LIDS-P-1383
JUNE 1984
EFFECTIVENESS ANALYSIS OF AUTOMOTIVE SYSTEMS
by
Alexander H. Levis
Paul K. Houpt
Stamatios K. Andreadakis
ABSTRACT
A methodology for analyzing and assessing the effectiveness of an
The
internal combustion engine powered automotive system is developed.
analysis is carried out by characterizing separately both the system and the
These
user's needs in terms of quantitative attributes of performance.
attributes are determined as functions of primitives (independent design
variables) that describe the vehicle system, the user's requirements, and
System capabilities
their context, for example, an E.P.A. test procedure.
and requirements are compared in a common attribute space by means of a
special geometric locus, with which certain partial measures of effectiveness
can be computed.
These partial measures are then combined to yield an
overall effectiveness measure with which design tradeoffs may be studied.
The methodology is illustrated by assessing the effectiveness of a diesel
powered passenger car with respect to fuel economy and emissions in the
context of a simplified E.P.A. drive cycle. A key feature of the methodology
is its ability to integrate complex data bases derived from simulation,
laboratory test and analytical models as often found in automotive design.
*Laboratory for Information and Decision Systems, Massachusetts Institute of
Technology, Cambridge, MA 02139.
fDepartment of Mechanical Engineering, Massachusetts Institute of Technology,
Cambridge, MA 02139.
1.
INTRODUCTION
System effectiveness
is an elusive concept that encompasses technical,
economic, and human-factor considerations.
When the system to be evaluated
is one which provides a service, such as an automobile, then the needs of the
users must be taken into account.
Furthermore, the service it provides may
change in value as the users' needs, attitudes and technologies change and as
the competitors' capabilities change.
Thus, any methodology that is proposed
for effectiveness analysis must be sufficiently broad and flexible so that it
can accommodate change and can evolve over time.
The
analytical
aspects
of
the
methodology
described
address mainly the relationships between component
structure,
Vehicle
and operating procedures
system
performance
operational goals.
to
denotes
the
ability
this
characteristics,
system performance
to
l],
achieve
paper
system
[2],
[3].
appropriate
It is assumed that the cost associated with any system
realization and operation can be computed:
costs for
in
the
total cost may reflect the
designing and manufacturing the vehicle system and the costs for
operating and maintaining it.
The basic premise of the methodology is that an automobile provides a
service to its user under a wide variety of conditions. The complementary
premise is that each user requires from an automobile services that it may or
may not
be
able
to
provide
and
that
the
requirements that it may or may not be able
there is the
public
establishes
to meet.
Thus,
performance
on one
side,
automotive system with a range of performance characteristics,
while on the other are the users and the public with their diverse needs and
requirements.
Therefore, the first step of the methodology is based on the
ability to model
terms
of
methodology
the system's capabilities and the users'
commensurate
attributes.
This
and
are described in the next section.
illustrative example is introduced.
the
other
In the
requirements in
steps
in
third section,
the
an
In section 4, the methodology is applied
to the specific example to analyze its system effectiveness.
2
2.
SYSTEM EFFECTIVENESS ANALYSIS
The methodology is based on six concepts: system, users' needs, context,
attributes,
primitives,
of
and measures
effectiveness.
The
first
three
describe the problem, while the last three define the key quantities in the
analytical formulation of the problem.
The
system consists of components,
A
operating procedures.
their interconnection and a set of
passenger car, a truck, and their associated power
plant and drive train are typical systems.
The users' needs are derived from a set of objectives and tasks that the
Their description must be as explicit and
users would like to accomplish.
specific as possible so that it can be modeled analytically.
requirement such as
useful
nto have a dependable engine' is too broad, while a more
specification would be
that delivers adequate power'
The context
For example, a
'to
have a reliable,
fuel efficient
engine
.
denotes the
i.e.,
set of conditions and assumptions,
A vehicle operating
environment, within which the user will use the system.
on a highway or city or combinations of the
the
two define
typical automotive
environments.
