Multidisciplinary Design optimization incorporating Robust Design Approach to tackle the uncertainti

1
Multidisciplinary Design optimization
incorporating Robust Design Approach to tackle
the uncertainties in the design of a Reusable
Aerospace Vehicle
Multidisciplinary Robust Design Optimization for
a Reusable Aerospace Vehicle

• 1st Progress Seminar after 6 months
• (Roll No. 02401701)

Under the guidance of Prof. K. Sudhakar Prof.
P.M. Mujumdar
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FULLY REUSABLE TSTO TYPICAL FLIGHT PROFILE
DEORBIT
SATELLITE DEPLOYMENT
RE-ENTRY
DOWN/CROSS RANGE MANEUVERS
RE-ENTRY
SEPARATION AT 80-100 KM, M 10-12
MANOEUVERS
PARACHUTE DEPLOYMENT
LANDING MANEUVERS LANDING ON AIR BAGS
TURN
HORIZONTAL LANDING
CRUISE AT M0.8 H10-12 KM
SHYAM / LVDG
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Expendable Launch Vehicle

• Participating disciplines are..
• Aerodynamics, Structures, Aero-thermodynamics,
  Navigation Guidance Control, Propulsion and
  Mission Trajectory.

Reusable Launch Vehicle

• Complexity Launch vehicle Space plane
• Should also account for Life cycle Disciplines..
• .. Economics, Reliability, Manufacturability,
• Safety Supportability
• And should account for uncertainties

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The Design Problem is

• Design of a reusable technology demonstrator for
  the First stage of Two Stage to Orbit fully
  reusable Launch Vehicle.

For which the mission is defined as
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TYPICAL MISSION PROFILE OF RLV-TD
ALT 150 km
RE-ENETRY / GLIDE / RANGE MANOEUVERS
2G TURN ALT 35 km
S12 SEPARATION ALT 60 km M 10.0
FLYBACK CRUISE ALT 12 km M0.8
LANDING
LIFT-OFF
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The Traditional Design Process
Mission Requirements
Historical Data base
Configuration Concepts
Engineering knowledge base
Trade off based on Figures of Merit
Historical Data base Eg Space Shuttle, X-34,
HYFLEX, ALFLEX, CRV
Concept Design Vehicle Sizing
Low fidelity Analysis
Aerodynamics
Weight Estimation, CG
Propulsion
Structures
Stability Control
No
Constraints met
Trajectory Analysis
yes
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Yes
Constraints met
No
Apply Small Perturbations in design variables
Low fidelity Analysis on Aero, Propulsion Weight
Estimation CG, Stability Control and
Trajectory
Select the best
No
High fidelity analysis on Aerodynamics,
Structures, Weight Cg estimation,
Aerothermal Propulsion, Stability Control and
Trajectory
Constraints met
yes
Detailed Design
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The methodology proposed in this research work
Vehicle Conceptual Design using engineering
methods (low fidelity) Aerodynamics, sizing,
Propulsion, Stability Control and Trajectory
Design variables
Noises factors
Multidisciplinary Analysis (High fidelity)
Sizing
Optimiser
Aerodynamics
Structure
Cost Model
Propulsion
CFD
FEM
INSCOST
Empirical
? f, ? f
Aerothermal
ObjectiveFunctions
MINIVER
Constraints
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The Configuration Concept selected
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Parameterization of the vehicle configuration
concept
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X7
For wing
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• X1 to X17 Length parameters
• t1,t2 Thickness parameters
• ?1, ?2 Angular variables
• R1,R2 radii
• di internal diameter

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• X3 to X8 and ?1, ?2 and the airfoil 1 are
  exclusively for the wing design.
• Since accommodating the 24 variables for
  multidisciplinary robust design optimization,
  will be computationally expensive, the wing can
  be optimized separately for its intended
  performance and to take care of the variations
  due to operational manufacturing uncertainties

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The Constraints

• The take off weight should not exceed 2000Kg ?
  GTOW ? 2T
• The maximum diameter of the fuselage should be
  between 0.9 to 1.2 m
• The volume requirement inside the fuselage for
  the avionics boxes, propulsion modules, landing
  gear wells and other auxiliary system are
  estimated as 3.0m3
• The nose cone length (x1) is estimated as 2250
  mm for the scramjet propulsion module performance
  point of view. ? x1 2.250m
• di, the internal diameter of the top half of the
  fuselage 1.00 m (considering the interfacing
  requirement with the solid boosters of 1 m
  diameter)

