U.S. patent application number 10/456179 was filed with the patent office on 2010-12-02 for autonomous experimental design optimization.
Invention is credited to Edgar Korner, Andreas Richter, Bernhard A. Sendhoff.
Application Number | 20100305925 10/456179 |
Document ID | / |
Family ID | 29716817 |
Filed Date | 2010-12-02 |
United States Patent
Application |
20100305925 |
Kind Code |
A1 |
Sendhoff; Bernhard A. ; et
al. |
December 2, 2010 |
AUTONOMOUS EXPERIMENTAL DESIGN OPTIMIZATION
Abstract
Iterative (nondeterministic) optimization of aerodynamic and
hydrodynamic surface structures can be accomplished with a computer
software program and a system using a combination of a variable
encoding length optimization algorithm based on an evolution
strategy and an experimental hardware set-up that allows to
automatically change the surface properties of the applied
material, starting with the overall shape and proceeding via more
detailed modifications in local surface areas. The optimization of
surface structures may be done with a computing device for
calculating optimized parameters of at least one (virtual) surface
structure, an experimental hardware set-up for measuring dynamic
properties of a specific surface structure, and an interface for
feeding calculated parameters from the computing device to the
experimental set-up and for feeding measured results back to the
computing device as quality values for the next cycle of the
optimizing step.
Inventors: |
Sendhoff; Bernhard A.;
(Bruchuobel, DE) ; Korner; Edgar; (Seligemstadt,
DE) ; Richter; Andreas; (Rodgau, DE) |
Correspondence
Address: |
FENWICK & WEST LLP
SILICON VALLEY CENTER, 801 CALIFORNIA STREET
MOUNTAIN VIEW
CA
94041
US
|
Family ID: |
29716817 |
Appl. No.: |
10/456179 |
Filed: |
June 5, 2003 |
Current U.S.
Class: |
703/8 ;
703/6 |
Current CPC
Class: |
Y02T 90/00 20130101;
G06F 2111/06 20200101; Y02T 90/50 20180501; G06F 30/15 20200101;
G06F 2111/10 20200101 |
Class at
Publication: |
703/8 ;
703/6 |
International
Class: |
G06G 7/48 20060101
G06G007/48 |
Foreign Application Data
Date |
Code |
Application Number |
Jun 21, 2002 |
EP |
02 013 826.9 |
Claims
1. A method for iteratively optimizing a shape of an object, the
method comprising: (a) calculating on a computer a set of parameter
values by a first optimization algorithm or a second optimization
algorithm depending on quality values from a set of initial
parameters, the set of initial parameters representing a shape of
an object having at least one continuous surface structure; (b)
automatically adjusting hardware setup comprising a plurality of
actuators coupled to the computer through an interface, the
plurality of actuators controlled according to the calculated set
of parameter values in order to alter a shape of the object with
respect to the set of calculated parameter values; (c) measuring
dynamic properties of the adjusted hardware setup; (d) retrieving
measured dynamic properties by the computer; (e) evaluating the
measured dynamic properties by the computer to obtain updated
quality values; (f) repeating (a) through (e) until a set of
optimized parameter values with respect to the measured dynamic
properties are obtained based on the updated quality values and (g)
storing the set of the optimized parameter values in a computer
memory.
2. The method of claim 1, wherein the step of calculating the set
of parameter values comprises the step of changing the number of
said parameter values.
3. The method of claim 1, wherein the first optimization algorithm
comprises an Evolutionary Algorithm (EA).
4. The method of claim 1, wherein the second optimization algorithm
comprises at least one of a Simulated Annealing (SA) and a Tabu
Search (TS) algorithm.
5-6. (canceled)
7. The method of claim 1, wherein the surface structure to be
optimized is superimposed to a second predefined surface
structure.
8-16. (canceled)
17. The method of claim 1, further comprising evaluating additional
quality values by a Computational Fluid Dynamics (CFD) solver
responsive to measuring the dynamic properties.
18. The method of claim 1, further comprising evaluating additional
quality values by an Artificial Neuronal Network (ANN) or a
Response Surface Model (RSM) responsive to measuring the dynamic
properties.
