1. Novel Technique to Reconstruct Instantaneous
Heavy Duty Emissions
Madhava R. Madireddy, Nigel N. Clark and Natalia A. Schmid
Dept. of Mechanical and Aerospace Engineering,
West Virginia University, Morgantown 26505, WV, USA.
Abstract: Transient vehicle emissions as measured in test cells or by on-board systems do not precisely
reflect the emissions at the exhaust because the instantaneous emissions are dispersed in time by the
sampling and analyzer systems. With increasing demand for accurate emissions measurement to optimize
engine controls and for atmospheric inventory models, research effort has been directed at compensating
for measurement distortions by the emissions analyzer system. This paper presents a new procedure
known as the modified deconvolution technique (MDT) which may be employed for the reconstruction of
instantaneous emissions signals. The method was applied to revising mass rates of emissions as a
function of speed and acceleration for the case of a transit bus. This revision (or reconstruction) led to a
higher range of emissions rates and for most high power speed-acceleration bins, the mass emissions rate
was increased. For bins with high deceleration, emissions rates were reduced.
List of Notations
SIT Sequential Inversion Technique
DCM Differential Coefficients Method
MDT Modified Deconvolution Technique
UDDS Urban Dynamometer Drive Schedule
1. Introduction
There is increasing interest in developing vehicle emissions models which predict instantaneous
emissions particularly for conformity studies to assess impacts of new traffic facilities or changes in
traffic controls. The instantaneous emissions values might be expressed as a function of vehicle operating
conditions. For example, mass emissions rates might be expressed based on vehicle speed and
acceleration [1, 2], and average emissions mass rates might be ascribed to speed-acceleration bins in a
matrix. Ideally, instantaneous emissions are the actual emissions produced by the engine at a specific
point in time at the engine manifold, or else they may be modified by after-treatment systems before they
leave the engine stack or tailpipe. A measurement system can be used to record these instantaneous
engine-out emissions, but the measurement system will distort the signal that corresponds to the
instantaneous emissions and produce an output signal, which represents the ‘measured’ emissions. For
some fast response research hardware [3, 4], the measured emissions will be much the same as the
instantaneous emissions. However, most sampling and analyzer systems used in transient test cells or in
on-board portable emissions measurement systems will report a distorted signal through the process of
measurement. For example, the emissions reported by the analyzer may be delayed and dispersed relative
to the instantaneous emissions. In contrast, measured speed and acceleration are usually faithful

2. 2
representations of the instantaneous values. Unfortunately, this means that the measured emissions may
not be related appropriately to the measured speed and acceleration of the vehicle. Traditionally
researchers and regulators have sought only to align the emissions [5-7] with the vehicle activity in time,
without considering the effect of diffusion in time. Failure to consider dispersion leads to inaccuracy in
resulting predictive models, typically resulting in emissions values in a bin which have been tainted by
vehicle activity which is actually outside of that bin. If the emissions can be related uniquely to each
speed and acceleration event, then this diffusion of information between bins can be eliminated. This
paper presents appropriate post-processing of emissions data, and confirms that the diffusion of emissions
information between speed-acceleration bins can be reduced by such post-processing.
2. The effect of time-dispersion of data on the average bin emissions
Figures 1 (a) and 1 (b) present a schematic of two hypothetical emissions measurement situations. In one
the emissions mass rate is low, then rapidly transitions to a high value, then rapidly returns to a low value.
In the other situation, a short constant acceleration event is mimicked. In Figure 1 (a), the solid rectangle
(and a solid trapezoid in Figure 1 (b)) represents the instantaneous emissions. However, when the
analyzer measures this rectangular (or trapezoidal) response, it will be distributed as the dotted parabolic
curve. This is the measured response and it can be noted that the measured response is distributed over a
larger time interval and has an average lower than the instantaneous (reconstructed) emissions.
Due to the analyzer response delay, the start of the dotted line should follow the start of the thick line.
However, when these two continuous sets of data (measured emissions and instantaneous emissions) are
time-aligned using cross correlation [8] (usually matches peaks and troughs), the measured response
shifts to the left and the response shown in Figures 1 (a) and (b) are after time alignment.
Hence the emissions measured in a particular activity bin may be the emissions which actually belong to
another activity bin. These emissions ‘bleed’ from one bin to another due to dispersion. Hence post-
processing the measured emissions is necessary to relate the emissions properly to their corresponding
operating conditions.
(a) (b)
Figure 1. Effect of reconstruction (and time alignment) on bin with (a) constant speed (b) constant
acceleration