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• The bottom surface of the demonstrator should be
  flat so that the scramjet modules integration as
  well as the inlet conditions are satisfied. Also
  for easy mounting of the Thermal Protection
  System tiles. This will compel the selection of
  an airfoil with flat bottom for the wings.
• The hypersonic L/D ? 1.5
• Subsonic L/D max 4.5
• The landing weight of the vehicle also should be
  taken as 2.00 T to take care of abort scenario.
• For subsonic cruise, Lift L 2000 kg, for Mach
  0.8 at 12 km altitude
• Wing leading edge sweep ? 45? and leading edge
  radius should be for minimum re-entry heating.
• For the subsonic cruise, the drag (D) of the
  vehicle should be equal to the thrust deliverable

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• The cruise range ? 800 km.
• The touch down speed ? 80 m/sec and the landing
  angle of attack will be 15 deg.
• The sink rate at touch down ? 4.5 m/sec.
• The runway roll ? 1.8 km.
• During the ascend boost phase the maximum dynamic
  pressure should be 120 KPa and angle of attack
  should be less than 3 degree and Maximum
  longitudinal acceleration should be 10 g
• During the re-entry phase the dynamic pressure
  should be less than 20 KPa and the maximum
  lateral acceleration should be 3 g
• During re-entry the overall heat flux should be
  less than 50 Watts/sq-cm

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The objective function -
Maximize the cruise range
Uncertainties Expected -
Manufacturing Uncertainty which will result in
surface roughness and the excrescence effects,
like mismatches ,gaps, contour deviation and
fastners flushness (rivets, etc) on the wetted
surface. Operational Uncertainty like
uncertainty in cruise Mach number.
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Literature Survey
Parametric Optimization of Manufacturing
Tolerances at the aircraft surface - A.K. Kundu,
John Watterson, and S. Raghunathan, Journal of
Aircraft, Vol.39, No.2, March-April 2002.

• Aimed at reducing life cycle cost of the
  passenger aircraft by relaxing the manufacturing
  tolerances on 11 key features in the nacelle.

• Parasite drag increase resulted by the
  degradation of the surface smoothness qualities,
  for example, the discrete roughness on the
  component parts and at their subassembly joints.
  These are seen as aerodynamic defects,
  collectively termed as one of the excrescence
  effects, typically,
• i) mismatches (steps etc.)
• ii) gaps,
• iii) contour deviation and
• iv) fastners flushness (rivets, etc) on the
  wetted surface.

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The four types of surface excrescence at the key
manufacturing features
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.
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Findings

• The results show that feature by feature
  percentage changes for one nacelle with a drag
  coefficient increment of 0.824 and a reduction
  of 2.26 on the nacelle cost.
• This will result to 0.421 overall reduction in
  DOC (Direct Operating Cost) of the transport
  aircraft.
• Tolerance relaxation tradeoff study between drag
  increase (loss of quality function) and
  manufacturing cost reduction (gain).
• Further research work is planned by the same
  group to extend the study to wing and fuselage.

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Probabilistic Approach to Free-Form Airfoil Shape
Optimization Under Uncertainty - Luc Huyse, AIAA
Journal, Vol. 40, No.9 September, 2002 Luc Huyse,
R. Michael Lewis, Aerodynamic Shape Optimization
of Two-dimensional Airfoil Under Uncertain
Conditions 16, NASA/CR-2001-210648

• This work is on the operating uncertainties
  which will affect the performance of an aircraft.
  The airfoil shape optimization is addressed.
• In airfoil design, the objective is to minimize
  drag with the specified cruise Mach number and
  target lift coefficient
• Robust design of airfoils for a transport
  aircraft. Here robust design technique accounts
  for the variation in cruise Mach number.

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The objective is lift constrained wave drag
minimization over the Mach range M ?
0.7,0.8 min Cd (d,M) d?D Sub to Cl (d,M)
? Cl over M ? 0.7,0.8 Where d is the
vector of design variables and D is the design
space. Cl is the minimum lift corresponds to
typical values found for commercial transport
airliners. In this study, the Mach number is the
only uncertain parameter.
This deterministic optimization model is not
necessarily an accurate reflection of the
reality. The formulation contains no information
regarding off-design condition performance. So
the drag reduction is achieved only over a narrow
range of Mach numbers. This is of concern if
substantial variability is associated with
operating condition.
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Consider different Mach numbers and to
generalize the objective function to a linear
combination of flight conditions  
m min ? Wi Cd (d,Mi) d?D i1 Sub
to Cl (d,Mj) ? Cl For j 1,2,..m  
Practical problems arise with the selection of
flight conditions (Mi) and with the specification
of the weights Wi. There are no clear theoretical
principles to guide the selection, which is in
fact, largely left to the designers discretion.
With multipoint formulation, Cd can be realized
over a wide range of Mach numbers M, however this
formulation is still unable to capture the full
range of uncertainty .
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Nondeterministic Approach
M is now treated as a random variable and the
optimization problem is now interpreted as a
statistical decision making problem. So using
the probability density function of the Mach
number, the objective function is stated as
min ? Cd (d, M) fM(M) dM Sub to Cl (d,Mj)
? Cl for all M, where fM(M) is the probability
density function of the free flow Mach number M.
The practical problem is that integration is
required in each of the optimization steps.
Theoretically sound but computationally
expensive. This work is an example of using
probabilistic approach in achieving robustness,
provided the distribution pattern of the noise
variable is known.
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Robert H. Sues, Mark A.Cesare, Stephan S.
Pageau, Justin Y.-T.Wu, Reliability Based
Optimization Considering Manufacturing and
Operational Uncertainties13, Journal of
Aerospace Engineering, October, 2001
Discuss about the approach of integrating MDO and
probabilistic methods to perform reliability
based MDO. RBMDO Demonstrated on Passenger
Airplane Wing Design problem

