Automated Sensitivity Analysis in Early Space Mission Design

www.DLR.de • Slide 1 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012

Automated Sensitivity Analysis

in Early Space Mission Design

Volker Schaus

> Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012 www.DLR.de • Chart 2

Overview

- Introduction

- Software Framework: Virtual Satellite

- Sensitivity Analysis

- Implementation of the algorithm

- Example – Dimensioning the fuel tank of a spacecraft

- Interpretation of the results of the Sensitivity Analysis

- Conclusion – Future Work


Virtual Satellite - Essentials

- Rich Client Application

- Integrated Design Environment

- Full support of parameter studies as they

are performed in Concurrent Engineering

environments

- Used as one Standard Tool in the

Concurrent Engineering Facility (CEF)

- Role Management through active directory

- Version control

- Truly distributed collaboration concept

- Collaborative configuration

- Orbit Visualization


Virtual Satellite - Interfaces

VirSat Application

Excel – IDM Workbooks

Catia V5 Skript Automation

QUDV-Standard

Quantities, Units, Dimension, Values

ECSS-TM-10-25

Engineering design model

data exchange (CDF)

Poster session

Data Model


𝑚𝑝 = 𝑚0 1 −1

𝑒 ∆𝑣𝑐

- Calculation explicit

- Parameters as sources and target Ziolkowski-Equation re-arranged for

the mass of the propellant 𝑚𝑝

Sensitivity Analysis – Why?

- Systems development life-cycle

- Model-based Systems

Engineering (MBSE)

- Digital master model as

central element for all the

design activity

- What is the best system design?

- Sensitivity Analysis is one way to

aid the evaluation of the system


Source: Wikipedia, last accessed: 26.09.2012

Evaluation

SA – Background

- Local methods

- Interactions between parameters

not respected

- One factor at a time (OAT)

- Global methods

- Interactions respected

- Problem: parameter input sets

needed

- Usually generated with Monte Carlo

methods

- Response surface plots


- Paper focusses on two implementations

- 𝑆𝐼 =𝑑𝑦

𝑑𝑥 0 and 𝑆𝐼𝐷 =

𝑥0

𝑦0

𝑑𝑦

𝑑𝑥 0

- Y … unknowns, calculated parameters

- X … boundary constraints

- Partial derivatives

Dimensioning the tank of a spacecraft

- Typical recurring task in early CE

- Three domains

- Mission Analysis

- Propulsion

- Structure


Source: Astrium EPDM – Bladder Tank BT 01/0 ∆𝑣 → 𝑚𝑝→ 𝑉𝑡 → 𝑚𝑡

Ziolkowski Volume and Area of a Sphere Barlow‘s formula (Kesselformel) Selection of the propellant:

Hydrazin → Density

Design Values – Working Point b

ou

nd

ary

co

nstr

ain

ts

𝑚0 = 3000 𝑘𝑔 in-orbit mass of the UV telescope mission

AEGIS

∆𝑣 = 165 𝑚 𝑠 required delta v for the AEGIS mission

𝑐 = 2300 𝑚 𝑠 exhaust velocity

𝜌𝑝 = 1008 𝑘𝑔 𝑚3 density of hydrazine

𝜌𝑡 = 4430 𝑘𝑔 𝑚3 density of the titan alloy used as material for the

reference tank

𝜎𝑡 = 895 ⋅ 106 𝑁 𝑚2 tensile strength of the titan alloy

𝑝 = 52 𝑏𝑎𝑟 = 52 ⋅ 105 𝑁 𝑚2 burst pressure of the tank

un

kn

ow

ns

𝑚𝑝 = 207.68 𝑘𝑔 mass of the required propellant

𝑉𝑡 = 0.206 𝑚3 volume of the needed tank

𝑚𝑡 = 7.95 𝑘𝑔 mass of the needed tank


Entering the Values for the Example in the Software


Implementation of the Algorithm

- Solver

- Find unknowns and boundary constraints of the design system

- Calculate the Sensitivity Index 𝑆𝐼 =𝑑𝑦

𝑑𝑥 0

- Variying each boundary constraint and solve the equation system

- At the working point

- Using the one factor at a time (OAT) method

- Derivative calculated with the finite difference method

- Store the index values in a matrix: Sensitivity Matrix (7 x 3)

- Display the result in the User Interface


Structogramm


Displaying and interpreting the results


- Sensitivity Data displayed as matrix

- Normalized to the interval [-1; 1]

- Color gradient

- Derivative 𝜕𝑚𝑝

𝜕∆𝑣 has largest value

- Valid locally around the working

point

- Unit change:

- Change ∆𝑣 by 1𝑚

𝑠

- ∆𝑚 = 1 0.06 𝑘𝑔 = 16.67𝑘𝑔

- Team leader can use this

information to drive the study

Boundary

Constr

ain

ts

Unknowns

Variying the mass

- Changing the working point

- Launch mass 𝑚0

- Gradients are changing accordingly

- Strongest connection shifted

- Dimensions affect the results!


𝑆𝐼 =𝑑𝑦

𝑑𝑥0

Interpretation of the results - dimensionless

- No variation due to dimensions any more

- Not looking at unit changes any more

- Percentual changes

- 𝑚0 is changed by 10%, the volume of

the tank 𝑉𝑡 also changes by 10%

- Proportionalality now reflected in the result


𝑆𝐼𝐷 =𝑥0𝑦0

𝑑𝑦

𝑑𝑥0

𝑉𝑡 =𝑚0

𝜌𝑝1 −

1

𝑒 ∆𝑣𝑐

Conclusion

- Implementation of Sensitivity Analysis in the Software Virtual Satellite

- Results can be generated on-the-fly

- Used by the team leader to guide the CE study


Future Work


Source: Browning – Applying the Design Structure Matrix

to System Decomposition and Integration Problems: A Review and New Directions

IEEE Transactions on Engineering Management, vol. 48, no. 3, August 2001

- Filter techniques needed for large

design problems

- Cyclic dependencies not respected

- Optimization

- Calculations in external tools are not

supported (Excel)

- Compare Sensitivity Analysis with

parametric-based design structure

matrix approach


Questions… yes please!

Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)

German Aerospace Center - Simulation and Software Technology |

Lilienthalplatz 7 | 38108 Braunschweig | Germany

Dipl.-Ing. Volker Schaus

[email protected]

Phone +49 531 295-2769

www.dlr.de/sc/en

LIVE DEMO of

VIRTUAL SATELLITE

SOFTWARE

Tomorrow, 18th of October 2012, 3 p.m.

Please register at the Conference Desk!

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Automated Sensitivity Analysis in Early Space Mission Design