Cellular dynamic models with built-in causal relation functions

In this paper a further development of the cause-effect relation (CER) dynamic models is proposed, namely the cellular dynamic (CD) models. These are a special incremental type of models that use a preliminary fixed number of dynamic cells. Each dynamic cell is a given by a Gaussian CER function and serves as a kind of hypothesis for the unknown process dynamics. Then the overall dynamic behavior is represented as a weighted sum of all the elementary dynamics of the cells. A modified version of the least squares algorithm is proposed for identifying the CD model under the assumption for predetermined parameters of all dynamic cells. Once identified, the CD models are used for simulation in the same way, as the usual CER dynamic models. The proposed cellular dynamic models show better robustness in identification against noisy input-output data and have much better interpretability, compared to the previously studied CER models. The final result of the identification of the CD models is easily converted into a meaningful and often logically interpretable CER function that can be further used for a human-like solution of decision making problems. Extensive simulations on test examples are used as a proof of the robustness and good interpretability of the cellular dynamic models. Finally a special recursive computation scheme for calculation of the inverse dynamics of dynamic processes with a single input, represented by CER functions is proposed and illustrated. It can be used for solving fault diagnosis and other decision-making problems in dynamic systems.