Ingegneria meccanica - Mechanical Engineering

Summary of the topics covered 1) Notes on The Fourier transform (FT) Impulse response and transfer function The time-frequency domain convolution theorem Shift and scaling properties, Hermitian symmetry Digital signal processing continuous vs discrete time signals • Sampled and windowed functions, • Nyquist-Shannon sampling theorem, • Time sampling and frequency sampling, observation time, aliasing, rippling effect, Discrete Fourier transform • Frequency content of a signal, narrow and wideband signals • Example of aliasing in MEMS ACC Worked exercises with Matlab: • FT of Sequence of unit and equally shifted impulses • FT of a rectangular function • FT of a cosine/sine function • FT of the Dirac delta 2) Introduction to Time-Frequency Analysis Mathematical and physical meaning of the FT Range of applicability and main limitations of the FT Worked exercises in Matlab: transient harmonic disturbance and frequency shift 3) The Short Time Fourier Transform (STFT) Mathematical formulation and physical meaning of the STFT The role of the window function Time and frequency characterization of a waveform Heisenberg - Gabor Uncertainty Principle Time frequency resolution, Heisenberg box Gabor transformation of trigonometric functions with large frequency fluctuations Range of applicability and main limitations of the STFT Worked exercises with Matlab: • STFT of a chirp • STFT of superposition of windowed trigonometric components • Worked examples in Matlab: Range of applicability and main limitations of GT 4) Wavelet transform (WT) Mathematical formulation and physical meaning Relation between scale and frequency The wavelet transform as a convolution integral Variable time-frequency resolution Range of applicability and main limitations Worked exercises with Matlab: • Time-frequency characterization of Mexican hat and Morlet wavelet • Analogies and differences between STFT and Wavelet transform, comparison between Morlet wavelet and Gabor atom • Filtering property of the wavelet transform • Identification of coherent structures • Edge detection • Analysis of a signal with “wavemenu” toolbox Lecture notes on: Structural health monitoring of a plate excited by ambient load by wavelet transform. 5) The Hilbert transform (HT) and analytic signal (AS) The need for analytic signal: its role on time-frequency analysis AS and HT: Mathematical formulation and physical meaning Bedrosian theorem Phasor representation of AS The instantaneous frequency (IF) Worked exercises with Matlab: • HT of a harmonically decaying function • AS of harmonic component with DC offset • AS of composition of harmonics • AS of a Chirp • AS of Harmonic amplitude modulated signal 6) Empirical mode decomposition (EMD) and Hilbert transformation Monocomponent and multicomponent signals, Intrinsic Mode Functions (IMF) Basic concepts of the EMD, main properties of IMF with examples Physical meaningfulness of IMFs: the length-of-day data Main advantages, range of applicability and main limitations of EMD+HT comparison with other time-frequency methods Inter-wave and Intra-wave frequency modulation Worked exercise with Matlab: • The sifting process • Introduction to the HHT-package code by Huang • EMD+HT of the Stokes wave • Analysis of damped oscillations with EMD+HT Lecture notes on: Damage detection in structures under traveling loads by Hilbert–Huang transform.

Il corso è insegnato in modo auto-contenuto, per quanto possibile. Tuttavia, lo studente dovrebbe essere già familiare con le nozioni fondamentali di cinematica, dinamica, analisi vettoriale e teoria delle matrici, e con la dinamica delle vibrazioni. Queste basi sono generalmente insegnate nei primi tre anni del corso di laurea. Le materie di riferimento sono Analisi I e II, Geometria, Meccanica Applicata alle Macchine, Fisica I e Meccanica Razionale, meccanica delle vibrazioni.

Reference books: N.Roveri lecture notes Cohen, L. 1995 Time frequency analysis. Englewood Cliffs, NJ: Prentice Hall G.Kaiser , A Friendly Guide To Wavelets, New York, Birkhäuser, 1994 A Wavelet Tour of Signal Processing, 3rd ed. Stéphane Mallat, Academic Press, dec. 2008 Hahn S., Hilbert transforms in signal processing. Artech House, 442 pp., 1995. Huang N.E., et al, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis, Proc. R. Soc. London A 1998; 454, 903 995. N.E. Huang, Hilbert Huang transform and its application, World Scientific

Attività di laboratorio settimanale (4 ore) Ricevimento settimanale (2 ore)

Test in calasse: analisi di un segnale proveniente da una struttura meccanica tramite software matlab e compilazione di un report riassuntivo ed esplicativo dei fenomeni osservati.

L’insegnamento si svolge attraverso lezioni frontali in aula e attività applicative al calcolatore, finalizzate a introdurre e sperimentare le principali tecniche di analisi numerica dei segnali in ambiente MATLAB. Durante il corso vengono proposti esempi e casi studio che costituiscono la base di riferimento per la prova d’esame finale, svolta in presenza su computer. L’esame consiste in un test pratico della durata di circa 4 ore, nel quale lo studente elabora e discute un report tecnico ispirato agli esercizi e ai progetti già affrontati in classe. La prova comprende: l’analisi numerica di uno o più segnali reali o sintetici mediante MATLAB; la descrizione delle procedure di elaborazione adottate; la discussione critica dei risultati e della loro interpretazione fisica. Le lezioni frontali, svolte con il supporto di materiale multimediale e codici MATLAB condivisi, sono integrate da esercitazioni pratiche guidate, in modo da rendere la parte di esame una naturale prosecuzione dell’attività didattica svolta durante il semestre.