Primitives
are the variables and parameters that describe the
system,
For example,
in the
case of an automobile, propulsion system primitives may include the
engine
the users' objectives and the public's requirements.
displacement, vehicle weight,
drive
train gear
ratios,
spark advance
EGR
schedules, and failure probabilities associated with the components to name
the
trip
length and the load. Let the system primitives be denoted by the set {x i
and
but a few.
the users'
Primitives
of the tasks may be
the annual mileage,
primitives by the set {yj).
Attributes
requirements.
are
quantities
System
that
attributes
describe
for
an
3
system properties
automobile
propulsion
or
users'
system may
include
and
cost, reliability, specific fuel consumption, exhaust gas emissions
driveability.
quantities as
Users'
requirements
the system attributes,
consumption, or maximum emissions.
(As) and the requirements
may
e.g.,
be
expressed
minimum
by
reliability,
the
same
and fuel
The system attributes are denoted by the
by (Arl.
Measures of Effectiveness are quantities that result from the comparison
of the system attributes and users' requirements.
They reflect the extent to
which the system meets the requirements.
The
first
step of
system primitives.
this
the methodology
consists
of
the
selection
By definition, they must be mutually
sense, the primitives are the independent variables
of
the
independent.
In
in the analytical
formulation of the methodology.
The
second
characterize
the
step
consists
properties
of
that
defining attributes
are
of
interest
for
in
the
the
attributes are expressed as functions of the primitives.
system that
analysis.
The
The values of the
attributes could be obtained from the evaluation of a function, from a model,
a computer simulation, or from empirical data.
Each attribute depends,
in
general, on some of the primitives, i.e.,
As = fs (XiV-x
s = 1,2,...,S
k)
Attributes may or may not be interrelated;
they
have
primitives
in
common.
A
primitives taking specific values {xi);
(1)
two attributes
system
realization
are related,
results
in
if
the
substitution of these values in the
relationships (1) yields values for the attributes {As).
Thus, any specific
realization can be depicted by a point in the attribute space defined by a
coordinate frame in which each coordinate corresponds to an attribute.
The third and fourth steps consist of carrying out a similar analysis
for the users' needs: Selection of the primitives that describe the variables
and
parameters
requirements.
of
the
objectives
and
tasks
and
definition
of
the
Then models are selected that map the primitives yj into the
4
requirements:
Ar = fr (Yl,.',Yn)
r = 1,2,...,R
;
interrelated through dependence
Some of the requirements may be
primitives.
It
the
between
is
possible
also
requirements,
(2)
to
e.g.,
a
introduce
trade-off
directly
constraints
some
relationship
on common
between
fuel
consumption and vehicle weight (e.g., for improved ride quality). However, it
through
the
functions or models that define attributes or requirements in terms of
the
is
that
preferable
such
trade-off
be
relationships
derived
Specification of values for these primitives results in a point
primitives.
or region in the requirement space.
The two spaces, the system attribute space As and the users' requirement
space
Ar ,
although
the
of
same
dimension,
may
be
in
defined
terms
of
different quantities, or quantities scaled differently. Therefore, the fifth
step consists of transforming the attributes and requirements
common, commensurate attributes
these
defined on a common attribute space A.
common attributes has been defined,
transformed
into commensurate
into a set of
sets
that
the two
{As }
sets
can be depicted
and
in the
Once
(Ar}
are
attribute
space A defined by a common coordinate frame.
A possible additional
operation
in this
step
is
the normalization of
the
various commensurate attributes so that their values are in the range (0,1].
If
all
the
attribute
attributes
is
space
graphically
the
are
normalized
in
the unit hypercube.
loci
of
the
sets
(A s }
this
This
and
manner,
is very useful
{Ar }
the
then
common
in depicting
and
in
analyzing
the
effectiveness
their
interrelationships.
The
sixth step
is
the
key
one
system in view of the users' needs.
in
the
system
properties
attributes
of
two
loci
and
in
of
a
It consists of procedures for comparing
users'
the
analyzing
requirements
attribute
allowable values that the primitives
space.
through
the
Consider
first
geometric
all
the
of a specific system design may take.
