Cell Mapping Model for Complex Systems with Statistical Trajectory Based on Data Mining

This paper proposes a new type of modeling framework for complex systems. This kind of systems has the characteristics: it is difficult to establish the mechanism model and its dynamics obey the statistical law. Firstly, in order to extract the statistical attributes, an iterative self-organizing data analysis techniques algorithm (ISODATA) of data mining is used to separate process data into a number of classes. Based on these classes, a pattern class space in which each class is taken as an element is established. Next, to describe the system dynamic with statistical law, a pattern class variable is defined in the pattern class space. To further solve the incalculable problem of the pattern class variable, a cell space is introduced where each pattern class variable is measured by cell centers. Based on this measure, an improved controlled autoregressive moving average (CARMA) model described by the pattern class variable is obtained, and model parameters are identified by an improved quantum-behaved particle swarm optimization (IQPSO) algorithm. The attractive of the algorithm lies in enhancing the ability of the global development and local exploration. Based on the model, the corresponding cell mapping model is derived by the state space representation, which avoid the expansion of categories. Then, the global performance of the pattern class space is analyzed via cell mappings. Finally, a simulation in the dynamic trajectory of a sintering process is given to demonstrate the feasibility of the proposed approach.