EPA-420-R-76-107
Calspan
AUTOMOBILE EXHAUST EMISSION MODAL ANALYSIS MODEL
J C. Bernard, H. T. McAdams and P. E. Yates
Calspan Report No. NA-5507-D-2
Prepared For;
ENVIRONMENTAL PROTECTION AGENCY
DIVISION OF EMISSION CONTROL TECHNOLOGY
ANN ARBOR, MICHIGAN
SEPTEMBER 1976
CONTRACT NO. 68-03-0435
Caispan Corporation
Buffalo, New York 14221
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ABSTRACT
This report on modal analysis of automobile emissions was prepared
for the United States Environmental Protection Agency's Division of Emission
Control Technology, Ann Arbor, Michigan, under EPA Contract No. 68-03-0435.
The work reported herein constitutes an application of a modal analysis emissions
model to emissions data from the FY 73 and FY 74 Emissions Factors Programs.
The model was developed under EPA Contract No. 68~01-0435 and was
extended and refined under the current contract. By means of the model,
it is possible to calculate the amounts of emission products emitted by
individual vehicles or groups of vehicles over an arbitrary driving sequence.
ii
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TABLE OF CONTENTS
Section Title Page
1 INTRODUCTION 1
2 MODAL ANALYSIS EMISSION MODEL: THEORY, APPLICATION
AND EVALUATION 4
2.1 Mathematical Basis of the Model 4
2.2 Application of the Model to Driving Sequences ... 8
2.3 Performance Evaluation of the Model:
Error Statistics 9
3 FACTORS AFFECTING MODEL PERFORMANCE 11
3.1 Model Input Data 11
3.2 Review of FY 71 and FY 73 Results 13
3.3 Direct Testing of Emission Rates 19
3.4 Discussion of Driving Sequences 26
4 FY 74 RESULTS 28
4.1 Model Coefficients and Error Statistics 31
4.2 Discussion of FY 74 Results 42
5 SUMMARY AND CONCLUSIONS 46
6 APPENDIX: AVERAGE GROUP COEFFICIENTS FOR FY 73 § FY 71. . 49
iii
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12
15
16
17
18
24
30
32
32
33
33
34
34
35
35
36
36
37
37
38
38
39
39
40
40
47
48
LIST OF TABLES
Title
Mode Versus Time in Mode
Percent Bias for Simple and Composite Emission Rate
Functions for FY 73 Program
Percent Standard Deviation for Simple and Composite
Emission Rate Functions for FY 73 Program
Percent Bias for Simple and Composite Emission Rate
Functions for FY 71 Program
Percent Standard Deviation for Simple and Composite
Emission Rate Functions for FY 71 Program
Test of 1972 Chevrolet Impala and Malibu
Comparison of Original A/D Modes and Corrected A/D Modes -
Vehicle 5011 -- Washington
Model Coefficients and Error Statistics
Performance Statistics for Washington (Composite Model)
Performance Statistics for Washington (Simple Function) . .
Performance Statistics for Chicago (Composite Function). .
Performance Statistics for Chicago (Simple Function) . .
Performance Statistics for Houston (Composite Function)
Performance Statistics for Houston (Simple Function) . .
Performance Statistics for St. Louis (Composite Function)
Performance Statistics for St. Louis (Composite Function)
Performance Statistics for St. Louis (Simple Function) . .
Performance Statistics for Phoenix (Composite Function)
Performance Statistics for Phoenix (Simple Function) . .
Pooled Performance Statistics for Above Cities (Composite)
Pooled Performance Statistics for Above Cities (Simple)
Pooled Coefficients for Above Cities
Performance Statistics for Los Angeles (Composite Function)
Performance Statistics for Los Angeles (Simple Function)
Coefficients for Los Angeles
Percent Bias for Simple and Composite Emission Rate
Functions for the FY 74 Program
Percent Standard Deviation for Simple and Composite
Emission Rate Functions for FY 74
IV
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1. INTRODUCTION
The modal emission model developed for the EPA under Contract No.
68-01-0435 and refined and extended under Contract 68-03-0435 makes possible
the computation of vehicle emissions over an arbitrary driving sequence.
The amounts of pollutants emitted over this sequence can be computed for
individual vehicles or for groups of vehicles pooled to represent meaningful
aggregations according to such constraints as model year or geographic
location.
The model was initially applied to data from 1020 automobiles as
obtained by Automotive Environment Systems, Inc. under EPA Contract No.
68-04-0042. These vehicles spanned model years 1957-1971 and represented
the total population of such vehicles in use in early 1972. As new genre
of vehicles enter the vehicle population and older vehicles are retired
from the population, adjustments in the model must clearly be made if it is
to be used for predictive purposes. Accordingly, it is important that the
modal emissions data generated as part of the Emission Factors Testing Program
be integrated into the modal emissions data base and that the modal emissions
model be updated as required to accommodate the new data. The results
reported herein represent efforts to integrate FY 74 emission factors data
into the modal emissions model and to review the FY 71 and FY 73 results
in the light of findings from the FY 74 program.
For many, if not most, purposes to which the modal emission model
will be put, the prediction of emissions from an individual vehicle is not
so much of interest as the prediction of emissions from an aggregate or
collection of vehicles subject to some set of constraints such as geographic
location, mix of model years, and time-history profile. For example, consider
the impact of two alternative traffic management systems on ambient air
quality. To determine relative desirability of the alternatives, it is more
appropriate to consider the aggregate emissions from a representative sample
of the vehicle population being controlled by the system than to consider
1
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emissions from individual vehicles in the population. The prediction of
group emissions benefits from the fact that the law of large numbers
operates to reduce the uncertainty in the predictions. If data from a
large number of individual vehicles are pooled to estimate the group
emission averages, those estimates are much more likely to reflect the
actual difference in environmental impact than are comparisons made on
individual vehicles.
In the FY 71 emission factors program, it was determined that model
years and certain geographical considerations, such as altitude, provided a
logical basis for stratification of vehicles into appropriate groups.
Accordingly, eleven groups were established for application of the modal
emission model to the FY 71 data. Similar considerations gave rise to six
vehicle groups in the FY 73 program and two groups in the FY 74 program.
The groups for FY 71, FY 73, and FY 74 are shown in the inset table. The
rationale for geographic classification is based on the fact that, in the
FY 71 and FY 73 programs, vehicles from Denver displayed, as a group,,
different emission characteristics than vehicles from low altitude cities.
Los Angeles vehicles were distinguished as a separate group because of
differences between emission standards for California and for other parts of
the United States. In the FY 74 program, data from Denver were not available
for analysis at the time this report was prepared.
In the ensuing sections of this report, the mathematical basis of
the model will be reviewed as a prelude to its application to the emissions
factors data for the various fiscal years. Included in this review will
be a reiteration of the statistical basis employed to evaluate the accuracy
and precision of the model in predicting emissions over the Surveillance
Driving Sequence (SDS) and the Federal Test Procedure (FTP). Results will
then be presented as tables of model coefficients for the several vehicle
groups and tables of performance in terms of model bias and variance.
2
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VEHICLE GROUP STRUCTURE
FOR EMISSION FACTOR PROGRAMS
Group 1
2
3
4
5
6
-7
/
8
9
10
11
Group 1
2
3
4
5
6
Group 1
2
FY 71 DATA
1957-1967 Denver
1957-1967 low-altitude cities (non-California
1966, 1967)
1966 and 1967 California
1968 low-altitude cities
1969 low-altitude cities
1970 low-altitude cities
1971 low-altitude cities
1968 Denver
1969 Denver
1970 Denver
1971 Denver
FY 73 DATA
1973 and 1974 Denver
1972 Denver
1973 and 1974 Los Angeles
1972 Los Angeles
1973 and 1974 low-altitude cities
1972 low-altitude cities
FY 74 DATA
1975 low-altitude cities ) mQst vehicles equipped with
1975 Los Angeles j catalytic converters
3
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2. MODAL ANALYSIS EMISSION MODEL: THEORY, APPLICATION AND EVALUATION
The modal emissions model is a regression model which applies
discrete data obtained from the Surveillance Driving Sequence (SDS) to
predict the instantaneous emission rate e of a vehicle or group of
vehicles as a function of speed v and acceleration a over any driving
sequence. The primary feature of the model is a scheme whereby emissions
from discrete time segments called modes can be expanded into a continuous
function of time.
2.1 MATHEMATICAL BASIS OF THE MODEL
The emission-rate function can be visualized as a surface in a
three-dimensional space in which the dimensions are speed v ,acceleration a ,
and instantaneous emission rate e . The surface is represented mathematically
in the form
e = f (v, a)
where e, v and a are all assumed to be continuous functions of time.
In general, the multiple regression equation for emission rate e
as a function of velocity and acceleration is written in the form
e (v,a) = Cjii (v,a) +• c2u2(v,a) + cRuk(v,a)
k
= c.u.(v.a) (1)
i = l 1 1
where the u. are called "basis functions" and are selected in such a way
l
as to best span the variation of instantaneous emission rate e in response
to instantaneous speed and acceleration. The basis functions need not
be orthogonal but are linearly independent.
4
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For a particular vehicle the emission rate surface e(v,a) is
completely specified by the model-generated coefficients (cj for any driving
sequence within the domain spanned by the basis functions. Since the regres-
sion model is a linear model, coefficients for groups of vehicles can be
computed by averaging the coefficients of all vehicles within the group.
Although Equation (1) represents an emission rate function e(v,a)
applicable over the entire (v,a)-plane, greater flexibility is afforded if
the equation is decomposed into two functions, one applicable when a = 0,
the other when a / 0. The first, denoted e(v,0), applies to constant-speed
operation and, since it is a function of v only, can be abbreviated es(v).
The second function, denoted e^ (v,a], characterizes vehicle emission rates
during periods of acceleration or deceleration. For purposes of spanning
the entire (v,a)-plane, the functions e^ (v,a) and eg(v) can combined
as the composite function
e(v,a) = h eg(v) + (1-h) eA(v,a)
(2)
where h is a weighting function dependent on acceleration a and bounded
in the interval 0 ^ h(a) ^1.
In the original version of the model the form of and e^ were:
es » bj ~ b2v . b3v'
2 2
e, = d. + d_v + d.a + d.av + dcv + d,a
A 1 2 3 4 5 o
2 2 2 2
+ d.,va + dgV a + d^v a
In matrix vector notation, (3) can be written
(3)
es = ill
eA = D G
A
(4)
5
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where IB = (b^ b )
F = C 1 V V2)
D - (d1 d2 d3 d4 d5 d6 d7 d8 d9)
2 7 7 7 7 7
= (lvaavv a va vava)
and .F and G^' denote, respectively, the transposes of the vectors F and G.
Let us consider a typical time segment or mode of the SDS of duration T.