• Objective Maximize expected cruise range
• Subjected to constraints
• 1. P (upper surface root stress 1 ? y )
  99.0
• -
• -6. P (take off distance 3000 ft ) 99.0

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3 case studied
Case A Six deterministic constraints with no
safety factor on yield stress Case B Six
deterministic constraints with safety factor of
1.5 on yield stress Case C Six probabilistic
constraints

• Manufacturing uncertainties are simulated on
  design variables
• Operational uncertainties are considered.

The results show that RBMDO ( case C ) gives
optimum solution that balances performance and
reliability
Case A
Case B
Case C
Range (NM)
1024.7
984.7
974.9
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99
96
Reliability ()
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P.B.S.Reddy and K.Nishina, Dr. Subash Babu
Taguchis methodology for multi-response
optimization- A case study in the Indian plastic
industry6- International journal of Quality
Reliability Management, Vol.15, No.6, 1998,
pp.646-668

• Taguchis methodology for carrying out a robust
  design is narrated in this.
• The salient features of robust design are
  presented and the robust design methodology
  applied to the case having multi responses (for
  an injection moulding process for the agitator of
  washing machine) is presented.
• The output responses considered were outer
  diameter, height pull out force.

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• The goal was minimizing the variance of the
  height,and outer diameter of the agitator while
  keeping the mean on target and pull out strength
  lt1.8 kg/sq-cm
• Based on cause-effect diagram seven factors were
  identified
• Three noise factors identified were - change of
  machine operators, variation in raw material
  quality and change in temperature environmental
  conditions.

• By performing robust design in the specific case
  of injection moulding process the rejection rate
  could be reduced from 20 to zero percent which
  helped the company in many ways related to cost,
  delivery, quality productivity.

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K.K.Choi, B.D.Youn, Issues Regarding Design
Optimization Under Uncertainty,
http//design1.mae.ufl.edu/nkim/index-files/choi4
.pdf
Discusses the mathematical formulation of robust
design problems
The conventional optimization model is defined as
Minimize OBJ (d) Sub. to Gi (d) ? 0, i
1,2,.NC dL ? d ? dU where OBJ is the
objective function, Gi is the ith constraint
function, NC is the number of constraints, d is
the design variable vector, dL dU are the
lower upper bounds of d.
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In robust design, Minimize OBJ ? R, ? R
 sub.to Gi (? ) k ? Gi ? 0 , i
1,2,.NC dL ? d ? dU where ? R, ? R are
the mean standard deviation of the response R,
Gi (? ) and ? Gi are the mean standard
deviation respectively of the ith constraint
function, k is the penalty function decided by
the designer, d is the design variable vector,
dL dU are the lower upper bounds of d.
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NPR OBJ ? R, ? R ? w1j
(? Rj Rj t ) 2 w2j ? 2 Rj
J1  sub.to Gi (? ) k ? Gi ? 0 , i
1,2,.NC dL ? d ? dU   Where, w1j is
the weight parameter for mean on target, w2j
that for the jth performance to be robust, ?Rj
and ?Rj the mean and standard deviation of the
jth performance, Rj t is the target value of the
jth performance and NPR is the number of
performances to be robust.
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For the robust design for best overall
performance over the entire life time the
objective function is based on the joint
probability density function of the random
variable x .
NPR OBJ ( d, x ) ? x ? wj Rj (d,x) f x
(x) dx J1 s.t Gi (? ) k ? Gi ? 0 ,
i 1,2,.NC dL ? d ? dU Where f x (x) is
the joint probability density function of the
random variable x, Rj (d,x) is the jth
performance function to be minimized and wj is
the weight parameter for the jth performance to
be robust.
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Mathematical formulation of reliability based
design (RBDO) problem
Minimize OBJ (d) s.t P ( Gi (d ) ? c ?
CFLi , i 1,2,.NC dL ? d ? dU where
CFLi is the confidence level associated with the
ith constraint, P denotes the probability, Gi (d
) is the ith constraint function and c is the
limiting value. Example P ( stress 1 ? ? y
) ? 99.0 , where ? y is the yield stress.
(ie) Since there are some uncertainty in the
material properties, instead of stating the
constraint as, stress 1 ? ? y, it is stated as
the probability of stress 1 ? ? y, is greater
than or equal to 99.0.
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Robust Reliability Based Design.
When the objective function is based on the
robust design principle, focusing on making the
response insensitive to the variations in the
design variables and the constraints are modified
to probabilistic constraints with the assigned
probability of each constraint function, the
result is a Robust Reliability Based Design
(RRBDO)
The mathematical formulation of such a method is
given below.
Minimize OBJ ? R, ? R  s.t P ( Gi (d )
? c ? CFLi , i 1,2,.NC dL ? d ? dU
 where NC is the number of constraints and the
objective function is defined as
NPR OBJ ? R, ? R ? w1j (? Rj Rj
t ) 2 w2j ? 2 Rj J1
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Plan of Action for the Next Two Years
Final thesis submission
Robust Reliability based MDO of the Aerospace
vehicle design
Integration of MDO architecture with robust
design techniques probability analysis
Draft thesis preparation, review modifications
Understanding, practising applying stochastic
techniques
Exploring the options for probabilistic design
applying to the problem
Activity
Identifying understanding the uncertainty
analysis methods
Identifying a proper strategy to attack the
problem
Review of the strategy modifications
Defining the design problem, identifying the
constraints, control variables, noise factors
objective functions.
2nd Progress seminar

