Determination of optimal measurement parameters from simulations

Increasingly complex mathematical models have become solvable by computer simulations. One particular class of such models are parameterized models, where the solutions depend on initial conditions determined by the parameters. For instance, these include the models of electromagnetic compatibility (EMC). In order to improve computational modelling, we have introduced a method for grouping the parameters and the corresponding solutions of the model into distinct classes [1, 2]. By solving the model with a large number of initially different cases, the overall behaviour of the model can be studied using a small number of representative parameters chosen from the classes obtained. The process of forming the classes is expected to be crucial in the choice of the measurement parameters. The classes can be visualised as patterns in the parameter space. Mathematically the patterns are the inverse images of a measuring function d, assigning real numbers to the solutions of the model. The overall behaviour of the model can be studied with the representatives of the classes if the function d correlates well with the measurements. The class formation process presented here follows from the partitioning of the image interval of the function d, but the partitioning can also be based on a more abstract algorithm [3]. Here, we consider different choices for measurement parameters, i.e., three choices of subintervals, the choice through distribution grouping and choice with principal component analysis. The image interval partitionings are the equal bin partitioning, the limiting value partitioning and the equal weight class partitioning. The parameters corresponding to physically different observations are determined by the grouping of the electric field amplitude histograms. Finally, we discuss the connections between principal component analysis and the grouping algorithm. What can be learned from the method and from the results of the case study? The choice of the parameters reduces the amount of configurations to be measured. Other choices than the PCA took into account the lowest resonance frequency 480 MHz, which is not surprising because a strong resonance is not statistically meaningful in the data set considered. However, from the shielding point of view it is very important to consider the cavity resonance. The first row contains three times the same frequency of 164.6 MHz, because it was the first parameter of our ordered input. Because it represents the typical behaviour of an empty cavity without resonating effects, it is a good choice. In the threshold value partitioning, we observed that the suitable way is simply to choose the values of the parameters randomly below and above the first cavity resonance frequency. The two other interval partitionings are more obvious. Finally, it should noted that a similar procedure can be applied to any other measurement and simulation problem, where there is the need to reduce the amount of measurements to be carried out.