The sequence is specified in terms of the speed at each of n discrete, equally
spaced points in time as shown in Figure 1. Note that time increases to the
left.
v,
The total emission e(T) produced during time duration T of the
mode is
e(T)
/.T
a)dt
(5)
and in discrete space can be approximated by
6
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n-1
Z eCvi5a ) At
i = l
(6)
where
v.
l
v(T.) + v(T. J
iy l+l-'
and
a.
1
v(Ti+i) - vf-T.)
(?)
At
n At = T.
In terms of (6), therefore, the average emission rate over time T is
v-1
< e >
= ^ ^ 4(Vi' ai)Z^T
i = l
C8)
Note, however, that this average emission rate can be computed from the total
emissions measured during the time duration of the mode. The total emissions,
called the "bag values" for the mode, are an estimate of and can be identified
with e(T). Therefore
< e > ,
e(T)/_
(9)
and from (2), (4), (8), and (9) one can write
T t-l
h. B F + (1 - h.) DG.
n-l
• I [f L hi + £ [t I Cl-h)
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Therefore, one can write:
e(T)/T = B F' + D G' [11)
where and G_ are the weighted time averages of the basis functions
vectors F^ and (] for the mode under consideration. Since the total
emissions for each mode are known, as well as the corresponding times in
mode, the weighted time averages £ and G can be computed using the
speed-acceleration profiles of the SDS for each mode. The coefficient
vectors and D_ can be computed through least squares regression analysis.
The emission rate regression equation is intentionally expressed as
a sum of two terms in (11) to stress the fact that emission rate is a composite
function consisting of a function of speed only and a function of both speed
and acceleration. Because of the linearity of the model, however, (11) could
just as well be expressed as
= if.' +£i' = A i' t12)
where A is a 12-element row matrix of coefficients, consisting of the
3 coefficients from B and the 9 coefficients from D. Similarly, X_ is
a 12-element column matrix, the elements of which are weighted time averages
(3 from £ and 9 from
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calculated for the Surveillance Driving Sequence (SDS) and for the first 505
seconds of the Federal Test Procedure (FTP) . Comparison of measured (bag)
values for these two sequences with corresponding values computed by the
model provide measures of model performance. In this connection, it is
convenient to regard the SDS as a "training sequence" and the FTP as a "test
sequence." The input modal data used in computing the regression coeffi-
cients for each vehicle are obtained from the SDS. When these coefficients
are employed to compute the SDS bag valuej therefore, there is present an
element of "reciting" what was learned in the training phase. When the
same coefficients are employed to compute total emissions for the FTP
sequence, however, no such reciting is involved because the FTP constitutes
an independent test. The same vehicles were evaluated by the emissions model
over both the SDS and FTP driving sequences.
2.3 PERFORMANCE EVALUATION OF THE MODEL: ERROR STATISTICS
Evaluation of the performance of the model is achieved by comparison
of measured emissions and emissions computed from the model. For this purpose
it is convenient to define "bag value error" as
R = C - 0
where 0 denotes the measured or observed bag value and C denotes the bag value
computed from the model. Note that R changes from one vehicle to another and
even from one test to another on the same vehicle. These variations can be
due to errors of measurement, whether of the modal input data or the bag value,
or they can be due to the fact that the model does not faithfully integrate the
time-varying emission contributions in the same way as they are accumulated in
the bag-value measurement. If one computes the error R for a number of vehicles,
however, one can assess probabilistically whether a bias exists in the computa-
tion. Statistical quantities of interest are R, the average bag error foT all
the vehicles, and CD, the standard deviation of the individual bag errors
about the mean value. A test of significance can then be applied to determine
whether R represents a bias or is most likely a consequence of random measure-
ment errors. Other statistics of interest are the root mean square deviation
of the bag error
9
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and the magnitudes of R, (f ^ and RMS relative to the average observed bag value
0. See the NOTATION insert for terms used in this report to discuss model
performance.
NOTATION
CBAR
• Mean of the calculated amount of the given pollutant
OBAR =
Mean of the observed amount of the given pollutant
RBAR =
Mean bag error
(Bag error = Calculated Amount - Observed Amo.unt)
SIGR =
= Standard deviation of the bag error
PSIG =
(SIGR/OBAR) X 100%
RMSR
= Root Mean Square deviation of the bag error
PERR
= (RMSR/OBAR) X 100%
10
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3. FACTORS AFFECTING MODEL PERFORMANCE
As a result of applying the model to data from the FY 71, FY 73,
and FY 74 Emission Factors Programs, a backlog of experience has accumulated
from which it is possible to isolate some of the factors which influence
model performance. Most notable are those associated with the emission
measurement process and its effect on the quality of the modal input data.
To provide the necessary perspective for meaningful interpretation of the
results reported in Section 5, it will be instructive to-review this
experience, as well as certain aspects of emission measurement.
3.1 MODEL INPUT DATA
First, let us consider the nature of the input data required by the
emission model. The model uses modal data as computed from each mode or time
segment of the total 1054 seconds of the SDS to predict the actual total
output of pollutant over any driving sequence. The SDS is divided into 65
time intervals or modes, 32 acceleration-deceleration modes, and 33 zero-
acceleration modes. Table 1 lists all 32 acceleration-deceleration modes with
their corresponding speeds, distances traveled, and times in mode.
Each acceleration-deceleration segment in the SDS is followed by
a cruise-mode segment. The second-by-second emission rate response of a
vehicle in executing the SDS is recorded by a strip-chart recorder. The
strip-chart response is then divided into segments corresponding to each of
the 65 modes of the SDS. The area under the emission response curve corre-
sponding to each of the 32 accel/decel modes is measured and is used as input
for the eA portion of the emissions model. The areas corresponding to the
33 cruise modes of the SDS are not input to model. Instead, separate tests
are performed at constant speeds for periods of 60 seconds. These stabilized
steady state emission rates are computed from the 60-second intervals, and
are then used as input for the eg portion of the model.
11
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MODE
NO.
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
Table 1
MODE VERSUS
TIME IN MODE
FROM-TO
DISTANCE
TIME
(MPH)
(MILES)
(SEC)
00-30
0.0602
12
30-00
0.0741
16
00-15
0.0201
8
15-30
0.0705
11
30-45
0.1360
13
45-30
0.1268
12
30-60
0.2163
17
60-45
0.1716
12
45-60
0.2043
14
60-15
0.3367
30
15-60
0.3136
26
60-00
0.1973
21
00-60
0.3313
32
60-30
0.2994
23
30-15
0.0579
9
15-00
0.0173
8
00-45
0,1759
22
45-15
0.1392
16
15-45
0.1528
18
45-00
0.1304
19
00-60
0.2654
25
60-00
0.2634
28
00-30
0.0737
15
30-60
0.3134
25
60-30
0.2362
18
30-00
0.0444
10
00-60
0.4009
38
60-00
0.3293
35
00-30
0.0886
18
30-60
0.2599
21
60-30
0.1813
14
30-00
0.0592
13
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3.2
REVIEW OF FY 71 AND FY 73 RESULTS
As initially developed the modal analysis model consisted of a
composite emission rate function consisting of an function based on
steady-state modes. The composite model with 12 basis functions had given
good performance in the FY 71 Emission Factors Program in the evaluation
of 1020 light-duty vehicles in six cities (see EPA Report No. EPA-460/3-74-005)
though in subsequent analysis there was found some evidence of significant
bias between observed and computed bag values (see EPA Report No. EPA-460/3-
74-024) . As a starting point in the analysis of the FY 73 Emission Factors
Program, therefore, the model in its initial form was applied to the FY 73
modal emissions data. Performance statistics for this form of the model as
applied to the SDS and FTP driving sequences for FY 73 data, however,
revealed that the mean emissions calculated from the model (CBAR) were con-
sistently lower than the observed means (OBAR) obtained by averaging the
observed bag values for the 450 vehicles. Statistical tests of significance
indicated that, for the most part, these differences could not be attributed
to chance and consequently suggested that the model was producing biased
results.
The following figure is offered as representative of a slice
through the emissions surface at constant speed.
Acceleration (Mph/Sec)
Figure 1
13
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Notice that the emissions rate vs. acceleration profile is discontinuous
at accelerations of -1 and +1. This discontinuity is a result of the fact
that the emissions surface is configured from two functions which are blended
together between accelerations of -1 and +1. The above figure is slightly
exaggerated to emphasize the fact that the steady state point at a = 0
is the lowest point on the curve. Since the model was negatively biased,
it was postulated that the steady state value was not representative of the
constant-speed operation during the SDS cycle. In particular, it was
conjectured that the cruise modes of the SDS did not afford sufficient time
for the emission rate to settle to a stable value truly -indicative of
constant speed operation and that the use of constant-speed data based on
periods of 60-second operation might be inappropriate.
An alternative to the initial form of the model was therefore
proposed. Compute the eA portion of the surface from the 32 A/D modes and
employ this surface to compute emission rates for all portions of the (v.aj-
plane, including those locations in which a = 0. The argument here is that
certainly yields emission rates for a = 0 and that these rates, being
based on transient performance., are more likely to be consistent with the
constant-speed portions of the SCS than are emission rates derived from tests
made under unrealistically stabilized conditions. When this alternative form
of the model was applied to the FY 73 emission factors data, it was found
that for both the SDS and FTP driving sequences the negative biases affecting
the computed emissions were, for the most part, adjusted in the positive
sense. In other words, large negative biases tended to be transformed into
smaller negative biases or, in some cases, into positive biases. These
results suggested that the FY 71 data be recomputed using the simplified
version of the model and that both versions of the model be compared with
regard to group emissions computed for both FY 73 and FY 71 data. For
purposes of reference the original version of the model, which employs a com-
posite emission rate function with both and components is called
the "composite" model. The new version of the model which employs only the
emission rate function is referred to as the "simple" model.
14
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The results using the composite and simplified forms of the model
for FY 71 and FY 73 data are summarized in the Tables 2 and 3. In these
tables, statistics are presented for homogeneous vehicle groups.
As may be seen in Tables 2-A and 3-A, with a high degree of con-
sistency, biases tend to be adjusted in the positive sense when the steady
state function is eliminated from the model. Equally important, however,
is the fact that there is an associated tendency for the percent standard
deviation to increase, as may be seen in Tables 2-B and 3-B. These results
suggested the need for a definitive test to assess the importance of the
postulated stabilization effect.
3.3 DIRECT TESTING OF EMISSION RATES
In order to evaluate the impact that variances in measurements of
input data would have on model performance, tests were conducted to determine
the difference between the emission rates of the cruise modes of the SDS
and the emission rates of the stabilized steady states. These tests were
conducted in such a way that emission rate could be monitored on a second-
by-second basis rather than being computed from total emissions and time in
mode.