Literature Survey exploring in-depth
information on robust reliability based design
practices, techniques the related research
works around the globe
August, 03
August, 04
August, 05
Month / Year
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Acknowledgement
I would like to express my sincere thanks to
Prof. K. Sudhakar and Prof. P.M. Mujumdar of
Aerospace Engineering Department for their
continuous guidance, encouragement and support.
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Methods of simulating the variation in noise
factors

• Monte Carlo Simulation
• Taylor Series Expansion
• Orthogonal Array based Simulation

• Monte Carlo Simulation
• A random number generator is used to simulate a
  large number of combinations of the noise factors
  called testing conditions.
• The value of the response is computed for each
  testing conditions and the mean and variance of
  the response are then calculated.
• For obtaining accurate estimate of mean
  variance, the Monte Carlo method requires
  evaluation of the response under a large number
  of testing conditions. This can be very
  expensive, especially if we also want to compare
  many combinations of control factor levels.

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Methods of simulating the variation in noise
factors- contd

• Taylor Series Expansion
• The mean response is estimated by setting each
  noise factor equal to its nominal value. To
  estimate the variance of the response, the
  derivatives of the response with respect to each
  noise factor is found out.
• Let R denote the response and ?12 , ?22,?n2
  denote the variance of n noise factors. The
  variance of R is then computed by the formula
• ?R2 ? (?R / ?xi)2 ?i2 , where xI is
  the ith noise factor.

n
i1
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Methods of simulating the variation in noise
factors- contd

• Orthogonal Array based Simulation
• Orthogonal arrays are used to sample the domain
  of noise factors. For each noise variable
  different levels are taken.
• The advantage of this method over the Monte
  Carlo method is that it needs a much smaller
  number of testing conditions yet the accuracy
  will be excellent. The orthogonal array based
  simulation gives common testing conditions for
  comparing two or more combinations of control
  factor settings.