19. A computer program stored in a computer readable storage medium
structured to store instructions executable by a processor for
iteratively optimizing dynamic properties of a shape of an object,
the instructions, when executed cause the processor to: (a)
calculate a set of parameter values by a first optimization
algorithm or a second optimization algorithm depending on quality
values from a set of initial parameters, the set of initial
parameters representing a shape of an object having at least one
continuous surface structure; (b) automatically adjust hardware
setup comprising a plurality of actuators coupled to a computer
through an interface, the plurality of actuators controlled
according to the calculated set of parameter values in order to
alter the shape of the object with respect to the set of calculated
parameter values; (c) measure dynamic properties of the adjusted
hardware setup; (d) retrieve measured dynamic properties; (e)
evaluate the measured dynamic properties to obtain updated quality
values; (f) repeat (a) through (e) until a set of optimized
parameter values with respect to the measured dynamic properties
are obtained based on the updated quality values; and (g) store the
set of the optimized parameter values in a computer memory.
20. A method for iteratively optimizing a continuous surface of a
road vehicle, comprising: (a) calculating on a computer a set of
parameter values by a first optimization algorithm or a second
optimization algorithm depending on quality values from a set of
initial parameters, the set of initial parameters representing a
shape of a road vehicle including at least one continuous surface;
(b) automatically adjusting hardware setup comprising a plurality
of actuators coupled to the computer through an interface, the
plurality of actuators controlled according to the calculated set
of parameter values; (c) measuring dynamic properties of the
adjusted hardware setup; (d) retrieving measured dynamic properties
by the computer; (e) evaluating the measured dynamic properties by
the computer to obtain updated quality values; (f) repeating (a)
through (e) until a set of optimized parameter values with respect
to the measured dynamic properties are obtained based on the
updated quality values; and (g) storing the set of the optimized
parameter values in a computer memory.
21. (canceled)
22. A closed-loop control system for iteratively optimizing a shape
of an object, the system comprising: a computing device for
calculating a set of parameter values by a first optimization
algorithm or a second optimization algorithm depending on quality
values from a set of initial parameters, the set of initial
parameters representing a shape of an object having at least one
continuous surface structure; an interface for automatically
adjusting hardware setup comprising a plurality of actuators by
controlling the plurality of actuators according to the calculated
set of parameter values in order to alter a shape of the object
with respect to the set of calculated parameter values; and a
measurement control unit for measuring properties of the adjusted
hardware setup, the measured properties evaluated by the computing
device to obtain updated quality values; wherein the computing
device, the hardware setup, and the measurement control unit repeat
calculating the set of parameter values, adjusting the experimental
hardware setup, and obtaining the updated quality values with
respect to the measured dynamic properties until optimized
parameter values are obtained based on the updated quality
values.
23. The system of claim 22, wherein the first optimization
algorithm comprises an Evolutionary Algorithm (EA).
24. The system of claim 22, wherein the second optimization
algorithm comprises at least one of a Tabu Search (TS) algorithm
and Simulated Annealing (SA) algorithm.
25-27. (canceled)
28. The system of claim 22, wherein the surface structure to be
optimized is superimposed to a second predefined surface
structure.
29. The system of claim 22, further comprising a second computing
device for evaluating the quality values by a Computational Fluid
Dynamics (CFD) solver.
30. The system of claim 29, wherein the second computing device
also evaluates the quality values by an Artificial Neuronal Network
(ANN) or a Response Surface Model (RSM).
31-38. (canceled)
Description
RELATED FOREIGN APPLICATIONS
[0001] This application is related and claims priority to European
Patent Application No. 02 013 826.9 filed on Jun. 21, 2002 by
Bernhard Sendhoff, Edgar Korner, and Andreas Richter, titled
"Autonomous Experimental Design Optimization".
FIELD OF THE INVENTION
[0002] The underlying invention generally relates to the
optimization of aerodynamic and hydrodynamic designs, in particular
to methods for an iterative (non-deterministic) optimization of
hydrodynamic and aerodynamic surfaces, e.g., aircrafts, ships and
vehicles, a computer software program for implementing such a
method as well as to systems for optimizing said surfaces.
BACKGROUND OF THE INVENTION
[0003] Some aspects of the invention involve the advantageous use
of technologies known in the art. In the following description some
of these basic technologies will be introduced, for example, CFD,
Gradient based methods, Evolutionary Algorithms (EA), and
Artificial 25 Neuronal Networks (ANN).
[0004] Computational Fluid Dynamics (CFD) has become an integral
part of aero/hydro-dynamic design processes, as, for example, the
aircraft design process. It involves the use of computational
methods to solve systems of nonlinear partial differential
equations in order to predict how fluids will flow, and what will
be their quantitative effects on the solids they are in contact
with. Thereby, CFD complements experimental and theoretical fluid
dynamics by allowing the efficient simulation of physical fluid
systems. Another advantage CFD provides is the ability to model
physical fluid phenomena that are difficult to measure in actual
experiments. However, CFD simulations are computationally very
expensive. What makes the problem more difficult is that EAs need a
relatively large number of evaluations in order to achieve a near
optimal aerodynamic design. To solve this dilemma, Artificial
Neural Networks (ANN) can be used to approximate CFD
computations.
