Aug 17, 2008 - internet through Globalspec, eCl@ss etc, and to a greater ... âEstimation Models for Concept Optimisati
Performance P f Estimation E ti ti Using U i Similarity Models and Design Information Entropy. Petter Krus Division of Machine Design Department of Management and Engineering Linköping University
Estimation Models for System y Design g ¾ The increasing computational resources means that large high fidelity models can be used for system analysis, so why bother with performance estimation models. ¾ High fidelity models requres a high fidelity design design, which is not available in early system level design. ¾ Estimation Models should have a predictive fidelity that is consistent i t t with ith th the d design i fid fidelity lit att that th t particular ti l stage. t ¾ Estimation models is not used directly for design of the component/subsystem they represent, merely to predict what can be achieved. This can later be used for component selection or as input for component design.
2008-08-17
Sid 2
Linköpings universitet
System y level development p p process
Identification of customer needs (compatible with capability)
Generating requirement and desirables specification
Concept generation
Concept selection
Quantitative Q tit ti refinement
Analysis A l i and d evaluation
Sensitivity and trade tradeoff analysis
2008-08-17
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Linköpings universitet
Performance Estimation ¾ Statistical models has been used for aircraft preliminary design for a long time to estimate weight of subsystems. This is related to similarity models (or allometric models) used in biology to describe morphology depending on size. These can be combined with analytical models for scaling relations ¾ M Modells d ll can also l be b derived d i d tto correlate l t performance f with ith th the degree of refinment. Here design information entropy is a useful quantity.
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Petter Krus
Information Entropy py ¾ Design information entropy is a measure of the contraction of design space during design. It is roughly proportional to the number of objects in the design space and thus a more convenient unit than the number of possibilities excluded. ¾ Relative Information entropy is a very useful state in evolutionary l ti llearning i processes. It iis consistent i t t with ith th the view i that the design process is a learning process. ¾ A general model is presented that links information to optimization, ti i ti refinement, fi t performance f and d cost. t ¾ The results indicate that it sometimes may be more efficient to increase the number of design parameters, rather than refining a few parameters to a high degree degree.
2008-08-17
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Petter Krus
Design Information Entropy is a Measure of the Size of the Design Space Lego example ¾ The design g space p of a set of Lego g bricks represents all combinations of arranging these bricks. ¾ With a set of only two bricks with four knobs on each there are 51 discrete possible arrangements ¾ Two of these represents picking only one brick. And one state is to p pick no one. ¾ The 51 different configuration (states) means that the amount of information needed to specify a particular design is:
I x = log 2 nDstate = log 2 51 = 5.7bits
2008-08-17
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Petter Krus
Amount of Information content (Information Entropy) The differential information entropy for continuous signals, defined by Shannon [1] as: ∞
H = − ∫ p( x) log 2 ( p( x))dx −∞
Kullback-Leibler divergence ∞
H rel
p( x) )dx = − ∫ p ( x) log 2 ( m( x ) −∞
Generalized ∞
H rel
2008-08-17
∞
p ( x1 K xn ) = − ∫ L ∫ p ( x1 K xn ) log 2 ( )dx1 L dxn m( x1 K xn ) −∞ −∞ Petter Krus
Sid 7
Amount of Information content (Information Entropy) The distribution m(x) should be a rectangular distribution in the bounded interval.
I x = H rel ( x) = −
xmax
∫
p ( x) log 2 ( p ( x) xR )dx
xmin
Generalized x1,max
Ix = −
∫
xn ,max
L
x1,min
∫
p ( x1 K xn ) log 2 ( p( x1 ,K xn ) xR1 L xRn )dx1 L dxn
xn ,min
More compact
I x = − ∫ p (x) log 2 ( p (x) S )dS S
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Petter Krus
Amount of Information content (Information Entropy) The information content I of a variable (in bits).
xmax
I = − ∫ p( x)log2 ( p( x) xR )dx
xR = xmax − xmin
xmin
If the range xr is divided in equal parts Δx the amount of information is:
xr 1 I = log2 = log2 Δx δx
or more general:
Δx
I = log2
Here Δx is the tolerance in x.
xmin 2008-08-17
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Petter Krus
x1
x2
xmax
S s
Design g Space p with Both Continuous and Discrete Variables ¾ The position of the inserted axis represents a continuous variables py ¾ The information entropy associated with that is dependent on the accuracy with which it is specified.
