The sequential inversion technique (SIT) and differential coefficients method (DCM) are two methods discussed to reconstruct true transient emission signals from measurements taken by analyzers, which introduce delays and dispersion. The SIT reconstructs the input second by second based on the measured response and dispersion characteristics. Testing with real data showed it can accurately reconstruct signals without noise. However, reconstruction fails if the dispersion characteristics change or there is signal noise. The DCM defines the real input as a linear combination of the output and its derivatives. It was more accurate than SIT when noise was present. Both methods aim to compensate for measurement delays and dispersion to obtain instantaneous emissions from analyzer readings.

1. 437
Sequential inversion technique and differential
coefficient approach for accurate instantaneous
emissions measurement
M R Madireddy* and N N Clark
Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, West Virginia, USA
The manuscript was accepted after revision for publication on 29 July 2006.
DOI: 10.1243/14680874JER00406
Abstract: The need for accurate emissions measurements has coerced researchers into trying
to reconstruct the true transient emission signal from that measured by the analyser. This
paper discusses two such methods and examines the validity of those methods by testing them
with real-time emissions data. The first method is the sequential inversion technique, which
tries to reconstruct the input second by second, based on the measured response at each
second and the dispersion characteristics of the analyser. The reconstruction was found to be
accurate, but there were some constraints associated with the dispersion characteristics and
the reconstruction failed if there was signal noise. The second method, the differential
coefficients method (DCM) of Ajtay and Weilenmann, reconstructs the input signal by approxi-
mating the analyser input as a linear combination of the output and the output derivatives.
When tested with real-time data, the DCM predicted the emission signal even when there was
noise imposed on the signal. While the DCM is clearly a better prediction technique, the
accuracy of the DCM is reduced when noise is added to the analyser input. The DCM, when
coupled with cross-correlation techniques, can be a powerful tool in retrieving ‘lost’ information
associated with the measurement delays and dispersion characteristics of the analyser.
Keywords: time-alignment, cross-correlation techniques, signal reconstruction, dispersion
function, sudden noise, continuous random noise
1 INTRODUCTION One reason for using windows 30 s wide is to account
for signal dispersion, as discussed later in this paper.
Several testing procedures have been developed toAutomotive engines produce exhaust that contains
carbon dioxide (CO
2
), carbon monoxide (CO), nitro- evaluate the continuous data of CO
2
, CO, NO
x
, and
HC emissions from engines. Continuous data are alsogen oxides (NO
x
), hydrocarbons (HCs), and particu-
late matter. Increasing restrictions on emissions valuable to manufacturers in optimizing transient
control strategies for engines and are essential forby the US Environmental Protection Agency (EPA)
require continuous emissions data to be measured the formulation of emissions inventory and hot-spot
models. For example, the EPA model called the motoras accurately as possible. The EPA has introduced the
‘not to exceed’ (NTE) limits [1] to control and moni- vehicle emission simulator (MOVES) [2, 3], employs
emissions as a function of vehicle-specific power andtor emissions. The NTE test procedure establishes a
region of operation with torque and speed bound- vehicle speed, while other approaches [4] use speed–
acceleration matrices. If continuous data are used toaries (the NTE zone) where emissions must not
exceed a specified value for any regulated pollutants. feed such models, it is desirable to avoid dispersion
of the actual emissions by the analyser.The emissions are averaged for at least 30 s and are
compared with the applicable NTE emission limits.