3. 3
3. Earlier work on emissions reconstruction
Earlier, the authors presented two different approaches for reconstruction of transient emissions from
heavy-duty engines [8-10]. They are the Sequential Inversion Technique (SIT) and Differential
Coefficients Method (DCM) [11]. SIT is a simple step by step de-convolution technique in the time-
domain. SIT failed to reconstruct any real-time data successfully without exhibiting runaway instability.
DCM was introduced by Ajtay and Weilenmann [11], and involves mapping the instantaneous emissions
as a linear combination of the analyzer output signal and its derivatives. A brief description of DCM
follows.
Let x(t) be the input to the analyzer and y(t) be the output and y/
(t) and y//
(t) be the first and second
derivatives of the output. In this method, the input can be expressed as the sum of the output and some
linear combinations of the first and second derivatives of the output. The input x(t) and output y(t) and its
derivatives are related by the following expression.
x(t) = y(t) + a1 y/
(t) + a2 y//
(t) Eq.1
Eq. 1 is subject to a constraint that the integrated input is the same as the integrated output over the
duration of observation as it is assumed that the analyzer accounts for all of the data even though the data
are delayed and diffused. For a known response to a unit impulse function (which can be determined
experimentally), minimizing the error between the left hand side and the right hand side of the equation 1
should generate the coefficients a1 and a2. These values can be used to generate the instantaneous input
from the measured output y(t) and its derivatives, y/
(t) and y//
(t). DCM was able to reconstruct
continuous emissions from real-time data. The results with the DCM were presented comprehensively
elsewhere [8, 10]. Trials were made to improve the DCM by adding more derivatives, and by trying
different numerical ways to compute the derivatives and improvements were possible [9].
4. Estimating the transient dynamics of the analyzer
To enable reconstruction, the transient dynamics of the analyzer need to be estimated. For this
purpose, the instantaneous impulse response characteristics of the two analyzers used for emissions
measurement were studied. The response tests were conducted on Rosemount 955 NO analyzer
(manufactured by Emerson Electric Co, St. Louis, MO) and Horiba AIA 210 CO2 analyzer (manufactured
by Horiba Automotive Test Systems, Ann Arbor, MI). All the data analyzed in this study were measured
only by these analyzers. The Rosemount 955 analyzer worked on a phenomenon called
chemiluminescence in which photons of light were produced by a chemical or electrochemical reaction.
The analyzer is capable of measuring either NO or total NOx. To determine NO, the sample NO is
converted to NO2 by oxidation using molecular ozone. During this reaction, about 10% of NO2 molecules
get elevated to an excited state and then when the molecules come back to non-excited state, photon
emission takes place. The emitted photons are detected and the response of the analyzer is proportional to
the total NO in the converted sample. To determine the total NOx, a similar procedure was followed,
except that the gas stream was passed through a converter which converts all the NO2 into NO. The
instrument response in this case, is proportional to the NO present in the original sample plus the NO
produced by the dissociation of NO2. To analyze CO2, Horiba’s AIA 210, a non-dispersive infra-red
(NDIR) analyzer was employed. Before the exhaust gas sample enters the analyzer, the sample is dried to

