11 Results

In this chapter, the results achieved with CNMccontrol-oriented Cluster-based Network Modeling shall be presented and assessed. First, in section 12, the tracking algorithm is evaluated by showing the outcome for 3 different dynamical model configurations . Second, in section 13, statements about the performance of modeling the Centroid Position Evolution (CPE) are made . They are supported with some representative outputs. Third, in section 14 the two decomposition methods are compared in terms of computational time and prediction quality in subsection 14.0.1 and 14.0.2, respectively . Fourth, it has been mentioned that 3 different regressors for representing the $Q / T$ tensor are available. Their rating is given in section 15. Finally, the CNMccontrol-oriented Cluster-based Network Modeling predicted trajectories for different models shall be displayed and evaluated in section 16.

For assessing the performance of CNMccontrol-oriented Cluster-based Network Modeling some dynamical model with a specific configuration will be used many times. In order not to repeat them too often, they will be defined in the following.

Model configurations

The first model configuration is denoted as SLS, which stands for mall Lorenz ystem . It is the Lorenz system described with the sets of equations 7.1 and the number of centroids is $K = 10$ . Furthermore, the model was trained with ${\vec{β}}_{t r} = [β_{0} = 28; β_{e n d} = 33], n_{β, t r} = 7$ , where the training model parameter values ${\vec{β}}_{t r}$ are chosen to start from $β_{0} = 28$ and end at $β_{e n d} = 33$ , where the total number of linearly distributed model parameter values is $n_{β, t r} = 7$ .

The second model is referred to as LS20. It is also a Lorenz system 7.1, but with a higher number of centroids $K = 20$ and the following model configuration: ${\vec{β}}_{t r} = [β_{0} = 24.75; β_{e n d} = 53.75], n_{β, t r} = 60$ .

The third model is designated as FW15. It is based on the Four Wing set of equations 7.4 and an illustrative trajectory is given in figure 11.1 . The number of centroids is $K = 15$ and it is constructed with the following configuration ${\vec{β}}_{t r} = [β_{0} = 8; β_{e n d} = 11], n_{β, t r} = 13$ .

Figure 11.1— *FW15* 7.4 trajectory for $β = 8$