* Corresponding author: Department of Mechanical and Aero- 2 DELAY AND DISPERSION
space Engineering, College of Engineering and Mineral Resources,
West Virginia University, Morgantown, WV 26506, USA. email: In a test cell, diesel engine exhaust is conveyed to a
dilution tunnel, where it is diluted with backgroundmadhava543@yahoo.com
JER00406 © IMechE 2006 Int. J. Engine Res. Vol. 7

2. 438 M R Madireddy and N N Clark
air. A sample stream of dilute exhaust is then carried 3 AVAILABLE DATA
via sampling lines to infrared analysers for CO and
The data used for testing these techniques were col-CO
2
, a chemiluminescent analyser for NO
x
, and a
lected from the federal test procedure (FTP) cycle onflame ionization detector (FID) for HCs. For on-
a 1992 Detroit Diesel Corporation (DDC) series 60board measurement, the exhaust is sampled raw,
engine and the testing was conducted in the Westusing infrared analysers for CO and CO
2
, zirconia,
Virginia University Emissions Research Laboratoryelectrochemical, or chemiluminescent analysers for
(WVUERL). Further details of the test cell and typicalNO
x
, and a spectral analyser or FID for HCs. Each
operation can be obtained elsewhere [8, 9]. Thecomponent of the exhaust is analysed by a different
instantaneous NO
x
data were collected using a fastanalyser and there is a significant delay between the
NO
x
analyser, which was manufactured by Cam-point in time when the engine experiences an
bustion Ltd, Cambridge, UK [10]. Since the responseoperating condition and the point in time at which
from the fast NO
x
analyser is rapid and has lowthe emissions related to that operating condition are
diffusion (T
10–90%
=12 ms), the data were treated asmeasured. The total delay time from the engine
instantaneous data. The NO
2
-to-NO converter wasexhaust to the analyser input has already been
not used before the measurements were taken.addressed [5] and is well understood at most
Hence, the NO
x
represents more NO and the smallresearch laboratories. Emissions data and operating
fraction of NO
2
was neglected. The dispersion func-variables are often time aligned visually or with
tion was used to diffuse the instantaneous (fast NO
x
)cross-correlation techniques, which are discussed
data to obtain the diffused NO
x
data.later in the present paper. Apart from the time delay,
the response can be dispersed over a period of time
when measured by the analyser. In other words,
the specific operating condition experienced by the 4 SEQUENTIAL INVERSION TECHNIQUE (SIT)
engine may be sudden or momentary, but the meas-
ured response can be dispersed in time with the 4.1 Reconstruction procedure using the SIT
amplitude of a peak or a dip smaller than that actu-
Before considering laboratory data, the researchers
ally experienced by the engine. Hence, the data read
examined the following idealized distribution. Con-
by the analysers do not represent the instantaneous
sider a 1 s injection of 100 ppm NO
x
into a dilution
emissions at the tailpipe. The problem of dispersion
tunnel that is connected to the input of an analyser.
or diffusion has already been raised by Ganesan and
Other than the 1 s injection, the tunnel carries no
Clark [6]. Their work focused on forward trans-
NO
x
. Let the readings of the analyser be 20 ppm,
forming the instantaneous emissions to measured
30 ppm, 40 ppm, and 10 ppm in the first, second,
emissions. third, and fourth seconds respectively. Then the ‘dis-
By compensating for the delay and the dispersion, persion function’ is defined as {0.2 0.3 0.4 0.1}. Even
the true emission signal can be reconstructed. In though a typical analyser responds for about 14 s to
other words, the measured emissions should be a 1 s input (which will be discussed later in this
reverse transformed to obtain the instantaneous paper) for a clear understanding the concept of
emissions. Two such procedures for reconstruction SIT, the analyser response was simplified and was
examined in this paper were the sequential inversion assumed to last for only 4 s. The dispersion function
technique (SIT) and the differential coefficients represents how the input to the analyser diffuses over
method (DCM). The SIT sequentially considers the a period of time and can be considered a character-
measured data and deduces the real data points istic of the tunnel and the analyser. If there were no
based on the dispersion characteristics of the ana- other sources of input to the analyser, the fractions
lyser. The DCM approach proposed by Ajtay and in the dispersion function should add up to unity.
Weilenmann [7] defines the real input as a linear In this paper, the continuous data (say U(t)) are
combination of the output and its differentials. The represented as (1, 3, 2, 1, 4, 0, 1), which means that
coefficients of the linear combination are computed 1 ppm of NO
x
is injected in the first second, 3 ppm
by minimizing the least-squares error between the in the second, and so on. The input U(t) is rep-
input and the linear combination of the outputs, resented as a function of time. The total input of a
and the real input is reconstructed from those co- species prior to the first second is assumed to have
efficients. In practice, since the input values are not zero concentration. The analyser diffuses the above
known, other methods may be used to determine the input U(t) according to the dispersion function and
generates the following output, say Y(t) of NO
x
incoefficients.
JER00406 © IMechE 2006Int. J. Engine Res. Vol. 7

3. 439Sequential inversion technique and differential coefficient approach
parts per million in each second, as follows: (0.2, 0.9, sequent time intervals. As can be seen in Fig. 1(a),
the reconstructed input values (asterisks) appear to1.7, 2.1, 2.2, 1.8, 1.9, 0.7, 0.4, 0.1). This is referred to
as the diffused or dispersed output in this paper. It lie on the analyser input data line. The diffused
output, when plotted against the original fast NO
x
should also be noted that, for constant tunnel flow,
it is immaterial whether concentration or mass flow data, was scattered as shown in Fig. 1(b), but the
reconstructed input agreed well with the fast NO
x
of a species is discussed.