4. 4
avoid moisture. There is a particular wave length of the infrared energy at which each of the gaseous
components is absorbed. The amount of energy absorbed at a wavelength corresponding to CO2 could be
measured and is directly proportional to the concentration of CO2 in the exhaust. The working principles
of these analyzers were described in more detail elsewhere [10].
The response of a Rosemount 955 NO analyzer to an instantaneous pulse of input of NO is shown in the
Figure 2 (a). In an engine test cell, a balloon was filled with one liter of NO with a concentration of 1000
parts per million (ppm) and inserted in the dilution tunnel. The balloon was burst to simulate a pulse of
short duration relative to the diffusion phenomena. The pulse traveled via the dilution tunnel and
sampling lines to the Rosemount 955 analyzer, and the analyzer output was collected. The time delay
showed in the Figure 2 (a) is a function of the length of the sampling lines and speed of the exhaust gas
travel through the lines. The response was found to be dispersed over a period of 6 seconds. The response
was of 5 hertz and the fraction of the response in each one interval (0.2 second) is represented by a point.
The shape of the response is obtained by connecting all such points with simple straight lines. If the
fractions of the response are less than 0.05 %, all such fractions were considered insignificant and were
added as one fraction on either side of the response. It should be noted that only the dispersion of the
instantaneous pulse by the analyzer system is of interest in this analysis. Similar procedure was followed
to obtain the response of Horiba AIA210 analyzer.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20 25
Time(sec)
Fractionofresponseperseco
Instantaneous input
Delay
Figure 2 (a). Impulse response of Rosemount 955 NOx analyzer to an instantaneous input

5. 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20 25
Time(sec)
Fractionofresponsepersec
Instantaneous input
Delay
Figure 2 (b). Impulse response of Horiba AIA 210 analyzer to an instantaneous input
5. Modified Deconvolution Technique (MDT)
A brief description of the reconstruction procedure is as follows. Based on the authors’ empirical
observations, the impulse response of the analyzer can be modeled as a gamma probability density
function (PDF). The analyzer system was modeled based on the assumption that it is linear and time-
invariant [12, 13]. Then the analyzer was completely characterized by an impulse response, a response of
the analyzer to an instantaneous pulse, denoted by H(t). The approximation of the gamma PDF depends
on the analyzer used. For example, Rosemount 955 NO analyzer will have a different gamma PDF from a
Horiba AIA 210 CO2 analyzer. A two parameter (k and θ) gamma PDF [14], denoted by G(t), is provided
by Eq.2:
)(tG = 

 /
1
)/( t
k
e
t 

, 0t . Eq.2
The maximum of the G(t) was equated to the maximum of the H(t) and the location of the maximum for
G(t) was equated to the location of the maximum of H(t).
Equating the maximum values of the real H to the maximum of the gamma distribution and differentiating the
distribution with respect to time, as shown in Eq. 3 generates the equations that yields the values of k and θ.
These values were considered the a priori information and were used while computing the back-transform.
0θ)(k,
dt
dG
 Eq.3
These two equations generated the values of the parameters k and . These parameters established a

6. 6
specific function G(t) to describe the response. Alternately, one might find G(t) from H(t) using a best fit
regression, but this method was not employed in this paper.
The values for k and  were found using the method described above for both CO2 and NOx as species.
For CO2 the values were k = 1.85 and  = 2.20 and for NOx the values were k = 1.88 and  = 2.22.
However, the continuous emissions data that were examined in this paper were obtained with a different
dilution tunnel than the one used for the response determination, and so the authors believed that it was
necessary to determine that these values of k and  were still applicable. The continuous data for CO2
and NOx were available along with values for instantaneous power. The authors assumed that CO2 and
NOx were strongly related to power, and there are compelling arguments on engine efficiency and
emissions compliance, along with existing data [15], to support this assumption. The measured CO2 and
NOx data were transformed, as described below, to yield the best estimate of instantaneous engine-out
emissions. These were compared, through correlation, with instantaneous power using the k and  values
presented above. Both k and  were then varied over a range of k = 1.67 to 2.04 for CO2 and k = 1.69 to
2.07 for NOx, and  = 1.98 to 2.42 for CO2 and  = 2.00 to 2.44 for NOx. The values of k and  that
correlated best under these circumstances were chosen for further use. The optimal values which were
found using this method were very close to the original values determined from the response functions.
The final values were k = 1.87 and  = 2.20 for CO2 and k = 1.91 and  = 2.20 for NOx. These were
used for further analysis.
The Fast Fourier Transform (FFT), employed previously by Madireddy [10], was involved to compute
efficiently the reconstructed input x(t) using the following simple procedure. Let X be the analyzer input,
Y, the analyzer output and H the transfer function of the analyzer. The FFT first transforms both
estimated impulse response and the output signal of the analyzer into a frequency domain (Eq.4 (a)). Then
a simple division (Eq. 4(b)) is employed in the frequency domain to compute the input in the frequency
domain. The Inverse Fast Fourier Transform (IFFT) of that input transfers the input into the time domain
(Eq. 4(c)).
X(n). Hw = Y(n); Eq.4(a)
Hence X(n) = Y(n)/ Hw and Eq.4(b)
IFFT (X(n)) = X(t). Eq.4(c)
6. Validation of MDT/ Comparison with DCM
To validate MDT, the data were collected from the chassis testing conducted in the WVU
Transportable Heavy-Duty Vehicle Emissions Testing Laboratory on a Peterbilt Truck with a Caterpillar
3406E engine fitted to a 19-speed Eaton Fuller transmission with 550 hp. The engine power was generated by
the Engine Control Unit, which is based on the fuel consumption and the engine efficiency curves. The
correlation of measured CO2 with power is calculated. The reconstruction of the data was attempted using
MDT. MDT increased the correlation of emissions with power. More importantly, the reconstructed input by
MDT correlated better (R2
of 0.9211) with power than the input generated by DCM (R2
of 0.9006).

