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BOEING is a trademark of Boeing Management Company.Copyright © 2008 Boeing. All rights reserved. 1

A Perspective on OptimizationKumar G. BhatiaBoeing Senior Technical FellowAeroelasticity and Multidisciplinary Optimization

12th AIAA/ISSMO Multidisciplinary Analysis and Optimization ConferenceVictoria, BC, September 12, 2008

Copyright © 2008 Boeing. All rights reserved. 2

Abstract

Optimization in its multitude of forms has entered all aspects of design. What was nascent has become functional to a degree but we still have a long ways to go. The disciplinary optimization pockets exist much more abundantly than the multidisciplinary optimization teams. Many of the current multidisciplinary optimization applications are not able to deal with the levels of fidelity required for making robust design decisions.

The growth of multidisciplinary optimization depends as much on organizational parameters as it does on the technology. To become truly effective multidisciplinary optimization needs to become an integral part of analysis and design process instead of being promoted as a specialty. It is interesting to consider the growth of the finite-element methods and the Computational Fluid Dynamics and how they have become pervasive in industrial environments. These two technologies have followed somewhat different paths of evolution in finding their places in the industry. We can discern how the penetration of multidisciplinary optimization in every day design environment might be accelerated by understanding the two evolutionary paths. A synergetic and enlightened technical and business relationship between the software vendors and the major manufacturers also will be necessary to support the development of better commercial applications which might provide a foundation for the manufacturers to develop their proprietary design or multidisciplinary applications


Acknowledgements

The Boeing Team whose work is the basis for some of the results and cycle times reported in this presentation:

• Frode Engelsen, Paul Frank, Tom Grandine, Krishna Hoffman, Bill Huffman, Geojoe Kuruvila, Joris Poort, Josh Stengel, Kannan Sundararajan, Zack Thunemann, Dave Young, Sean Wakayama, Jason Wu

Boeing internal Application Development funding supported by Robert McIntosh and Steve Sawyer

Dr. Joaquim Martins for sharing his course notes for his MDO class at the University of Toronto


Outline

Introduction and Multidisciplinary Optimization Vision

Engineering Optimization

Challenges and Approaches for Optimization

Balancing the Aerodynamic and Structural Optimization

Lessons Learned

Concluding Remarks


Introduction

This talk contains my personal views in the spirit of sharing with the larger technical community the technical challenges we face in making MDAO as an everyday design tool in order to contribute towards creating a more efficient societyMy views are shaped by my professional career at Boeing Commercial Airplanes and about two years spent as an NRC Associate Post-Doctoral Fellow in the Aeroelasticity Branch at NASA Langley Research Center during early seventiesI am grateful for the many opportunities to learn and am particularly fond of the 8 years or so working on the High Speed Civil Transport where optimization and improved methods were required and very welcomeMy background is more in the areas of Structural Optimization with Aeroelastic Constraints but I have aspired to learn more about Aeroservoelastic Optimization, Aero-Structures Optimization and the broader aspects of Multidisciplinary OptimizationMany of my colleagues have contributed to what I am presenting, and I will verbally acknowledge their contributions throughout the presentation


Optimization Vision Configuration and Planform Optimization Rapid Cycling with Parametric Design Scenario


Optimization Vision: Configuration Synthesis


Outline





Lessons Learned

Concluding Remarks



The foundation for numerical optimization was formed by the practical development of the finite-element method. The first publication was by the legendary Boeing engineer Jonathan M. Turner with R. Clough, H. Martin and L.Topp in 1956 (Stiffness and Deflection Analysis of Complex Structures, J. Aero. Sciences). The first usage of the term finite element is said to be by R. Clough (2nd Conf. on Electronic Computation, ASCE, 1960).

The first engineering application of nonlinear mathematical programming to optimization was by Lucien Schmit as set forth by the structural synthesis concept (2nd Conf. on Electronic Computation, ASCE, 1960). Schmit brought the ideas of Operations Research to Structural Optimization and suggested “coupling finite element structural analysis and nonlinear mathematical programming to create automated optimum design capabilities for a rather broad class of structural systems” (Structural Synthesis-Its Genesis and Development, AIAA J., Oct. 1981).


