ity (high COV(IMEP)). It is demonstrated that the detec- tion of these categories can result in faster determination. (prediction) of high variability compared to only ...
2004-01-0522
An ion current algorithm for fast determination of high combustion variability Stefan Byttner, Ulf Holmberg and Nicholas Wickstr o¨ m Intelligent Systems Laboratory, IDE Halmstad University S-301 18 Halmstad SWEDEN Abstract It is desirable for an engine control system to maintain a stable combustion. A high combustion variability (typically measured by the relative variations in produced work, COV(IMEP)) can indicate the use of too much EGR or a too lean air-fuel mixture, which results in less engine efficiency (in terms of fuel and emissions) and reduced driveability. The coefficient of variation (COV) of the ion current integral has previously been shown in several papers to be correlated to the coefficient of variation of IMEP for various disturbances (e.g. AFR, EGR and fuel timing). This paper presents a cycle-to-cycle ion current based method of estimating the approximate category of IMEP (either normal burn, slow burn, partial burn or misfire) for the case of lean air-fuel ratio. The rate of appearance of the partial burn and misfire categories is then shown to be well correlated with the onset of high combustion variability (high COV(IMEP)). It is demonstrated that the detection of these categories can result in faster determination (prediction) of high variability compared to only using the COV(Ion integral).
1
INTRODUCTION
Exhaust gas recirculation (EGR) is today a standard method for controlling the emissions of nitrogen oxides (NO x ) in automobiles. The incoming air-fuel mixture is diluted with inert exhaust gases which results in lower combustion temperature which reduces the formation of NO x . Also, recirculating exhaust gas to the intake manifold increases the manifold pressure and results in decreased pumping losses. The problem is that the EGR dilution leads to slower burn rate which results in more incomplete burn
cycles, more misfires, and a higher variability in output torque. This can result in reduced drivability and higher hydrocarbon (HC) emissions. The EGR flow in modern vehicles is typically controlled by using an experimentally tuned look-up table using e.g. engine speed and manifold pressure as inputs. The EGR valve is then adjusted in a closed loop fashion until the desired flow is achieved. The control is however essentially open loop because no check is made if the actual EGR ratio inside the cylinders corresponds to the desired one (the total EGR is also a sum of the residual gases and external EGR and does not necessarily match a value estimated from external EGR only). There is currently no good way of determining exactly how much exhaust gas that is being recirculated. In a laboratory setting it is possible to sample the cylinder gas in a bag [6] or measure the hydrocarbon content in the gas [4]. These techniques are however unfeasible for online measurement in a production car. Because of these difficulties in measuring the actual amount of EGR, automobile manufacturers have an upper limit on how much EGR they will be using in a given vehicle. This means that a more defensive approach than is necessary is taken to insure that the vehicle will not have problems igniting the air-fuel mixture. Another popular method is the lean burn concept where the intake charge is intently mixed with excess amounts of air. The lean burn strategy can result in significantly reduced fuel consumption and CO2 emissions, but there is also a risk of inducing a too high combustion variability resulting in e.g. producing non burning cycles (misfires), shifting of the combustion into the expansion phase and an increase of HC emissions. The approach adopted in this paper is to estimate the variation in the produced work from the engine (the co1
Corr. coef. 0.94887
Corr. coef. 0.92074
0
0
COV(Ion integral)
10
COV(Ion integral)
10
−1
10
−1
−2
10
1
−1
10
0
10 COV(IMEP)
1
Corr. coef. −0.13528
1
Both the ion current and the cylinder pressure are sampled at a resolution of one crank angle degree. The ion current integral is defined as Z θ2 Ion integral = I(θ)dθ (1) θ1
where I(θ) is the measured ion current over crank angle θ and the limits θ1 and θ2 are chosen so that the ignition related disturbance (coil ringing) of the ion current is excluded from the integral. The limit θ 2 is chosen so that all ionization has ended at this angle (no matter what ignition timing has been used) and the limit θ 1 is calculated as θ1 = τ +
8∗N 1500
(2)
where N is the engine speed in RPM and τ is the time of ignition in crank angle degrees relative the top dead center (TDC). This expression was taken from [3] after verification that it matched our engine well. The coefficient of variation for the indicated mean effective pressure, COV(IMEP), is a commonly accepted variable for combustion stability [5], and is defined as COV(IMEP) =
σ(IMEP) µ(IMEP)
(3)
where σ and µ are the standard deviation and the mean value, respectively, over a number of consecutive combustion cycles. Measurements have been made using a SAAB 9000 during normal(steady state) driving on a Swedish highway. The engine was a 2.3 litre low pressure turbo engine (B234E MY96) with cylinder one equipped with a Kistler 6121 cylinder pressure sensor and a NGK UEGO sensor. The measured data is only for a single cylinder at an engine speed of 1500 and 2000 RPM. The intake
2
10 std(IMEP)
3
10
Corr. coef. −0.080353
std(Ion integral)
10
0
ION CURRENT MEASUREMENTS
1
10
10
10 −2 10
2
10
10
std(Ion integral)
efficient of variation of IMEP (COV(IMEP)) from the ion current. This has already been suggested in previous SAE publications [1][2], but the approach of using the COV(Ion integral) uses many combustion cycles to produce an estimate (typically a hundred cycles or more). The algorithm is based on that partial burn (and misfire) combustion cycles are (almost) only present when there is a high combustion variability. It is therefor possible to detect high combustion variability by detecting these cycles in an early stage (i.e. without measuring a complete block of a hundred combustion cycles or more).
