Determining the Model Order of Nonlinear Input-Output Systems by Fuzzy Clustering

Selecting the order of an input-output model of a dynamical system is a key step toward the goal of system identification. By determining the smallest regression vector dimension that allows accurate prediction of the output, the false nearest neighbors algorithm (FNN) is a useful tool for linear and also for nonlinear systems. The one parameter that needs to be determined before performing FNN is the threshold constant that is used to compute the percentage of false neighbors. For this purpose heuristic rules can be followed. However, for nonlinear systems choosing a suitable threshold is extremely important, the optimal choice of this parameter will depend on the system. While this advanced FNN uses nonlinear inputoutput data based models, the computational effort of the method increases along with the number of data and the dimension of the model. To increase the efficiency of the method this paper proposes the application of a fuzzy clustering algorithm. The advantage of the generated solutions is that it remains in the horizon of the data, hence there is no need to apply nonlinear model identification tools. The efficiency of the algorithm is supported by a data driven identification of a polymerization reactor.