If the primitives are allowed to vary over their admissible ranges, then the
5
variations
define
requirement
hypercube.
a
Ls
locus
in
the
attribute
locus Lr can be constructed.
space.
Similarly,
a
Both loci are defined in the unit
The geometric relationship between the two loci can take one of
three forms:
The two loci do not have any points in common; they do not
(a)
overlap, i.e., the intersection of Ls with Lr is null:
Ls n
Lr =
(3)
In this case, the system attributes do not satisfy the users' requirements
and
one
would
define
the
effectiveness
to
be
zero,
regardless
of
which
specific measure is used.
(b)
The two loci have points in common, but neither
locus is included in the other:
L Ln
s
(4)
r
but
L
In this case,
satisfy
s
nL
r
<
L
s
and
L
s
nL
r
<
L
(5)
r
only some of the values that the system attributes may take
the users'
describe the extent
requirements.
to which the
these measures may be considered
Many
different measures
system meets
as
the
a measure of
normalized, takes values in the open interval (0,1).
measure in the normalized attribute space.
can be used
requirements.
to
Each
of
effectiveness which,
if
For example, let V be a
Then an effectiveness measure can
be defined by
E = V(L
s
n L r)/V(L s)
(6)
which emphasizes how well matched the system is to the users' needs.
6
The requirements locus is included in the system locus:
(c)
L
In
this
s
n L
r
case,
= L
(7)
r
it
follows
from
Ls
(7) that
is
larger
them
First, only certain system attribute values
can be interpreted in two ways.
the
the
of
requirements
users.
since
resources
This
is
with
consistent
the
The second interpretation is that the use
interpretation given in case (b).
of this system for the
and,
This result
consequently, the ratio defined by (6) will be less than unity.
meet
Lr
given requirements represents an inefficient use of
system
the
the
exceed
capabilities
needs.
users'
Inefficiency, in turn, implies lower effectiveness.
If the system locus is included in the requirements locus, then
the system's effectiveness is identically equal to unity, i.e.,
L
The
measures
s
nL
r
s
measure
that
(8)
=L
of
effectiveness
can be
defined
in
given by
the
partial measures be denoted by {Ep}.
(6)
common
is
one
attribute
of
function u.
k
now
are
However,
the
arguments of u must belong
valid
to the
these
To combine these partial measures into
considered
for
partial
Let
space.
The k partial
a single global measure, utility theory may be used [4],[5].
measures El,...,E
many
to
be
the
application
arguments
of
utility
of
a utility
theory,
the
positive orthant of Rk*.
The subjective judgements of the system designers and the users can be
incorporated
directly
into
the
methodology
in
two
ways:
(a) by
choosing
and (b) by selecting a utility function.
different partial measures,
The
global effectiveness measure is obtained, finally, from
E =u
(E
,E.. )
1 ,E2,
(9)
k
k-dimensional Euclidean space
7
The
seven
steps
of
the methodology
shown schematically in Figure 1.
and
their
interrelationships
are
The diagram emphasizes that the system and
the users' needs must be modeled and analyzed independently, but in a common
context.
users'
The system capabilities should be determined independently of the
needs
and
the
users'
requirements
considering the system to be assessed.
should
be
derived
Otherwise, the assessment is biased.
GLOBAL
EFFECTIVENESS MEASURE
PARTIAL
EFFECTIVENESS MEASURES
SYSTEM
REQUIREMENTS
LOCUS
LOCUS
COMMENSURATE
COMMENSURATE
SYSTEM ATTRIBUTES
REQUIREMENTS
I REQUIREMENTS
REQUIREMENTS
SYSTEM
ATTRIBUTES
SYSTEM
MISSION
PRIMITIVES
PRIMITIVES
SYSTEM
Figure 1.
without
CONTEXT
MISSION
The Methodology for System Effectiveness Analysis
8
AN EXAMPLE
AUTOMOTIVE EFFECTIVENESS ANALYSIS:
3.