The continuous effluent response of two light-duty vehicles were
investigated over the SDS. Particular attention was focused on the time
required for each effluent to stabilize after reaching each cruise condition
within the SDS. For purposes of this study, therefore, the cruise portions
of the SDS were lengthened in time to 60 seconds duration to assure that
stabilization had been achieved, and to allow comparison of stabilized emission
rates with actual cruise mode emission rates during the zero-acceleration modes
of the SDS.
Two cars were selected for the tests: a 1972 Chevrolet Impala and
a 1976 Chevrolet Malibu. These two vehicles were chosen as representative
of cars built before and after the use of NOX controls and catalytic con-
verters. The 1972 Impala was previously used on EPA Contract No. 68-02-0698
15
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Table 2-A
PERCENT BIAS FOR SIMPLE AKD COI-ri'OSITE EMISSION RATE FUNCTIONS
FOR FY 73 PROGLIAM
SDS DRIVING SEQUENCE
o»
FTP DRIVING SEQUENCE *
Group
N
HC
CO
NOX
HC
CO
CO,
U
NOX
s
I
1
1973 and 1974 Denver
45
-16.4
-26.5
-5.9
+15.3
-16.5
-5.6
-11.7
0.0
+9.0
-1.4
-2,2
+4.7
- +14.5
+41.1
-4.0
-5.5
;
2
1972 Denver
30
-22.9
-32.8
-8.6
i
+15.2
15.7
-0.8
-14.9
-5.6
+3.8
-6.0
-2.8
+3.1
+21.9
+54.7
-6.4
-12.0
j
i
3
1973 and 1974
45
-12.7
-5.5
-4.4
+5.2
-27.5
-16.7
-4.7
+3.1
Los Angeles
+5.9
-7.9
-4.4
+18.6
-5.5
-14.2
-3.4
+19.4
4
1972 Los Angeles
30
-6.8
+2.2
-6.6
+15.2
-21.5
-10.4
-6.6
+14.2
.
:
+8.1
+8.4
-7.0
+33.4
-3.0
+4.7
-5.6
+34.1
f:
i
5
1973 and 1974 low
180
-15.5
-25.6
-10.6
-10.4
-17.8
-12.0
-8.8
-15.4
i
altitude cities
+6.2
-4.6
-4.6
-3.9
+9.0
+21.9
+D.3
-4.6
i
i
i
i
5
1972 low altitude
120
-18.3
-24.1
-S.8
-9.0
-16.9
14.0
-8.0
-16.6
}
cities
+7.9
-6.6
-3.3
-2.7
+18.1
+11.7
+0.5
-5.9
ii
f
Pooled
450
-17.1
-25. C
-9.0
-4.3
-18.5
-11.5
-8.7
-9.7
[
If
+6.8
-4.3
-4.1
+2.2
+11.4 .
+24.1
-1.2
-0.9
f
a
MODEL
C
S
C
c;
c
s
c
s
c
c
c
s
*First 505 seconds
C ¦= Composite
S = Simple
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Table 2-B
PERCENT STANDARD DEVIATION FOR SI:-FL2 AND COMPOSITE EMISSION
RATE FUNCTIONS FOR FY 73 PROGRAM
SDS DRIVING SEQUENCE
FTP DRIVING SEQUENCE *
Group N
I 1973 and 1974 Denver 45
2 1972 Denver
4 1972 L.A.
30
3 1973 and 1974 L.A. 45
30
5 1973 and 1974 lew 180
altitude cities
6 1972 low altitude 120
cities
Pooled 450
HC
15.4
14.7
15.2
7.6
21.6
24.1
23.1
23.3
29.7
23.9
25.7
20.6
CO
21.5
10.9
20.2
9.2
16.4
21.9
28.8 49.4
13.8 100.9
29.9
22.0
32.6
25.4
35.2
22.8
CC,
/
6.1
9.8
11.6
5.8
9.3
13.4
21.5
10.3
11.4
15.0
13.3
11.6
12.4
NOX
18.3
12.6
23.7
9.1
13.5
18.9
23.3
23.8
18.4
21.8
16;4
17.4
21.8
23.1
UC
29.4
40.7
17.3
22.9
25.5
28.7
17.3
30.5
31.1
33.7
29.2
48.2
28.0
39.2
CO
29.6
54.0
30.5
51.6
20.8
43.6
69.7
131.1
45.2
61.7
30.6
40.2
37.9
67.4
^2
8.1
7.2
11.6
13.8
6.1
10.8
17.4
26.3
8.5
10.4
9.0
11.5
9.1
12.3
NOX I) MQ2EL
22.2
30.6
18.1
23.1
18.9
27.4
16.0
24.0
24.2
31.8
22.6
26.1
ii
22.1 j!
M
31.2 !i
li
C
3
C
S
s
c
5
c
s
c
S
* First 505 seconds
C = Composite
S = SItoiIc
-------
Table 3-A
PERCENT BIAS FOR SIMPLE AXD CWG'OSITE EMISSION RATE FUlsCTIOrS
FOR
FY 71
? i ,0,7 F -AI'1!
SDS DRIVI
KG SEQUENCE
T
IF ?RI v Xr-¦;
Croup
N
HC
CO
CC2
NOX
HC CO
CQ2
N0X
.
(
I
1
1
1957-1967 Denver
97
-14.2
-6.3
-19.3
+24.5
-15.3
+1.3
-U i- m
+2.1 j! C
+3.1
+10.4
-36.5
+12.9
+7.9
+27.7
"< 0' 1
JO I Ji
-7.4
C
o
2
1957-19.6 7 low
altitude cities
458
-12.9
+5.7
-6.3
+2.3
'-2.9
-3.1
+4.4
+10.0
-12.6
+12.2
-7.7
+S.S
-5.2
-3 * 5
-1.5
+7.9
i
| c
S
3
1966 and 1967
California
33
-14.8
-6.2
-15.0
-14.5
-11.0
-U.3
+0.2
+8.4
-13.8
-4.4
-13.8
-10.8
—O "7
-7.8
-7.8
+3.5
i r
! L
i s
4
1968 low altitude
cities
84
-8.0
+11.4
+1.9
+4.1
-3.2
-2.0
-1.8
+8.3
-7.9
+15.8
-0.9
+8.0
-4.5
-1.1
-9.1
+3.8
i
! c
1 S
j
5
1969 low altitude
cities
39
-9.3
+9.4
-6.5
-0.9
-3.5
-2.1
+5.5
+15.2
-9.9
+15.2
-7.1
+4.5
-4.2
+0.2
+0.0
+13.7
] ^
j L
i s
j
6
1070 low altitude
cities
66
-10.1
+3.8
-8.9
-2.4
-5.4
-4.3
+3.1
+12.0
-11.4
47.2
-10.1
+3.4
-'3.4
-l.S
-3.1
+S.4
[ r
j
i s
7
1971 lev altitude
101
-9.9
-7.7
-5.8
+2.3
-6.8
+11.5
-3.7
-A.l l! C
cities
+3.9
-6.1
-4,0
+14.3
+12.8
+2C.2
-3.5
+11.0 i! s
8
1968 Denver
18
-22.2
-9.5
-25.2
+37.0
-21.1
+5.8
-23.1
+12.2
!
-11.3
+7.5
-4 3.2
+21.2
-6.2
+35.3
-42.4
-2.1
s
9
1969 Denver
17
-30.1
-1.7
-23.3
+16.8
-31.6
+2.1
-25.2
-7.0
c
-27.6
+7.4
-38.4
+28.9
-26.1
+20.2
-33.5
+6.0
s
i
10
1970 Denver
17
-27.6
-10.3
-19.3
+26.6
-23.7
+3, 5
-23.2
-5.6
5
i c
*
-13.9
+12.7
-31-3.
+20.8
-4.5
j
+41.9
-33.1
-7.9
¦
i 5
11
1971 Denver
20
-15.9
-11.8
-14.9
+34.8
| -14.9
+7.2
-15.9
-4.8
! c
i
-0.1
+15.7
-20 ..7
+28.0
] +7.6
+54.5
-2C.3
-9.4
f
' s
i
Pooled
1020
-13.5
-6.9
-6-2
15.6
1 -13.3
-4.3
-8.9
-2.7 |j C
+4.1
+3.9
-8,1
+11.9
j +10,0
+13.3
-7.3
+7.1
1 S
*
First
505 seconds
1
j
C =
-
r * ' i' f-.
-------
fa6fe J-g
PERCENT STANDARD DEVIATION FOR SI^LF, AN!) COMPOSITE EMISSION RATE FUNCTIONS
FOR FY 71 PR DGRi'.M
Group
.1 1957-1967 Denver
2 1957-1967 low
altitude cities
3 1966 and 1967
California
4 1968 low altitude
cities
5 1969 low altitude
cities
6 1970 low altitude
cities
7 1971 lew altitude
cities
8 1968 Denver
9 1969 Denver
10 1970 Denver
11 1971 Denver
Pooled
N
97
458
33
84
89
86
101
18
17
17
20
1020
SDS DRIVING SEQUENCE
HC CO CO.,
16.5
18.7
21.4
30.7
15.8
29.4
17.8
31.0
17.2
27.1
17.0
22.3
31.3
26.3
22.1
35.1
27.2
41.3
24.8
29.6
22.1
29.4
22.4
30.4
12.5
13.5
24.9
33.8
23.6
24.1
28.2
33.2
25.9
43.5
31.5
55.7
29.5
43.1
11.6
11.4
9.9
13.3
21.1
14.9
13.6
14.0
22.9
30.5
19.4
33.2
9.9
12.8
14.7
24.4
11.8
14.2
10.4
14.3
13.0
17.7
12.2
15.9
23.4
38.5
21.0
36.9
18.9
34.3
18.9
30.4
13.7
21.3
N0X
43.1
46.0
29.4
37.0
36.8
56.9
21.8
29.4
20.7
33.8
19.1
33.1
20,7
27.7
19.8
20.3
12.9
34.1
28.3
37.1
24.2
33.9
26.5
36.2
FT? DRIVING S:
* First SOS seconds
HC
18.2
18.3
27.2
42.3
49.4
68.7
40.3
55.6
24.6
44.5
37.9
48.0
30.1
62.8
22.4
39.8
19.9
35.9
21.6
37.7
14.8
26.8
29.1
43.4
CO
17.2
26.8
29.3
40.5
21.0
28.9
23.0
38.9
23.3
44.7
47.6
76.5
55.2
85.1
15.3
29.4
24.2
30.0
25.0
32.2
24.1
41.9
28.9
45.1
C
S
19.4
34.3
IS.3
21.1
15.6
4L. t • 5
13.1
16.3
14.9
17. A
12.0
18.7
30.5
31. S
21.2
33.3
17.4
35.C
15.0
34.0
17.2
2? .1
20.0
26.7
Composite
Sironic
NOX
33.8
53.2
29.3
42.9
33.2
51.6
31.1
42.3
24.8
37.6
22.7
40.6
22.2
33.4
38.6
38.3
15.9
30.8
23.9
38.1
27.7
32.6
28.0
42.3
MCDEL
-------
and had been driven 20,000 miles on unleaded indolene and EPA reference
fuel. This car was equipped with a 350 CID V-8 engine, a two-barrel
carburetor, and an automatic transmission. The 1976 Malibu was equipped
with a 305 CID V-8 engine, a two-barrel carburetor, automatic transmission,
and an oxidation catalyst. This vehicle had been driven about 1000 miles.