Let U(t
j
) and Y(t
j
) be the input and the output data.
However, it was observed that, when the value ofrespectively in the jth second. Let the elements in
the dispersion function be C
1
, C
2
, C
3
, and so on. The C
1
was decreased, the technique failed. To find the
value of C
1
at which this technique begins to fail, thedispersion function relates the input and output at
each second as [6] first element was gradually decreased. When it was
reduced to 0.137, a deviation was observed at the
Y(t
1
)=C
1
U(t
1
)
85th time interval (in this case), as shown in Fig. 2(a).
The deviation was noted to be oscillatory. By furtherY(t
2
)=C
1
U(t
2
)+C
2
U(t
1
)
reducing the first element C
1
to 0.130, the deviation
Y(t
3
)=C
1
U(t
3
)+C
2
U(t
2
)+C
3
U(t
1
)
began at an earlier time interval (81st) and the size
of the deviation also increased, as shown in Fig. 2(b).In short, the above equations can be represented by
a system according to If the first element (C
1
) of the diffusion function
were 0.6, the magnitude of the error (which is the
Y(t
j
)=C
1
U(t
j
)+C
2
U(t
j−1
)+C
3
U(t
j−2
)+,
difference in the amplitude of the reconstructed
signal and the real signal) was found to be of the+C
k
U(t
j−k+1
) (1)
order of 10−15 but, with a decrease in the first
where j takes values from 1 to n (where n is the
element, the order of the error increased exponen-
number of seconds of output data considered) and
tially. The logarithm to the base ten of the error was
k represents the number of elements in the disper-
computed and was plotted against the magnitude of
sion function. The set of equations can be solved in
the first element in Fig. 3. The order of the error also
sequence starting from the first equation when j=1.
increased with increasing time interval at which the
Since the computation of the input U(t
j
) at any
error was computed. This was because the number
time interval from the output Y(t
j
) depends on the
of computations for the reconstruction increased the
input U(t
j−1
) at the previous time interval, numerical
error sequentially.
errors will be propagated throughout the compu-
tation. The computational error includes the loss of
significant digits due to truncation, and the magni- 4.3 The effect of noise on the SIT
tude of the error increases with the number of data
Analyser signals can be subject to disturbances
points or time intervals.
which can be termed noise. The noise can be sudden
and momentary [11], which causes a large difference
4.2 The role of dispersion function in the SIT
in the response at one point in time or during a small
duration of time. Such a noise can be electrical orFor a dispersion function {C
1
C
2
C
3
C
4
}, the role
played by the size of C
1
was examined, keeping the from interference from other gases or suspended
particle species.other elements C
2
, C
3
, and C
4
equal. (It should be
noted that still C
1
+C
2
+C
3
+C
4
=1 to achieve mass The noise can also be continuous such as a wave
along the time axis of the data. There can also be anbalance.) To start with, the fast NO
x
data collected
from the FTP test conducted in the WVUERL were inherent inaccuracy in the measurement by the ana-
lyser, which can be due to the analogue-to-digitalconsidered as the instantaneous NO
x
at the engine
manifold. The data were dispersed in time using conversion. For example, if the digital device can
measure up to six decimal places, the remaining parta dispersion function to obtain the diffused data.
Before considering the realistic dispersion character- of the signal (from the seventh decimal) is either
equated to zero or the sixth decimal place is in-istic of an analyser, the present authors examined
the reconstruction of the emission signal for a simple creased by 10−6 for rounding. Such a noise is defined
as quantization noise [12] and the magnitude ofdispersion function such as {0.4 0.2 0.2 0.2}. For
this dispersion function, the computation involved this kind of error depends on the sensitivity of the
analogue-to-digital converter of the analyser. Thisdivision with a large value of C
1
, and the input in the
first time interval was computed accurately. Conse- noise can be continuous and random.