I x = log l 2 nDstates + log l nCstates + log l 2 ¾ The axis can be in three position and If the position of th axis the i within ithi one h hole l iis specified within 10% the total information entropy is:
xR Δx
1 I x = log l 2 51 + log l 2 3 + log l 2 = 10.6bits bi 0.1
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Petter Krus
x
Design Information entropy ¾ The design g information entropy y represents a measure of the precision by which a design is defined relative to the design space in consideration. ¾ It is also proportional to the dimensionality of the design problem. ¾ It can also be seen as a measure of a probability that a random design in the design space is found, that is within the given t l tolerance region. i ¾ Design information entropy, as defined here, should not be taken as a direct measure of complexity. A very simple design can represent a large information content if it has been picked from a large design space.
2008-08-17
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Petter Krus
Design g space p expansion p ¾ The design information entropy can be increased in two ways ¾ Refinement ¾ Design D i space expansion i
¾ Design space can be increased in several ways like: ¾ Adding more bricks ¾ Adding other types of bricks ¾ Releasing more design parameters in a design
xR′ xR xR′ xR xRn xR I x = log 2 = log 2 = log 2 = n log 2 Δx Δx xR Δx xR Δx = nI p
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Petter Krus
Growth of design g information entropy py during the design process I R = log 2
Design space expansion
S0′ S0
S0′
m
∑ si
n
∑s
i =1
Design space generation
S0
i =1
Concept generation m
I I = − log 2
∑ si i =1
S0
Concept screening
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Petter Krus
Concept optimization and selection
n
I II = − log
∑s
i =1 2 m
j (i )
∑s i =1
2008-08-17
j (i )
i
I III = − log2
sδ n
∑s i =1
j (i )
sδ
Influence factor of design parameters
System characteristics Generalised system performance
y = f x ( x)
z = g(y) z = z( x)
ψ (i )= z i ( xR ,i , x p ,opt ,i ) − z i −1 ( xR ,i −1 , x p ,opt ,i −1 )
An aproximate modell of this is:
ψ (i)= c pi 2008-08-17
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Petter Krus
−λ
Total influence up to the n:th parameter: n
n
i =1
i =1
Ψ ( n)= ∑ψ (i ) = c p ∑ i
−λ
= c p H ( n, λ )
H ( n, λ )
(
is the harmonic function
)
zopt ( n ) = z n x p ,opt = Ψ (n) − z0 = n
= cp ∑ i i =1
−k
−z0 = c p H (n, λ ) − z0
⎛ 1 ⎛ 1 ⎞⎞ ≈ c p ⎜ c (λ ) + ⎜1 − λ −1 ⎟ ⎟ − z0 λ −1 ⎝ n ⎠ ⎠ ⎝ 2008-08-17
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Petter Krus
Asymptotic y p behaviour
(
)
zopt ( n ) = z n x p ,opt = Ψ (n) − z0 = n
= c p ∑ i − k −z0 = c p H (n, λ ) − z0 i 1 i=
⎧ ∞ when λ ≤ 1 lim H (n, λ ) = ς (λ ) = ⎨ n →∞ ⎩finite value > 1 ς (λ )
4 3.5 3 2.5 2 1.5 1 0.5 2
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Petter Krus
3
4
λ
5
Sorted spectrum of parameter influence
ψ (i)= c p i
−λ
λ =1
Influence
12 10 8 6 4 2 0 1
2
3
4
5
Figure 3. Sorted parameter influences
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Petter Krus
6
7
8
9
Total influence up to the n:th parameter: n
n
i =1
i =1
Ψ ( n)= ∑ψ (i ) = c p ∑ i
−λ
= c p H ( n, λ )
H ( n, λ )
(
is the harmonic function
)
zopt ( n ) = z n x p ,opt = Ψ (n) − z0 = n
= cp ∑ i i =1
−k
−z0 = c p H (n, λ ) − z0
⎛ 1 ⎛ 1 ⎞⎞ ≈ c p ⎜ c (λ ) + ⎜1 − λ −1 ⎟ ⎟ − z0 λ −1 ⎝ n ⎠ ⎠ ⎝ 2008-08-17
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Petter Krus
Accumulated influence ⎧ ∞ when λ ≤ 1 lim H (n, λ ) = ς (λ ) = ⎨ n →∞ ⎩finite value > 1 40
18
35
16
30
14 12
25
10 20
λ =1
15 10 5 0
8
4 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
80 70 60 50 40
λ = 0.5
30 20 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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λ=2
6
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Petter Krus
Performance model
z ( n ) = k p H ( n, λ ) − z 0 zopt (n) − zopt ( n, δ x ) = k p H ( n, k )δ x
δx = 2
−
Performance loss due to uncertaintyy
Ix n
Ix n
zopt (n, I x ) = k p H (n, k )( )(1 − 2 ) − z0
2008-08-17
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Petter Krus
Example: optimization of a beam
F 1
2
...........