All testing was done in Calspan's Vehicle Emissions Research
Laboratory. In each of the tests, the gas sample to be analyzed was drawn
from a location in the stabilized flow stream established by the constant
volume pump. Consequently, the sample was proportional to the instantaneous
mass emissions of the vehicle. Therefore, it was possible to measure emission
rates on a continuous basis.
Results obtained from these tests made it apparent that measuring
system delay times were of greater magnitude than stabilization times.
These results further suggested that integrated modal outputs would be
correctly predicted by the model if the modal input data were more appro-
priately phased in relation to the modal speed profile.
For purposes of clarifying the results of this investigation, the
following sketches are offered as a simplified representation of the emission
response during a steady-state (mode n-1), acceleration (mode n), steady
state (mode n+1) sequence. The emission rate responses in the following
sketches approximate the actual emission rate response observed on the strip
chart recordings referred to in Section 3.1.
Sketch A shows a portion of the SDS as executed by the driver in
accelerating from a 30 mph cruise mode to a 60 raph cruise mode, kn idealized
version of the emission response to this maneuver is postulated in Sketch B.
Though the triangular shape of the emission-response pulse is deliberately
oversimplified for convenience in presentation, it is reasonable to believe
that during acceleration the emission first increases, then reaches a maximum,
and finally decreases to an essentially constant level.
20
-------
(A)
(B)
(C)
time
21
-------
In terras of the driver maneuver, the times denoting the beginning
and the end of the acceleration mode are as shown by the event markers at
and in Sketch A. The time elapsed between these two markers consti-
tutes a modal "window" corresponding to the actual acceleration of the
vehicle. Note, however, that in Sketch B the emission pulse does not begin
until some time ^ + ^t, where At denotes a delay time associated with
sample transport time and instrument response time. Consequently, only a
portion of the emission response pulse falls within the clock-time interval
between t^ and t^, and the integrated emission during this interval is
unrepresentative of the actual acceleration response.
Now consider Sketch C, in which the modal window, of time duration
t^-t^, is shifted by the delay time At. Now most of the emission response
pulse falls within the time interval between t^ + At and t^ + At,
and the integrated emission during this interval is much more representative
of the actual emission response. The fact that the emission has not come
to a constant level at time t^ + At can be interpreted to mean that the
vehicle requires an additional period of time for stabilization to a new
steady-state mode of operation. As represented in Sketch C, however, this
"stabilization time" is short relative to the delay time At and introduces
relatively little error in the integrated emission over either the accelera-
tion mode or the cruise mode immediately following it.
Now consider that the inputs to the emission model are the stabilized
steady states as computed apart from the SDS, and the acceleration-deceleration
emission rates as computed from the SDS. Thus, if acceleration-deceleration
values were computed without regard to delay times of the measuring system,
the shaded portion of the following Sketch D would represent the input to
the emissions model. On the other hand, if modal values were computed by
re-positioning the modal time window to adjust for measuring system delay
time, the corresponding representation of the input to the model would look
like the Sketch E below.
22
-------
Time
Note that in both cases (Sketches D and E), some area under the actual
response curve of the vehicle during acceleration is deleted. The extent to
which the predicted values vary from the observed values depends upon both
the measuring system delay time and the time it takes the vehicle response to
stabilize once it has reached steady state. Measuring system delay times
appear to be of the order of 7 to 20 seconds, whereas stabilization times
appear to be between 0-4 seconds. Stabilization times can only be defined and
measured after the appropriate correction for the measuring system delay time
has been made.
23
-------
HC
TT~
15
16
17
18
19
20
CO
14
15
16
17
18
19
20
OX
14
15
16
17
18
19
20
Table 4
Test of 1972 Chevrolet Impala
Relative Area
Assuming No Delay
Time Due To
Instrumentation
Relative Area
Assuming Constant
Delay Between Vehicle
Response and Instrument
Response
Assuming 7.5 Sec Delay
850
1460
192
780
294
1136
420
1330
960
102
840
504
1050
360
Assuming 18 Sec Delay
850
4080
768
3480
882
3960
1860
1108
3660
744
3600
1064
3780
1710
Assuming 12 Sec Delay
51
1948
336
600
712
2025
660
680
1680
156
480
756
1800
167
24
-------
Table 4 ,[CONT'D.)
Test of 197i_> Chevrolet Malibu
Relative Area
1
Assuming No Time
Relative Area
Delay
With Delay
}3C
7.5 Sec Delays
14
160 J
700
15
1200
600
16
24
800
17
750
128
18
14
100
19
250
180
20
300
300
CO
12 Sec Delay
14
150
800
15
3200
2100
16
24
480
17
800
400
18
40
400
19
2400
2200
20
960
600
NOX
18 Sec Delay
14
51
306
15
3600
4800
16
1200
300
17
1400
660
18
170
560
19
2000
1900
20
600
60
25
-------
Table 4 represents the relative areas under the emission rate
response as measured on the actual strip chart recordings for HC, CO, and NOX
for tests conducted on a 1972 Chevrolet Impala and a 1976 Chevrolet Malibu.
Relative areas are presented for the case when measuring system
delay times are ignored and for the case when appropriate system delay time
shifts are taken into account. Relative areas reported in Table 4 were only
approximated and are presented only for comparison. Note that the areas as
measured with and without a time shift can differ considerably. Also, note
that the greater the delay time shift, the more this difference is exaggerated.
Differences in relative areas of each modal segment are also a function of the
length of time defining a modal segment. Delay times of 15 seconds or more
that are not applied to modal segments of less than 15 seconds duration imply
that the entire emission response of that modal segment may be mistakenly
added to another mode.
The areas corresponding to cruise modes in Table 4 are areas computed
over the 60 second time duration of the extended SDS. The effect of ignoring
measuring system delay times during the normal 15 second duration cruise modes
of the SDS can result in greater differences in relative areas than are noted
in Table 4. Areas for each mode segment of the emission response could
increase or decrease after adjustment of the modal window by the delay time,
depending on the time duration of the successive modes relative to the delay
times involved.
3.4 DISCUSSION OF DRIVING SEQUENCES
It is indicated from results obtained from tests of the 1972 Impala
and the 1976 Malibu over the SDS cycle that if adjustments of the modal windows
by appropriate delay times are not applied to the emission response for each
acceleration and deceleration mode, then errors will occur in the measurement
of the modal response of these A/D modes. Since stabilization times are of
much smaller magnitude than measuring system delay times, little or no errors
occur in the use of stabilized steady state emission values for the cruise
mode portions of the SDS.
26
-------
Inspection of the velocity-time profile of the SDS sequence shows
that every acceleration and deceleration segment of the SDS cycle is followed
by a steady-state period of approximately 15 seconds. That is, almost half
of the SDS cycle, which may be regarded as a "training sequence" is composed
of steady-state or cruise mode periods over which little or no errors occur
in the measurements of emissions.
Inspection of the velocity-time profile of the Federal Test
Procedure (FTP), which may be regarded as a "test sequence," shows that less
than twenty percent of the FTP cycle is composed of cruise mode or zero-
acceleration segments. All cruise mode segments of the FTP are idle modes
where the velocity is zero. When comparing the SDS cycle performance with
the FTP cycle performance, it is evident why the SDS cycle performs more
accurately in predicting total emissions. The SDS contains more steady-state
portions and measurements of these portions are accurately representative
of the zero-acceleration modes. Measurements of acceleration-deceleration
segments, however, may be inaccurate due to phasing problems as discussed
in Section 3.
Also, since the regression coefficients are obtained from inputs
from the SDS, calculation of SDS bag values from these coefficients involves
an element of "reciting" what was input or "learned" in the training phase.
When the same coefficients are employed to compute total emissions for the
FTP sequence, however, no such reciting is involved because the FTP con-
stitutes an independent test.
27
-------
4. FY 74 RESULTS
Results of the continuous emission response test reported in
Section 3.3 indicated that the measuring system delay times could introduce
a phase lag between driver actions and the actual emission response as
recorded by the instrumentation strip charts. The result of the phase lag
was that the emission outputs could be associated, in part, with the wrong
nominal mode of the SDS. The second finding, however, led to a completely
different cause for the negative bias observed in the model. If the driver
maneuvers and emission responses are properly phased, there may be only minor
differences between stabilized steady state emission rates and cruise mode
emission rates. According to this second finding, it is reasonable to
believe that the stabilized steady state values as input to the composite
model are representative of the cruise mode or zero-acceleration portions
of the SDS.
The result of the first finding from the continuous emission rate
tests of two vehicles implies that the acceleration-deceleration modes,
as reported, are not representative of the emission response of the vehicle
in executing an accel or decel segment. If we now return to the sketches
in Section 3.3, it will be helpful in demonstrating an approximate method
for correcting the A/D input data. If the phasing lag has not been removed,
then the emission response of a vehicle in accelerating from a 30 mph cruise
mode to a 60 mph cruise mode, as seen in sketch A, might be represented by
approximation in sketch B.
As pointed out in Section 3, if the phase lag was not accounted for,
the input to the model would be represented by the shaded portions of sketch D
In sketch D, the shaded areas of mode n+1 and mode n-1 are the stabilized
steady state values that are input to the model. Mode n is an acceleration
mode. Sketch D"graphically demonstrates that because mode n was misaligned
due to the phase lag, the unshaded portion of mode n+1 was mistakenly omitted
from mode n.
28
-------
If the phase lag was properly accounted for, the emission response
to the acceleration sequence shown in sketch A might look like the approxi-
mated curve in Sketch C. Although not used as input to the emission
model, the cruise mode data from Washington is available. If the phase lag
was not accounted for, the shaded area of mode n+1 in Sketch F below would
correspond to the "cruise" mode as measured from the strip chart recording.
time
If the phase shift was not made, part of the emission output from
mode n could be incorrectly associated with mode n+1. Even if the phase
lag was not adjusted, however, the emission output from mode n can be
adjusted to a first approximation. If the stabilized steady state output
from mode n+1 in Sketch D is subtracted from the cruise mode output from mode
n+1 in Sketch F, the resulting delta output is reclassified as belonging to
mode n. Table 5 gives a comparison of the 32 accel-decel modes before and
after adjustment by the above method for one vehicle from Washington.
Note that, in most cases, the A/D modal values have been increased after
adjustment and, in some cases, decreased in magnitude after adjustment.
