In the following, the measurement design for the identification of the global-local model struc- ture is presented. Since a stationary model structure is applied, stationary measurements are used for model training and validation. Thus, the significant measurement dynamics of emission meas- urements are avoided. For the collection of stationary measurements, closed loop controls for the engine speed, the air path states and the crank angle of 50% mass fraction burnt are utilised. Each measurement point is hold for 15 s such that the dynamic effects of the system and the measurement dynamics are decayed. The measurements are averaged over the last 1:5 s such that noise effects are reduced.
The choice of the holding time is based on the time constants of the system and the measurement dynamics. It is an upper bound with a safety distance such that all dynamic effects are decayed. After data collection, the measurement data is checked for outliers and if the holding time was chosen sufficiently long. This is a laborious task, which is mainly based on visual decision. It is also possible to analyse the data already at data collection automatically, which reduces the meas- urement time and increases the data quality. An example is the automatic detection of stationary states, instead of applying the upper bound holding time of 15 s. Such an automatic data collec- tion is one of the objectives of a current research project at the Institute of Automatic Control and Mechatronics [191].
Distribution of measurements
The distribution of the measurement data over the engine operation points is depicted in the left part of Fig. 3.5. The training data is placed in the local model centres, compare to Fig. 3.4, and the validation data in between. For each operation point, several data points are distributed over the local drivability space, as is illustrated in the right part of Fig. 3.5. The drivability space of the j -th local model is denoted by Dj and envelopes the reachable points. The drivability space
may be determined with separate experiments or, as applied here, incorporated in the measurement design. A rough description of Dj is derived from the semi-physical air path model, to determine
the measurement design in each engine operation point. Then the measurements are performed and the final drivability space Dj is defined by the convex hull surrounding the collected data points.
Other structures than the convex hull can also be applied for Dj, if the drivability space is not
describable by a convex hull.
Measurements are performed on several days in the summer and several days in the winter with varying environmental conditions. The identified models can therefore be regarded as non sensitive to changes in environmental conditions. The measurement data consists of 4584 data points for model training and 2262 data points for model validation.
The measured combustion outputs are NOx, soot, engine torque, crank angle of 50% mass fraction
burnt, opacity, exhaust gas temperature, exhaust gas pressure and further emissions, such as CO or HC. For the presented optimisations the emissions NOx and soot and the engine torque are of
~ ~ ~~
Figure 3.5: Distribution of the training and validation data over the engine operation points.
The training data is collected in the model centres and the validation data in between. In each operation point the local drivability space Dj is covered with measurements. The varied local
inputs are mair, p2i, 'mi and T2i. There are 4584 stationary data points collected for model
training and 2262 data points for model validation.
interest. NOxis measured by an NGK NOx-sensor and measurements for soot are taken by an AVL
Micro Soot sensor. Both are measured as concentrations and are transformed to an emission mass flow rate by eq. (3.12) and eq. (3.13) respectively. The torque is measured by a torque shaft sensor and the crank angle of 50% mass fraction by in-cylinder pressure sensors in combination with an indicating system.
For an excitation of the local model inputs, measurements are equally distributed over the local driv- ability spaces, see Fig. 3.6. The drivability spaces, shown by surrounding lines, are well covered. For the presented distribution of measurements, no a-priori information about the model structure is applied. Since polynomial models are identified, a D-optimal design, as described in Sect. 2.2.2, would be advantageous. However, a D-optimal design would favour a polynomial model structure, compared to other model structures. This would bias the comparison of model structures presented in Chap. 6, why a rastered input distribution is applied. But, if the task is to calibrate the combustion model, a D-optimal design should be applied such that the measurement design is adapted to the model structure.
The manipulated local input variables are the air mass per cycle mair, the intake pressure p2i, the
crank angle of 50% mass fraction burnt 'Q50 and the intake temperature T2i. These inputs are
adjusted by closed loop control with actuators for the guide vanes of the turbocharger st, for the high-pressure egr valve segr, for the low-pressure egr valve slp egr and the crank angle of main injection 'mi. Since no thermal conditiong system is available, the temperature T2i is excited by
the proportion of hot high-pressure egr and cold low-pressure egr. If exhaust gas is recirculated to the engine, this exhaust gas can either be taken from the low-pressure or the high-pressure egr system. Hence, the intake temperature T2i is colder if the egr is taken from the cold low-pressure
Figure 3.6:Two-dimensional projections of training data on the input dimensions for the op-
eration points: black: neng D 2000rpm, uinj D 15mm3=cyc and grey: neng D 2000rpm,
uinj D 20mm3=cyc. The drivability spaces of the local models are shown by the convex hulls
surrounding the measurements.
hot high-pressure to cold low-pressure egr exites only the temperature and not the gas composition, it is applied to manipulate the intake temperature.
Avoidance of extrapolation
With the collected measurement data, a drivability space Dj is defined in each engine operation
point by the convex hull surrounding the local measurement data. The drivability space Dj is then
applied to check if the local model operates in extrapolation region. Therefore, a local measure is defined for the j -th local model,
EMj.u/ D 8 < : 0 W u 2 Dj 1 W u 62 Dj: (3.20)
These local measures are summed up to a global measure by means of the weighting function ˆj,
EM.z; u/ D
M
X
j D1
ˆj.z/EMj.u/: (3.21)
The global extrapolation measure EM takes values between 0 and 1, depending on how many local models operate in extrapolation region and on their weighting functions ˆj. A threshold for
extrapolation can then be chosen between 0 and 1. The threshold depends on the extrapolation performances of the local models, which on the other hand depend on the applied model structure and the distances between the local models.
The applied polynomial models are well suited for interpolation, but polynomial models tend to infinity in extrapolation region. To ease these asymptotic effects, the inputs and outputs of the local models are limited by a bounding box to their minimum or maximum observed training values.
To enable some extrapolation, the bounding box of the inputs can be extended by ˙10%. Thus, extrapolation is enabled without the risk of unreasonable values.
Since the drivability spaces differ for different engine operation points, see Fig. 3.6, the risk of extrapolation depends on the distances of the local models. A dense distribution of local models lowers the risk of extrapolation, but requires a high calibration effort. Hence, the required number of local models depends on the variations of the drivability spaces over the engine operation points. It further depends on the variation of the physical behaviour from one local model to another. The number of local models is therefore a trade-off between the calibration effort on the one hand and the extrapolation risk and model accuracy on the other hand.
There are 21 local models identified over the engine operation points with the equidistant resolution of neng D 500rpm and uinj D 5mm3=cyc, see Fig. 3.4. Applying this distribution, the variation
of the drivability space from one operation point to another is acceptable, as can be seen in Fig. 3.6. The coverage in the mair dimension is improved by applying the air mass per cycle rather than
the measured air mass flow rate, see [203]. Model qualities for training and validation data are presented in the following section.