In this section, the effectiveness analysis methodology is illustrated
The problem is to evaluate the system effectiveness
with a concrete example.
of
fixed power plant which is
a particular
to be
in a hypothetical
used
For this study, the context is a simplified version of a
family of vehicles.
drive-cycle used in the U.S. Environmental Protection Agency test standards.
Context is defined in this case by a set of prescribed velocity versus time
trajectories
which
the
vehicle
must
follow.
Attributes
of
interest
are
confined to fuel-consumption (FC,g/mi), unburned hydrocarbons (HC, g/mi), and
oxides
of
nitrogen
(NOx,g/mi).
(a) the vehicle weight
simplicity:
associated with the shift point
defined
Only
by
a
constraint
two
corresponding
to
considered
for
and
(b) a parameter
transmission.
The mission is
load);
(including
in a manual
are
primitives
federally
mandated
emission
standards and fuel economy.
3.1
System Modeling
Modeling vehicle performance in the context of E.P.A. test procedures
has received extensive attention since the tests were established in 1974.
One
approach
which
has
in
been
widely
used
and
engine
initial
industry
can
be
broadly
characterized as follows:
STEP
1:
Define
ambient
conditions
(hot/cold)
for
specified procedure; fix control laws for spark-timing, air-fuel ratio, and
exhaust gas recirculation, etc.; define velocity versus time trajectories for
test
(e.g.,
combination of urban and highway driving).
For effectiveness
analysis, any other primitives are also fixed in this step.
STEP 2:
For the given vehicle and power train, determine the speed and load
(torque and/or power) seen at the crankshaft as functions of time as the test
trajectories are swept out.
Compute a matrix of engine speed (RPM) vs torque
(or power) and time spent at
each speed/load point from the trajectories.
Figure 2 illustrates a typical matrix for a 4500 lb. vehicle with automatic
transmission resulting from the original urban and highway drive
[6]; a single combined test procedure has been employed.
9
schedules
Urban Schedule (18 Cycles)
4500 lbs. in. wt.
47-
2407
-
--
196.7
1.3t
2000
1RW
Iwo
O849
184d0
-174
-2.?71
4.33
1933
92.8
1&.33
W1859
63.
17.43
.09
2.14
~1600
- -
1739
59.1
15.75
if
1645
81.2
9.47
1400-
>
-
1739
57.4
7.42
.
1.
143.1 14691
3.154
I
17.6
5.1
4.13
1312
34.0
1.02
1257 IM
101.6 114.9
56
9.31
1258
64.5
54.33
- -i3
W~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1070
10t
t
' 8l4ll
11157112
1077
1
l
1092
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15
Q815
894
952
94.0
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807--34.1 9.5
728 603 656
19.6
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69.22 90.62 49.16
708
6
624
34.3 43.7
33.69 20.64
607---
6.20
I
i
Speed (rev/mi)
__
1
T
597
43.1
1312 1359
155.1 67.8
15.24 6 92
Speed___
763
7 7
3.
62.3
(1
Time
s)
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T T TT TTTITTTTT
407-~...
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70
60
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11.45 1.66
9.97
1153
140.5
6.6
96.4 101.4 115.7 179.2
49.4 57.6
7.9
17.6
3654 49.91 19.92 18.17
13.76
3.94 47.62
11.4
11.4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3.9
76
968
919
908
914
9180
932 93
92
96
102.2 112.6
74.0t 7".
31.7 .
50.3 6,0
m2
9.4
6.893
19.251 13.71
829
37.6
117.40 3.3
9.3
12.3
12.30
1702 181.919.7
9-62
1301
142.2
2679
1729
21.5
I.
1
1493 1562
1465
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127!
129.7
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2100
6.07
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1670 1667
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M3
Torque (N.m)
am~
2200 - --i
z~~o
. o
52
II
1831
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24.4 34.7
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9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~21.68
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7
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8.I
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i,;
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~~~~~~l
_
Highway Schedule
4500 lbs. in. wt.