[0005] ANNs are an important tool in soft computing that can
advantageously be applied to solve a plurality of problems. The
original purpose of an ANN is to simulate a biological neural
system (e.g. a brain). To date, several neural network models have
been developed, which can be applied to function approximation,
classification, control tasks, and the like. An important issue
that is closely related to ANNs is learning. Thereby, learning
theory in ANNs has large overlap with that in Machine Learning
(ML), Bayesian Theory and statistics.
[0006] In the following some background on optimization algorithms
will be provided. The most well known ones are gradient-based
methods (GMs), which probe the optimum by calculating local
gradient information. These methods are efficient and the optimum
obtained from these methods will be a global one, if the objective
and constraints are differentiable and convex. Consequently, this
approach has been widely used for many design problems including
wing design, nozzle design, supersonic wing-body design, and more
complex aircraft configurations. The quality landscape for an
aerodynamic design problem, however, is usually multimodal. For GMs
to find a global optimum, the optimization process has to be
started repeatedly from a number of initial points and then checked
for consistency of the obtained optima. In this sense, GMs are
neither efficient nor robust for design optimization. Furthermore,
for design optimization problems, the gradient information needed
by GMs must be numerically estimated. This process can be
computationally expensive and in general it is not very robust
against noise.
[0007] By contrast, soft computing techniques such as Evolutionary
Algorithms (EAs) form a new kind of iterative pseudostochastic
optimization techniques that try to emulate mechanisms of natural
evolution, where a biological population evolves over generations
to adapt to its environment by means of selection, recombination
and mutation. Such a population consists of a number of individuals
composed of chromosomes, which are in turn composed of genes. These
genes encode the parameters that need to be optimized for a given
problem. If an EA is used for structure optimization, the
parameters that describe said structure are encoded in said
chromosomes. To eliminate unfavorable modifications and to proceed
with modifications that increase the overall quality of the
underlying population, a selection operation is used. Since
techniques from computational intelligence like Evolutionary
Algorithms (EAs) that employ objective function information
(fitness values) instead of derivatives or other auxiliary
knowledge--are known to be very robust, they have been enjoying an
increasing popularity in the field of numerical optimization for
practical engineering applications in recent years. EAs have been
applied to aeronautical problems in several ways, including
parametric and conceptual design of an aircraft, preliminary design
of turbines, topological design of non-planar airfoils and
aerodynamic optimization based on CFD.
[0008] Originally, there were three main streams of evolutionary
computation-namely Genetic Algorithms (GA), Evolution Strategies
(ES) and Evolutionary Programming (EP). More recently, Genetic
Programming (GP) has been developed and has matured into the fourth
major direction. When EAs are applied to optimization problems,
individuals, genes and fitness values usually correspond to a
design candidate, a number of design variables and an objective
function value, respectively. One of the key features of EAs is
that these algorithms search the design space population based,
instead of moving from a single point like GMs do. Moreover, due to
their stochastic component and the recombination of individuals the
global optimum can be found, for most EAs theoretically even with
probability one. Other advantages such as robustness, efficiency,
suitability to parallel computing and simplicity make them
particular useful candidates for a combination with CFD methods.
The number of parameters (design variables) and the way in which
the parameters describe the structure or surface, e.g., B-splines,
Polygons, or alternative codings, are usually called the
representation or the encoding of the design in evolutionary
algorithms.
[0009] Experimental design optimization techniques using
evolutionary algorithms (EAs) in particular evolution strategies,
for example, as described in "Evolutionstratgie '94"
(Frommann-Holzboog Verlag, 1994, incorporated herein by reference
in its entirety) by I. Rechenberg and "Experimentelle Optimierung
einer Zweiphasenduse--Teil (AEG Forschungsinstitut Berlin, Bericht
35-11.034/68, 1968, incorporated herein by reference in its
entirety) by H.-P. Schwefel was one of the first application
domains of this type of optimization methods. The necessary changes
of the experimental design were carried out manually by adjusting
devices that changed the design subject to said optimization. An
example for this technique is the optimization of a pipe for
re-directing the flow of a fluid or gas 90 degrees, in which screws
were attached to the flexible material of the pipe. In this case,
the employed evolution strategy was restricted to a
(1+1)-population, so that the manual adjustment process remained
feasible.
