Ing Ind - Inf (Mag.)(ord. 270) - MI (471) BIOMEDICAL ENGINEERING - INGEGNERIA BIOMEDICA
054062 - MODEL IDENTIFICATION AND MACHINE LEARNING [I.C.]
In modern-day engineering, problems of analysis and design are more often than not solved by using mathematical models to describe the salient features of the systems under study, be they technological systems or industrial devices, biological or natural phenomena, economic or financial processes, etc. However, the mathematical descriptions that can be obtained from basic prnciples of the various engineering disciplines are not always satisfactory. In fact, it can often happen that the value of some parameters of a model obtained in this way remains uncertain; sometimes, the designer faces up problems which lay on the boundary of the body of current scientific knowledge and no basic principles are are available; finally, it may happen that the model that is eventually is too complex to be usable for any kind of analysis and design. In all these cases, it is of great value to resort to experimental observations made during the system operation and automatic model identification procedures. These procedures, which allow data to be converted into simple and adequate models, are the subject of the course. As one of the main criteria for building models from data is their predictive ability, the study of prediction methods for time series and systems is the subject of the initial part of the course; prediction methods are of considerable conceptual significance, as they are the basis for the analysis of uncertain data and systems, and practical significance, due to the considerable impact in applications.
Risultati di apprendimento attesi
The objective of this courseg is to provide the basis for modeling from experimental data, together with the development of techniques for the prediction of variables and the estimation of parameters through virtual sensors. Through the lessons and exercises, the student:
- will acquire the basic notions of stochastic systems and will be able to evaluate their main properties (DD1);
- will be able to solve an estimation and optimal prediction problem and will be able to evaluate the properties of the solution found (DD2,DD3);
- will know the main algorithms for data processing in order to identify a model starting from experimental data; will be able to assess the quality of the implemented algorithms and will be able to make proper design choices for the identification algorithm in order to optimize the obtained result (DD2,DD3).
Models in engineering and science
Model accuracy and complexity. Estimation from experimental observations. Models for classification, prediction, control, simulation and management. Data processing techniques
Stochastic models, spectral analysis and prediction
Stochastic processes and stochastic models for time-series and input/output systems. Model classes (AR, MA, ARMA, ARX, ARMAX, Box-Jenkins). Correlation analysis and spectral analysis. Kolmogorov-Wiener prediction theory.
Identification of input/output models
Parameter and variable estimation problems. Model identification from experimental data and the prediction error minimization (PEM) approach to identification.Least squares and maximum likelihood algorithms for AR, MA, ARMA, ARMAX model. Choice of complexity (AIC, MDL, etc.). Yule-Walker equations and Durbin-Levinson algorithm. Non-parametric identification.
Kalman filtering and prediction
State-space stochastic models. Filtering, prediction and smoothing. Kalman filter. Steady-state Kalman filter. Extended Kalman filter. Use of the Kalman filter in model identification.
Basic notions of systems theory and automatic control. Basic facts of probability and statistics.
Modalità di valutazione
2-hour written exam consisting of 4 numerical exercises and 2 theoretical questions on the course topics. In some exercises, questions will be posed so as to highlight the student's ability to develop links between the various topics of the course. Specifically, the student is required to:
- be able to analyze the main properties of a stochastic dynamic system and to calculate its mean, the covariance function and the spectrum of the output stochastic process;
- demonstrate knowledge of the main definitions and concepts of stochastic dynamical systems, the problem of output and state prediction and the problem of model identification from experimental data;
- know how to use the main analytical results given in the course in order to calculate the predictor of I/O or state-space models; be able to evaluate the predictor properties and its dependence on the problem parameters; be able to compare different results and choose the most suitable for the problem of interest;
- know the main model identification algorithms and ther numerical implementation;
- be able to analyze the properties of the model identification algorithms; be able to choose the most significant design parameters (for example the most suitable model class and its complexity) in order to optimize the final result.
The exam is offered together with the exam of the part of Machine Learning, which with the current course forms the integrated course MODEL IDENTIFICATION AND MACHINE LEARNING [C.I.].
S. Bittanti, Model identification and data analysis, Editore: Wiley, Anno edizione: 2019
T. Söderström, Discrete-time stochastic systems, Editore: Springer
T. Söderström, P. Stoica, System Identification, Editore: Prentice Hall
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