An NO
x
analyser with a simple dispersion functionquently, the reconstruction was accurate in the sub-
JER00406 © IMechE 2006 Int. J. Engine Res. Vol. 7

4. 440 M R Madireddy and N N Clark
Fig. 1 Reconstruction using the SIT: (a) continuous emissions; (b) parity plot
{0.4 0.3 0.2 0.1} was considered. A sudden noise, Random noise was added at all the time intervals
to the diffused analyser output. A random numberwhich has the same amplitude as the measured
response, was added in the 300th time interval. generator was used to select −1, 0, and 1 and these
were added (as parts per million) to every data pointBecause of this noise, the reconstructed response
deviated from the desired value around the 300th in the measured response. The random error was
within 2 per cent range of the response when thetime interval, as shown in Fig. 4. The spike in the
reconstructed input was the result of the added response was larger than 50 ppm. However, when the
response was as small as 5 ppm, there was a signifi-noise. It can be seen that the error due to the noise
was not just reflected at one time interval but that it cant percentage of noise in the response. The prob-
lem of overestimation of the noise can be againpropagated over a few time intervals after the noise
had occurred. Hence, it can be concluded that the observed, as shown in Fig. 5.
Hence, for the SIT to predict the true engine-outSIT ‘overestimates’ (predicts a higher amplitude of)
the sudden noise. emissions accurately, it is necessary that the first
JER00406 © IMechE 2006Int. J. Engine Res. Vol. 7

5. 441Sequential inversion technique and differential coefficient approach
Fig. 2 The SIT applied to an NO
x
analyser: (a) when C
1
=0.137; (b) when C
1
=0.130
element of the dispersion function should be higher reconstruct the instantaneous emissions using the
SIT for the realistic diffusion function is not war-than the rest of the elements. This requires that the
response of the analyser in the first time interval ranted. In other words, since the SIT failed for simple
diffusion function, it will fail for a realistic diffusionshould be larger than or at least comparable with the
response in the following time intervals. As this is function as well.
not the case for most dilution and analyser systems,
the examination of the cases with the realistic disper-
5 DIFFERENTIAL COEFFICIENTS METHOD (DCM)sion function (shown in Fig. 6) is unnecessary. Since
the numerical error increases exponentially for every
5.1 Reconstruction procedure using the DCM
computation, this method is not practical for recon-
structing the emission signal from the data measured Ajtay and Weilenmann [7] have discussed a math-
ematical approach to reconstruct the true emissionby the current analyser systems. Hence an effort to
JER00406 © IMechE 2006 Int. J. Engine Res. Vol. 7

6. 442 M R Madireddy and N N Clark
Fig. 3 The effect of C
1
on the order of the error in
Fig. 5 The impact of continuous random noise onthe SIT
the SIT
Fig. 6 Analyser response to a 1 s unit pulseFig. 4 The impact of sudden noise on the SIT
signals from the measured output of the analyser. tion (Fig. 6) was obtained from the dispersion model
proposed by Ramamurthy et al. [13]. The output wasFollowing their analysis, let U(t) be the input to the
analyser and Y(t) be the output and Y∞(t) and Y◊(t) spread over 14 s and the peak amplitude of the
output was less than a quarter of that of the input.be the first and second derivatives respectively of the
output. The method assumes that the input can be The analyser response to an instantaneous 1 s pulse
of unit input is shown in Fig. 6 and this provides theexpressed as the sum of the output and some linear
combinations of the first and second derivatives of dispersion function used to generate the diffused
data.the output. The input U(t) and output Y(t) and its
derivatives are related by This dispersion function was considered as the
output Y(t) and was differentiated numerically to
U(t)=Y(t)+a
1
Y∞(t)+a
2
Y◊(t) (2)
obtain Y∞(t) and Y◊(t) over a period of the dispersion.
These time steps for the numerical differentiationEquation (2) is subject to a constraint that the inte-
grated input is the same as the integrated output over can be 1, 0.5, or 0.1 s, but a 1 s time step was con-
sidered. The numerical derivatives for this study werethe duration of observation as it is assumed that the
analyser accounts for all the data even though the computed using backward differences in 1 s time
intervals. Then the derivatives were mapped with thedata are delayed and diffused. This dispersion func-
JER00406 © IMechE 2006Int. J. Engine Res. Vol. 7

7. 443Sequential inversion technique and differential coefficient approach
unit impulse input, the time sequence was fitted over
the dispersion period, and the error was then com-
puted at each second as the absolute value of
U(t)−Y(t)−a
1
Y∞(t)−a
2
Y◊(t). The least-squares error
was computed as the sum of the squares of the com-
puted errors at all points and this was minimized for
the best fit that generated the values of a
1
and a
2
,
the coefficients of the derivatives of the output. The
values of a
1
and a
2
were then used to obtain the input
U of the analyser from the output Y of any given data
from the analyser. The inherent assumption in the
method was that the analyser was consistent in its
dispersion behaviour and that its behaviour will not
change in the long run.