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Amy E. Kumpel, Peter A. Barros Jr., and
Dimitri N. Mavris Quality Engineering Approach
to the determination of the Space Launch
capability of the peace keeper ICBM utilizing
probabilistic methods 1 - AIAA 2002-10-6
Discuss about the use of a comprehensive and
robust methodology for the conceptual design of
an expendable launch vehicle employing the
existing Peacekeeper ICBM This methodology
includes an Integrated Product and Process
Development (IPPD) approach, coupled with
response surface techniques and probabilistic
assessments. It also provides a probabilistic
framework to address the inherent uncertainty in
vehicle requirements in an analytical manner by
representing payload, mission, and design
requirements as distributions instead of point
values. The three primary objectives identified
are (i) to design for the minimization of the
time-to-launch, (ii) minimization of development
and production costs, and (iii) the maximization
of useable payload
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The first step in the design process was to
define the problem by mapping the customer
requirements to engineering characteristics. A
Quality Function Deployment approach, utilizing a
House of Quality, was employed. Possible engine
and propellant types, as well as staging
arrangements, were organized in a Morphological
Matrix of design alternatives. Several vehicle
concepts from the Morphological Matrix were then
evaluated in terms of performance, cost,
availability, reliability, safety, commonality
with existing space systems, and compatibility
with various launch sites.
Ranges were assigned to several significant
design variables, and a sensitivity analysis was
performed on the responses to see how small
perturbations in the design variables would
affect the outcome. A parametric study was also
performed on some of the assumptions made in the
design process so that the exact effects of the
estimates on the vehicle concept could be
determined. A Response Surface Methodology (RSM)
in conjunction with a Monte Carlo simulation was
used for these tasks. This methodology was an
iterative process and was repeated until both
technical feasibility and economic viability were
achieved.
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The tool employed in the problem definition stage
of this study was the Quality Function Deployment
(QFD) process which is a "planning and problem
solving tool that is finding growing acceptance
for translating customer requirements into the
engineering characteristics of a product. The
broad requirements of the engineering
characteristics are transformed into an
interrelationship digraph (ID). A statistical
analysis software package called JMP is used to
create the DoEs. A Monte Carlo simulation is
used in conjunction with response surface
equations in order to model thousands of designs
in seconds. The software package Crystal Ball by
Decisioneering is used for this task. Crystal
Ball is a risk analysis software package and an
add-in to Microsoft Excel. It allows for the
definition of design variables as probability
functions bounded by a range or a set of values.
It then uses the defined ranges in a Monte Carlo
simulation. For each uncertain design variable, a
probability distribution is used to define the
possible values. Distribution types include
normal, triangular, uniform, logarithmic, etc.
The Monte Carlo simulation creates Probability
Distribution Functions (PDFs) and Cumulative
Distribution Functions (CDFs), in order to
illustrate the probability of success for a
response.
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A PDF is the mathematical function that maps the
frequency of the response to metrics within the
given range. The PDF is then integrated to
determine a CDF. The CDF is the mathematical
function that maps the probability of obtaining a
response to the metric within the given range.
If the amount of feasible design space is
unacceptable, three options exist for the
designer/decisionmaker   1. Modify the design
variable ranges 2. Relax the constraints 3.
Select a different alternative concept.   At this
point in the design process, the system is
evaluated to check if the responses satisfy the
customer requirements as established in the
problem definition phase. If any of the
requirements are violated at any point in this
iterative process, the design process will be
repeated.
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Brent A. Cullimore , Reliability Engineering
Robust Design New Methods for Thermal / Fluid
Engineering14, C R White Paper, Revision 2,
May 15, 2000
Mention that overdesign provides robustness but
it is costly in areas such as aerospace. He
modified SINDA/FLUINT, the thermodynamic analyzer
software to make the design robust by
statistically integrating the probabilities of
design variables to control the probability of
response. The paper dwells on the SINDA/FLUINT
software and also mention about the add on
software named Relaibility Engineering module,
which will estimate the reliability of a point
design based on uncertainties in the dimensions,
properties, boundary conditions etc.
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Few possible capabilities of Reliability
Engineering Module in SINDA/FLUINT (1) A design
can be selected using the solver and then (in the
same or later run) the reliability of that design
can be estimated. (2) The reliability of a design
can be used as an objective (maximize reliability
or minimize the chances of failure). (This
feature can be useful to the present
problem). (3) The reliability of a design can be
used as an optimization constraint (find the
minimum mass design that achieves a reliability
of at least 99). (4) The range or variance of a
random variable can be used as a design variable
What variations can be tolerated how tight must
tolerance be ?. The paper also mention about a
commercial tools named Engineous iSIGHT that
can perform optimization, reliability estimation
and robust design generation.
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Wei Chen, Kemper Lewis, A Robust Design
Approach for Achieving Flexibility in
Multidisciplinary Design2, http/www.uic.edu/la
bs/ideal/pdf/Chen-Lewis.pdf (2001)
Explained the two types of robust design. In type
1, the robust design concept is applied to the
early stages of design for making decisions that
are robust to the changes of downstream design
considerations (called Type I robust design).
Furthermore, the robust design concept is
extended to make decisions that are flexible to
be allowed to vary within a range (called Type II
robust design) 2,18. In Type II robust design,
the performance variations are contributed by the
deviations of control factors (decision
variables) rather than the noise factors. The
concept behind Type II robust design for
determining flexible design solutions is
represented in Figure below.
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For a typical optimization model that is stated
below
The robust optimization can be formulated as a
multiobjective optimization problem shown as the
following
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?f and ?f are the mean and the standard
deviation of the objective function f (x),
respectively. In the above equation, the mean
locations and the range of design solutions are
identified as x and ?x. To study the variation of
constraints, the worst case scenario is used,
which assumes that all variations of system
performance may occur simultaneously in the worst
possible combination of design variables. To
ensure the feasibility of the constraints under
the deviations of the design variables, the
original constraints are modified by adding the
penalty term to each of them, where kj are
penalty factors to be determined by the designer.
The bounds of design variables are also modified
to ensure the feasibility under deviations.
Depending on the computation resource, ?f and ?f
could be obtained through simulations or
analytical means such as Taylor expansions.
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Improving the quality of a product through
minimizing the effect of the causes of variation
without eliminating the causes
To assure proper levels of safety (Probability
of being safe) for the system designed
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Wei Chen, Xiaoping Du, Efficient Robustness
and Reliability Assessment in Engineering
Design, www.icase.edu/colloq/data/colloq.Chen.Wei
2001.5.9.html (2001)
Narrates the difference between Robust Design
Reliability based Design and Integrated Robust
Reliability Assessments and schematically
presented the procedure for optimization under
uncertainty.
Uncertainty Classification
Catastrophe
Risk analysis Reliability based Design
optimization
Impact of events
Cost benefit analysis Robust Design optimization
Performance loss
Everyday fluctuations
Extreme events
Frequency of events
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And the difference in problem formulation for
Conventional Optimization model Robust Design
model is given as below.
Integrated Robustness Reliability Assessments
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Stephen M. Batill, John E. Renaud, Xiaoyu Gu
Modeling Simulation Uncertainty in
Multidisciplinary Design Optimization
AIAA-2000-4803
Dwell on the technical risk uncertainty in the
model based design of physical artifacts. The
issues of physical process variability,
information uncertainty and the influence of the
use of models simulations on the design
decision process are discussed. This paper only
qualitatively addresses these issues. It suggests
Monte Carlo simulation for uncertainty analysis
in which variations in the design variables
parameters are selected from an appropriately
selected population of random numbers.
57
Daniel P.Schrage Technology for rotorcraft
affordability through Integrated Product/Process
Development (IPPD) 19 55th Annual Forum of
American helicopter Society, May 25th 29th,
1999.
Highlights the Robust Design Simulation as the
main approach in the roadmap to Affordability. He
defines the benefit-cost ratio (BCR) as an
objective and defines robust design as the
systematic approach to find optimum values of
design factors which results in economical
designs which maximize the probability of
success. The steps in economic risk analysis
other research activities in the related areas at
Georgia Tech are mentioned.
58
Focus on to the specific Aerospace Vehicle Design
Problem