n
L
FL m= η kσ max 2008-08-17
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Petter Krus
η ∈ ]0,1]
Efficiency y as a function of information 0.9 η
5 segments
0.8 0.7 0.6 1 segment 0.5
5
10
15
20
25
Ix
30
Figure 6. The efficiency of the structure as a function of information Ix
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Petter Krus
The optimal number of design parameters as a function of design information entropy
n
λ=1
20
15
Bounded performance
Unbounded performance
10
λ=2 5
20
2008-08-17
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Petter Krus
40
60
80
Ix
100
Influence values
ψ (i )= c p i − λ 07 0.7 0.6 0.5 0.4
Influence
0.3
Model
02 0.2 0.1 0 1
2
3
4
5
6
7
8
9
Figure 7. Influence of increasing the number of elements in the beam model. Exact solution and a model based on a negative power law relationship with λ=2.
2008-08-17
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Petter Krus
Influence values
ψ (i)= c pi −λ
9.00 8.00 7.00 6.00 5 00 5.00
I fl Influence values l
4.00
Adjusted model
3.00 2.00 1.00
tc
t
ise Vc ru
C
T
r C
W e
W f
xw
Bh t
B
0.00
Figure 10. Sorted influences for different design parameters of a transport aircraft aircraft. Adjusted model with λ=1.4. =1 4
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Petter Krus
Performance model Ix n
zopt (n, I x ) = c p H (n, λ )(1 − 2 ) − z0 I x = C / kc
Substituting information with cost
zopt (n, C ) = c p H (n, λ )(1 − 2
C / kc n
) − z0
Or as a continuous function
zopt (n, I x ) = c′p 2008-08-17
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Petter Krus
1 n
(1 − 2 λ −1
C kCI n
) − z0′
4
4
3.5
3.5
3
3
performance [G Hz eqv]
performance [GHz eqv]
Example p
2.5 2 1.5 1 0.5
2.5 2 1.5 1 0.5
0
0
0
1000
2000
3000
price [SEK]
4000
5000
0
1000
2000
3000
4000
price [SEK]
Processor performance as a function of price for Intel Pentium and Celeron processors (2004), with fitted model
2008-08-17
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Petter Krus
5000
Modelling of components/subsystem for system level design Design parameters
Reduced design parameters
ii.e. e max torque torque, speed, etc
Secondary characteristics
i.e. weight, volume, cost, power loss
Component model
i.e. geometrical dimensions
Functional characteristics h t i ti
Functional (primary) characteristics
Allometric All ti Component model
Allometric models are derived under Secondary the assumption that the design characteristics parameters t in i the th component/system are optimized with respect to the secondary characteristics (Design parameters)
General Power Transformation i.e electric motors, hydraulic motors, mechanical gears, etc
e1 f1
Power transformer
e2 f2
Power losses e
are effort variables i.e. voltage, force, pressure
f
are the flow variables ii.e. e current current, speed speed, flow
P=ef
Modelling of components/subsystem for system level design
Secondary characteristics
Functional characteristics
Mass, m
Max power, P
Volume V Volume, Max torque, T
Estimation model
Mom. inertia, J Efficiency Cost Life Reliability
Table of hydraulic y motor data