Structural Optimization - 1

Schmit describes reaction to his proposals in 1959: it was already done and the proposal was “hopelessly complicated and impractical.”

1960-1970: Two system level structural synthesis programs were developed:• Gallagher and Gellatly at Bell Aerosystems (Aeronautical Qtly, 1966)• Karnes and Tocher at Boeing (AIAA 73-361, 1971) which Schmit considers

as “the most general and sophisticated structural synthesis program available at the end of the 1960-1979 decade.” It had design variable linking and “partial derivatives were recalculated when the design moved outside a user defined hypersphere.”

By 1970: “The finite element analysis with mathematical programming techniques required inordinately long run times to solve structural design problems of only modest practical size.”

This situation led to the development of the Fully Stressed Design and Optimality Criteria Methods led by Venkayya and others (Venkayya, Khot and Reddy, 2nd Conf, on Matrix Methods in Structural Mechanics, AFFDL-TR-68-150, 1969), and the development of computer systems such as FASTOP.


Structural Optimization - 2

The seventies also saw additional developments towards overcoming some of the shortcomings of mathematical programming and the practical inclusion of additional disciplines to the Optimization family:

• Analytic flutter sensitivities (Rudisill and Bhatia, 1971, 1972)• Automated Flutter and Matched Point Solution (Bhatia, 1973)• Wing Strength and Flutter Sizing (WIDOWAC, Haftka, 1973)• Rapid Iterative Reanalysis for Automated Design (Bhatia, NASA TN D-

7357,1973)• Accuracy of Taylor Series Approximations for Structural Resizing (Storaasli

and Sobieski, 1974)• Approximation Concepts for Efficient Structural Synthesis (Schmit and

Farshi, 1974 and Schmit and Muira, 1976)• Preliminary Design of Composite Wings (Starnes and Haftka, 1978)• Combining Approximate Concepts and Dual Methods (Schmit and Fleury,

1980)With these and other developments much of the foundation for Structural Optimization was laid but still there were hardly any industrial applications


Structural Optimization: The Paradigm Shift

“The use of mathematical programming for structural optimization breathed new life in 1974 when Schmit and Farshi published the concept of approximate techniques for structural synthesis” as observed by Vanderplaats (AIAA-97-1407).

According to Schmit (1981): “The introduction of approximation concepts leading to a sequence of tractable approximate problemsvia the coordinated use of design variable linking (and/or basisreduction), temporary constraint deletion (regionalization and truncation), and the construction of high quality explicit approximations for retained constraints (using intermediate variables and Taylor series expansions), has led to the emergence of mathematical programming based structural synthesis methods that are computationally efficient.”


Aerodynamic Optimization – 1

There have been several good survey papers on Structural Optimization over the years but there does not appear to be any comprehensive survey paper on Aerodynamic Optimization!

An Assessment of Airfoil Design by Numerical Optimization (Hicks, Murman and Vanderplaats, 1974)

Wing Design by Numerical Optimization (Hicks and Henne, 1978)

Aerodynamic Design via Control Theory (Jameson, 1988)

Practical Design and Optimization in Computational Fluid Dynamics (Huffman et al, 1993)

Issues in Design Optimization Methodology (Young et al, Several Boeing Reports, around 1994

Practical Considerations in Aerodynamic Design Optimization (Jou et al, 1995)


Aerodynamic Optimization - 2

Constrained Multipoint Shape Optimization Using and Adjoint Formulation and Parallel Computers (Reuther, Jameson, Alonso, Rimlinger, Sauders, 1997)

A comparison of the Continuous and Discrete Adjoint Approach to Automatic Aerodynamic Optimization (Nadarajah and Jameson, 2000)

Effect of Shape Parametrization on Aerodynamic Shape Optimization (Castonguay and Nadarajah, 2007) – an undergraduate student is the first author!