7. 7
y = 0.0999x + 3.1012
R
2
= 0.849
y = 0.1081x + 2.1868
R2
= 0.9211
-10
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600
Engine power (hp)
CO2(g/s)
(Measured)
(Reconstructed)
Figure 5-13 (a). Validating MDT: MDT in reconstruction of CO2 emissions from Peterbilt truck
with Caterpillar 3406E engine tested on UDDS cycle
The previous work involving the validation studies of DCM and MDT techniques by the authors proved
that MDT can reconstruct the transient emissions better than DCM [8, 10]. The improvement in
predicting the emissions with DCM (on an average for eight data sets, four for NOx and four for CO2) is
about 1.5%. The corresponding marginal improvement with MDT was about 2.5%. While these numbers
may be dependent to some extent on the data itself, the overall conclusion is that MDT was able to predict
more accurately the true instantaneous emissions. Hence MDT was the only method chosen for the
reconstruction presented in this paper. The data were time-aligned using cross-correlation [16-18].
7. Available data
Continuous CO2 and NOx emissions data were available for a New Flyer 2006 model year transit bus
with a Cummins ISM 280 diesel engine tested on a UDDS drive cycle [10]. The continuous data for bus
speed and acceleration were also available. More details of the study are available in reference [19].
While this method is applicable to most of the continuous data streams, reconstruction will be adversely
affected when the analyzed emissions species is subjected to after-treatment methods.
8. Data analysis
8.1 Comparison of Measured and Reconstructed Emissions
At each point in time, the measured emissions were available, and MDT was used to produce a

8. 8
corresponding, predicted instantaneous (reconstructed) value. The measured and reconstructed data sets
for the bus were compared (Figure 3); the best correlation between the measured and reconstructed data
sets yielded a slope close to unity and an intercept close to zero. However, the range of the reconstructed
data was greater than the range of the measured data because the peaks and troughs associated with
transient operation of the vehicle were diffused by the measuring system. If the reconstructed data were
considered to be the true emissions, it can be implied from Figure 3 that for any true emissions value, the
corresponding measured values vary over a range. For example, the reconstructed emissions of 30 g/sec
yielded measured values from about 23 to 37 g/sec. From Table 1 it can be implied that, while the
averages of the measured and the reconstructed data sets were much the same, the standard deviation and
the range of the whole reconstructed set were higher. For a sufficiently long sampling time, the average
value of the reconstructed signal will approach closely the average value of the measured signal, but this
will not hold true for short time periods: for an instantaneous comparison, as in Figure 3, the difference
will be a maximum. A small negative value for the emissions rate represented the minimum after
reconstruction.
y = 1.0002x - 0.0076
R2
= 0.8947
-10
0
10
20
30
40
50
0 5 10 15 20 25 30 35 40
Measured mass rate (g/s)
Reconstructedmassrate(g/s)
Figure 3. Comparison of the measured and reconstructed CO2mass-rate (g/sec) for a New Flyer transit bus
2006 tested on UDDS.