• To design a reusable technology demonstrator (
  for the First stage of Two Stage to Orbit fully
  reusable Launch Vehicle.)

TSTO Features

• 10 T to LEO (Low earth Orbit) payload capability
• Vertical take off
• Semicryogenic booster stage with Isp of 330 sec
  (mission average) cryogenic orbiter stage Isp
  400 sec (mission average)
• Total lift off weight lt 700 tons
• Winged body booster which should boost the
  orbiter to Mach 10 at altitude of 80-100 km then
  separate, return to launch site land horizontally
  in a conventional runway of 2.5 km stretch.

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• The vehicle structures should be designed for 100
  flights engine/ stage systems should be for 50
  flights
• Turn around time should be 30 days
• The service life life of the vehicle should be 15
  years
• Ideal velocity at 400 km circular orbit 9.8
  km/sec
• Number of missions lt Ten per year
• Payload fraction 2 (Measure of efficiency of
  the vehicle)
• Cost effectiveness lt 1000/kg for the LEO payload
• Realizability Total development time lt10 years
• Reliability gt0.995
• (Other features which are not relevant to the
  specific design problem are not mentioned)
• The mission profile of the TSTO vehicle is shown
  in the next slide.

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Flying regimes and related parameters of the TSTO
first stage

• Vertical lift off with T/W of 1.3 (GLOW lt 700
  tons)
• Maximum acceleration (longitudinal) during ascend
  phase lt 10g
• During the ascend boost phase the maximum dynamic
  pressure should be 120 KPa and angle of attack
  should be less than 3 degree
• Separation altitude velocity 80-100 km Mach
  10
• Re-entry altitude 100-80 Km
• Angle of attack during re-entry 40 deg
• During the re-entry phase the dynamic pressure
  should be less than 20 KPa and the maximum
  lateral acceleration should be 3 g
• Maximum Heat flux during re-entry lt 50 Watts
  /sq-cm
• Turn around manoeuvres by aero control surfaces
  Elevons rudders

61

• Cruise Mach number 0.8
• Cruise altitude 12 km
• Down range at cruise start 800 km
• Angle of attack at touchdown lt 15 deg
• Horizontal velocity at touch down 80-100 m/sec
• The sink rate at touch down lt 4.5 m/sec
• The landing roll shall be lt 2 km

So the task is to design a Technology
demonstrator for the first stage of this TSTO
62
Design Guidelines