[0010] In "A Surrogate Approach to the Experimental Optimization of
Multi-Element Airfoils" (Multi-Disciplinary Optimization Branch,
NASA Langley Research Center March, 1996, Report RTR 505-59-53-08;
WWW address:
http://fmad-www.larc.nasa.gov/mdob/MDOB/hilites/h1.96/Surrogates-
.sub.--3.96.html, incorporated herein by reference in its entirety)
by J. C. Otto, D. Landman and A. T. Patera, the process described
above is applied to the optimization of a multi-element airfoil, in
which actuators are used to position the flap relative to the main
element (2D change). Again, the measurement process is performed
autonomously, the results are transmitted to the optimization
algorithm, which uses a steepest ascent method and determines the
best set-up of the relative wing positions for the next test.
However, Otto et al. do not disclose the use of EAs for said
optimization process.
[0011] In the article "Evolution Strategies for Computational and
Experimental Fluid Dynamics Applications" (L. Spector, et al.
(editors): Proceedings of the Genetic and Evolutionary Computation
Conference (GECCO-2001), Morgan Kaufmann Publishers, San Francisco,
Calif., 2001, incorporated herein by reference in its entirety) by
F. Sbalzarini, S. D. Mueller, P. Koumoutsakos and G.-H. Cottet, an
optimization of trailing vortices distraction using evolution
strategies is disclosed. Thereby, Sbalzarini et al. study an
implementation of two- and multi-membered evolution strategies to
optimization problems for CFD applications in an experimental and
computational environment, respectively.
[0012] Generally, the invention proposes a closed-loop combination
of an optimization algorithm running on a computing device and an
experimental hardware set-up that allows to automatically change
the surface properties of the applied material.
[0013] In view of the explanations mentioned above, it is an object
of the invention to propose a method for an efficient 35
optimization of the structure of a surface. This and other objects
and advantages of the invention are apparent in the following
detailed description and drawings. This written description and
accompanying drawings are not to be construed as limiting the
invention as it is recited in the attached claims.
[0014] One embodiment according to the underlying invention is
generally dedicated to the use of optimization methods for design
parameters of aerodynamic and hydrodynamic surfaces. In this
context, the invention presents a method for the optimization of
specific structures (and not only of a single parameter) of
surfaces, e.g., of aircrafts, ships and road vehicles, a computer
software program for executing such a method and a system for
optimizing said surface structures.
[0015] For this purpose, in one embodiment, a hybrid approach is
proposed which encompasses a combination of an optimization
algorithm, thereby realizing a closed loop for an autonomous
experimental optimization, and an experimental hardware setup that
can be used for modifying the (three-dimensional) surface of an
aerodynamic or hydrodynamic body by automatically altering specific
surface properties of the applied material. The method can start
with the overall shape and proceed via more detailed modifications
in local surface areas. The model, structure, shape or design to be
optimized is described by parameter sets that comprise different
object parameters. As mentioned before, the number of parameters
and the way in which they describe the design is generally called
the representation.
[0016] In another embodiment using an evolution strategy, these
object parameters are mutated to create offsprings of the parameter
set. After that, the quality of these offsprings is evaluated. The
parameter set furthermore comprises at least one strategy parameter
representing the step size of the mutation (e.g., the variance of
the normal distribution of associated object parameters).
[0017] Using different techniques from computational intelligence
(e.g., ANNs and evolutionary computing methods) in order to solve
complex optimization problems within a hybrid-approach embodiment
as described above, has several advantages. For example, the
approximation strength of ANN can be combined with experimental and
CFD based evaluation methods of the design candidates to speed up
the optimization process, which in turn is based on evolutionary
algorithms to be able to search the quality landscape globally.
[0018] In another embodiment of the present invention, it is
proposed a method for the optimization of surface structures which
comprises the steps of optimizing parameters of at least one
(virtual) surface structure, adjusting the surface structure of an
experimental set-up according to the optimized parameters,
measuring dynamic properties of the adjusted experimental surface
structure, and feeding measured results back as quality values for
the next cycle of the optimizing step. According to another aspect
of the present invention a method for a hierarchical design
optimization is also proposed, wherein in addition to the values of
the parameters, the representation of the design and
correspondingly the experimental set-up can be adapted (mutated)
during the optimization process.
[0019] Furthermore, another embodiment of the invention refers to
the usage of these methods for the optimization of road vehicle
surfaces. Moreover, these embodiments can be produced in several
mediums, for example, a computer software program which implements
the methods when executed in a computer system.