5.2 Testing the DCM to reconstruct NO
x
data
The fast NO
x
data were again considered as instan-
taneous NO
x
, representing the values of U(t), and
were dispersed in time to generate the diffused NO
x
,
Y(t). This diffused NO
x
signal represented a typical
conventional NO
x
analyser output. Then the pro-
cedure described above was used to reconstruct the
NO
x
. A portion of the reconstructed data is magnified
in Fig. 7(a). The diffused data were smoother and had
lost some high-frequency detail, but the recon-
structed data points lie close to the fast NO
x
curve,
regaining the detail. Moreover, the original fast NO
x
data have better correlation (with a correlation
coefficient R2 of 0.976) with the reconstructed input
than with the diffused output (R2 of 0.519) as shown
in Fig. 7(b).
Fig. 7 NO
x
reconstruction using the DCM: (a) continu-5.3 Testing the DCM to reconstruct CO
2
data
ous data; (b) parity plot
One way to evaluate the high-frequency detail in
emissions data is to correlate CO
2
with power. For
diesel engines, the CO
2
corresponds closely to the product curve PE should be a maximum. A simple
trial-and-error method was applied to check the timefuel consumed, and the brake specific fuel consump-
tion is fairly constant over much of the engine- shift that generates the maximum sum of the product
of P and E. In other words, the time shift s was deter-operating envelope. The engine power data are not
diffused in time, so that a high correlation of CO
2
mined to maximize WP
i
E
i+s
.
The power was dispersed according to a realisticwith power suggests that the CO
2
data are not excess-
ively diffused. dispersion function shown earlier in Fig. 6 and then
CO
2
was time aligned and expressed as a function ofThree more cases of the FTP runs conducted on
the DDC series 60 engine in the WVUERL were col- dispersed power. The CO
2
was better correlated (R2
of 0.978) with the dispersed power than with thelected. The engine power was calculated from the
engine speed and engine torque and then the con- un-dispersed power (R2 of 0.890); this was expected
because of the dispersion associated with thetinuous data of CO
2
were time aligned with the
engine power using the cross-correlation technique measurement of the emissions. Then the continuous
data were considered again and the data were recon-described as follows. Let the continuous data of
power be represented by P
i
and that of CO
2
be rep- structed using the DCM. The reconstructed data cor-
related better (R2 of 0.950) with the undispersed axleresented by E
j
. It is known that E lags P. If both P
and E are time aligned, the peaks and troughs of power than with the measured data (R2 of 0.890), as
can be seen in Fig. 8(a). Moreover, the correlation ofP align with those of E and hence the area under the
JER00406 © IMechE 2006 Int. J. Engine Res. Vol. 7

8. 444 M R Madireddy and N N Clark
Fig. 8 CO
2
reconstruction using the DCM: (a) parity plot; (b) continuous data
Table 1 R2 values for the three FTP runs examined tothe measured data with the dispersed power (R2 of
test the validity of the DCM0.978) was comparable with the correlation of recon-
structed (instantaneous) data with the undispersed Reconstructed
Correlating CO
2
versus CO
2
versus CO
2
versus(instantaneous) power (R2 of 0.950). A section of the
variables power dispersed power powerreconstruction is magnified in Fig. 8(b) and both the
delay and the dispersion of the data can be clearly Run 1 0.890 0.978 0.950
Run 2 0.899 0.974 0.957observed. Also, the reconstruction brought back the
Run 3 0.887 0.979 0.947
lost transient detail from the measured CO
2
data. All
the three FTP runs from the DDC series 60 engine
showed similar results and the correlation co-
5.4 The effect of sudden noise on the DCM
efficients between the CO
2
emissions and power are
listed in Table 1. In all the three cases, the recon- Sudden noise was added at the 120th second to the
diffused data. The amplitude of the added noise wasstructed CO
2
correlated better with the power than
the measured CO
2
did. the same as the amplitude of the signal itself at that
JER00406 © IMechE 2006Int. J. Engine Res. Vol. 7

9. 445Sequential inversion technique and differential coefficient approach
point. Then the original data were reconstructed caused fluctuation, the amplitude of which was over-
estimated as in the case of the reconstruction usingfrom the noisy diffused output. Because of the noise
added, the reconstructed response deviated from the the SIT.