displacem max ent power [cm3] 59 00 59.00 103.00 5.00 10.00 14.00 19.00 22.00 28.00 40.00 56.00 71.00 125.00 250.00
max torque
[W] [Nm] 44000 331 00 331.00 62000 572.00 24730 33.00 45338 66.00 60142 96.00 71919 127.00 62000 140.00 79000 178.00 106000 255.00 134000 357.00 132000 509.00 190000 895.00 321000 1790.00
volume [cm3] 2203 3076 742 1082 1282 1683 1596 1596 2738 2374 5967 9389 20838
diameter [mm] 117 123 84 94 102 114 118 118 150 133 170 200 265
mass
moment of inertia
[kg]
[kg cm2]
85 8.5 12.50 5.00 7.5 8.3 11.00 11.00 11.00 15.00 21.00 34.00 61.00 120.00
1.6 3.9 4.2 11.00 15.00 15.00 43.00 85.00 121.00 300.00 959.00 Average values
power intensity kp [kW/kg]
5 18 5.18 4.96 4.95 6.05 7.25 6.54 5.64 7.18 7.07 6.38 3.88 3.11 2.68 5.45
mean pressure (torque power torque density) density intensity pm kT ρp [bar] [W/cm3] [Nm/kg] 1 50 1.50 19 97 19.97 38 94 38.94 1.86 20.16 45.76 0.44 33.33 6.60 0.61 41.90 8.80 0.75 46.91 11.57 0.75 42.73 11.55 0.88 38.85 12.73 1.12 49.50 16.18 0.93 38.71 17.00 1.50 56.44 17.00 0.85 22.12 14.97 0.95 20.24 14.67 14.92 0.86 15.40 1.00
34.33
17.74
Inertia fraction
εJ
NA NA 0.018 0.024 0.019 0.031 0.039 0.039 0.051 0.092 0.049 0.049 0.046 0.042
Table of electric motor data
Voltage [V] 8.4 8 24 24 24 50 460 460 460
max power [W] 210 320 609 1440 3580 15992 73763 198499 491751
speed at load
max torque
[rad/s] [Nm] 1068 0.20 1378 0 23 0.23 523 1.164 450 3.2 471 7.6 419 38.20 175 420.74 215 922.87 175 2813.33
volume
mass
[cm3]
[kg] 0.1716 0 29 0.29 1.10 2.4 3.9 9.36 215.00 215.00 907.00 Average values
55 54 343 729 729 4539 23487 86524 165518
power intensity kp [kW/kg] 1.22 1 10 1.10 0.55 0.60 0.92 1.71 0.34 0.92 0.54 0.88
mean pressure (torque power torque density) density intensity pm kT ρp [bar] [W/cm3] [Nm/kg] 0.04 3.84 1.15 0 04 0.04 5 95 5.95 0 80 0.80 0.03 1.78 1.06 0.04 1.98 1.33 0.10 4.91 1.95 0.08 3.52 4.08 0.18 3.14 1.96 0.11 2.29 4.29 3.10 0.17 2.97 0.09
3.38
2.19
Table of planetary yg gearbox data
max power
max torque
[W] [Nm] 329 92 550 176 1125 372 1272 304 1333 38 2543 607 6283 110 6597 1000 18473 560 18850 1440 18850 1440 28589 1820
gear ratio
51 51 51 50 9 50 10 50 10 10 10 20
volume [cm3] 152 729 1331 975 452 1610 462 2839 2162 4180 4180 2185
diameter [cm] 5.7658 9 11 3.54 8.001 11.5062 7 13 13 16 16 14
mass
moment of inertia
power intensity kp
[kg]
[kg cm2]
[kW/kg] 0.66 0.79 0.70 0.61 1.11 0.94 2.17 0.44 1.61 0.70 0.70 1.86
0.5 0.7 1.6 2.1 1.2 2.7 2.9 15 11.5 27 27 15.4
0.38 4.96 4.1 12.3 12.3 6.85 Average values
1.02
mean pressure (torque density) pm
power density
ρp
[bar] [W/cm3] 6.05 2.16 2.41 0.75 2.79 0.85 3.12 1.30 0.84 2.95 3.77 1.58 2.38 13.60 3.52 2.32 2.59 8.54 3.44 4.51 3.44 4.51 8.33 13.08 3.56
4.68
torque intensity kT
Inertia fraction
εJ
[Nm/kg] 184.00 251.43 232.50 144.76 31.67 224.81 37.93 66.67 48.70 53.33 53.33 118.18
NA NA NA NA NA NA 0.0107 0.0078 0.0084 0.0071 0.0071 0.0091
120.61
0.008
Moment of inertia All mass is contributing g to the moment of inertia and located at the diameter of the machine
⎛d ⎞ J max = m⎜ ⎟ ⎝2⎠
d
2
The inertia fraction is defined as the ratio between the actual moment of inertia, and the theoretical max value.