0
−1
10
0
10 COV(IMEP)
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10 1 10
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10 std(IMEP)
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Figure 1: The coefficient of variation and standard deviation for the ion integral and IMEP. An engine speed of 1500 and 2000 RPM and the 5:th gear was used. There were a total of 28000 combustion cycles (14000 cycles of each engine speed). Ignition is set at 30 CAD BTDC (approximately MBT timing). Each point is calculated over 100 combustion cycles. charge contained excess air as dilution (which affects the ion current in the same way as exhaust gas recirculation), the normalized air-fuel ratio (λ) was varied from 1.0 to 1.6 in uniform steps of 0.1. Ignition was fixed at 30 CAD BTDC (approximately MBT timing).
3 EXPERIMENTAL RESULTS As previously described, COV(IMEP) is a standard measure of combustion stability. This section will first demonstrate that it is possible to estimate this variable by computing the COV(Ion integral). It will then be shown how a cycle-to-cycle based classification can be used to detect high combustion variability. Figure 1 shows the correlation between the standard deviation (std) and coefficient of variation (COV) for the ion integral and IMEP. The std(Ion integral) has virtually no correlation to the std(IMEP). The COV(Ion integral) has a good correlation to both COV(IMEP) and std(IMEP). Figure 2 shows the mean ion current versus the std(IMEP) and COV(IMEP). The correlation is good but not as good as when using the COV(Ion integral) (Figure 1).
Cycle-to-cycle based classification Experiments have indicated that detecting if e.g. a misfire has occured (a cycle-to-cycle level classification), can 2
Corr. coef. 0.83131
0
10 1/mean(Ion integral)
1/mean(Ion integral)
Corr. coef. 0.78077
0
10
−1
10
−2
10
−1
10
−2
−2
10
−1
10
0
10 COV(IMEP)
1
10
10
1
10
2
10 std(IMEP)
3
10
Corr. coef. 0.77979
2
mean(Ion integral)
10
1
10
Erate =
0
10 2 10
3
10 mean(IMEP)
4
10
Avg. IMEP > 85% 46-85% < 46% 30%
Table 1 Cycle classification relative the average IMEP at a specific operating point and the corresponding actual EGR flow [5].
be used for making an estimate of the approximate region of COV(IMEP). Figure 4 shows the frequency (or rate) of different types of burn cycles (defined in Table 1) as a function of COV(IMEP). The figure shows that partial burn and misfire cycles only occur at high COV(IMEP) (high means > 0.1). This indicates that by detecting a partial burn (or misfire) there is a high probability that the engine is operated in a region of high COV(IMEP). Ion current measurements contain information about these four categories as is show in Figure 3. The figure shows an average of 1000 ion current measurements for each of the 4 different categories. Both the chemical and thermal ionization peak is only clearly visible for normal combustion, both slow and partial burn ion curves typically only contain a single peak. Misfire combustion cycles typically has no or very little ionization. When designing the classification methods that are pre-
where K is the number of categories (in this case 4) and Cij is the confusion matrix which is defined as Cij = Nij /Ntotal
(5)
where Nij is the number of samples in category i that is classified to category j and Ntotal is the total number of samples of each category. The numbers in the matrix is then to be interpreted as the relative percentage of correct and incorrect classification of each category. Both classifiers has been designed using a data set from the 5:th gear that contains an equal amount of data for each category (1941 combustion cycles of each category). Nearest neighbors method The 1-nearest neighbor classifier uses the mean ion current vector (a 51-dimensional vector) for each category (requiring a storage space of 4·51 = 204 memory locations). The vectors are the mean ion currents for each of the four categories in the training data set. A new measurement is classified into belonging one of these vectors (categories) by computing the euclidian distance. The category is chosen as the category associated with the closest vector (closeness means the minimum euclidian distance). The performance is shown in Table 2. Artifical neural network method The artificial neural network (ANN) is of the multi-layer perceptron type with a 1-hidden layer network, 10 hidden nodes and 3 output nodes (requiring a storage space of 51·10 + 10 + 10·3 + 3 = 553 memory locations). The hidden nodes uses hyperbolic tangent activation functions and the output nodes uses linear activation functions. The output signal was coded with a so-called thermometer coding [7] which helps the network understand that the output signal (category of IMEP) is defined in an ”ordered” fashion. Table 3 shows the result of the neural network. 3
0.8
0.7
Model output Normal burn Slow burn Partial burn Misfire
Normal burn
0.6
Ion Current [V]
0.5
N 78 13 0 0
S 22 86 16 0
P 0 1 57 1
M 0 0 27 99
Slow burn
0.4
Partial burn 0.3
Misfire
0.2
0.1
0 −15
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5 10 15 Crank Angle ATDC [deg]
20
25
30
35
Table 3 Confusion matrix for the neural network classifier using data from the 5:th gear, non bold-face is the model output, bold-face is the true category. The numbers in the matrix is the percentage of where the cycles for each (true) category has been placed. Mean error rate is 20%.