[0020] Finally, yet another embodiment of the present invention
involves a system for the optimization of surface structures, which
comprises a computing device for calculating optimized parameters
of at least one (virtual) surface structure, an experimental set-up
for measuring dynamic properties of a specific surface structure,
and an interface for feeding calculated parameters from the
computing device to the experimental set-up and for feeding
measured results back to the computing device as quality values for
the next cycle of the optimizing step.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021] Further advantages and possible applications of the
underlying invention will become evident from the following
description of the preferred embodiment of the invention, which is
depicted in the following drawings.
[0022] FIG. 1 presents an overview diagram showing the principle of
the autonomous experimental aerodynamic design optimization
technique.
[0023] FIG. 2 presents an experimental hardware set-up with devices
for altering the surface structure of the design according to the
present invention.
[0024] FIG. 3 exhibits a 3D diagram that shows a discontinuous
(discrete) representation of a surface with an example of a virtual
block definition according to the present invention.
[0025] FIG. 4 exhibits a 3D diagram that shows a continuous
(smooth) representation of a surface with underlying pistons and a
flexible surface material according to the present invention.
[0026] FIG. 5 illustrates the integration of the experimental
optimization process in a design optimization framework consisting
of a CFD-based and meta-model-based evaluation according to the
present invention.
[0027] FIG. 6 shows a technology for implementing a hierarchical
design optimization using evolutionary algorithms according to the
present invention.
DETAILED DESCRIPTION OF THE INVENTION
[0028] In the following description, embodiments of the present
invention as depicted in FIGS. 1 to 6 shall be explained in detail.
As an overview, the following is a brief description of the
elements in the diagrams, charts, and illustrations of the
figures.
[0029] System 100 embodies the principle of the autonomous
experimental aerodynamic design optimization technique according to
the one embodiment of the present invention. Interface 101 is the
interface between the computing device 102 and the wind tunnel 104
in one embodiment of the present invention. Computing device 102 is
a client PC needed for the selection process according to the
evolution strategy and the calculation of optimized parameter sets
according one optimization algorithm embodiment of the present
invention. Server 103 is a first application server connected to
the client PC 102 via the Internet 504 or any corporate network
(Intranet), which hosts the optimization algorithm according to one
embodiment of the present invention. Server 103a is a second
application server connected to the first application server 103,
which is needed for the CFD-based evaluation 502a according to an
optimization algorithm embodiment of the present invention. Server
103b is a third application server connected to said first
application server 103, which is needed for the meta-model based
evaluation 502b according to an optimization algorithm embodiment
of the present invention. Windtunnel 104 is needed for the
experimental evaluation, which is used to change the underlying
design surface of aircrafts and road vehicles and to measure their
fluid dynamics, air resistance index, and the noise according to
one embodiment of the present invention.
[0030] Now referring to FIG. 2, experimental set-up 200 is one
embodiment of an experimental hardware set-up according to one
embodiment of the present invention. This embodiment comprises
actuator devices 204 needed for altering the flexible surface
material 202, which is a flexible (magnetic) surface material of
the design altered by a number of variable actuator devices 204.
Actuator devices 204 may be variable piston devices or magnets
needed for altering the flexible surface material 202 of the
design. In addition, the actuator devices 204 are controlled by a
device control unit 206a. The system 200 further comprises a
measurement control unit 206b.
[0031] Now referring to FIG. 3, 3D discrete diagram 300 shows a
discontinuous (discrete) representation of a surface 202 with an
example of a virtual block definition 302 according to one
embodiment of the present invention. Cuboids 301 or rectangular
parallelepipeds serve as adjustment elements that are used for a
modification and aerodynamic optimization of a discontinuous
(discrete) surface 300 according to one embodiment of the present
invention. Virtual block 302, consists of four cuboids 301 having
the same length and the same cross-sectional area according to one
embodiment of the present invention.
[0032] Now referring to FIG. 4, 3D smooth diagram 400 shows a
continuous (smooth) representation of a surface 202 with underlying
pistons and a flexible surface material according to one embodiment
of the present invention.
[0033] Now referring to FIG. 5, system 500 is shown as an
integration of an experimental optimization process in a design
optimization framework consisting of a CFD-based and meta-model
based evaluation according to embodiment of the present invention.
Process 502 represents an autonomous experimental evaluation of the
parameter sets according to one embodiment of the present
invention. Sub-process 502a represents a CFD-based evaluation as a
first part of the hybrid optimization algorithm according to
embodiment of the present invention. Similarly, sub-process 502b
represents a meta-model based evaluation as a second part of an
optimization algorithm embodiment of the present invention. As
previously mentioned, the system is interconnected by network 504,
which in one embodiment could be the Internet, a corporate network
(Intranet), or the like.
