Dynamical fuzzy autocatalytic set of combustion process in circulating fluidized bed boiler using transition matrix / Hazwani Hashim - Hashim, Hazwani (2014)
A chemical reaction occurring during combustion process in circulating fluidized bed boiler (CFB) has been modeled using concept of Fuzzy Autocatalytic Set (FACS) of fuzzy graph type-3 whereby fifteen important species identified in the process are represented as nodes and catalytic relationship among the species are represented by fuzzy edges in the graph. A study has been conducted to explain dynamical behaviour of the species during the combustion process by using Perron-Frobenious eigenvector of adjacency matrix as an indicator for the concentration of species at certain time t. However the result reveals that by-product of the process is not in accordance to the real process. Thus, this study is carried out to investigate further the dynamical nature of the process using alternative matrix representation of FACS namely transition matrix of FACS. Here, specific transition matrix of FACS in CFB is developed and its basic properties which relates to Perron-Frobenius theorem are investigated. The development of an algorithm to calculate left Perron vector or steady state vector of the transition matrix is required in order to investigate dynamical behaviour of the system through graph dynamics of FACS. Thus it leads to the establishment of an improvised Graph Dynamics Algorithm which is used to assist the analysis of graph dynamics of FACS in CFB. The improvised GDAis able to reduce computer running time as compared to previous algorithm and able to deals with a sparse graph. Implementation of the algorithm to graphical FACS model of CFB shows that it is able to better explained the combustion process in terms of depletion species over time t and important species which denotes as by-product of the combustion is shown to be in accordance to the real process. Thus transition matrix of FACS of CFB is able to give better interpretation of combustion process in CFB as compared to adjacency matrix. It shows that result gathered from this study conformed to the result obtained from the previous study on the application of transition matrix of FACS in explaining clinical waste incineration process. Hence, this study provides enrichment to the explanation of FACS through different type of matrix representation in describing any dynamical system.