The decrease corresponds to adjustments of deceleration modes as the same
argument above applies.
29
-------
Table 5
COMPARISON OF ORIGINAL A/D MODES AND CORRECTED A/D MODES -
VEHICLE 5011* -- WASHINGTON
Original A/D Modes A/D Modes Corrected for Phasing Error
Mode HC CO C02 NOX HC CO C02 NOX
1
2.66
16.35
1012.9
9.55
3.18
16.79
1471.4
10. 26
2
0.83
12. 18
310 .0
0. 73
0.96
17.58
359 .9
0.83
3
3.51
18.35
838.0
11.32
5.41
28.08
1340.5
13.06
4
1.49
8.80
559.3
8.06
1.90
10.59
996.4
8.73
5
0.89
4.14
485.7
7.69
1.06
7.37
742.1
9.59
6
0 .48
4.89
299.1
3.80
1.23
7.87
291.0
4. 17
7
2 .20
41.02
655.3
11.18
3.38
49.82
842.9
12.84
8
0.36
4.92
295.4
2.16
2.14
8.41
235.3
2.72
9
0 .85
12.81
631.7
10.60
1.06
16.77
773.3
11.80
10
1.70
7 .14
347.9
0.91
2.08
9.19
347.1
0.90
11
1.36
34.96
782.6
14.62
1.49
35 .36
872.8
15.26
12
2.32
8.48
404.2
1.48
2.50
11.46
421.3
1.52
13
1.26
17.16
826.5
14.94
1.37
17.51
928.9
15.68
14
2.01
5.94
344.2
1.42
2.24
6.96
321.8
1.36
15
0.67
6.95
363.2
1.34
1.52
19.10
358.6
1.38
16
2.31
19.81
712.2
1.27
3.47
50.59
871.2
1.70
17
1.56
8.51
878.9
11.60
1.70
9.04
984.9
11.89
18
1.12
7.29
326.8
0.49
1.47
11.49
324.9
0.54
19
1.33
10 .38
700.1
13.48
1.60
10.67
928.3
14.11
20
1.23
9 .03
383.5
0.67
1.38
13.00
411.9
0.73
21
2.05
57 .14
930.9
15.15
2.39
59.14
1046.2
16.07
22
2.25
7.38
336.0
1.15
2.49
9.40
346.4
1.18
23
2 .44
13.09
557.1
9.44
2.86
14.12
779.8
9.71
24
0.99
9.75
607.5
10.61
1.17
11.44
701.9
11.39
25
1.73
5.72
321.9
1.18
2 .64
7.37
306.9
1.16
26
0.91
10.39
436.4
0.76
1.30
22 .38
498.3
0.93
27
1.05
7.91
536.7
12.02
1.16
8.18
585.0
12.69
28
1.75
6.04
369.7
0.72
1.82
7.55
377.1
0.74
29
1.92
9.37
836.5
8.17
2.27
9.91
993.1
8.34
30
2.12
19.45
523.9
12.50
2.79
21.76
660.9
14.07
31
1.34
5.97
339.4
1.19
2.15
8.66
302.4
1.20
32
0.88
8.48
448.5
1.22
1.13
17.01
500.4
1.35
*This table is representative of corrected input data for one vehicle from
Washington. Input data for all 35 vehicles from Washington were corrected
in the same manner.
30
-------
The adjusted A/D modes were then employed with the stabilized
steady state modes as input to the composite model. These results are
presented in Table 7 of Section 4.1. Note that the biases as well as the
percent RMS errors are lower than the composite model employing the original
data in Table 6. Since both biases and RMS errors are lower when the
adjusted A/D modes are used in the model, one must conclude that the adjusted
A/D modal values are more representative of actual modal responses than the
original A/D values.
The results presented suggest that a phasing error exists for the
Washington data. Manipulation of the accel/decel data is possible to a first
approximation by employing the cruise mode emission rates. This manipulation
reduces the phasing error and improves model performance. Although improve-
ment of model performance is possible by the above method, proper adjustment
of the phase lag before accel-decel data is computed is greatly desirable in
improving model performance.
4.1 MODEL COEFFICIENTS AND ERROR STATISTICS
Unfortunately, the "cruise mode" values available for Washington
are not available for any of the remaining data for FY 74. Presented in the
Tables 8-23, therefore, are model performance statistics for individual
cities as well as the pooled group of cities excluding Los Angeles. Coeffi-
cients for the pooled group and Los Angeles are also presented.
At this point it is well to consider results particular to the FY 74
data. Most vehicles within this data set were equipped with catalytic converters.
As a result, in general, all the modal values for FY 74 were much lower than
the values for FY 73 and FY 71. Upon examination of the individual model
predictions for each of the vehicles using the simple form of the model, it was
discovered that some vehicles had negative predicted emissions. Further,
upon examination of the observed modal steady-state values for these vehicles
with negative predictions, it was discovered that all or almost all steady state
raw input values were reported as "true" zeroes. It is conjectured that the
31
-------
Table 6
MODEL COEFFICIENTS AND ERROR STATISTICS
PERFORMANCE STATISTICS FOR WASHINGTON
SDS Driving Sequence
Composite Function
(Units = GMS/MI)
Number of cars in this group = 35 (Model Year 75)
CBAR =
OBAR =
REAR =
PRBR =
SIGR =
PSIG =
RMSR =
PERR =
HC
0.867
0.898
-0.031
-3.458
0.161
17.974
0.164
18.304
CO
20.586
21.857
-1.271
-5.815
5.830
26.675
5.967
27.302
C02
556.124
567.466
-11.342
-1.999
22.109
3.896
24.848
4.379
NOX
4.935
4.778
0.157
3.279
0.532
11.141
0.555
11.614
Table 7
PERFORMANCE STATISTICS FOR WASHINGTON
SDS
A/D Modes Adjusted
Composite Model
(Units = GMS/MI)
cars
in
this group
= 35 (Model Year 75)
HC
CO
C02
CBAR
=
0.911
22.404
576.489
OBAR
=
0.898
21.857
567.466
RBAR
=
0.013
0.547
9.023
PRBR
=
1.457
2.503
1.590
SIGR
=
0.137
4.346
19.666
PSIG
=
15.290
19.885
3.466
RMSR
=
0.138
4.381
21.637
PERR
=
15.359
20.042
3.813
NOX
5.057
4.778
0.278
5.825
0.307
6.420
0.414
8.669
32
-------
Table 8
PERFORMANCE STATISTICS FOR WASHINGTON
SDS Driving Sequence
Simple Function
(Units = GMS/MI)
cars in
this group
= 35 (Model
Year 75)
HC
CO
C02
NOX
CBAR =
1.016
19.881
603.600
6.073
OBAR =
0.898
21.857
567.466
4.778
RBAR =
0.119
-1.975
36.134
1.294
PRBR =
13.204
-9.038
6. 368
27.087
SIGR =
0.258
7.508
34.443
0.958
PSIG =
28.698
34.350
6.070
20.054
RMSR =
0.284
7.763
49.920
1.610
PERR =
31.589
35.519
8.797
33.702
Table 9
PERFORMANCE STATISTICS
FOR CHICAGO
SDS
Composite Function
(Units = GMS/MI)
cars in
this group
= 35 (Model Year 75)
HC
CO
C02
NOX
CBAR =
0.700
23.724
545.629
3.188
OBAR =
0.811
28.170
561.643
3.224
RBAR =
-0.112
-4.446
-16.013
-0.036
PRBR =
-13.778
-15.781
-2.851
-1.122
SIGR =
0.139
4.150
18.881
0.377
PSIG =
17.142
14.731
3.362
11.686
RMSR =
0.178
6.081
24.757
0.378
PERR =
21.993
21.588
4.408
11.740
33
-------
Table 10
PERFORMANCE STATISTICS FOR CHICAGO
SDS
SIMPLE FUNCTION
(UNITS = GHS/MI)
cars
in this group =
35 (Model
Year 75)
HC
CO
C02
NOX
CBAR
0.770
23.649
572.171
3.629
OBAR
0.811
28.170
561.643
3.224
RBAR
-0.041
~4.521
10.528
Q.406
PRBR
-5.110
-16.050
1.875
12.587
SIGR
0.156
6.824
25.016
0.620
PSIG
19.210
24.226
4.454
19.242
RMSR
0.161
8.186
27.141
0.741
PERR
19.878
29.060
4.832
22.993
Table 11
PERFORMANCE STATISTICS FOR HOUSTON
SDS Driving Sequence
Composite Function
(Units = GMS/MI)
Number of cars in this group
HC
= 35 (Model Year 75)
CO
CO 2
NOX
CBAR =
0.623
15.316
546.917
4.094
OBAR =
0.711
17.199
566.700
4.163
RBAR =
-0.088
-1.883
-19.783
-0.070
PRBR =
-12.333
-10.949
-3.491
-1.671
SIGR =
0.151
3.366
15.184
0.397
PSIG =
21.194
19.572
2.679
9.528
RMSR =
0.174
3.857
24.938
0.403
PERR =
24.521
22.426
4.401
9.674
34
-------
Table 12
PERFORMANCE STATISTICS FOR HOUSTON
SDS Driving
Sequence
Simple Function
(Units =
GHS/MI)
: cars
in this group
= 35 (Model Year 75)
HC
CO
C02
NOX
CBAR
0.724
15.169
569.158
4.739
OBAR
0.711
17.199
566.700
4.163
RBAR
0.013
-2.030
2.458
0.575
PRBR
1.881
-11.801
0.434
13.813
SIGR
0.147
4.846
13.846
0.586
PSIG
20.640
28.177
2.443
14.072
RMSR
0.147
5.254
14.063
0.821
PERR
20.725
30.548
2.482
19.718
Table
13
PERFORMANCE STATISTICS FOR ST. LOUIS
SDS
Composite Function
(Units =
GMS/MI)
cars
in this group
= 35 (Model Year 75)
HC
CO
CO 2
NOX
CBAR
0.591
11.969
507.309
3.881
OBAR
0.598
13.186
521.331
4.093
RBAR
-0.007
-1.217
-14.023
-0.212
PRBR
-1.147
-9.229
-2.690
-5.191
SIGR
0.307
3.582
25.280
0.469
PSIG
51.254
27.165
4.849
11.458
RMSR
0.307
3.783
28.909
0.515
PERR
51.267
28.690
5.545
12.579
35
-------
Table 14
PERFORMANCE STATISTICS FOR ST. LOUIS
SDS
Composite Function
(Excluding One Outlier)
(Units = GMS/MI)
Number of cars in this group = 34 (Model Year 75)
HC
CO
C02
NOX
CBAR =
0.547
11.829
507.684
3.885
OBAR =
0.603
13.427
521.426
4.091
RBAR =
-0.055
-1.598
-13.743
-0.205
PRBR =
-9.205
-11.903
-2.636
-5.016
SIGR =
0.108
2.824
25.605
0.474
PSIG =
17.916
21.033
4.911
11.590
RMSR =
0.121
3.245
29.060
0.517
PERR =
20.143
24.168
5.573
12.629
Table 15
PERFORMANCE STATISTICS FOR ST. LOUIS
SDS
Simple Function
(Units = GMS/MI)
Number of cars in this group = 35 (Model Year 75)
HC
CO
C02
NOX
CBAR =
0.568
11.521
527.425
4.434
OBAR =
0.598
13.186
521.331
4.093
RBAR =
-0.030
-1.665
6.093
0.341
PRBR =
-5.075
-12.627
1.169
8.328
SIGR =
0.122
4.900
44.557
0.480
PSIG =
20.421
37.164
8.547
11.732
RMSR =
0.126
5.176
44.971
0.589
PERR =
21.042
39.251
8.626
14.388
36
-------
Table 16
PERFORMANCE STATISTICS FOR PHOENIX
Composite Function
of cars
in
tliis group =
35 (Model
Year 75)
HC
CO
CO 2
CBAR
=
0.727
20.918
503.700
0BAR
=
0.861
25.101
522.429
RBAR
=
-0.135
-4. 184
-18.728
PRBR
=
-15.626
-16.667
-3.585
SIGR
=
0.141
8.302
12.762
PSIG
=
16 .351
33.072
2.443
RMSR
=
0 .195
9. 296
22.663
PERR
=
22.617
37.035
4.338
Table 17
PERFORMANCE
STATISTICS FOR PHOENI)
Simple Function
of cars
in
this group =