Optimum Transonic Wing Design Using Control Theory (Antony Jameson, 2002)


Aero-Structural Optimization

A Coupled Aero-Structural Optimization Method for Complete Aircraft Configurations (Reuther, Alonso, Martins and Smith, 1999)

Complete Configuration Aero-Structural Optimization Using a Coupled Sensitivity Analysis Method (Martins and Alonso, 2002)

Aero-Structural Wing Planform Optimization (Leoviriyakit and Jameson,2004)

An Adaptive Approach to Constraint Aggregation using Adjoint Sensitivity Analysis (Poon and Martins, 2007) has a very good explanation of Kreisselmeier–Steinhauser (KS) function used by many to aggregate structural constraints

Wing Design by Aerodynamic and Aeroelastic Shape Optimisation (Morris, Allen and Rendall, 2008)


Multidisciplinary Optimization -1

Main focus has been on the wing with a few exceptionsIntegrated Multidisciplinary Optimization of Actively Controlled Fiber Composite Wings, UCLA Dissertation, Livne, 1990 showed the advantages of simultaneous optimizationIntegrated Aeroservoelastic Optimization and Status: Status and Direction (Livne, 1999) has a very good summary with special focus on Structural Synthesis and AeroservoelasticityMultidisciplinary Aerospace Design Optimization :Survey of Recent Developments (Sobieski and Haftka, 1996) has a good summary andconsidered the cost of each structural analysis to be much lower than the cost of the aerodynamic analysisMOB A European Distributed Multi-Disciplinary Design and Optimisation Project (Morris, 2002) uses a BWB configuration for a demonstration of MDOMDOPT – A Multidisciplinary Design Optimization System Using Higher Order Analysis Codes (LeDoux, Herling and Fatta, 2004) describes an advanced framework, option of various aerodynamic methods coupled with ELAPS


Multidisciplinary Optimization -2

Blended-Wing-Body Optimization Problem Setup (Wakayama, 2000) demonstrated one of the most complete vehicle synthesis processes for preliminary configuration design (incorporated in WingMOD)

Design Trades for a Large Blended-Wing-Body Freighter (Wakayama, Gilmore and Brown, 2003) has one of the best MDO applications again using WingMOD


Some Observations about MDO Applications - 1

Often the structural design problem is under appreciated in the Aerodynamics community and is oversimplified as a Ku=P linear problemMost MDO applications are Aerodynamics centric and appear to be based on the belief that the structural design problem is a much simpler problem than the aerodynamic design problem. In fact all disciplines have their own challenges.Higher order CFD codes (Navier-Stokes, Euler, Full Potential) have been coupled with structural analyses which are too simple and structural design conditions considered have been too incomplete to be of much practical useThe bundling of stress constraints in a KS function causes me some discomfort since in actual practice instead of stress constraints, margins are determined for multiple failure conditions (e.g., about 20+ failure conditions for each stiffened panel)In the current design environment, structural design conditions include many design conditions (O(10) in preliminary design to O(10,000) in detailed design) covering static loads, dynamic loads and flutter calculated with an active flight control system often to reduce loads and sometimes to increase damping


Some Observations about MDO Applications - 2

The airplane design is optimized iteratively and somewhat informally by multiple disciplines over a period of time

Formal Optimization needs to automate these iterations over muchshorter periods of time. Herein lies the promise and the challenge.

I am not aware of any balanced MDO system where each discipline is addressed at a consistent and appropriate level of fidelity. WingMOD for early PD may be one of the exceptions where the emphasis is on including many design elements with emphasis on speed.

Any credible MDO application should have acceptance and approval from all the included domains and disciplines


Outline





Lessons Learned

Concluding Remarks


Challenges for MDO

Lack of faith, and therefore lack of coordinated and integrated effort to develop an MDO framework and capabilities

• Management is not sure how practical and encompassing MDO can be and the proponents have not demonstrated it either.