Summary of the topics covered 1) Notes on The Fourier transform (FT) Impulse response and transfer function The time-frequency domain convolution theorem Shift and scaling properties, Hermitian symmetry Digital signal processing continuous vs discrete time signals • Sampled and windowed functions, • Nyquist-Shannon sampling theorem, • Time sampling and frequency sampling, observation time, aliasing, rippling effect, Discrete Fourier transform • Frequency content of a signal, narrow and wideband signals • Example of aliasing in MEMS ACC Worked exercises with Matlab: • FT of Sequence of unit and equally shifted impulses • FT of a rectangular function • FT of a cosine/sine function • FT of the Dirac delta 2) Introduction to Time-Frequency Analysis Mathematical and physical meaning of the FT Range of applicability and main limitations of the FT Worked exercises in Matlab: transient harmonic disturbance and frequency shift 3) The Short Time Fourier Transform (STFT) Mathematical formulation and physical meaning of the STFT The role of the window function Time and frequency characterization of a waveform Heisenberg - Gabor Uncertainty Principle Time frequency resolution, Heisenberg box Gabor transformation of trigonometric functions with large frequency fluctuations Range of applicability and main limitations of the STFT Worked exercises with Matlab: • STFT of a chirp • STFT of superposition of windowed trigonometric components • Worked examples in Matlab: Range of applicability and main limitations of GT 4) Wavelet transform (WT) Mathematical formulation and physical meaning Relation between scale and frequency The wavelet transform as a convolution integral Variable time-frequency resolution Range of applicability and main limitations Worked exercises with Matlab: • Time-frequency characterization of Mexican hat and Morlet wavelet • Analogies and differences between STFT and Wavelet transform, comparison between Morlet wavelet and Gabor atom • Filtering property of the wavelet transform • Identification of coherent structures • Edge detection • Analysis of a signal with “wavemenu” toolbox Lecture notes on: Structural health monitoring of a plate excited by ambient load by wavelet transform. 5) The Hilbert transform (HT) and analytic signal (AS) The need for analytic signal: its role on time-frequency analysis AS and HT: Mathematical formulation and physical meaning Bedrosian theorem Phasor representation of AS The instantaneous frequency (IF) Worked exercises with Matlab: • HT of a harmonically decaying function • AS of harmonic component with DC offset • AS of composition of harmonics • AS of a Chirp • AS of Harmonic amplitude modulated signal 6) Empirical mode decomposition (EMD) and Hilbert transformation Monocomponent and multicomponent signals, Intrinsic Mode Functions (IMF) Basic concepts of the EMD, main properties of IMF with examples Physical meaningfulness of IMFs: the length-of-day data Main advantages, range of applicability and main limitations of EMD+HT comparison with other time-frequency methods Inter-wave and Intra-wave frequency modulation Worked exercise with Matlab: • The sifting process • Introduction to the HHT-package code by Huang • EMD+HT of the Stokes wave • Analysis of damped oscillations with EMD+HT Lecture notes on: Damage detection in structures under traveling loads by Hilbert–Huang transform.

Il corso è insegnato in modo auto-contenuto, per quanto possibile. Tuttavia, lo studente dovrebbe essere già familiare con le nozioni fondamentali di cinematica, dinamica, analisi vettoriale e teoria delle matrici, e con la dinamica delle vibrazioni. Queste basi sono generalmente insegnate nei primi tre anni del corso di laurea. Le materie di riferimento sono Analisi I e II, Geometria, Meccanica Applicata alle Macchine, Fisica I e Meccanica Razionale, meccanica delle vibrazioni.

Reference books: N.Roveri lecture notes Cohen, L. 1995 Time frequency analysis. Englewood Cliffs, NJ: Prentice Hall G.Kaiser , A Friendly Guide To Wavelets, New York, Birkhäuser, 1994 A Wavelet Tour of Signal Processing, 3rd ed. Stéphane Mallat, Academic Press, dec. 2008 Hahn S., Hilbert transforms in signal processing. Artech House, 442 pp., 1995. Huang N.E., et al, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non stationary time series analysis, Proc. R. Soc. London A 1998; 454, 903 995. N.E. Huang, Hilbert Huang transform and its application, World Scientific

Attività di laboratorio settimanale (4 ore) Ricevimento settimanale (2 ore)

Test in calasse: analisi di un segnale proveniente da una struttura meccanica tramite software matlab e compilazione di un report riassuntivo ed esplicativo dei fenomeni osservati.

L’insegnamento si svolge attraverso lezioni frontali in aula e attività applicative al calcolatore, finalizzate a introdurre e sperimentare le principali tecniche di analisi numerica dei segnali in ambiente MATLAB. Durante il corso vengono proposti esempi e casi studio che costituiscono la base di riferimento per la prova d’esame finale, svolta in presenza su computer. L’esame consiste in un test pratico della durata di circa 4 ore, nel quale lo studente elabora e discute un report tecnico ispirato agli esercizi e ai progetti già affrontati in classe. La prova comprende: l’analisi numerica di uno o più segnali reali o sintetici mediante MATLAB; la descrizione delle procedure di elaborazione adottate; la discussione critica dei risultati e della loro interpretazione fisica. Le lezioni frontali, svolte con il supporto di materiale multimediale e codici MATLAB condivisi, sono integrate da esercitazioni pratiche guidate, in modo da rendere la parte di esame una naturale prosecuzione dell’attività didattica svolta durante il semestre.