# In Search for Mathematical Model: The Potential of Optimization Algorithms in System Identification

In Search for Mathematical Model: The Potential of Optimization Algorithms in System Identification

System identification is a method to find the mathematical model of a dynamic system which uses statistical methods to build mathematical models from measured data. Two types of models are common in the field of system identification: grey-box model and black-box model. Grey-box model refers to the model where some information is partially known from first principle while the rest of the information is obtained from experiment. On the other hand, a black-box model uses no priori physical knowledge of the system. A number of model structures have been proposed in the area of black-box identification system. The most common models are autoregressive model with exogenous inputs (ARX), autoregressive moving average with exogenous inputs (ARMAX), and Box-Jenkins (BJ) model.

Most essential stages of model identification process can be summarized into four main stages. The first stage is collecting experimental data. Then, the model order and structure are chosen. The next stage is to estimate the parameters of the model and finally, the mathematical model is validated.

Model order selection and parameter estimation are two significant aspects of determining the mathematical model for system identification. In this research, an approach termed as Simultaneous Model Order and Parameter Estimation (SMOPE) based on Particle Swarm Optimization (PSO) and Gravitational Search Algorithm (GSA), have been developed to combine these two parts into a simultaneous solution. In this technique, both the model order and the parameters of the system are computed simultaneously to obtain the best mathematical model of a system.