• Maximum landing speed (horizontal) is ? 85 m/sec
• Subsonic L/D max 4.5.
• The vehicle should have near neutral stability at
  subsonic speeds.
• The vehicle should be trimmable at all Mach
  numbers.
• The vehicle takes off vertically and lands
  horizontally hence the wing design should be for
  landing and checked for the other flight regimes.
• It should have minimum pitching about CG for
  mated configuration, with the solid boosters.
• 7.    The hypersonic L/D shall be ? 1.5 for
  better cross range.

contd
63

• The landing weight of the vehicle is taken as
  equal to the take off weight to take care of the
  abort missions.
• The wing loading should be selected in such a way
  that the structural weight is minimum.
• Wing plan form should be selected for the best
  performance in hypersonic as well as subsonic
  regimes.
• Wing should provide a lift equal to the GTOW
  during cruise at subsonic speed (Mach 0.8) at
  altitude of 12 km.
• The airfoil should be selected to have maximum Cl
  at landing and lower heating at hypersonic speed
  as well as for mounting of tiles, the bottom flat
  airfoil is preferred.
• The control surfaces should be sized to trim the
  vehicle with minimum force and maintain the
  attitude at hypersonic speed.

contd
64

• Fuselage fore body should be shaped so as to
  minimize the re-entry heating, to have minimum
  drag and for good directional stability.
• Wing leading edge sweep shall be not less than 45
  deg.
• Wing leading edges shall be blunted to reduce
  re-entry heating.
• Low aspect ratio wing with highly swept leading
  edge angle shall be considered to reduce heating
  and drag.
• Thickness of airfoil shall be selected based on
  lift, drag leading edge bluntness requirements.
  
• Vertical tail area should be designed to provide
  positive directional stability and rudder shall
  be designed for landing conditions at high angle
  of attack in cross-wind and aft C.G conditions.

contd
65

• The gaps between control surfaces and
  aerosurfaces shall be kept minimum to reduce the
  heating problems to improve the performance.
• The fuselage should be sized considering the
  volume requirements for accommodating the
  avionics systems, propulsion modules, landing
  gears and other auxiliary systems and also for
  better interfacing with the carrier solid
  boosters.
• The vehicle should be capable of testing the
  scramjet module in a dedicated mission.
• The vehicle should have a supersonic cruise
  capability at Mach 3.0 using the ramjet engine.

66
After analysing the additional requirements in
terms of technology, from all the entities the
major objectives of the RLV-TD are listed as
follows 23.

• (i) To evaluate the aero-thermo dynamic
  characteristics of wing body vehicle and
  associated control surface effectiveness at
  various flight regimes i.e. from sub-sonic to
  hypersonic zones.
• (ii) To assess the autonomous navigation,
  control and guidance schemes to function in the
  demanding environment of re-entry, cruise flight
  and auto-landing phase with constraints on loads
  and thermal environment.
• (iii) To demonstrate the auto-landing
  technologies including landing gear, aerodynamic
  control, deceleration systems etc.
• (iv) To evaluate the thermal protection system
  (TPS), re-usable light weight structures for
  multiple missions (say about 100), evaluation of
  air-breathing propulsion system, to design and
  validate redundant electro-mechanical actuators
  to control the vehicle at severe environment
  condition.
• (v) To evaluate the integrated flight management
  and ground operation requirements.
• (vi) To demonstrate the scramjet propulsion
  module.

67
The Challenges

• The multidisciplinary nature
• The coupling with different disciplines and a
  large design variable set
• Uncertainties of parameters and model structure
• The computational burden