[0034] In one approach proposed within the scope of one embodiment
of the present invention, the autonomous experimental optimization
can be combined with a hierarchical design optimization approach.
Surface properties of the applied materials 202 are autonomously
changed in an experimental set-up 200. As depicted in FIG. 1, their
fluid dynamics and other properties are measured and fed back to
the computing device (client) 102 that hosts the optimization
algorithm. The computing device and the experimental set-up are
connected with each other by means of an interface to thus form a
closed-loop. In the following description, some characteristics of
this approach shall be described:
[0035] Autonomy: The whole process operates without the necessity
of a manual controller. The surface shape 202 is modified
automatically with the aid of suitable actuator devices 204
described below and controlled by an appropriate optimization
algorithm residing in a computer 103. Those surface properties that
are the subject of optimization are measured, and then the results
are further processed in the next optimization step of the
algorithm inside the computer.
[0036] Surface properties: The surface 202 of a design is
represented in an experimental set-up 200, which allows the
hierarchical alteration of the structure of surface 202. For
example, two main cases can be distinguished, in which either a
discontinuous approximation or a continuous representation of the
surface 202 is applied. In case a discontinuous (discrete)
approximation 300 of the surface 202 is desired, metallic cuboids
301 of variable size that directly represent the surface 202 are
used, and the properties of a three-dimensional grid are measured
directly. The length of these cuboids 301 can be controlled by a
computer 102, e.g., by using micro motors as shown in FIG. 3. The
depicted application could be used for an optimization of the
underside of a car. In case of a continuous (smooth) surface
representation 400, several embodiments of methods according to
this principle of the invention are proposed on how such an
experimental set-up 200 could be achieved.
[0037] In one embodiment, the surface 202 consists of a flexible
material, whose shape is controlled by a two-dimensional array of
pistons 204 that vary in length and in the force they exert on the
surface 202. Examples are shown in FIG. 4 and a sample set-up in a
2D scenario in FIG. 2. Other embodiments can be designed using
indirect methods instead of the direct connection of the pistons
204 to the surface 202, e.g., where magnets may exert the force on
the surface 202.
[0038] In another embodiment, the surface 202 is filled with a
material that can be used to alter its shape. Pockets of possibly
variable size can be filled with a liquid (e.g. water or oil) or a
gas. By varying the pressure of the liquid the shape of the surface
202 changes, which is basically similar to an inflatable mattress.
Again, the pressure is controlled via the computer 102, and
necessary containers can be hidden inside the design (e.g. the
cockpit in the case of a racing car).
[0039] In yet another embodiment, the material of the surface 202
is of such a kind that its shape can directly be controlled e.g.
with the aid of electrical currents of varying strength. In this
case, the electrical field or direction/strength of the electrical
current has to be varied in such a way that the desired shape can
be produced. For example, materials with a memory of their shape
and with varying stiffness (according to electrical fields) can be
used.
[0040] Hierarchical design optimization: The term "hierarchical
design optimization" encompasses different aspects. Generally, the
optimization can be carried out on different hierarchical levels,
as, e.g., regarding the range (fine/rough optimization), time
scale, and the representation of the design and the experimental
set-up. Generally not only the parameter values, but also the
representation of the design as well as the corresponding
experimental set-up characteristics can be modified ("mutated" in
case an evolutionary algorithm is used for the optimization). The
modification of the representation can be achieved in the
experimental set-up by different methods, some of which are
described below.
[0041] Reference is also made to FIG. 6 showing an embodiment of an
application of the above hierarchical design optimization principle
in the case of evolutionary algorithms. According to this technique
the representation as well as the strategy and object parameters
are mutated. Some principles of this technique are derived from
European Patent Application EP 01104723.0, filed Feb. 26, 2001 by
Markus Olhofer and Bernhard Sendhoff (also in corresponding US App.
No. 2002165703, filed Feb. 21, 2002), entitled "Strategy Parameter
Adaptation in Evolution Strategies" now issued as European Patent
EP 1 235 180 A1, the disclosures of which are hereby incorporated
by reference in their entirety.
[0042] Another aspect of the hierarchical design optimization
according to one embodiment of the present invention refers to the
combination of an optimization algorithm, e.g., an evolution
strategy and an experimental set-up 200 of the surface alterations
that allows to change surfaces starting with the overall shape and
proceeding via more detailed changes in local surface areas. Since
the design optimization problem in principle is a very
high-dimensional one, adequate measures have to be taken to
decompose the problem. This way, the optimization of fine details
in local areas can be combined with overall changes of the shape.
