Research On Parameter Identifiability Of DAE Systems

Dynamic systems described by differential algebraic equations (DAEs) have been widely studied during the past decades. DAE systems are used to describe many systems in science and engineering, such as electronic circuit systems, chemical engineering systems and constrained mechanical systems. The unknown parameter identifiability of DAE systems are some of the important topics in the field of system engineering. Identifying the unknown parameters of the models and matching the real systems are essential for model-based control and optimization of real systems. This dissertation studies the problem of parameter identifiability of DAE models. Based on the DAE model of batch free radical polymerization, the parameter identifiability of the model is analyzed, and then the values of unknown parameters are also identified by dynamic optimization. Furthermore, the product design of free radical polymerization is conducted on the identified DAE model by dynamic optimization. The results of simulation and optimization about batch free radical polymerization show the reasonableness of the parameter identification and the necessary of optimization.The main contents and original contributions of this dissertation are presented as follows:1. The definitions of parameter identifiability of DAE systems are given from the aspect of input-output; The primary theory of traditional differential algebraic (D-A) approaches is discussed; The internal mechanism of applying D-A approaches to test the identifiability of dynamic systems described by ordinary differential equations (ODEs) is analyzed; The sufficient conditions in which D-A approaches can be used to test the identifiability of ODE systems is proved. Finally, these sufficient conditions are extended to DAE systems.2. As the traditional D-A approaches will encounter the problem that the sufficient conditions of D-A approaches are not be satisfied, a new approach based on extended space is proposed to deal with the identifiability of index-1DAE systems. The correctness of the new approach to index-1DAE systems is proved 3. The algorithm of the improved D-A approach is designed and implemented. Some examples have been presented to demonstrate the efficiency of the new approach.4. Based on the DAE model of batch free radical polymerization, the D-A approach on extended space is used to analyze the identifiability of unknown parameters of the model and the unknown parameter values are obtained by dynamic optimization. As the DAE model is global identifiable, the optimal values of parameters are globally optimal values of unknown parameters. Moreover, the product design of free radical polymerization is conducted by the identified DAE model from the perspective of process system engineering. The results of optimization demonstrate that the temperature and the initial charge amount of the initiator have the important significance in the the polymerization of industrial production.At last, the research work is concluded and future perspective of the research is also presented.