A Perspective on Optimization - American Institute of ... Presentations/Bhatia...Introduction and Multidisciplinary Optimization Vision Engineering Optimization Challenges and Approaches
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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
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
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
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).
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.
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
“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.”
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)
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)
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
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
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
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
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?
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
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
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
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
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
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
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.