In the context of the proposed solutions for the alteration of the
shape, a hierarchical two-dimensional array of pistons 204 with
variable lengths (looking like a 3D grid) can be designed. Thereby,
a number of pistons 204 (or in a discrete embodiment, cuboids 301)
are used for the overall shape control during the initial phase of
the experimental design optimization, whereas the devices 206a+b
controlling the detailed shape are subsequently added in later
optimization phases according to appropriate measures.
[0043] Alternatively, blocks 302 of pistons 204 or cuboids 301 may
define (virtual) larger blocks 302 while simultaneously being
controlled; the size of these blocks 302 is reduced in later
optimization phases. Additionally or alternatively the position of
pistons 204 can be mutated during the optimization process.
Therefore, the term "virtual" block structure or design refers to
the arrangement of sub-blocks or in general sub-structures that are
controlled in such a way that they behave as one solid block or
structure. Whether each sub-block or structure is adapted
individually or as a virtual block or structure is controlled by
the changes in the representation.
[0044] Another embodiment according to the present invention
includes a hierarchical set-up 200 for other shape control
scenarios. In case of fluid-filled pockets, again (virtual) blocks
of pockets can be defined for a simultaneous control. In addition,
pocket walls can be designed in such a way that they are variable
and can be moved by simple mechanical procedures to modify the
representation. For magnetic or electric field based control, the
area of influence of these devices can also be adapted. This leads
not just to a hierarchical experimental set-up 200 but also to one
where the overlap between different magnetic control units is
altered.
[0045] Generally, the mutation rates of the optimization with
different hierarchical levels are set such that the mutation rate
is the lower the higher the hierarchical level. E.g. the mutation
rate of the representation is usually set to be lower (slower) than
the mutation rate of the values of the parameters. Therefore,
according to one embodiment of the invention, different
hierarchical levels of optimization can be performed.
[0046] Optimization: In one embodiment of the present invention,
the optimization algorithm can run on any computer 103 and/or
103a+b connected in one way or the other to the computer 102, which
controls the experimental set-up 200. In an alternative embodiment,
the optimization algorithm uses the experimental set-up 200 only as
one particular method for evaluating the quality of designs. This
method may be combined in one embodiment with, for example, a CFD
solver and meta-models, like ANNs or response surface models. In
this embodiment, the computer 103b might belong to a computer
cluster that is physically remote from the experimental hardware
set-up 200. Thereby, the computer 103 which hosts said optimization
algorithm is in contact with the computer 102 which controls the
experimental set-up 200, for example, via any form of a computer
network, e.g. local area network, wireless network, corporate
network (intranet), a secured Internet connection 504, or the like.
The results of the experimental optimization can directly be
combined with other methods due to its autonomy. The interaction
between and the control of the different evaluation methods can be
taken from FIG. 5. The results of the experimental optimization can
in turn be used to update and improve the model fidelity in, for
example, neural networks using online learning. In one embodiment
of the present invention, the focus is on using EAs as optimization
tools due to their robustness and reliability even for complex
problems. However, other embodiments of the proposed methods of the
present invention can be combined with any optimization algorithm
that does only need the quality of different designs for the
optimization; examples are Simulated Annealing and Tabu Search
(Tabu search is an iterative procedure designed for the solution of
optimization problems, see e.g., J. W. Barnes, M. Laguna and F.
Glover, "Intelligent Scheduling Systems", D. E. Brown and W. T.
Scherer (Eds.), Kluwer Academic Publishers, 101-127 (1995),
incorporated herein by reference in its entirety. Simulated
annealing is a Monte Carlo approach for minimizing such
multivariate functions).
[0047] Following, an optimization for application domains shall be
presented in two sample embodiments. In an EA embodiment according
to the present invention, optimization steps to be applied can be
described as follows:
[0048] Process Initialization: A population of specific parameter
vectors (possibly of varying length and representations) is stored
within the EA running on a computer 102. For instance, the
parameter vectors may describe the position of pistons 204 (or
blocks thereof for the hierarchical case) or, alternatively, the
strength of magnets altering the surface 202 of a design consisting
of a flexible (magnetic) material that is subject to the fluid
dynamics (FD) tests in the wind tunnel 104 as depicted in FIG.
2.
[0049] Set-Up Adjustment P2 (adjusting the surface structure 202 of
an experimental set-up 200 according to the optimized parameters):
The parameter set mentioned above is autonomously sent to the unit
206a that controls the pistons 204 or magnets, which results in a
newly formed surface 202 of the underlying design to be
optimized.