35 (Model
Year 75)
HC
CO
C02
CBAR
=
0.833
22.629
523.767
OBAR
=
0.861
25.101
522.429
RBAR
=
-0.028
-2.473
1.338
PRBR
=
-3.275
-9.851
0.256
SIGR
=
0.148
4.895
11.499
PSIG
=
17.228
19.499
2.201
RMSR
=
0.151
5.484
11.577
PERR
=
17.536
21.846
2. 216
NOX
3.994
4.107
-0.113
-2.747
0.471
11.472
0.484
11.796
NOX
4.429
4.107
0.323
7.862
0.514
12.526
0.607
14.789
37
-------
Table 18
POOLED PERFORMANCE STATISTICS FOR ABOVE CITIES
Composite Function
Number of cars in this group
HC
175 (Model Year 75)
CBAR =
OBAR =
RBAR =
PRBR =
SI GR =
PSIG =
RMSR =
PERR =
0.701
0. 776
-0.074
-9.587
0.195
25.089
0.208
26.858
CO
18.502
21.103
-2.600
-12.321
5.498
26.054
6.082
28.820
C02
531.939
547.914
-15.978
-2.916
19.402
3.541
25.134
4.587
N0X
4.018
4.073
-0.055
-1.347
0.464
11.384
0.467
11.464
Table 19
POOLED PERFORMANCE STATISTICS FOR ABOVE CITIES
Simple Function
Number of cars in this group
HC
= 175 (Model Year 75)
CBAR =
OBAR =
RBAR =
PRBR =
SIGR =
PSIG =
RMSR =
PERR =
0.782
0.776
0.006
0.822
0. 181
23.290
0.181
23.305
CO
18.570
21.103
-2.533
-12.002
5.928
28.090
6.446
30.547
C02
559.224
547.914
11.310
2.064
31.155
5.686
33.145
6.049
NOX
4 .661
4.073
0.588
14.431
0.743
18.240
0.947
23.258
38
-------
Table 20
POOLED COEFFICIENTS FOR ABOVE CITIES
Basis
Function
HC
CO
C02
NOX
) 1
0.00806836
0.21578518
2.28404948
0.01081596
{ v
-0.00040017
-0.01257778
-0.02627984
-0.00122498
) a
0.00090038
0.05147729
0.06559008
-0.00073537
CA
^ av
0.00006497
-0.00234263
0.05392222
0.00053943
Function
^ 2
) v
0.00000663
0.00016779
0.00212888
0.00004444
) 2
^ a
-0.00073571
-0.00157560
-0.16557200
-0.00329725
I 2
) va
0.00008982
0.00028233
0.03023214
0.00052657
) 2 2
^ v a
-0.00000028
0.00012527
-0.00009010
0.00000312
< 2 2
) v a
-0.00000058
0.00004850
-0.00041269
-0.00000840
es
) 1
0.00538160
0.11655782
1.46895685
0.00265085
Function
) \
-0.00014550
-0.00462987
0.00706689
-0.00035369
( 2
) v
0.00000205
0.00006995
0.00161369
0.00002341
Table 21
PERFORMANCE STATISTICS FOR LOS ANGELES
Composite Function
cars in
this group
= 33 (Model
Year 75)
HC
CO
C02
NOX
CBAR =
0.233
7.106
576.160
3.291
OBAR =
0.241
8.947
594.936
3.318
RBAR =
-0.008
-1.841
-18.776
-0.028
PRBR =
-3.321
-20.577
-3.156
-0.831
SIGR =
0.111
4.291
22.326
0.401
PSIG =
46.106
47.958
3.753
12.087
RMSR =
0.111
4.669
29.171
0.402
PERR =
46.226
52.186
4.903
12.115
39
-------
Table 22
PERFORMANCE STATISTICS FOR LOS ANGELES
Simple Function
Number of cars in this group
HC
= 33 (Model Year 75)
CBAR =
OBAR =
RBAR =
PRBR =
SIGR =
PSIG =
RMSR =
PERR =
0.199
0.241
-0.042
-17.255
0.055
23.046
0.069
28.790
CO
6.012
8.947
-2.935
-32.804
4.768
53.290
5 .599
62.577
C02
590.584
594.936
-4.353
-0.732
27.507
4.624
27.849
4.681
NOX
3.544
3.318
0. 225
6.792
0.391
11.772
0.451
13.591
Table 23
COEFFICIENTS FOR LOS ANGELES
Basis
Function
HC
CO
CO 2
NOX
Function
1
v
a
va
2
va
2
v a
2 2
v a
Function
1
v
-C .0009054?
0.00012708
0.00033065
-0.00002369
-0.00000186
0.00055315
-0.00005786
0.00000121
0.00000162
0.00104760
-0.00000516
0.00000013
O,04637552
-0.00331952
0.03405101
-0.00423590
0.00002119
0.01143820
-0.00182000
0.00013682
0.00007624
0.00859732
-0.00056630
0.00001144
2.21799416
-0.00712464
0.10090503
0.05336254
0.00185543
-0.09739484
0.02457471
-0.00022188
-0.00026850
1.70297875
0.01441993
0.00155828
0.00921564
-0.00070116
0.00029334
0.00038903
0.00002696
-0.00198106
0.00031261
0.00000196
-0.00000375
0.00206893
-0.00016999
0.00001728
40
-------
observed modal steady state values for these vehicles could actually have
been negative emission values (i.e., emissions lower than ambient), but
were reported as zero.
As seen in the above figure, the utilization of the simple model
could result in the prediction of a negative emission, since the simple model
does not use steady state values (which, in this case, would be zero
but not negative) as input to calculate coefficients which define the
emissions surface. The negative emission is possible for the SDS (or
even the FTP) sequence because, even though part of the emission surface
is positive, the majority of the driving sequence takes place in the region
where the surface is negative.
The simple, although arbitrary, procedure to solve this problem is
to set all negative emissions predicted by the model to zero. This was done
before model performance statistics were computed for all cities using the sim-
ple model. Examination of the FTP driving sequence shows that while there are
no steady state models other than v = 0, negative values predicted by the model
are certainly possible since many accelerations in the FTP are very small and
very close to zero (i.e., between -1 and +1 mph/sec -- see above figure).
41
-------
4.2 DISCUSSION
Perhaps it would be best to review the emissions model results for
FY 71, FY 73, and FY 74 data by observing, as we have previously, a slice
through the emissions surface at constant velocity. For FY 71 and FY 73 data,
all coefficients produced by the emissions model have resulted in an emissions
surface entirely above the velocity-acceleration plane. As the effect of
emissions controls succeeded in limiting the amounts of pollutants emitted by
a vehicle, the emissions surface has come closer to the velocity-acceleration
plane, at the same time retaining its essential shape for FY 71 and FY 73.
The shape of this surface in emission rate acceleration space is closely
represented by a skewed parabola approximated below in Sketch G.
acceleration {mph/sec)
The solid curve represents the composite form of the model and the
dotted line the simple form of the model, both of which are blended together
at approximately +1 mph/sec. As the emission surface descends and finally
touches and intersects the v-a plane, as it does for FY 74 data, its shape
changes. The surface represented by the composite model gets "squashed"
against the v-a plane as a rubber ball would get squashed upon impact against
a hard surface. We have mentioned that the reason the composite surface is
42
-------
effectively squashed, stems from the fact that any modes measured during
the SDS as having emissions below ambient get reported as zero.
Examine for a moment the plot of the test design points on the
average speed and acceleration plane in the following figure. If all
or most all of the steady state emissions are reported as zero and if the
steady state portion of the model e^ is blended into the model between
accelerations of +1, then the surface will eventually flatten out or squash
between tl mph/sec as it descends into the v-a plane. There is no such
restriction on the simple form of the model (only as long as no negative
emissions for A/D modes are measured). The simple model certainly predicts
a surface at a = 0, but the simple model has no prior inputs between a = 11
mph/sec that would alter the form of the surface from the form determined by
the "outer" design test points (i.e., -I>a>+1).
For FY 71 and FY 73 data, it is apparent that the lowest point on
the emission surface, for the composite model, is the stabilized steady state
point. It appears as if the stabilized SS point causes a distortion in the
emissions surface, As we have shown, however, it is the A/D modal values
or "outer'1 design test points that are in error. In fact, when the A/D
modal data are corrected as by the approximation reported for the FY 74
Washington data, the effect is to appropriately increase or in some cases
(especially for decelerations) decrease the A/D values, such that the
emission rate surface for the composite model using adjusted data from
Washington now appears as in Sketch H.
o
+J
M
e
o
• H
Ch
•H
S
<3>
/
/
(H)
-1 0 +1
acceleration (mph/sec)
43
-------
For corrected A/D input data, steady state values are "naturally"
blended into the form of the emissions surface. That is, as long as the
emissions surface is entirely above the v-a plane, there is no difference
between the shape of the surface for the composite model and the simple
model. Performance statistics for the two models should be the same except
perhaps for the fact that the simple model may have a slightly higher standard
deviation because of a reduced number of degrees of freedom.
The above discussion attempts to describe the effects on the
emission surface and thereby on the emissions model as the input data is
changed from FY to FY to reflect the changes in vehicle population, emissions
regulation (i.e., catalytic converter for FY 74), vehicle group structure,
and even emissions measuring procedure; for the reporting of emission rates
lower than ambient as zero is arbitrary at best. This procedure coupled with
measurements of A/D modal values that are uncorrected can have deleterious
effects upon model performance. Model performance for Washington, for
instance, was very good indeed even prior to adjustment of the A/D modes.
