Behaviour-Based Engine Models

The increase of control demanding technologies, like variable valve timing, advance ignition management, variable exhaust gas recirculation, variable geometry turbine, and many more, has a great impact on the complexity of the engine control process. However, behaviour-based engine models can neglect the complexity of a system by simply hiding the relation of inputs and outputs within their structure. Look-up tables, response surface methodology, and artificial neural networks are contained within this modelling technique.

3.2.1.1 Look-up Tables

Several inputs of the internal combustion engine can be represented in multidimensional look-up tables or maps. The main drawback of look-up tables in engine modelling is the exponential growth of the data points with increasing number of inputs. Therefore, in terms of practicality, a look-up table engine model usually uses one- or two-dimensional input space [127]. As illustrated in Figure 3.2, a one-dimensional look-up table includes one output that is depended on one input, whereas a two-dimensional table will consist of a set of data points within its grid with each data point having two inputs.

An estimation parameter is employed to link the data points together. The accuracy of the model strongly depends on the number of points on the grid.

38

Figure 3.2: One-dimensional look-up table for one input at the left and two-dimensional look-up table for two inputs at the right

3.2.1.2 Response Surface Methodology

Response Surface Methodology (RSM) is a set of statistical techniques developed for solving black-box-based optimisation problems [130]. Design of experiments are created to determine the relationship between the design variables (inputs) and the responses (outputs) of the simulation. The method relies on the fit of empirical equations to identify the key inputs of the design and analyse the effect of the inputs on the objective function to optimise an output or a set of outputs [131]. The choice of efficient experimental designs can make the application of RSM reduce the cost of expensive analysis methods, such as finite element or computational fluid dynamics simulation [132].

Figure 3.3: Profile example of surface response generated from a RBF-model with three variables (input A’, B’, C’) in the optimisation of response A’

39

Due to the huge advantage over the classical one-factor-a-time optimisation analysis, the RSM is largely used for generating a large amount of information from a small number of experiments. However, because of the relatively few data sets required, the real global optimum might be missed in the search if the experiment is not able to capture a sufficient design space [133]. It might be the case that the response surface developed is invalid for regions other than the studied ranges of factors. It should also be noted that the main limitation of the method is that RSM is a black-box approach, hence it is very difficult to estimate the accuracy of the approximation [134].

3.2.1.3 Artificial Neural Network

A very powerful method among behaviour-based engine modelling is the artificial neural network technique. Inspired by the organisation of neurons in the brain, the major feature of this type of engine model is its ability to learn how to perform a particular task [135, 136]. The artificial neural networks will then extrapolate the frame between input and output data [137]. This method can be used to distinguish engine data that is similar to the examples given during the training stage. Figure 3.4 illustrates the simplified architecture of an artificial neural network engine model. Within the black-box there are layers of neurons, which are basically the data computational elements of the system. Typically, there is one input layer and one output layer of neurons;

however intermediate layers can be introduced.

40

Figure 3.4: General architecture of an artificial neural network engine model Generally, neurons receive inputs, and process them to obtain an output.

Hence, the neurons in the output layer will gather information from all the neurons in the intermediate layer or directly from the input layer of neurons if there are only two layers. Each data sent to the neurons in the following layer have an individual weight factor that will determine the outcome being transferred to the next set of neurons. The data flow inside the network follows only one feed-forward direction; input data are processed in the input layer’s neurons and the results of the operation are passed to the neurons of the intermediate or output layer.

The simplicity of an artificial neural network has been used for predicting engine performance, such as torque, power and specific fuel consumption [138, 139, 140, 141]. Wu and Gisca [142, 143] adopted artificial neural network models for defining the functioning parameters of the internal combustion engine such as in-cylinder pressure and mixture strength. A neural network based solution is efficient in terms of time; however, great knowledge in the design selection of the network is needed. Furthermore, because of its black-box nature, artificial neural networks are prone to over-fitting data with several consequences, such as becoming excessively

41

complex and with poor predictive performance. Additionally, the training outcome of the network will depend crucially on the choice of the inputs.