[0050] Measurement P3 (measuring dynamic properties of the adjusted
experimental surface structure 202) and Feedback P4 (feeding back
the measurement results as quality values for the next cycle of the
optimizing step): The FD properties of the new design (or results
of these properties like down pressure, or the like.) are tested
and then autonomously sent back to the computer 102.
[0051] Looping: the first two steps are repeated until all
parameter vectors in the population have been tested and the
quality values of their corresponding designs have been
determined.
[0052] Optimization Process P1 (optimizing parameters of at least
one virtual surface structure 202): The EA running on the computer
102 uses the quality values to select the best parameter vectors
for the parent population of the next generation. Additionally, the
resolution of the 2D array of pistons 204 may be adapted in a
hierarchical manner. For this purpose, a variable length
representation for EAs has to be used. Applying the usual
evolutionary variation operators, like mutation and recombination,
creates the next generation of parameter vectors.
[0053] Process Termination: In case the best solution has already
been found, the optimization process P1 is stopped; otherwise the
second through fifth steps are repeated.
[0054] Several other useful embodiments according to the present
invention shall briefly be described.
[0055] Optimization of the underside of automobiles: In this
embodiment, a full model of a car is subject to measurements in the
wind tunnel 104. The underside is represented by rectangular
parallelepipeds 301 (cuboids) which are made of an appropriate
material. Thereby, the relative positions of said cuboids 301 to
each other and the rest of the car are controlled by micro motors.
The mechanical control unit 206a is hidden inside the model car.
Since a hierarchical representation is applied, an evolution
strategy can be chosen. In this context, virtual blocks 302 of
cuboids 301 are defined and represented whose size (and thus the
length of the representation) is optimized during the evolutionary
search besides the actual optimization P1 of the length of said
cuboids 301. Thereby, measured properties could be the air
resistance index and the noise level.
[0056] Optimization of the front or rear wing of a racing car: In
this embodiment, the front wing of the racing car is given by a
stiff but flexible material 202 that contains different pockets
which are filled with oil. The pressure of the oil is controlled by
means of a unit 206a that is hidden in the cockpit of the car.
Walls whose permeability can be controlled with the aid of
electrical currents separate the pockets. In this way, the
optimization process P1 can again be organized in a hierarchical
fashion, which is very important due to the complexity of the
problem. The pressure of the different pockets and the permeability
of the walls are represented by real-valued numbers. Thereby, the
algorithm changes the numbers according to the applied optimization
method. The experimental set-up 200 is combined with a CFD solver
and an ANN that serves as a meta-model. In this way, the accurate
data obtained by the experimental simulations can directly be used
for an online learning process to improve the accuracy of the
network model. In this connection, measured properties of the
racing car model can be, for example, air resistance values or down
pressure.
[0057] Optimization of a transonic compressor cascade: One
embodiment of the present invention can be designed to resolve a
major issue is the development of a new aerodynamic design for a
transonic compressor cascade, i.e., a series of airfoil layers
consisting of rotor and stator blades found within the gas turbines
that power jet-propelled aircraft. This issue is essentially a
fluid dynamics optimization problem: the streaming conditions
around the fixed "stator" blades, and the rotor blades determine
the efficiency of the whole turbine.
[0058] The embodiments of the present invention described above
present several benefits and advantages vis-a-vis conventional
solutions. Some of these advantages and benefits are summarized
below.
[0059] Optimization algorithms based on experimental measurements
have one main advantage compared to those based on simulations:
They are more exact, in particular because they take secondary flow
field effects into account. Of course, this comes at the expense of
a much more difficult, time- and resource-consuming hardware set-up
200. By contrast, one embodiment of present invention proposing a
method of an autonomous set-up minimizes these drawbacks by using
appropriate approaches to modify the shape and the surface 202 of a
given design. For this purpose, it combines the experimental
optimization with the CFD- and meta-model based evaluation of a
design by setting up a networked overall optimization environment.
Thereby, the best of both domains can be obtained-accuracy when it
is needed by the optimization algorithm and speed when accuracy is
not decisive. The experimental data can directly be used to improve
the meta-model, e.g., an ANN. Hierarchical design optimization can
be used to achieve a decomposition of the overall problem. In the
embodiments of the present invention using this principle, the
algorithmic variable length representation is combined with a
hierarchical organization of the modified shapes or surfaces 202
by, for example, defining (virtual) blocks 302 of adjustment
elements 301.
* * * * *
References