)

Illustration of thrusters on the bottom and GEO

position keeping strategy


The solar power discipline computes the area of solar arrays to provide sufficient

available power.

Solar power discipline modeling

0 0 0(1 ) ( 1)cosr s e sa c pP p S XX X X A F T

The NASA AP8 Approximation Model is utilized to compute the omnidirectional

radiation flux of protons, the non-ionizing energy loss (NIEL) of solar arrays (Gallium

Arsenide) is computed by the interpolation result of experimental data.

0 20 40 60 80 1000

0.01

0.02

0.03

0.04

0.05

0.06

E

NIE

L

Ga

As

GaAs

( ) ( ) ( )dD E E NIEL E

log(1 )drx

Dp K

D

2

21 2 3

( , )

2

( )

0

2 3

0 1 2 3 4 4 5

( , , ) ( , )

cos

( , )

( , )

b L E l

a E a a L

L E a L E e

rL

R l

a L E a e

b L E b b E b L b EL b EL b L b L

Power Degradation Coefficient Calculation


The structure discipline establishes the structural finite element (FE) model of the

satellite based on the given configuration to obtain the mass properties and natural

frequencies. The structural FE model of the all-electric GEO satellite is established by

Patran/Nastran including 6235 elements and 5991 nodes.

Structure discipline modeling

Finite element model

of the Structure

1st order rotational

modals of X axis

1st order rotational

modals of Y axis

1st order translational

modals of Z axis

Outline

Introduction




Summary


To reduce the computational cost in solving MDO problems with expensive functions,

surrogate-based analysis and optimization (SBAO) technologies have been widely

employed. In SBAO, a surrogate model is constructed to represent the true

computationally expensive analysis model or multidisciplinary design analysis (MDA)

process for simulation-based optimization.

FEM

The adaptive response surface method with intelligent space exploration strategy

(ARSM-ISES) is used to solve the optimization problem.

Review of ARSM-ISES

Approximation Optimization

Surrogate Model NLP Optimizer


Initial Maximin LHD Sampling

in Entire Design Space

Obtain Responses at

Sample Points

Construct/Refit RSM

RSM-based Optimization

Obtain true Response at

Pseudo-optimum

SDS Identification

for Space Reduction

Iterative Sequential Maximin

LHD Sampling in SDS

Invoke

Respond

Invoke

Respond

N

Y

Termination

Criteria Satisfied?

Stop

Optimization

Design Library

Identify Potential

Optimum and Responses

Expensive

Simulations

（e.g. FEA/CFD...）

Build design optimization model

Initial

Design Space

Objective

Constraints

Design

Variables

1k

1k k

Adjust Penalty

Factor and Update

Design Library

1 Set initial conditions

2 LHD sampling

3 Invoke analysis model at the

samples

4 Build RSM using current samples

5 Obtain the potential optimum of

the iterative metamodel using GA

6 Invoke analysis model at the

potential optimum

7 The termination criterion is

checked, if satisfied, turn to step 9,

otherwise go to step 8

8 Generate new samples using

SDS method 9 The process terminates

Flowchart of ARSM-ISES


The optimization yields 66.1kg decrease in total mass, i.e., about 5.4% of the satellite

components being optimized.

Optimization Results

1 2 3 4 5 6 72480

2485

2490

2495

2500

2505

2510

2515

Mass/k

g

Iteration

1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Max C

onstr

ain

t V

iola

tion

Mass

Constraint Violation

History curves of objective and maximum constraint violation


Design variable Symbol Unit Range Initial

design

Optimal

design

Thrust angle in the first GTO stage α ° [0,60°] 0 29.79

The T position of thruster dT mm [500,1180] 1180 503.28

The N position of thruster dN mm [800,1050] 1050 962.40

Solar array area Asa m2 [100,120] 110 117.49

Core thickness of service cabin

SN\EW plates SH mm [17,25] 20 17.6

Core thickness of communication

cabin SN\EW plates CH mm [17,25] 20 17.1

Core thickness of central cylinder TBH mm [17,25] 20 22.4

Ply thickness of service cabin

SN\EW plates SP mm [2.8e-4,5.2e-4] 4e-4 3.8e-4

Ply thickness of communication

cabin SN\EW plates CP mm [2.8e-4,5.2e-4] 4e-4 3.3e-4

Ply thickness of bearing cylinder TBP mm [7e-5,1.3e-4] 1e-4 7.8e-5


Constraint Symbol Unit Range Initial

design

Optimal

design

Total orbit transfer time tf Day ≤180 166.11 130.10

EWSK accuracy max ° ≤0.05 0.035 0.027

NSSK accuracy maxi ° ≤0.05 0.036 0.036

Beginning-of-life power PBOL kW ≥22.90 21.41 22.90

Ending-of-life power PEOL kW ≥16.30 19.86 21.20

First order rotational modal round X fX Hz ≥12 13.48 12.25

First order rotational modal round Y fY Hz ≥12 13.39 12.16

First order translational modal round Z fZ Hz ≥25 25.55 26.17

Outline

Introduction




Summary

Summary

A surrogate assisted MDO framework consisting of MDO problem definition,

disciplinary modeling, and surrogate assisted optimization, is introduced to

efficiently implement the state-of-the-art all-electric GEO satellite system design.

A surrogate-based optimization method is utilized to reduce the computational cost

of the satellite MDO problem. The total transfer time is reduced by 21.7%, while

the total mass yields a 66.1kg decrease after optimization. The reduced mass leads

to a lighter satellite with lower launch cost, and it could also be dedicated to

additional payloads which means more revenue from customers’ perspective.

The optimization results illustrate that the proposed surrogate assisted MDO

framework is feasible and effective to improve the quality and efficiency of all-

electric GEO satellite system design. The work could be referred for further all-

electric spacecraft system research. In future work, we will try to apply this

proposed framework to other spacecraft systems design and optimization.

Thank You

multidisciplinary design optimization for an all-electric geo … · 2019. 9. 5. · aets comprises...

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