Figure 3: The mean ion current for the 4 categories defined in Table 1. 0
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COV(IMEP)
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40 60 80 Percent of normal burn
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COV(IMEP)
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40 60 80 Percent of partial burn
100
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Figure 4: Rate of appearance for 4 different categories in 100 combustion cycle long blocks as a function of COV(IMEP). The categories are defined in Table 1. Model output Normal burn Slow burn Partial burn Misfire
N 82 27 0 0
S 17 68 6 0
P 1 5 51 0
M 0 0 43 100
Table 2 Confusion matrix for the 1-nearest neighbor classifier using data from the 5:th gear, non boldface is the model output, bold-face is the true category. Mean error rate is 25%.
of 10% as the threshold limit was motivated partly by that the vehicle had a noticable decrease in response and an increased level of vibration when COV(IMEP) was well above 10%. References in the literature can also be found, in [5] the coupling between driveability and COV(IMEP) is described as ”...vehicle driveability problems usually result when COV(IMEP) exceeds about 10 percent”. A separate data set with 33200 combustion cycles was used for comparing the COV(Ion integral) method with the classification method (using the neural network). Data was divided into 332 blocks each consisting of 100 combustion cycles. The COV(IMEP) was computed for each block (using all of the 100 combustion cycles in each block), approximately 55% of the blocks had a COV(IMEP) greater than 10%. The methods uses only a fraction of the combustion cycles in each block for making the prediction, the first 5 and the first 50 combustion cycles respectively. The prediction error is defined as Epred =
NF A + NM A 2
where NF A is the number of false alarms (the method predicts COV(IMEP) above 10% when true value is below) and NM A is the number of missing alarms (the method predicts COV(IMEP) to be below 10% when the true value is above). The COV(Ion integral) method computes an estimate of COV(IMEP) by using a linear model COV(IMEP) = 0.69 · COV(IonIntegral) − 0.08
Comparison of COV(Ion integral) and the classification method The two methods are compared by letting them predict if the COV(IMEP) value is above or below 10%. The choice
(6)
(7)
The classification method computes the COV(IMEP) estimate in a simple way; counting the number of cycles that are classified as either misfire or partial burn. If the number of detected misfire or partial burn cycles exceed or equals a certain threshold the block is predicted to have 4
N=5 N=50
COV(Ion) 13.3% 5.1%
ANN 5.9% 4.7%
Table 4 Prediction error (defined in eq. 6) in percent of the total test data set (332 blocks) when comparing the COV(Ion integral) and the classification (ANN) based approach. N denotes the number of cycles that were used to produce a prediction.
a COV(IMEP) greater than 10%. The 5-cycle predictions have a threshold of 1, the 50-cycle predictions a threshold of 4 (these values have not been optimized). Table 4 shows the performance on the test data set. The table shows that if the number of cycles that are used for the prediction is small the COV(Ion integral) method misclassifies about 13% of the test data (the 332 blocks), while the neural network based classifier has an error of about 6%. When the number of cycles that are used for the prediction increases the two methods result in similar performance. The classification based approach does however have approximately the same performance when using only 5 combustion cycles as when the COV(Ion integral) method uses 50 combustion cycles. Increasing the threshold limit to e.g. COV(IMEP)=15% results in slightly better performance for the classification approach, but similar performance for the COV(Ion integral) method. A higher threshold means the frequency of partial burn and misfire cycles is higher, and thus more likely to be detected (and appear in the small prediction window).
4
CONCLUSION
The use of exhaust gas recycling is today a standard method for controlling NOx emissions and reducing fuel consumption. There is a possibility to make faster estimation of combustion variability by detecting partial burn and misfire combustion cycles in an early stage. The average error for the two classifiers is 25% for the 1-nearest neighbor method and 20% for the neural network. However, for the neural network method, only 1% of the slow burn cycles and none of the normal burn cycles were classified as partial burn. The low error rate makes it possible to detect the high region of variability if significantly more than 1% of the combustion cycles are classified as either partial burn or misfire. Many of the partial burn cycles (16%) would however go undetected.
There is also an additional benefit with implementing the classification approach, the cycle-to-cycle based classifications can be used in e.g. a diagnostics system (both on-line and off-line diagnostics). The COV(Ion integral) method was compared to the classification based approach and it was found that if only a small number of measurements were used (5 combustion cycles), the classification based approach results in less than half the number of errors compared to the COV(Ion integral) method. Improved estimation accuracy can also be expected if ion measurements from all four cylinders are used to form a joint estimate of combustion varibility (at least for a disturbance caused by external EGR since it can be assumed that the exhaust gases are distributed equally to each cylinder). Acknowledgements This research was supported by the Swedish National Energy Administration (STEM).
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