This favorable model performance indicated that measurement of A/D values
was conscientious and all, or most, steady state values were positive values.
For Los Angeles, however, model performance is not comparable to Washington.
First of all, Los Angeles was statistically determined to be presented
separately from the rest of the city groups. Examination of the pollution
levels for Los Angeles show pollutant levels much lower than other low-
altitude cities. A third of the predicted emissions for the 33 vehicles in
Los Angeles were negative predictions for CO. The percent bias for CO was
-20.6% when using the composite model and -32.8% when using the simple model.
The percent RMSR error was 52.5% for the composite model and 62.6% for the
simple model. We can see that the simple model no longer reduces the percent
bias or changes the bias in a positive sense. Instead, both percent bias
and percent RMS error increase when the simple model is used.
Obviously, measurement of all modal values accurately is essential
for good model performance. Degradation of model performance is most likely
due to inaccuracies in measurements of the A/D modes. The effect of these
44
-------
inaccuracies is most surely heightened as emission levels decrease, as is
evident from examination of model performance statistics for Los Angeles.
Although corrections of A/D modal data input is possible, there is no
substitution for proper adjustment of the data during the sequence in which
the vehicles are tested.
45
-------
5. SUMMARY AND CONCLUSIONS
The modal emissions model performance is affected by two major
phenomena:
1. Measuring system response delay times can introduce
a phase lag between driver actions and the emission
response to these actions as recorded on the instru-
mentation strip charts. The result is that emissions
outputs resulting from driver maneuvers can be asso-
ciated, at least in part, with the wrong nominal mode
of the Surveillance Driving Sequence (SDS). The
modes affected by the time lag are the acceleration-
deceleration modes of the SDS.
2. Although constant speed or zero acceleration emissions
input data accurately reflect the cruise mode portions
of the SDS, model distortion can arise as total
emissions from FY to FY decrease, causing a flattening
of the emissions surface against the v-a plane. This
flattening results because emissions that are measured
lower than ambient are reported as zero, constraining
the emissions surface to be above the v-a plane. Any
errors in correctly measuring the accel-decel emission
modes can greatly degrade model performance, since total
emissions become smaller from FY to FY.
If A/D modal input was correctly adjusted prior to the emissions
model, the emissions surface generated by the simple emissions model (i.e.,
model without steady state), would be identical or at least very close to the
emissions surface generated by the composite model, as long as all modal
emissions for all modes were measured greater than ambient.
Presented in the following tables are the summarized results for
the FY 74 program. Table 24 compares the percent bias results for both the
simple and composite forms of the model and Table 25 compares the percent
standard deviation for both forms of the model for all city groups.
46
-------
Table 24
PERCENT BIAS FOR SIMPLE AND COMPOSITE EMISSION RATE FUNCTIONS
FOR THE FY 74 PROGRAM
CITY
HC
CO
CO-
NOX
MODEL
Washington
35 -3.458
13.204
1.457
-5.815
-9.038
2 .503
-1.999
6. 368
1.590
3. 279
27.087
5.825
C
S
C [adjusted)
Chicago
35 -13.778
-5.110
15.781
16.050
¦2.851
1. 875
-1.122
12.587
Houston
35 -12.333
1. 881
¦10.949
-11.801
-3.491
0.434
-1.671
13.813
C
S
St. Louis
35 -1.147
(34) -9.205
-5.075
-9.229
-11.903
-12.627
-2.690
-2.636
1.169
-5.191
-5.016
8.328
C (minus
outlier)
S
Phoenix
35 -15.626
-3.275
¦16.667
-9.851
-3.585
0.256
-2.747
7.862
C
S
Pooled
175 -9.587
0. 822
-12.321
-12.002
-2.916
2.064
-1.347
14.431
C
S
Los Angeles
33 -3.321
-17.255
-20.577
-32.804
-3.156
-0.732
-0.831
6.792
C
S
47
-------
Table 25
PERCENT STANDARD DEVIATION FOR SIMPLE AND
COMPOSITE EMISSION RATE FUNCTIONS FOR FY 74
CITY
HC
CO
CO-
N0X
MODEL
Washington 35
17.974 26.675
15.290 19.885
28.698 34.350
3.896
3.466
11.141
6.420
(Modified A/D Inputs)
6.070 20.054 S
Chicago
35 17.142 14.731
19.210 24.226
3.362 11.686
4.454 19.242
C
S
Houston 35 21.194 19.572 2.679 9.528
20.640 28.177 2.443 14.072
C
S
St. Louis 35 51.254 27.165
(34) 17.916 21.033
35 20.421 37.164
4.849 11.458
4.911 11.590
8.547 11.732
(minus outlier)
S
Phoenix 35 16.351 33.072 2.443 11.472
17.228 19.499 2.201 12.526
C
S
Pooled
175 25.089 26.054 3.541 11.384
23.290 28.090 5.686 18.240
C
S
Los Angeles 33
46.106 47.958 3.753 12.087
23.046 53.290 4.624 11.772
C
S
48
-------
6. APPENDIX: AVERAGE GROUP COEFFICIENTS FOR FY 73 AND FY 71
49
-------
AVERAGE GROUP COEFFICIENTS FOR FY 73 FOR
BOTH SIMPLE 5 GROUP EMISSION RATE FUNCTIONS
HC
CO
C02
NOX
GROUP
N
GROUP 1 - 1973 and
1974 Denver - Simple
emission rate function
1
C .0367327 9
1.10400859
2.60419B41
0.00310424
V
—0.00199239
-0.07945368
-O.05360373
0.00001506
a
-0.00088590
0.05630319
0.05482671
-0.00077950
va
0 .00037P07
0.00170772
0.01517054
0.00018693
v2
0.O0004643
0.00161816
0.00207580
O.OCOOl103
a2
-0.00412 351
-0.17064409
-0.2199<>30a
-0.00058944
0 .000 56 53 9
0.01930341
0.02470781
0.00009365
v2a
-0.00000277
0.00020100
0.00006307
-0.00000053
v2a2 !
—0.0000089?
-0.00026332
-0.00035096
-0.00000159
I
for composite emission rate function include the following
0.01262324
0.25955876
1.21196046
0.00199461
V
-0.00026730
-0.00759697
0.01720046
-0.00024173
V2
0.0000114V
0.00026727
0.00125049
0.00001981
JKOUH
N
GROUP 2 - 1972
Denver - Simple emission rate function
1
0.0 5405 56 7
1.49310401
2.22999486
0.00144976
V
-0.0026 892 5
-0.10349673
-0.02441241
0.00043599
a
-0.00101342
0.00722273
0.05660318
0.00017710
Va
0.00019053
0.00591609
0.00234623
0.00002336
V2
0.0000562 3
0.00200536
0.00159217
0.00001192
a2
—0•00556067
-0.23721019
-0.16246379
0.00018445
va2
0.000692^6
0.02622559
0.01698271
0.00001644
r2a
-0.00000090
0.00002392
0.00004330
-0.00000066
,2a2
-0.00001145
-0.00039850
-0.00024700
-0.00000112
for composite emission rate function include the following
1 >
0.0 12H1331
0.328/7001
1.20695927
0.00233554
v ;
-0.00021 JOB
-0.009172 6 7
0.01750029
-0.00040469
V2 :
0.00001241
0.00029820
0.00104091
0.00003392
GROUP
N
1
v
a
va
v2
va
v2a
v2a2
1
V
GROUP 3 - 1973 and
1974 Los Angeles -
Simple emission rate function
0.02667524
0.20974290
1.66130810
0.00096731
-O .00147237
—0.01284891
0.02272887
—0.00 005? 36
0.00338008
0.09635962
0.14670172
-0.00075958
0.00008997
-0.00663593
0.05285483
0.00069431
i 0.00002910
0.00018599
0.00122293
0.00002439
!-0-00319628
0.02192463
-0.03175795
-0.00102613
0.00041041
-0.00156659
0.02299226
0.00033396
0 . 00000063
0.00027883
0.00004743
0.00000060
-0.00000438
0.00012293
-0.00028821
-0.00000449
for composite emission rate function include the following
0.00864129
0.11387944
1.61624131
0.00194663
-0.00007578
-0,002868 58
0.02409572
-0.00021615
0.00000427
0.00004719
0.00113920
0.00002051
50
-------
GROUP
N
GROUP 4 - 1972
Los Angeles - Simple emission
rate function
1
V
0.02753334
-0.00155636
0.28853572
-0.01231569
1.54830571
0.01656593
-0.00235249
-0.00019142
a
va
-5
0.0 041)7 88 0
0.000 00915
0.09240786
-0.00315050
0.18629377
0.04171278
-0.00225345
0.0009239?