• Practical MDO capability is difficult and expensive to develop• Different “MDO experts” believe in and promote their own approaches• Industry has the true expertise but does not have sufficient appetite• Not all the domain experts believe that MDO is practical and that they should

invest their time to automate their processes to support MDO iterations• Discipline leaders are focused at best on automation in their own domains

where they have control and see no definite, further advantage in tightly integrated systems which will require even more of their stretched resources and perhaps lead to a loss of control or at least diminish their control.

• How do we integrate knowledge from different domains into a cohesive and practical MDO system?


An Approach for MDO Development

Focus on the total cycle time which includes the time required to create analysis models and set ups as well as the solution time

Since a good MDO system will take a long time to develop, it must follow certain good software development principles and a well thought out strategy:

• Knowledge Environment• Neutral (specific domain “independent”) optimization framework• Modular Architecture • Ability to explore different approaches (e.g., approximations, optimizers, etc.)• Standard domain or discipline processes preferably the same processes

through the design cycles (with the fidelity and completeness increasing going from early preliminary design to detailed design)

• Avoid software obsolescence

Start with Preliminary Design, followed by Detailed Design and Manufacturing, and ultimately the Life Cycle Cost Optimization


A Preferred MDO Architecture

• Leverage all relevant, existing, known Knowledge

• Developing in a Proprietary environment

• Object model facilitates maintaining and leveraging relationships between different representations

• Only file transfers are to the solvers, and no file transfers should be necessary between disciplines

• Variable fidelity models with minimum process changes throughout design progression

• Think about options for intelligent engineering – natural language user interfaces using intelligent agents

• Will need object data bases with a suitable object model architecture for large scale applications

Design and AnalysisKnowledge Base

ConfigurationKnowledge -Based

System

Configuration Definition

Configuration Recommendations

Weights

Sizing

Empirical Aerodynamics

Linear Aerodynamics

CFD

Static Loads

Dynamic Loads

Flutter

Finite -Element Model

Flight Controls

Wireframe

CAD System

BAPNastran

..

Database

Kno

wle

dge

Env

ironm

ent


Parametric Aero-Structural Wing-Body Model

Parametric Planform• Semi-span• Taper ratio• Aspect ratio• Quarter chord sweep• Yehudi parameters• Airfoil maps• …

Parametric Airfoils• CST parameterization• Airfoil locations• LE radius• TE angle• TE thickness• Shape functions• …

Parametric Structure• Rib spacing• Stringer spacing• Fuselage frame spacing• Floor locations• …

Parametric Spars• Spar break locations• Limit lines


Parametric Structural Layout

Stringer spacing in Section 12 carries into Section 11

10” Stringer Spacing 20” Stringer Spacing

Variable number of longitudinal stations in Section 11 properly integrate with Sections 41 and 46

Station 20

Station 0

Station 12

Station 0


Outline





Lessons Learned

Concluding Remarks


Balancing the Aerodynamic and Structural Optimization Cycles

Tranair Multi-point Design (5 Mach numbers) for a Production Size Airplane Model (1-2 Million Grid Points, 100-150 Shape Functions for a typical wing design problem)

• ~ 24 hrs with 6 Processors (1 Day)Structural Optimization for an Aeroelastic Production Type FEM

• NASTRAN Sol 200• ~400 DV, 13 Static Load Cases• Approximate Constraints: 90K Total, up to 7500 Retained, up to 300 Active • Fixed Aerodynamic Data Base• ~9 Hours (Single CPU) per Optimization Cycle with Loads Update (Sol 144)• ~50 Cycles for convergence (20 Days)!

For the reported time, the structural model does not have sufficient number of load cases for an adequate design. It neither includes dynamic load cases not does it have flutter constraints.

Tranair is a very efficient aerodynamic optimization process

There is a need to speed up the Structural Optimization solutions


MDAO Implementation with BOPT Optimization Framework

Initial Design

Analysis 1

Converge?