εJ =
J J max
=
J ⎛d ⎞ m⎜ ⎟ ⎝2⎠
2
hence
2 ) d )⎛ ⎞ J = ε J m⎜ ⎟ ⎝ 2⎠
Estimation of motor characteristics Mass, m Max power, P Max torque, T
Diameter, d
) m = P / ρP ) V = T / pm 2 ) d )⎛ ⎞ J = εJm⎜ ⎟ ⎝2⎠
Volume, V
Mom. inertia, J
ρP, pm, and eJ are technology parameters. They are reasonably constant for a technology regardless of size size.
Conservative mass and volume estimation) ) ) m = max((mP , mT ) ) ) ) V = max(VP , VT ) 2 ) )⎛ d ⎞ J = ε J m⎜ ⎟ ⎝2⎠
where
) mP = P / ρ P ) VP = P / k P ) mT = T / kT ) VT = 2πT / p m
Multiple p regression g models ) log m = a10 + a11 log P + a12 log T ) log V = a 20 + a 21 log P + a 22 log T ) l J = a30 + a31 log log l P + a32 log l T This can also be written as
) a10 a21 a22 Vs = 10 P T ) m s = 10 a10 P a11 T a12 ) a30 a31 a32 J s = 10 P T
Note: N t Becomes B zero when P or T is zero (unrealistic)
Estimation model of mass for hydraulic motor Mass relation
Mass relation 3
2 Y Predicted Y 1
log(mass [kg])
log g(mass [kg]
3
2 Y Predicted Y
1
0
0 4
5 log(power [W])
6
1
2
3
log(torque [Nm])
4
Mass and volume estimation Hydraulic H d li motor
) ms = 7.26 ⋅10 −5 P 0.99T 0.202 ) Vs = 0.53 ⋅10 −6 P 0.493T 0.53 ) −0.734 2.12 J s = 1.34 P T This can be used together with the other expressions for a conservative estimation
) ) ) ) V = max(Vs ,VP ,VT ) ) ) ) ) m = max(ms , m P , mT ) 2 ) ) )⎛ d ⎞ J = max( J s , ε J m⎜ ⎟ ) ⎝2⎠
Alternative form ⎛P⎞ ) m = m0 ⎜⎜ ⎟⎟ ⎝ P0 ⎠
a11
) ⎛P⎞ V = V0 ⎜⎜ ⎟⎟ ⎝ P0 ⎠
a 21
) ⎛P⎞ J = J 0 ⎜⎜ ⎟⎟ ⎝ P0 ⎠
a31
⎛T ⎞ ⎜⎜ ⎟⎟ ⎝ T0 ⎠
a12
⎛T ⎞ ⎜⎜ ⎟⎟ ⎝ T0 ⎠
a 22
⎛T ⎞ ⎜⎜ ⎟⎟ ⎝ T0 ⎠
Can be used for scaling of an existing motor
a32
Model of mass as a function of power ) m = 7.26 ⋅10 P (h d li motor) (hydraulic t ) −5
s
0 99 0.99
0 202 T 0.202
) Vs = 0.53 ⋅10 −6 P 0.493T 0.53
) J s = 1.34 P −0.734T 2.12 Mass[kg]40
1000
20
800
0
600 400
50000 100000
200 150000
Power[W]
200000 0
Torque [Nm]
) ) ) ) m = max(ms , mP , mT )
Model of volume as a function of power ) m = 7.26 ⋅10 P T (h d li motor) (hydraulic t ) −5
0 99 0.99
0.202 0 202
s
) Vs = 0.53 ⋅10 −6 P 0.493T 0.53
) J s = 1.34 P −0.734T 2.12 8000 6000 4000 2000 0
Volume [cm3]
1000 800 600 Torque [Nm]
400
50000 100000 Power[W]
200 150000 200000 0
) ) ) ) V = max(Vs , VP , VT )
Main axis of data points (electric motor) "Line of natural ratio" y = 1.2696x - 3.6972 R2 = 0.9881
3 2
Series1 Linear (Series1)
1 0 1
2
3
4
5
6
-1 log(Power[W]) 4 lo og(torque[Nm])
log g(Torque[Nm])
4
Hydraulic
y=1 1.3805x 3805x - 4.4009 4 4009 2 R = 0.7225
3 2
Series1 Linear (Series1)
1 0 1
2
3
4
-1 log(powe r[W])
5
6
Principle p Component p Analysis y ¾ Introduces new set of artificial design parameters. Could be close to real parameters such as ”size” and aspect ratio ¾ Removes the need to handle the extreems. ¾ Useful for minimizing waste in the design space. ¾ It also differnentiate the impact p of the design g p parameters to a maximum degree. (Maximizes the decay exponent λ)
log(T ) log( x2 )
log( x2 )
log( x1 )
4
4.00
3
3.00
2
2.00
1
1.00
0 0
1
2
3
4
6
7
0.00 0.00
-1
-1.00
-2
-2.00
-3
-3.00
log( P ) 2008-08-17
5
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Linköpings universitet
1.00
2.00
3.00
4.00
log( x1 )
5.00
6.00
7.00
Estimation models using PCA design parameters (2-parameter case) Size