V*
a2
va2
v2a
v2a2
0.0000307°
-0.00351729
C.00016614
0.00707022
0.00107667
-0.02311154
0.00004448
-0.00126582
0.00044819
0.00000019
0.00046436
0.00014813
0.01892498
0.00016261
0.00045565
0.00000192
-0 .000 00 56 5
0.00005659
-0.00021464
-0.00000762
1
0.00898459
for composite emission rate function include the following
0.15976294 1.46922220 0,00195007
V
v2
-0.0000*90fo
0.00000568
—u.00652330
0.00010359
0.02363722
0.00097246
-0.0002 2206
0.00003236
GROUP
N
GROUP 5 - 1973
and
1974 low altitude cities -
Simple emission rate
function
1
0 .02626262
0.54005560
2.90645519
0.011R7600
V
a
-0.00110 58 0
0.00130 303
-0.03959409
0.G28 32118
-O.05130095
-0.00944663
-0.00072420
-0.00077164
va
V2
0 .00006337
0.00002336
0.00144263
0.00070014
0.02837012
0.00237781
0.00027149
0.00003251
a2
va2
-0.00186747
0.00025699
-0.05709695
0.00732978
-0.25426778
0.03370509
-0.00249363
0.00034106
v2a
v2a
0.00000033
-0.00000 311
O.OO005355
-0.00008588
-0.00005903
-0.00051395
0.000C0082
-0.00000539
1
V
V2
0 .01045 2 /9
-0.00019408
for composite emission rate function include the
0.20t013tl 1.66736J8* O.00«8216
-o.nrisnfti ;<¦ n.ni5*l<>13 —-0.00036151
0.00 CiOO 67
0.0000055b
0.00131556
0.000026H**
GROUP 1
N
1
GROUP 6 - 1972
low
altitude cities - Simple emission rate function
d .1)4434662
0.57665520
2.61400935
0.014P6188
V
a
va
V2
-0.002 21667
0.00068992
-0.03627741
0.02157196
-0.04138154
-0.02310735
-0.00072346
-0.00044333
0.00013456
0.00004133
0.00294424
0.00063650
0 .02 886318
0.00215970
0.00032002
0.00004031
a2
va2
v^a
v2a2
-0.00534209
0 .00060573
-0.05285343
0.00694145
-0.25081254
0.032P5040
-0.00339756
0.00045425
-0.00000133
-0.00000964
-0.00001756
-0.00009447
-0.00004957
-0.00049582
0.00000104
-0.00000763
for composite emission rate function include the following
1
v
0.01310196
-0.00024442
0.25530096
-0.007694S5
1.49414969
0.01919612
0.00340546
-0.00050338
V2
0.000008it
0*00013531
0.00121897
0.00003816
51
-------
GROUP AVERAGE COEFFICIENTS FOR FY 71
FOR BOTH SIMPLE S COMPOSITE EMISSION RATE FUNCTIONS
HC
CO
C02
GROUP
N
GROUP 1 - 1957-1967 Denver - Simple emission rate function
1 0.G9193CS2
v -0 . 00 4 6 2 605
a 0.0039293 8
va 0.00057714
v 0.00008735
a -0.01177275
va2 0.00141214
v2a -0.00000 619
v2a2 -0.O00O2401
1 O .G 30 L 7 74'<>
v2 -0 . 0002241: 5
V 0.00001 69**
1.01939646
-0.04771040
0.00074659
0.02156(325
0.00110084
-0.15253911
0.01991216
-0.00012003
-0.00029160
for composite emission
0. 3 ? G V 1 •> 7 (
—G.0024152 2
u.OC0 32G59
Q*7$*99322
0.01152654
,0.075368^3
NOX
-0.00305700
0.00050317
0.000^2683
0.01649186
0.0005501B
0.00702534
0.00428403
0.00004008
-O.00003355
rate function include the
0.86*39376
0.01073421
G.00124642
-0.00001250
.. 0.00000649
0.00198891
-0.00016629
0.00000242
0.000002f?L
following
0.002°73IV
-0.00 030207
0.00002282
GROUP
N
1
v
a
:*
a2
va2
v2a
v2a2
GROUP 2 - I9S7-1967 low altitude cities* - Simple emission rate function
0.07623901
-0.0033578 2
0.005 5765 3
0 .00029385
0.00006357
-0.00765667
0.00096193
-0.00000 303
-0.00001630
0.63519355
-0.02517176
0.0398 2681
V . 005 56602*
0.00047038
—0.04830223
0.00635515
-0.00000291
-0.00007479
1.25022438
0.02228016
0.08512990
jO .00463792
0.00014202
0.00007608
O.03687863
0.00091322
0.00303730
0.00864681
0.00002828
-0.00006759
0.00044335
0.00002215
-6.00029964
0.00017920
0.00000155
-0.00000301
1 O.G2 75 51J:2
V —0.00028 560
V2 , 0.00001451
for composite emission rate function include the following
G.30 342393 0.90209652 0.003516
—0.0u273503 O.01276564
0.00013472 0.00133361
7
-0.00046493
0.00003240
GROUP
N
1
v
a
v|
V
a2
va2
v2a
vV
1
v
GROUP 3 - 1966 and 1967 California - Simple emission rate function
0 . 027 3 0 842
-0 . 0004 2 39 5
0.00208875
0.00048092
0.00001614
-0.00080988
0.00022 506
-0.00000581
-0.0000038 2
_G_.019 74p4 0
0 .0002250 2""
0.00000273
0.27989996
-4). 00498866
0.04242040
0.00155372
1.86924557
0.00234203
0.16609689
0.02692388
0.00869070
-0.00059465
-0.00070495
0.00070165
0.00011530
-0.00235636
0.00101693
0.00000706
-0.00000490
for composite emission
0.22926731
0.00116331
-0.05894861_
0.01433370
0.00011010
-0.00018606
rate function include
1.28089607
0.00003425
-0.00266144
0.00048951
-0.00000204
-0.00000861
the following
0.00322353
—0. 004ul950
0.00012243
*non California 1966, 1967
52
0.02726103
0.0010226 3
-0.00044518
0.00002993
-------
GROUP 4 - 1968 low altitude cities - Simple emission rate function
GROUP
N
1 0.04931905
v -0.00216938
a 0.00373793
va 0.00009513
v2 0.0000401A
a2 -0.00530121
va2 0.0006470 3
v*a -0.000 0012 2
v2a2 -0.00001054
1
V -0. OC'02314 t' "
v2 0.0 00 00 72 3
GROUP GROUP 5 - 1969
N
1 0.05025577
v -0.00230273
a 0.00221975
va 0.00018041
v2 0.00004093
a2 -0.00626336
va2 0 . 000 6 8 70 3
v2a -0.00000117
v2a2 -0.00001060
1 J . 01 9 o b 4-5 6
V -0.000246ft2 _
V2 : " 0. 0000060 I
GROUP GR0UP 6 . 1970
N
1 0.02778199
V -0.00106505
a 0.00278733
va 0.00003901
v2 0.00002242
a2 -0.002 2883 5"
va2 0.00030622
v2a 0.00000089
v2a2 -0.0000042 7
1 , 0.01214718
V ! -0.0001102C
V2 0.0000068 6
0.50832557
-0.01621125
0.060 54505
-0.00034837
0.000 24459
-0.009 J2161
0.00138 6B0
0.00009970
0.00GG2778
for composite emission
u . 5 10
-Urn
-------
GROUP
N
1
v
a
va i
:•
va
2a? '
2a2
GROUP 7 - 1971 low altitude cities - Simple emission rate function
0.02387170
-0.0009389 2
0 ,00190 53 7
0.00009884
0. 0000191 5
—0 .0018255 5
0.00025134
-0 .00000010
-0 .00000 323
0.37338899
-0.01503251
0.06764833
-0.00314375
0.00020130
0.GOO57390
0.000 26241
0.00013265
0.00004680
2.33113963
-0.01420001
O.07696648
0.04623667
0.00149476
-0.12730560
0.01051507
-O.0UO53625
-0.003f 369B
0.00110935
0.00004619
-0.00451347
0.02257528
-O.00008096
-0.00029945
1
4
V
GROUP
N
1
v
a
va
va^
v2a
v^a2
1
v
v2
GROUP
N
1
v !
a
va
v2
a2
va2
v2a
2a2
1
v
y 2 i
0 . 01043 694
-G .OOOOS30 1
¦"> .00000516
0.00073^42
-0.00000 541
-0.00001357
for composite emission rate function include the following
0.00 5 77* 0 2
-0.0007076
0 .00004330
0.22516425
-0 . <>04609 59
0 • 6V 79
1.45908313
r-.rr9b3462
0.00141076
GROUP 8 - 1969 Denver - Simple emission rate function
0 .0449013 2
-0.00227597
0.00128843
0.00042103
0.0000499 2
—0^. 00669 26 6_
o.oboes 194
-0.00000314
-O.00001500
0.01800S3 3
-0 .00016620
O .f'0001437
1.05429790
-0.06943045
0.04712450
0.01336219
0.G014691O
-0.17414647
0.74615 791
0.02110150
-0.01475054
0.02680134
0.00034770
—Q.O?724796
-0.01341946
0.00161219
—0.00108798
0.00023321
-0.00000956
0.00 3595 46
0.0224265 5
0.00007263
-0.000 31433
for composite emission
C). 3052U380
—u.00656131
0. Ul,036294
0.00686935
-0.00016431
-0.00008498
rate function include the
0.9O307769
0.02028057
0.0G1O9V75
GROUP 9 - 1969 Denver - Simple emission rate function
_ 0^0335772 j
-0.00160934
0.00136514
0.00022437
0.00003290
-0.00391496
_0 .00049 794
-0.0000009 5
-0.00000796
0 .01454846
0.0000040 3
0.0000093 8
1.19717609
Q,fe968iJ?63
-0.05215655
0.08151960
0.00562416
0.00104906
-0.09712129
0_. 0j.42_50.0j
0.00015691
-0.00015502
for composite emission rate function include the
-0.00033100
_ -0.00COO234
0.00000516
following
0.0O3l4H0b
—0.0003042 0
0.00002452
n.nn^06419
0.004*9378
-0» 00.07.0476
0.02585258
0.00055116
-0.04984784
0.00731408
0.00018235
-0^00351125
0.00067441
0.Q0001946
-0.00116670
0.00020889
-O.00009728
-0.00007255
—0.00000R43
-Q.QQG0Q4Z8
0.199 742 57
-0.00776361
0.000 33751
1.17531764
0.018092 30
0.00104337
following
0.00 372786
-0.00046996
0.00002788
54
-------
va
2
v^a
GROUP 10 - 1970 Denver - Simple emission rate function
1 .22872281
GROUP
N
1 0.05206897
V -o.o 02 6 6 509
a 0.00025524
va 0.-100 5175 8
v2 O .00005 2$ 1
a2 -0.0071069 3
2 () .000B4P1 3
-0 .COO0!)43 5
v2a2 -0.00001418
i • c.ci«02o;n
V ~O • O00 1 694 ,?
v2 O.OCO::1115
1 •09134300
-0.07413160
0.04172969
0.01422696
0.00149024
-0.18479960
0.02352125
0.00006572
—0 . 000 32908
0.00254560
0.03491994
0.02550732
0.00084449
-0.05919603
0.01056317
-O.00006632
-0.00014492
0.00043387
0.00046245
0.00047936
0.00007920
0.00001353
0.00092582
—0.00004556
for composite emission rate function include the
0. 31745<.t"<* 1.11161829
-O.uuV70994 0.012^5046
0.^o03l33r 0.00134523
0.00000092
0.00000007
following
0.00361932
-0.00040599
0.0000319 6
GROUP
N
1
v
a
va
v2
a2
va2
v2a
v2a
1
v
GROUP 11 - 1971 Denver - Simple emission rate function
0.0397 6 24 1
-0 .00210474
0.00352024
0.0001550 5
0.0000447 3
-0.00352917
0.00047602
0.00000430
-0 . 0000 0 55 3
0 . u 12 6 f 95 2
-0.0000156 0
0 .00C (" fHW3
1.17291937
-0.08788155
0.07816697
0.0036 3532
O.OOl78530
-0. 18577261
0.02430256
A*00025009
-0.000 32093
1.55096134
Ji«00624295
0.10723281
0.03361190
0. 00099627
-0.02B33368
0.01130088
•*O.OOOt7174
-0.00014693
-0.00501945
Q.00073873
-0.00114299
0,00050725
0.00001002
... 0.00150P6B
-0.0000210 8
-0.00000842
-0.00000094
for composite emission rate function include the following
0.30541509 1.31557277 0.0034668K
-0.0Ct>7«//13 0.02523382 -0.00037850
0.0002*5di 0.00107375 0.00003049
55
------- |