Analysis 2 Analysis 3 Analysis n… …

Approximate Model 1

Approximate Model 2

Approximate Model 3

Approximate Model n… …

Merge Models & Perform Optimization

Output DesignNo Yes

Within/CrossDisciplines

As Required


Exploration with Structural Optimization

We thought that we can explore more efficiently by developing a prototype code on our ownApproach:

• Understand completely the NASTRAN Sol 200 formulation and data management

• Develop an object-oriented code in MATLAB • Use NASTRAN Toolkit to extract large data sets efficiently from the

NASTRAN data base• Use the Boeing developed SOCS-OPTLIB optimizer initially• Implement different approximation concepts


MSC Nastran Implementation of Structural Optimization


Notations for NASTRAN Sol 200 Structural Optimization

Super-script represents type of property and response

Type 2 response can be an input argument for another type 2 response; Omitted for shorter expression

Notation Example

x Design Variable (DV) Ratio

p1 =p1(x) Linear relationship between DV and gauge

p2 =p2(x) Relationship between the design and smeared model properties

r1 =(x,p2) Weight

r2 =(x,p1,p2,r1 ) Tech constraints; objective function

r3 =(x,p1,p2,r1,r2) Margins from the strength server

Copyright © 2008 Boeing. All rights reserved. 32BOPT

1

132121 ,,,,

x

xrrrpp

at sconstraint and objective gcalculatin for

at of gradients compute

and evaluate

Detailed Sol 200 Flow

Initial Design

Structural Analysis

Sensitivity Analysis

Constraint Screening

Approximate Model

Optimizer

Improved Design

Converge?

N

sconstraint and objective

ngconstructi for 32121

0 ,,,,, rrrppx

xxx Δ+← 00

xxx δ+= 01

YStop

loopmany times

xΔ

retained constraints

only

0x

0

32121 ,,,,x

rrrpp at

of iessensitivit

x

Non-linear Line Search

xΔxx Δ←Δ 9.0


Optimization Region Wing Box Structure

Optimization set up (single load case test)• 438 Design variables• 484 Technology constraints• 6,678 Stress constraints

Design Zone Definition


Design variable definition FEM idealization (Nastran)

Panel section

Skin layer thicknessesT0, T45, T90

Stringer cap widthsWoc, Wic

I-stringer layer thicknessesToc0, Toc45, Toc90 Tic0, Tic45, Tic90

Skin

~FWDUP

I-Section Wing Panel

Stringer (outer chord)

Stringer (inner chord)

Design model is derived from the smeared model


Failure Mode Tension Comp.Beam column 1 Skin x x

2 Skin flange x x3 Web x x4 Cap x x

Stability 5 Crippling - cap x6 Crippling - web x7 Lateral instability x8 Skin buckling x

BVID 9 Barely Visible Impact Damage xResidual Strength

10 DaDT x

Sample Strength Constraints for Sol 200 DRESP3 Formulation


Examination of Stress Constraint Sensitivity indicates more linear behavior than expected


Approximate Model Formulations Explored

Approx. Model Type DV type Objective DRESP2

ConstraintDRESP3 Constraint

Recalculation (Sol200-like)

Direct Linear Linear Non-linear*

Mixed Dir-Inv Model Direct Linear Linear Nonlinear

Linear Model (LP) Direct Linear LinearLinear

QP Model Inverse Quadratic Linear** Linear**

•Recalculate strength margin with direct DRESP3 call

Invariant DRESP3** Update NASTRAN sensitivity with chain rule w.r.t. inverse gauge


Approximate Model Exploration: Cycle History

Approx. Sol200 Recalc. Mixed LP QP

Time (min.) 68 55 17 19 17

0.00E+00

5.00E+03

1.00E+04

1.50E+04

2.00E+04

2.50E+04

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Sol200RecalcMixedLPQP

Objective

Cycle


Outline





Lessons Learned

Concluding Remarks


Lessons Learned and Improvements Identified for Structural Optimization Process

Significant improvements in cycle time were made by using direct design variables, eliminating expensive margin re-calculations and using SOCS optimizer