accurate value around that interval, as shown in
Fig. 9. Similar to the SIT, it can be observed that the
6 CONCLUSIONSDCM also overestimated the sudden noise. The noise
affected the reconstruction not only at the time of
The true emission signal can be reconstructed fromoccurrence but also in the vicinity of the time interval
the analyser output by the use of the SIT, but the firstaround which the noise was added. Despite this
element of the dispersion function should be largeproblem, the real input is more correlated with the
enough in order to avoid numerical errors in thereconstructed input than with the diffused output.
reconstruction. Moreover, the other drawback while
using the SIT is that it requires continuous data start-5.5 The effect of continuous noise on the DCM
ing from the first time interval. Also, when the output
Continuous random noise was added to the diffused has a sudden noise or a continuous random noise,
output. The amplitude of the random noise was the reconstruction overestimated the noise.
obtained randomly, picking a number from −1, 0, On the other hand, the DCM of Ajtay and
and 1 ppm. The reconstruction was good, as shown Weilenmann [7] reconstructed the emission signal
in Fig. 10. It can also be noted that the random noise for any given realistic dispersion function. However,
when the output was superimposed with noise, the
predicted noise was higher than the added noise, as
was the case with the SIT. The real-time emissions
data from several runs were used to verify the validity
of the method and the reconstructed emissions
agreed well with the real emissions in all the con-
sidered cases. Hence the DCM, when coupled with
time-alignment techniques, can be a powerful tool
in reconstructing the emission signal from the output
measured by an analyser.
ACKNOWLEDGEMENTS
This research was conducted with support from the
US Department of Transportation (WV-26-7003), to
assist in future emissions data interpretation. The
present authors thank Mr Matt Spears of the EPA forFig. 9 The impact of sudden noise on the DCM
drawing their attention to reference [7], Gregory
Thompson, Mahesh Govindareddy, and Chamila
Tissera for providing the continuous CO
2
and fast
NO
x
data, and Jayendran Srinivasan for assistance
with the manuscript preparation.
REFERENCES
1 NTE test procedure and NTE limits,
www.dieselnet.com, www.dieselnet.com/standards/
us/hd.html, 31 August, 2005.
2 Koupal, J. Design and implementation of MOVES:
EPA’s new generation mobile source emission
model. In International Emission Inventory Con-
ference, 2003.
3 MOVES2004 energy and emission inputs. USEPA
draft report EPA420-P-05-003, Office of Transport-
Fig. 10 The impact of continuous noise on the DCM ation and Air Quality, March 2005.
JER00406 © IMechE 2006 Int. J. Engine Res. Vol. 7

10. 446 M R Madireddy and N N Clark
4 Weinblatt, H., Dulla, R. G., and Clark, N. N. sources. MS Thesis, Department of Mechanical and
Aerospace Engineering, West Virginia University,A vehicle activity based procedure for estimating
emissions of heavy duty vehicles. In Transportation Morgantown, West Virginia, USA, 2004.
9 Wayne, W. S., Corrigan, E., Clark, N. N., Gautam,Research Board Meeting, 2003.
5 Messer, J. T., Clark, N. N., and Lyons, D. W. M., Lyons, D. L., and Evans, J. Measuring diesel
emissions with a split exhaust configuration. SAEMeasurement delays and modal analysis for a
heavy-duty transportable emissions testing labora- paper 2001-01-1949, 2001.
10 Fast gas analyzers, available online at http:tory. SAE paper 950218, 1995.
6 Ganesan, B. and Clark, N. N. Relationships between //www.cambustion.com/instruments/index.html
(accessed 29 June, 2006).instantaneous and measured emissions in heavy
duty applications. SAE Trans., J. Fuels Lubricants, 11 Bell, L. H. Industrial noise control fundamentals and
applications, 1982, p. 77 (Marcel Dekker, New York).2001, 110, 1798–1806.
7 Ajtay, D. and Weilenmann, M. Compensation of the 12 Betts, J. A. Signal processing, modulation and noise,
1971 (Elsevier, New York).exhaust gas transport dynamics for accurate instan-
taneous emission measurements. Environ. Sci. 13 Ramamurthy, R., Clark, N. N., Atkinson, C. M., and
Lyons, D. W. Models for predicting transient heavy-Technol., 2004, 38, 5141–5148.
8 Nayak, G. A. Development of test method to measure duty vehicle emissions. SAE paper 982652, 1998.
in use emissions from stationary and portable diesel
JER00406 © IMechE 2006Int. J. Engine Res. Vol. 7