Component identification by Design-of-Experiments

The data-based pump model is made up of an n-dimensional hyper matrix for n input signals that describe specific sensitivities. Model input considers several boundary conditions. The high pressure pump characteristics are calculated out of a DoE model that is set up in advance. The tool used here is called ASCMO (3) developed by ETAS Corporation. It will be commercially available in 2012. ASCMO can be used in a broad range of applications. It enables the user to characterize complex unknown systems. The DoE method is much more efficient with respect to measuring effort compared to a factorial testing plan based approach. Starting out with a tool prescribed test plan automated test bench software triggers a number of experiments that train the model. Several test bench input channels allow simulation of boundary conditions in order to fill the model’s hyper matrix. The involved parameters for the high pressure pump are the fuel temperature, the rail pressure, the electrical FMU current, the FMU current step and the engine speed. Other influences like pump inflow pressure or pressure within the pump backflow have been neglected in the regarded scenario however they are straightforward to implement. Finally the ASCMO package provides a post processing algorithm that allows a comfortable access to the hyper matrix in order to gain a model output for a certain set of input values. Interface functions that allow a Matlab based control are available. The model can be exported for further analysis with Matlab. Its output here consists of a scalar value representing the pump delivery quantity.

A sensitivity or "intersection plot" (ISP) of the pump model can be seen in Fig. 5 for several input parameters. Each plot shows one-dimensional sensitivities at a specific operation point with the other parameters kept constant (the dashed line indicates this point in the hyper matrix). As expected the model output — i. e. the pump flow

— is dominated by the electrical current that varies the FMU cross section
mechanically via the solenoid. Fluid temperature as well as rail pressure just show a minor effect on the macroscopic scale. Sensitivity towards engine speed is significant in an area of low values only. A fifth figure shows a value equivalent to hysteresis.

Component identification by Design-of-Experiments

Engine speed temperature rail pressure FMU current delta current Fig. 5: Intersection plot of the high pressure pump model

The left hand side of Fig. 6 gives a first hint towards model quality. However deviations do not only reflect model deficiencies but also measurement uncertainties. The quality of the data logging procedure during the DoE training process plays a crucial part. Basically the modelling effort is drastically reduced when using DoE (compared to a physical modelling approach) while the measuring part has to be done very accurately including the corresponding effort. Here the model quality is tested against the measuring points that were used during its synthesis. Since the points represent training data it is hardly amazing that they show only small errors. Another model check can be seen on the right hand side of Fig. 6. Using the so-called "leave-one-out" technique the spread of model errors increases. This method investigates successively the reproduction quality of a measured operating point that is not part of the model synthesis any more i. e. that is left out. Since a leave-one-out point is not part of the training data anymore model tolerances increase for this test.


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Fig. 6: Model validation using training points

Further model error increase can be noticed in Fig. 7. The testing points regarded here have not been part of the model synthesis so they might be regarded as "true" test points. The figure shows the comparison of model output und test bench measurement for several engine speeds, rail pressures and temperatures. It can be seen that the model shows a slight waviness in the range of maximum pump

Delivery. A possible countermeasure for that problem is the usage of additional training points. However, this range is not relevant for the investigation discussed here since no valid engine operation points (consisting of engine speed and load) exist in that area. Moreover temperature impact on fuel delivery is marginally overestimated. It must be noted that model quality also depends on the parameter choice. The used temperature has to be relevant to the model output. The temperature chosen here is measured at the inflow of the pump. The largest errors are found in an area of maximum pump delivery where the model tends to oscillate thus producing additional error terms. It becomes clear that this area is not relevant if "real" engine operation points are taken into account (see Fig. 9).

Component identification by Design-of-Experiments


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