The best solution to tackle the uncertainties is
the robust design solution (ie) by making a
design insensitive to the variations in noise
factors and to tackle the variation in the
control factors a reliability based solution in
which the constraints are stated
probabilistically to get the probability of an
objective function for a known deviations in the
control factors.
68
Information flow of a Multidisciplinary System
69
Complexities of MDO under Uncertainties
Xs- the sharing variables Xi-the design variables
of subsystem (discipline) i, Yij-linking
variables of subsystem Zi-output of subsystem i
70
A Typical model with uncertainties
71
The major disciplines involved in the design of
the aerospace vehicle are Aerodynamics,
Structures, Aero-thermodynamics Propulsion and
control.
(1) Aerodynamics F1 (Xs, X1,Y21----Y51) ?1 (Xs,
X1,Y21----Y51)
(2) Structures F2 (Xs, X2,Y12--Y52) ?2 (Xs,
X2,Y12--Y52)
(3) Propulsion F3 (Xs, X3,Y13--Y53) ?3 (Xs,
X3,Y13--Y43)
RMDO
(4) Control F4 (Xs, X4,Y14--Y54) ?4 (Xs,
X4,Y14Y54)
72
K.K.Choi, B.D.Youn, Issues Regarding Design
Optimization Under Uncertainty,
http//design1.mae.ufl.edu/nkim/index-files/choi4
.pdf
Emphasizes the different ways of applying the
term robustness as, Definition 1- Identify
designs, which minimize the variability of the
performance under uncertain (manufacturing or
operation) conditions, Definition 2 -Provide the
best overall performance over the entire lifetime
of the structure or device and Definition 3-
Mitigate the detrimental effects of the
worst-case performance. The design with the
best worst-case performance is selected as the
robust solution as per definition 3.
The conventional optimization model is defined as
Minimize OBJ (d) s.t Gi (d) ? 0, i
1,2,.NC dL ? d ? dU where OBJ is the
objective function, Gi is the ith constraint
function, NC is the number of constraints, d is
the design variable vector, dL dU are the
lower upper bounds of d.
73
In robust design, of definition 1 the objective
is to keep the mean on target minimize the
variation. So the mean standard deviation of
the response will constitute the objective
function. So the formulation will be Minimize
OBJ ? R, ? R   s.t Gi (? ) k ? Gi ? 0 ,
i 1,2,.NC dL ? d ? dU where ? R, ? R
are the mean standard deviation of the response
R, Gi (? ) and ? Gi are the mean standard
deviation respectively of the ith constraint
function, k is the penalty function decided by
the designer 5, d is the design variable
vector, dL dU are the lower upper bounds
of d.
Here the objective function takes care of the
signal noise factors and the constrained
functions are modified such that the allowed
variation in them are limited by the sigma
bounds.
74
NPR OBJ ? R, ? R ? w1j (? Rj
Rj t ) 2 w2j ? 2 Rj
J1  s.t Gi (? ) k ? Gi ? 0 , i
1,2,.NC dL ? d ? dU Where, w1j is the
weight parameter for mean on target, w2j that
for the jth performance to be robust, ?Rj and ?Rj
the mean and standard deviation of the jth
performance, Rj t is the target value of the jth
performance and NPR is the number of performances
to be robust
75
And for the robust design for best overall
performance over the entire life time
(definition2) the objective function is based on
the joint probability density function of the
random variable x . According to the theory of
probability statistics, integral of the
probability density function will give the
probability and when this is multiplied by the
performance function, the expected value
corresponding to that probability will be
obtained. The expression given below is based on
this theory.   NPR OBJ ( d, x ) ? x ? wj
Rj (d,x) f x (x) dx J1 s.t Gi (? ) k
? Gi ? 0 , i 1,2,.NC dL ? d ? dU
 Where f x (x) is the joint probability density
function of the random variable x, Rj (d,x) is
the jth performance function to be minimized and
wj is the weight parameter for the jth
performance to be robust.
76
In the Reliability Based Design Optimization
(RBDO) problems, the objective is to maximize
expected system performance while satisfying
constraints that ensure reliable operation.
Because the system parameters are not necessarily
deterministic, the objective function
constraints must be stated probabilistically. For
example RBDO can determine the manufacturing
tolerance required to achieve a target product
reliability because the method considers the
manufacturing uncertainties, such as dimensional
tolerance as probabilistic constraints. RBDO
will ensure proper levels of safety reliability
for the system designed. The mathematical
formulation for RBDO is shown below18.  
Minimize OBJ (d) s.t P ( Gi (d ) ? c ?
CFLi , i 1,2,.NC dL ? d ? dU  where
CFLi is the confidence level associated with the
ith constraint, P denotes the probability, Gi (d
) is the ith constraint function and c is the
limiting value.
77
The following example 8 will clear the concept
of probabilistic constraint. P ( stress 1 ? ?
y ) ? 99.0 , where ? y is the yield stress.
(ie) Since there are some uncertainty in the
material properties, instead of stating the
constraint as, stress 1 ? ?y, it is stated as
the probability of stress 1 ? ?y, is greater
than or equal to 99.0.
When the objective function is based on the
robust design principle (with mean standard
deviation of the response), focusing on making
the response insensitive to the variations in the
design variables and the constraints are modified
to probabilistic constraints with the assigned
probability of each constraint function, the
result is a Robust Reliability Based Design
(RRBDO) The mathematical formulation 18 of
such a method is given in the next slide.  
78
Minimize OBJ ? R, ? R  s.t P ( Gi (d )
? c ? Poi , i 1,2,.NC dL ? d ? dU
where NC is the number of constraints and the
objective function is defined as NPR OBJ
? R, ? R ? w1j (? Rj Rj t ) 2
w2j ? 2 Rj J1   The
different parameters in the above definition are
already explained in the formulation for robust
design. This approach will yield a design whose
response is insensitive to the effects of noises
whose reliability can be predicted based on the
reliabilities apportioned to the different
constraints.