g( P) ⎞ ⎛ cos ϕ ⎛ log( ⎜ ⎟=⎜ ⎝ log(T ) ⎠ ⎝ sin ϕ
, x1,max ] g( x1 ) ⎞ x1 ∈ [ x1,min − sin ϕ ⎞ ⎛ log( , , ⎟ ⎟⎜ cos ϕ ⎠⎝ log( x2 ) ⎠ x2 ∈ [ x2,min , x2,max ]
) a10 Vs = 10 P a21 T a22 ) m s = 10 a10 P a11 T a12 ) a30 a31 a32 J s = 10 P T
2008-08-17
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Linköpings universitet
Auxiliary parameter 1
Modelling for system level design Performance parameters (PCA-set) i.e. size
Allometric component model
Functional (primary) characteristics
ii.e. max ttorque, speed, etc
Secondary characteristics
i.e. weight, volume, cost, power loss
Allometric (similarity) models are derived under the assumption that the design parameters in the component/system are optimized with respect to th secondary the d characteristics. h t i ti Models based on PCA-parameter sets are useful for trade-of studies and system optimization
Using g component data directly y
Voltage [V] 8,4 8 24 24 24 50 460 460 460
max power [W] 210 320 609 1440 3580 15992 73763 198499 491751
speed at load
max torque
[rad/s] [Nm] 1068 0,20 1378 0,23 523 1,164 450 3,2 471 7,6 419 38,20 175 420 74 420,74 215 922,87 175 2813,33
volume [cm3] 55 54 343 729 729 4539 23487 86524 165518
mass [kg] 0,1716 0,29 1,10 2,4 3,9 9,36 215 00 215,00 215,00 907,00
power intensity kp [kW/kg] 1,22 1,10 0,55 0,60 0,92 1,71 0 34 0,34 0,92 0,54
mean pressure (torque power torque density) density intensity pm kT ρp [bar] [W/cm3] [Nm/kg] 0,04 3,84 1,15 0,04 5,95 0,80 0,03 1,78 1,06 0,04 1,98 1,33 0,10 4,91 1,95 0,08 3,52 4,08 0 18 0,18 3 14 3,14 1 96 1,96 0,11 2,29 4,29 3,10 0,17 2,97
¾ Component data is increasingly being made available from the internet through Globalspec, eCl@ss etc, and to a greater extent machine readable. y level design g ¾ This makes use of real data for system optimization possible.
Design optimization using component data directly Design on demand, Micro Aerial Vehicles, MAV
Baseline
Optimized
motor
Astroflight 010
Hacker B20 31S
propeller
Graupner 6x3 folding APC 5x5
motor controller
Astroflight 10
YGE 4
Battery
Etec 1200 2s1p
Tanic 1100 3s1p
S AR
MAV baseline
P
P
b
d
ηd
ηb
MAV propulsion l i system.
0.12 m2
0.12
1.33
1.33
Endurance at cruise
22 min
Max speed T/W ratio
75 km/h 0 95 0.95
Pm ηm
42 min 12 1.2
Pout ηp
ηtot=ηb*ηd*ηm *ηp
MAV optimized geometry
Result: Shopping list and geometrical dimensions
David Lundström, Petter Krus
Conclusions ¾ Models for performance prediction can be based on statistics from existing subsystems and components is a simple and well established practice although it has had limited use outside aircraft design design, and is not present in the university curriculum to the extent it deserves. ¾ Design information entropy can be used to describe the impact of further refinement and design space expansion. This is a promising area for further study. Also potential for forecasting of performance ¾ Principal Component Analysis PCA can be used to produce parameters sets for models suitable for system optimization. It produces design spaces that minimize waste of the design space space.
2008-08-17
Sid 49
Linköpings universitet
References
2008-08-17
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