automated sensitivity analysis in early space mission design
TRANSCRIPT
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
www.DLR.de • Slide 3 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
www.DLR.de • Slide 4 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
www.DLR.de • Slide 5 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
www.DLR.de • Slide 6 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
www.DLR.de • Slide 7 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
- 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
www.DLR.de • Slide 8 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
www.DLR.de • Slide 9 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
Entering the Values for the Example in the Software
www.DLR.de • Slide 10 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
www.DLR.de • Slide 11 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
Displaying and interpreting the results
www.DLR.de • Slide 13 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
- 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!
www.DLR.de • Slide 14 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
www.DLR.de • Slide 15 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
www.DLR.de • Slide 16 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
Future Work
www.DLR.de • Slide 17 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
www.DLR.de • Slide 18 > Volker Schaus • Schaus_SECESA_2012.pptx > 17th October 2012
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
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!