Nonlinear system identification

System identification is a method of identifying or measuring the mathematical model of a system from measurements of the system inputs and outputs. The applications of system identification include any system where the inputs and outputs can be measured and include industrial processes, control systems, economic data, biology and the life sciences, medicine, social systems and many more.

A nonlinear system is defined as any system that is not linear, that is any system that does not satisfy the superposition principle. This negative definition tends to obscure that there are very many different types of nonlinear systems. Historically, system identification for nonlinear systems^[1]^[2] has developed by focusing on specific classes of system and can be broadly categorized into five basic approaches, each defined by a model class:

Volterra series models,
Block-structured models,
Neural network models,
NARMAX models, and
State-space models.

There are four steps to be followed for system identification: data gathering, model postulate, parameter identification, and model validation. Data gathering is considered as the first and essential part in identification terminology, used as the input for the model which is prepared later. It consists of selecting an appropriate data set, pre-processing and processing. It involves the implementation of the known algorithms together with the transcription of flight tapes, data storage and data management, calibration, processing, analysis, and presentation. Moreover, model validation is necessary to gain confidence in, or reject, a particular model. In particular, the parameter estimation and the model validation are integral parts of the system identification. Validation refers to the process of confirming the conceptual model and demonstrating an adequate correspondence between the computational results of the model and the actual data.^[3]

^ Nelles O. "Nonlinear System Identification: From Classical Approaches to Neural Networks". Springer Verlag, 2001
^ Billings S.A. "Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains". Wiley, 2013
^ Nesaei, Sepehr; Raissi, Kamran (2011-12-01). Das, Vinu V.; Ariwa, Ezendu; Rahayu, Syarifah Bahiyah (eds.). Data Processing Consideration and Model Validation in Flight Vehicle System Identification. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering. Springer Berlin Heidelberg. pp. 269–274. doi:10.1007/978-3-642-32573-1_46. ISBN 978-3-642-32572-4.

[Nelles-1] Nelles O. "Nonlinear System Identification: From Classical Approaches to Neural Networks". Springer Verlag, 2001

[SAB1-2] Billings S.A. "Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains". Wiley, 2013

[3] Nesaei, Sepehr; Raissi, Kamran (2011-12-01). Das, Vinu V.; Ariwa, Ezendu; Rahayu, Syarifah Bahiyah (eds.). Data Processing Consideration and Model Validation in Flight Vehicle System Identification. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering. Springer Berlin Heidelberg. pp. 269–274. doi:10.1007/978-3-642-32573-1_46. ISBN 978-3-642-32572-4.

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