1371
1371
70.2
9.90
1575
14
5.61
7311
1
4.96
9.14
1549 747
514
131.5 14.7
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].5.5
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907
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7
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743
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0
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-
0
10
655
19.9
23
34.9
2.28
20
2.03
30
6W
'
44.6
7.73
48
50
60
Speed (rev!min)
Torque (N.m)
800 - -
Time (s)
I,
70
8L'
TTTT
90
70
170
1717 130
145
t150
lO
170
191
91
T0
Torque (N.m)
Figure 2.
Speed-Torque Martix with accumulated Time
Resulting from GPSIM Simulation of
(a) Urban Schedule,
(b) Highway Schedule [6].
10
707
210
T
12 22
30
STEP 3:
Obtain "calibration" maps for
the
engine under
study which
give
rates of fuel consumption and emission production per unit time as functions
of engine speed and load.
total
fuel
Then, from data in Step 2, integrate to obtain
and
consumed
emissions
For
produced.
example,
with
a
grid
discretization of the map into cells
EFC (g/mi)]
Zoa
dsa(dFC/dt)(Time
in Cell)
total distance in test
=
all speed
torque cells
Note
that
in the
calibration
computations
maps
to
change
in
Step
with
3,
time,
it
is
possible
for
e.g.,
cold
to
allow
start
the
initial
conditions, hot soak, or changes in ambient, so that very complex scenarios
or contexts may be defined.
FC, HC and NOx
extrema
over
Also, in practice, the surfaces corresponding to
rates are continuous but
the
speed/torque
not convex and may have multiple
Note
coordinates.
that
the
frequency
distribution over the grid on speed/torque coordinates can be obtained from
highly
detailed
simulations
vehicle
(the
source
for Figure
2),
or
from
experimentally derived test data.
Completion of Steps 1-3 defines implicitly values for system dependent
variables as functions of certain primitives.
For this example,
attention
has been limited to the system attributes corresponding to fuel consumption,
unburned
hydrocarbons
and
oxides
of
nitrogen.
This
complex
model
thus
defines the relationship required by equation (1).
3.2
Case Study:
A Diesel Powered Passenger Car
To illustrate the methodology of effectiveness analysis, a hypothetical
vehicle powered by a particular diesel engine studied in reference [7] was
used,
as
illustrated
in
Figure
3.
The
diesel
was
selected
somewhat
arbitrarily because of the availability of published performance maps, and
the simplicity resulting from not having to consider spark advance and EGR
schedules as primitives.
The
effectiveness analysis
is easily applied
spark ignited engines with these added design variables.
to
(a)
so
240
60
22
OSe6-_i
C
2
20
i-
_
..
0-t
I0
O
800
350
Specific
_300
1200
1600
fuel consumption
2000 2400 2800 3200
Engie speed rev/min.
/
3600
250
&000
(b)
Figure 3.
255 Cubic Inch Displacement Diesel [7]
(a) Engine, (b) Nominal Performance Characteristics.
12
Figure
4 illustrates the performance of
consumption,
hydrocarbon
emissions,
oxides
the
diesel
of
nitrogen,
in
terms
and
functions of specific power (BMEP) and crankshaft speed (RPM).
of fuel
smoke
as
This was for
a particular injection advance, optimized in the study in reference [7].
In
principle, one could include the advance schedule as one of the primitives,
but this will not be done here.
If the brake torque or power and speed are
specified, the rate of change of attributes with respect to time are computed
by spline interpolation of the specified points on the various 'maps'.
In this
focus
is
variables
example,
on
the engine parameters
tradeoffs
associated
with
are
the
vehicle
have been selected as primitives.
which can be
thought
vehicle loading.
of both
in
terms
of
assumed to be
First
and
fixed;
drivetrain.
the
Two
is the vehicle weight,
classes
of vehicles
or
simply
Second, is a single drive-train parameter corresponding to
the shift-point (in RPM) associated with a manual four-speed transmission.
The motivation for considering the shift point as a primitive can be viewed
as an
optimization problem.
For
example,
if
a
optimum upshift point to the driver were to be
shift take place (as in the Volkswagen system)?
signal
light
employed, where
to
indicate
should the
Alternatively, one may ask a
sensitivity question such as how a distribution over shift points
individual
driver
or
over
a
population)
degrades
system
(by an
performance
attributes.
