Frequency Domain Identification For Linear Systems With Mixed Noises

As a powerful technological and theoretical research subject,system identification is a method to establish mathematical models based on observed input and output data.With the development of the era and the progress of society and technology,there are many problems in people's production practice and scientific experiment activities,and we hope to establish the mathematical model of the research object by identification methods by that we can understand the various properties of the object.At present,system identification has been widely used in computer science,medical treatment,chemistry,aviation,economy,energy fields and so on.Based on this background,this thesis proposes a new frequency-domain identification method for linear time-invariant systems.In terms of frequency-domain identification system,there is a direct link between the frequency responses and the system transfer functions.An approximate transfer function is always found for identification system that is a linear time-invariant in frequency domain,so this thesis first introduces the transfer functions structural characteristics,including orthogonal rational bases and other important concepts related to modelling.Secondly,considering the truth that there maybe some kinds of unknown mixed noises in the system,we set up a new model structure which can remove the unknown mixed noises,augmented Lagrangian optimization method and accelerated proximal gradient algorithm are used to calculate the optimal solution of the model on the basis of the previous study.Finally,a new method of frequency domain identification for discrete linear systems is presented.The simulation results are given by using MATLAB.The frequency-domain identification method proposed in this thesis is very helpful for removing the unknown mixing noises.We can find the poles quickly without knowing the true poles of system.Besides the simulation results show the feasibility and effectiveness of this method.Another advantage of this method in the thesis is that identification process is simple.As long as we record the actual system' input and output data,we can achieve the purpose of identifying the actual system,which is an adaptive identification method.