In general, engine mapping and calibration is the process of defining the engine calibration data, which is embedded into the ECU in order to control engine actuators. As a result of modern engines using more technologies, exploring the whole space of control parameters by using traditional one factor at a time experiment-based calibration process has became very expensive. Therefore, mathematical and statistical techniques are attractive for finding optimal solutions that produce low emissions and better engine performance, by using Design of Experiments (DoE), statistical modelling, and optimisation methods.
A typical model based engine calibration approach for steady-state engine tests is illustrated in Figure 3.11 (Sampson, 2010), and has been commonly used both for gasoline and Diesel engines, and can be summarised as follows:
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1. Design of Experiment (DoE): is a more efficient way of exploring the design space by planning engine tests and aiming to reduce the cost of engine testing;
2. Engine Test & Data Collection: carry out the engine tests and collect the
engine testing data according to the experiment design;
3. Engine Responses Modelling: based on the engine testing data, fit
empirical mathematical models to predict the engine responses;
4. Optimisation & Engine Control Map Calibration: the engine response models are used for the optimisation to search for an optimal solution of the engine actuator settings; the aim is to fill the engine maps with local optimal engine actuator settings and to smooth the actuator transitions map between these settings;
5. Implementation: embed the calibrated engine control map into ECU and validate at system level (engine and vehicle installation).
Figure 3.11 Illustration of Model Based Calibration Process (Sampson, 2010)
Steady-state model based calibration refers to the steady-state engine tests, which are to measure and collect engine response data while the engine is running at a constant engine load and speed condition. Therefore, this type of engine calibration
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approach is called steady-state model based calibration. Engine response models based on this type of engine test data can predict the engine response only at specified engine load-speed conditions. Such engine response models are commonly called “local models” (Roudenko et al., 2002). Optimisation with this type of engine model would normally be carried out individually at different engine load- speed conditions. Alternatively, the total objective formulation over the full range of engine load and speed conditions has to be integrated by summing all the weighted engine local models value (Hafner and Isermann, 2001 , Roudenko et al., 2002). Optimisation based on steady state engine models produces an optimal solution for a set of engine actuator settings for different engine load and speed conditions. With this set of optimal solutions, the engine control map is filled across the full range of engine load speed space. This steady-state model based engine calibration approach has been taken up by most commercial software tool packs, such as AVL CAMEO (Stuhler et al., 2002), MBC toolbox in MATLAB software environment (Styron, 2008) and so on. In the literature, a large number of applications of Diesel engine calibration are based on the steady-state engine calibration (Alonso et al., 2007 , Baert et al., 1999 , Brooks and Lumsden, 2005 , Haines et al., 2000 , Jankovic and Magner, 2004 , Jankovic and Magner, 2006 , Roudenko et al., 2002 , Sampson, 2004).
From another point of view, the steady-state engine calibration for a gasoline engine typically requires more than 30 different engine load/speed points in order to populate the look-up table over the range of engine load-speed (Sheridan, 2004). Comparing the gasoline and Diesel engine calibration processes, the gasoline engine calibration will require more expensive engine testing and more model fitting and optimisation to be carried out. In order to reduce the cost of engine testing and
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modelling, and to characterise the engine responses on the entire engine operating condition, a global engine modelling approach has been introduced (Alonso et al., 2007 , Atkinson et al., 2008 , Atkinson et al., 1998 , Seabrook, 2000). The global engine response model is a function of all engine control variables and parameters including engine load and speed. The idea of the global engine response modelling approach is to represent the engine behaviour over the whole engine operating range with a single global engine model rather than using a number of local engine models. Global engine response models can reduce engine test cost by producing a Design of Experiments (DoE), which involves engine load and speed as design variables. A global engine model has the ability of predicting the engine response across the full range of engine load speed space (Atkinson and Mott, 2005).
Research has been carried out to demonstrate and compare the use of local steady- state models and the use of global models (Hafner and Isermann, 2001 , Roudenko et al., 2002 , Stuhler et al., 2002 , Rask and Sellnau, 2004). To find the optimal solution of engine actuator settings, optimisation is carried out at each of the engine load/speed points according to the look-up table. The use of steady-state engine local models requires engine tests and statistical modelling at each of these engine load/speed points. Whereas, the use of global engine models reduces engine testing effort by carrying out DoE that involves all engine controls and engine parameters (speed and load). The optimisation problem at each of the engine load/speed points is formulated as a single optimisation problem, in Equation 3.1 (Hafner and Isermann, 2001): Minimise:
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Subject to:
Equation3.1 is the optimisation objective defined as a weighted sum of NOx, “Opacity” (a measure of smoke or particulates emissions), and “fuel” consumption. The control
variables need to be within the range defined by LB (Lower Bounds) and UB
(Upper Bounds), and other engine responses are defined as nonlinear constraints within the user defined limit. At each of the engine load/speed points, the optimal solution of controls is generated and entered into the look-up table.
Vossoughi and Rezazadeh (Vossoughi and Rezazadeh, 2005 , Vossoughi and Rezazadeh, 2004) (2004; 2005) applied a similar process with the global engine models. In their research, the optimisation problem was formulated as a multi- objective problem locally at each engine load/speed point. The optimisation at each engine operating point is to minimise both fuel consumption and the weighted sum of emissions (e.g. NOx, Opacity, HC and CO). Evolutionary Genetic Algorithms (GAs) have been tested to solve the multi-objective optimisation problem. Wu et al (Wu et al., 2006) also introduced an engine calibration approach to maximise torque output and minimise the fuel consumption and NOx emissions. In the optimisation process, an attempt to produce a smooth engine control map has been made by adding a penalty function (related to engine stability conditions) to the objective function.
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