Seite - 40 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3. ModelingMicrowaveHeating White-boxmodeling The white-box modeling is the opposite of black-box modeling. In a white-box system, all properties and details of the system are well defined by first principles, and system parameters are also perfectly known [JHB+95]. Although white-box modeling is theoretically clear, it is rarely used to solve real problems. In many cases the white-box model is too complicated or even impossible to implement and solve withinagiventime. Grey-boxmodeling Grey-box modeling is a combination of the black-box and the white- box modeling, where not all but a certain part of the physical insight isavailable [JHB+95]. Themodelstructurecanbedirectlydetermined by prior knowledge and physical insight, but many system param- eters still remain unknown. These unknown parameters have to be estimated using experimental data via either online or offline system identification (SID) methods. In many cases, the grey-box model is sufficiently accurate to interpret the relationship between inputs and outputsof thesystem,withoutgoing intounneededdetails. A pure white-box system seldom exists in practice, therefore for real problems, the black-box modeling and the grey-box modeling are mainly used. Both of them have their advantages and disadvantages. Black-box modeling is essentially more flexible and it can be applied to all kinds of systems. In theory, black-box modeling can reach arbi- trarily high accuracy given an adequate amount of experimental data [JHB+95]. Nootherknowledgeoradditionalassumptionsareneeded. But on the other side, the performance of a black-box model depends on many factors, which means the model itself has to be tuned and optimizedtogetanacceptableperformance. For instance, as one of the most popular black-box modeling meth- ods, theneuralnetwork(NN)methodhasbeenimplementedinmany areas. The performance of a neural network is determined by sev- eral components, such as the number of hidden layers or the num- ber of nodes in each hidden layers. There is no sophisticated guide how to choose these elements. All elements have to be compared and 40