To apply the effectiveness analysis methodology, a common scenario or
context is required.
test
In general, this might be as complex as a full E.P.A.
procedure.
Here,
we
limit
attention
to
a
series
of
acceleration/deceleration and cruise conditions for the vehicle as shown in
Figure 5.
Parameters of the context include the total duration of the test,
the acceleration and
deceleration on
each change
in velocity,
the
cruise
velocities, and the dwell time at each cruise condition.
Given the velocity time profile, a simple inverse kinematic model was
developed, as
brake
load
shown in block diagram form by Figure
on the
engine.
For
specified
13
vehicle
5(b),
mass,
to
drag
compute
the
coefficient
170 ~ I10'~-"Ito
i l
6-0
.1
1
I
32300
50
350
Soo
6-r0
60
NO
1.00
1,0
30
0
i 0.-
o
2200
~
2850
200
350150
m 511~~~~~~~7
I2O0
/
3
0IEnoine
2000 speed
2i00 revmmv.
200
SF.C.
310
310~~~~~5
3200 / 3600
60
330
000
800 1200
vmmin.
ee
1600
36000
00 2000
2.00 2000
,me spJEwgd
&O
6-1
3~o
290
:3SO ~ ~ --..--~
290
310
/
"
2~'0,
3-0 (
37S
1-0
1 00
I20
1600
2O
2
2002100 21100 3200 3600
Engine speed revimm.
Figure 4.
O
/,(XX
Maps of HC, NOx, and Fuel Consumption
at optimum timing for performance [7]
14
3200
,
:
Figure 5(a)
Vehicle speed vs
time trajectories for
case study context
Vehicle
At50
D
TE
Gear
>'C
! T/Selection
3i0
sIHC
DaZ
fParameters
i
e e-- a I2f
sI
i
Figure
5(b).
Drag
Forces
Blok diagmeiers
compu
Drive
Shof t
T - torque [N-M]
NE
E
Engine
Shaf t
to
N - speed [RPM]
Engine
Maps
NOx
* HC
TE
Figure 5(b).
iSeectioncs
Block diagram of inverse kimenatics to
compute load seen at engine shaft
15
(which for this analysis is an effective drag coefficient to model cumulative
friction losses), gear selection, and other parameters (Table I),
computes
from
the
velocity
instantaneous
and
acceleration
the
the model
crankshaft
speed and torque required to follow the given trajectory.
TABLE I
From the
digitized
1.2
Differential Ratio
4
Tire Radius
0.34m
Gearbox Ratios
0.28
calculated
versions
interpolation)
N Sec 2 /m2
Drag Coefficient
to
of
obtain
engine
the
shaft
maps
the
hydrocarbon and NO T generation.
in
load,
0.52
the
Figure
instantaneous
0.81
1.12
computer model
4
(with
rates
of
then uses
bi-cubic
fuel
spline
consumption,
These are then integrated over the scenario
By varying vehicle weight and the shift
trajectory to obtain nbag" totals.
point described above, a trajectory sweep yields values for the attributes
which
define
surfaces
in
3-dimensional
space.
These
surfaces
are
illustrated in Figures 6, 7, and 8, for fuel consumption, nitrogen oxides,
and hydrocarbons respectively.
The attributes locus is derived from the data in Figures 6-8 by ploting
the contour of upper and lower bounds of admissible shift points and vehicle
mass into the three dimensional attribute space whose axes are FC, HC, and
NOx , each with dimensions of (g/mi).
shown in Figure 9.
16
A perspective view of this surface is
FC
100
g/mi
95
90
17 27
2.2
31
'3S
2
RPM x 100
N
Figure 6.
Fuel Consumption as a function of
and Weight
KgxSpeed
85o
N
F
as a function of Speed and
6igure
Fel
7. ConsOmption
17
Weight
HC
0.313
0.311
0. 309
0. 307
g/mi
0. 305
RPMx10oo
N 7w3
Figure 8.
ic
HC as a function of Speed and Weight
2.4
0.313
gmia
0.311
22
0.309
g/mi
0.307
2.1
FC
Figure 9.