9. 9
Table 1. Comparison of the parameters of the measured and reconstructed data sets of CO2mass rate
(g/sec) for a New Flyer transit bus 2006 tested on UDDS.
Measured (g/s) Reconstructed (g/s)
Average 10.32 10.31
Standard deviation 8.80 9.31
Maximum 36.98 45.03
Minimum 0.11 -2.31
Cumulative distributions for the measured and the reconstructed data are shown in Figure 4. The plots are
visually similar partly because they are forced to be similar for periods of idle (about 4 g/sec) and steady
state operation, where diffusion of the true emissions by the analyzer does not play a role. However, the
two plots do deviate at low emissions values associated with deceleration and high emissions value
associated with acceleration and high speed.
0
200
400
600
800
1000
1200
-10 0 10 20 30 40 50
Emissions mass rate (g/sec)
Numberofpointsbelowvalue
Measured
Reconstructed
Figure 4. Frequency distribution of measured and reconstructed CO2 mass rate for a New Flyer 2006
transit bus tested on UDDS.
8.2 Average emissions for different operating conditions
While one parameter such like speed, acceleration or load is not sufficient to uniquely represent an
instantaneous operating condition of a vehicle, a combination of speed and acceleration of the vehicle at
an instant in time was earlier proved [2] to represent a vehicle operation. Instantaneous power is a
function of speed and acceleration, and for unthrottled diesel engines instantaneous mass rate of CO2 is

10. 10
closely related to instantaneous power. Moreover while measured emissions are dispersed, the measured
values of speed and acceleration are usually closer to their instantaneous values. For these reasons, each
operating condition was represented by a combination of a range of speed and range of acceleration. For
species such as carbon monoxide and particulate matter, other engine parameters may be needed for
emissions prediction, but the diffusion problem will impact the model in the same way as is illustrated for
CO2 below.
One data point was available at each second over the UDDS. The data were divided into 63 (9 X 7) bins
based on speed and acceleration ranges as shown in Table 2 (a). Each bin had a specific speed range and
specific acceleration range, and the resolution was coarse out of necessity because there are relatively few
data. The vehicle speed ranged from 0 to 57 mph for a UDDS. Hence the range of speeds for bins across
the rows was from 0 to 6.333 (which is 57/9) mph for the first column, 6.333 mph to 12.666 (which is
2X57/9) mph for the second column and so on. The acceleration range was divided similarly into 7 equal
rows. Each bin contained data for several instances of operation.
Variability of emissions values in each bin occurred due to size of the bin, transient effects, diffusion of
emissions data and lack of repeatability of the bus and measurement system. The emissions values in
each bin were averaged. Analyzing the emissions in each of these bins associated the operating conditions
(in a small range) with emissions data. The continuous sets of measured data were reconstructed using
MDT. These data were also divided into bins in the same procedure as the one followed for the measured
emissions. After the data were reconstructed, the emissions values in each of the bins changed. The
results are shown in Table 2 (b). Consider the bin with the lowest average acceleration (of -1.50 m/s2
).
For this bin, the ratios of the averages and standard deviations of reconstructed to measured CO2 were
computed (Figure 5 (a)). It can be inferred that, when the vehicle was decelerating, the reconstructed
values were lower than the corresponding measured values. Figure 5 (b) shows how the ratios slightly
increased for a bin with highest acceleration (of 1.06 m/s2
). This was because the analyzer system under-
read the highest amplitudes (peaks), which usually correspond to high vehicle acceleration and over-read
the lowest amplitudes (troughs), which usually correspond to the vehicle deceleration. Hence, the ratio of
reconstructed to measured of bin averages increases during acceleration and decreases during
deceleration.