Further improvements can be gained by using a parallel LP solver

Additional improvements are necessary and can be achieved by making the sensitivities calculations more efficient and parallelizing them

• We should revisit the ideas of intermediate design variables for sensitivity calculations (Bhatia, 1973)

• Take advantage of the observation that the stiffness matrix sensitivities with respect to truss and plane-stress design elements are invariant as observed by Livne (1999)

Significant improvements are necessary in the loads recalculation process

We need a major revamp of structural optimization codes to take advantage of the new insights, and the progress in hardware and software architectures and capabilities

The goal is to be able to do structural optimization with 20K design variables and 100 load cases while updating the loads for each design cycle

It is not difficult to see why the structural optimization is not more widely used and why it is overly simplified for most of the Aero-Structural Optimization


Two-Pronged Approach with Common Elements

Create a rapid preliminary design focused multidisciplinary optimization system base on the following premises:

• “Real” parametric configurations• Structural design and material parametric choices• Completely automated and guaranteed to execute without a single

error in a knowledge environment• Standard processes deriving speed from multiple processors• Automated reports and documentation

Create a higher-fidelity system to perform simultaneous multidisciplinary optimization with appropriate fidelity for all the relevant disciplines

There are common elements to achieving both the objectives


Emergent Applications

For parametric configurations, I favor creating discrete “real” configurations which can be assessed rapidlyWe have the ability to use shape functions as an input to the structural optimization processes, and determine weight sensitivities to shape functions. We should assess inclusion of the loads sensitivities to shape functions and their effect on the gage sensitivities.However, there is increasing use of topology and related optimization applications being used in structural design. There are several vendors providing such capabilities and some of them are:

• Altair• MSC• VR&D

I would like to see topology optimization linked more closely with the overall structural design process. For example, the topology optimization should be linked tightly with the stress sizing routines similar to what is being done for gage optimizationWe don’t have time to go into details of their capabilities today but it is an important development which will help bring the analysis and design closer together, and eventually analysis, design and manufacturing together


Outline





Lessons Learned

Concluding Remarks


Optimization Vision: Configuration Synthesis We Need Additional Disciplines Included!


Concluding Remarks - 1

We have a few glimpses of good MDO applications specially for PD

A configuration synthesis capability still remains a dream

There are more real applications of high-speed aerodynamic optimization than of structural optimization

Structural optimization is much more involved and complex than most researchers seem to believe and composites provide their own set of challenges and opportunities

Structural optimization implementations need to be reviewed and the best formulations and software practices need to be incorporated

Advances are needed for solving more realistic structural designproblems involving pad ups and discrete composite layups along with manufacturing considerations


Concluding Remarks - 2

Structural topology optimization applications need to be coupled with realistic stress analysis and design methods to provide meaningful results

Additional aerodynamic considerations for high lift, and S&C need to be incorporated in MDO but before these can be incorporated the prediction methods need to validated

For realistic applications, significant automation is needed for preparing the models and inputs for optimization, and extracting meaningful output from the optimization runs especially if these fail to converge

PD applications hold the most promise for configuration optimization

We need to create parametric “real” configurations for assessment using optimization unless we can make the “real” configuration constraints as a part of the overall optimization problem


Selling MDA and MDO is hard because some assembly and development is required. Also on several past occasions the chainsaw did not work as advertised!

Art Courtesy of

Dr. J. Sobieski

NASA Langley


The only way to overcome skepticism is by delivering results

It ought to be remembered that there is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of new processes. Because the innovator has for skeptics all those who have done well under the old processes, and lukewarm defenders in those who may do well under the new. This coolness arises from the incredulity of men and women, who do not readily believe in new and improved processes until they have had a long experience of them.

Paraphrasing Machiavelli

We MUST Deliver More Than What We Promise!

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