The system attribute locus
18
(BC, No x ,
RC)
3.3
System Requirements
In
this
problem
the
requirements
or
mission
constraints on emissions and fuel consumption.
locus
is
defined
by
For example, current E.P.A.
specifications call for:
HC (total)
< 0.41
g/mi
NO
(total)
<
1.0-1.5
CO
(total)
<
3.5
(10)
g/mi
(11)
g/mi
There are no hard specifications on fuel consumption, only on corporate wide
average fuel economy (CAFE), such as 15 miles per gallon, and a tax on gross
fuel consumption.
Thus, for this example, an upper limit on fuel consumption
is assumed to be a user requirement: 30 mpg which corresponds to
FC (total)
The
three
locus, Lr.
,
87 g/mi
constraints,
(12)
(9),
(10)
and
(11),
define
the
requirements
It is a rectangular parallilepiped bounded by the planes
HC = 0
HC = 0.41
NO
NO
x
=0
FC = 0
x
= 1.5
FC = 87
as shown in Figure 10.
19
FC
0.408
/
\
Figure 10.
4.
The Requirement Locus
SYSTEM EFFECTIVENESS ANALYSIS
In the previous section, the two loci necessary for the assessment of
effectiveness were defined;' the system locus Ls was depicted in Figure 9 and
the requirements locus Lr in Figure 10.
the
same
coordinate
frame,
Since both loci have been defined in
it is possible
to
assessment by superimposing Figure 9 on Figure 10.
carry
out
a qualitative
For the selected range of
primitives, i.e., 1,000 to 1,600 kilos for vehicle weight anbd 2,700 to 3,700
RPM for the shifting point, it is clear that no part of the system locus is
within the requirements locus.
20
Ls
Lr
84.96
<
FC
<
101.69
FC
<
87
0.305
<
HC
<
0.313
HC
<
0.41
2.015
<
NO x <
2.364
NO x <
because of the condition on NOx .
s
1.5
Consequently,
r
and, in accordance with Eq. (3), the effectiveness of this particular dieselpowered passenger car is identically zero.
As
earlier,
stated
this
particular diesel engine.
a
is
hypothetical
powered
vehicle
by
a
The initial choice of design parameters for the
What the designer
vehicle led to a locus totally outside the requirements.
would do then is to modify the design parameters in an effort to move the L s
This is best done interactively with the
locus within the Lr parallilepiped.
aid of
any
of
the
graphics
3-D
available
designer would
The
software.
continue modifying the parameters until a high measure of effectiveness is
obtained,
design.
the
or
until
the
design
limits
are
a
reached without
satisfactory
During
In the latter case, alternative designs will be considered.
interactive
qualitatively
design
by
process,
observing
intermediate
the
relationship
designs
would
between
Ls
be
evaluated
and
Lr
and
quantitatively by computing the measures of effectiveness.
To
illustrate the procedure
to be
used when Ls
system requirements for this example will be changed.
direct
and
serves
to
illustrate
requirements can be expressed as
21
the
methodology
and
Lr overlap,
the
This procedure is more
better.
The
three
HC
< a
;
NO
b
x
FC
c.
Consider the case in which:
a = 0.310
:
b = 2.250
c = 0.96
;
Then the two loci overlap,
LLs h L
0
as shown in Figure 11.
FC
FC 0.3 13
0.311
2.
N
0
.309
90
95
100
HC
Figure 11.
The system and requirements loci;
case
Lr #
the Ls
22
In this case, a measure V is required that will allow the assessment of
the system with respect to the requirements.
Let the first measure
to be
considered be the volume of the system locus.
V = I I I
f(FCNOx HC) dFC dNO
(13)
dHC
Then, a possible measure of effectiveness is the ratio of the volume within
the Lr locus to the total volume of the system locus (as in Eq. (6)).