11. 11
Table 2 (a). Measured CO2 mass emissions (g/s) for different speed and acceleration bins of a New Flyer
2006 transit bus tested on UDDS.
Average bin speed (m/s) 1.4 4.2 7.0 9.9 12.7 15.5 18.3 21.1 23.9
Average bin accel. (m/s/s) ↓
-1.50 1.15 2.56 2.21 2.87 3.96 4.23 6.24 8.01 12.78
-1.08 0.99 0.76 1.97 3.41 6.68 11.56 18.35 24.45
-0.65 0.97 0.58 0.52 6.02 8.83 14.79 25.46 28.86
-0.22 1.42 1.34 1.20 2.52 8.32 13.26 21.24 29.34
0.20 0.31 1.45 7.77 15.84 25.54 27.22
0.63 1.87 1.29 15.66 19.34 26.41
1.06 5.39 19.78 25.58 34.79
Table 2 (b). Reconstructed CO2 mass emissions (g/s) for different speed and acceleration bins of a New
Flyer 2006 transit bus tested on UDDS.
Average bin speed (m/s) 1.4 4.2 7.0 9.9 12.7 15.5 18.3 21.1 23.9
Average bin accel. (m/s/s) ↓
-1.50 0.71 2.21 1.76 2.57 3.94 4.20 5.70 6.59 8.81
-1.08 0.84 0.94 2.83 3.76 5.99 9.11 17.91 21.77
-0.65 1.18 0.79 0.64 7.85 8.30 14.87 25.31 32.43
-0.22 1.84 1.77 1.58 3.43 9.44 12.71 22.29 29.30
0.20 0.29 1.95 10.87 16.06 26.07 27.37
0.63 2.66 1.76 16.75 19.01 26.49
1.06 7.60 20.09 25.57 37.62

12. 12
(a)
(b)
Figure 5. Ratios of average and standard deviation of the reconstructed to measured CO2 for the bin
with (a) lowest acceleration and (b) highest acceleration for a New Flyer 2006 transit bus tested on
UDDS.

13. 13
9. Discussion and Applications
If continuous emissions data for a thousand seconds were considered, the average of the emissions rate
measured by the analyzer was found approximately equal to the average rate of the true (instantaneous)
emissions. However, for a given operating condition (defined by vehicle speed and acceleration), the
average of measured emissions differed from the instantaneous average. This is because of the dispersion
associated with the measurement system. In most circumstances, the measured emissions may be
sufficient to support an inventory model. However, if the model is required to perform accurately over
small time and space scales, such as in a conformity study for a traffic control signal that results in
periodic vehicle acceleration, then the reconstruction will improve the inventory estimation at that
location.
For inventory models, it is of interest to associate emissions with vehicle activity. MDT could improve
the instantaneous emissions inventory models based on speed-acceleration matrices, or other
combinations of vehicle speed and acceleration, as are used in MOVES [20, 21]. If one wishes to divide
activity into speed-acceleration bins and assign emissions mass rate values to each bin, it can be achieved
by using instantaneous data, as shown in this study and by assigning the emissions value at each moment
in time to the related bin. The ultimate value in that bin, to be used for modeling purposes, can be found
by averaging all values placed in that bin. This procedure can be used to compensate for the delay and
dispersion of the emissions data used to populate a model. The result would be a tool for instantaneous
emissions modeling which has superior time resolution and more accurate predictions of emissions for
sustained high and low load operation. This procedure could also be incorporated into other emissions
prediction models such as COPERT [22].
Acknowledgements
The authors are thankful to ABM Khan for assisting with the data analyzed in this study. Support for this
analysis was provided by the US Department of Transportation (contract number
10009291.1.1.1003596R).
List of Captions for the Figures and Tables
Figure 1. Effect of reconstruction (and time alignment) on bin with (a) constant speed (b) constant
acceleration
Figure 2 (a). Impulse response of Rosemount 955 NOx analyzer to an instantaneous input
Figure 2 (b). Impulse response of Horiba AIA 210 analyzer to an instantaneous input
Figure 3. Comparison of the measured and reconstructed CO2mass-rate (g/sec) for a New Flyer transit bus
2006 tested on UDDS.
Figure 4. Frequency distribution of measured and reconstructed CO2 mass rate for a New Flyer 2006
transit bus tested on UDDS.
Figure 5. Ratios of average and standard deviation of the reconstructed to measured CO2 for the bin
with (a) lowest acceleration and (b) highest acceleration for a New Flyer 2006 transit bus tested on
UDDS.
Table 1. Comparison of the parameters of the measured and reconstructed data sets of CO2mass rate

14. 14
(g/sec) for a New Flyer transit bus 2006 tested on UDDS.
Table 2 (a). Measured CO2 mass emissions (g/s) for different speed and acceleration bins of a New Flyer
2006 transit bus tested on UDDS.
Table 2 (b). Reconstructed CO2 mass emissions (g/s) for different speed and acceleration bins of a New
Flyer 2006 transit bus tested on UDDS.
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