The total volume of Ls was computed to be:
V (L)
=
0.416
The volume of the portion of the L s locus within the Lr is obtained from Eq.
(13):
V1 (L n
L ) = 0.205
and the resulting measure of effectiveness is
0.205
0.416
1
0.493
This measure weighs equally all operating points or all points in L s, i.e.,
all
values
of
the
attributes
are
equally
significant.
however, to introduce weights in the measure of V1 ,
i.e.,
It
is
possible,
the integral
(13)
may be generalized:
V
= I R g(FCN,HC)
C)f(FCNOBC)
(FCNO
dFC dNO
dHC
Alternatively, one may assign different relative weights to the primitives.
For example, there may be a preference toward having the shift point at lower
23
RPM.
This can be expressed as a weighting coefficient
C1 = 1.370 - 0.0001 SP
where SP is the shift point in RPM.
This coefficient assigns a weight to the
locus points corresponding to that value of SP.
Similarly, for the vehicle
weight:
Weight W:
1000-1100
Coefficient C :
1100-1200
1.00
1200-1300
1.15
1.10
1300-1400
1.05
1400-1500
1.00
When the corresponding integrations are carried out,
V (L)
V2 (L
= 0.457
L ) = 0.231
and the measure of effectiveness is
E
The
two
0.231
=
0.457
0.506.
partial
measures
El
and
E ,
each
one
reflecting
different
weights, can be combined into a global measure of effectiveness through the
use of an appropriate utility function.
Consider, for example, the global
measure
E =
{EI E
=
0.499
All the steps of the methodology have been carried out and a specific measure
of effectiveness for the particular vehicle and a set
been determined.
24
of requirements
has
If the requirements were changed to:
FC < 100
,
NO
< 2.31
HC < 0.311
and
;
then the partial measures of effectiveness are:
EB = 0.720
E2 = 0.733
E = 0.726.
and
If an alternative design is considered, then the methodology can be applied
to
the second design and a measure
between the
two
designs
of effectiveness
could be made
then
both
obtained.
Comparison
qualitatively using
the
attributes (system) loci and the requirements loci, and quantitatively using
the measures of effectiveness.
5.
CONCLUSION
A general methodology for assessing
been described briefly and then shown
powered
passenger
effectiveness
is
vehicle.
the
The
comparison
expressed
space.
The
underlying
of
software.
the
is
suitable
for
the
concept
system's
of
case
systems
of a
for
capabilities
has
diesel
measuring
to
the
Both capabilities and requirements
in terms of multi-dimensional
approach
effectiveness
to apply to
requirements of its users (the mission).
are
the
loci defined in the attribute
inclusion
in
computer
aided design
Graphical representation of the loci would enhance the designer's
intuition and assist him in exploring design alternatives.
25
6.
REFERENCES
Analysis of C 3
Vol. SMC-14, No.
[1]
Bouthonnier, V., and A. H. Levis, 'Effectiveness
Systems,' IEEE Trans. on Systems, Man and Cybernetics,
1, January/February 1984.
[2]
Dersin, P. and A. H. Levis, Large Scale Systems Effectiveness Analysis.
Report LIDS-FR-1072. Laboratory for Information and Decision Systems,
MIT, Cambridge, MA, 1981.
[3]
Dersin P. and A. H. Levis, 'Characterization of electricity demand in a
power system for service sufficiency evaluation,' European J.
of
Operation Research, Vol.11, No.3, November 1982.
[4]
Debreu, G.,
Equilibrium,
Theory of Value:
An
Wiley, New York, 1968.
Axiomatic
Analysis
[5]
Phlips, L.,
Applied Consumption
Elsevier, New York, 1974.
Analysis,
North-Holland/American
[6]
Cassidy, J. F., Jr., 'A Computerized Approach to Calculating Optimum
Engine Calibrations,' General Motors Research Laboratory, Research
Publication GMR-2286, December 1976.
[7]
W. M. Scott,
International
October 1980.
of
Economic
'Development of a 225 Cubic Inch Diesel Engine,'
Symposium on Automotive Propulsion Systems, Vol.
26
5th
20,