Introduction TO SHM

Introduction to Structural Health Monitoring (SHM)

To present the fundamental ideas to implement modern structural health monitoring methods in mechanical, aeronautical, and civil structures.

Methodology: The course is given through slideshows and a whiteboard with practical hands-on examples in Matlab and Python using data sets of various benchmarks proposed by SHM Lab (UNESP/Ilha Solteira) available in

Evaluation: The evaluation procedure will be performed through seminars and projects held by the students.

Topics: Introduction to SHM, Vibration-based damage detection, Electromechanical impedance-based SHM, an SHM approach using Machine Learning

Prerequisites: Vibration, Statistics, Signal Processing

A short version of this course can also be offered. Past courses:

  • March, 2022: Short-Course (20 h) - Introduction to Structural Health Monitoring (SHM) - University of Bourgogne-Franche-Comté, Besançon/France, EIBHI - BFCP Graduate School Cross Disciplinary Science and Technology, Master in Smart Mechanics, link


1. Introduction to SHM

  • Motivation

  • Levels of SHM strategy

  • Statistical pattern recognition approaches

  • Current methods: vibration-based SHM methods; wave-guided, electromechanical impedance, and others

  • Challenges for real-world applications

2. Vibration-based damage detection

  • Types of common damages in structures

  • Extraction of features sensitive to damage: model-based versus data-based

  • Classification of structural states by using supervised methods, semi-supervised, Reinforcement or non-supervised approaches

  • Definition of thresholds: statistical approaches for hypothesis thesis

  • Probability of false alarm: Type I error (false positive) and Type II error (false negative)

  • Receiver operating characteristic (ROC) curve

3. Electromechanical impedance-based SHM

  • Concepts of active structures

  • Model of electromechanical coupling between a piezoelectric patch and a host structure

  • Estimation of impedance signatures by spectral analysis

  • Root means square deviation of the real and imaginary part of impedance signatures as a damage feature

  • Temperature effects and compensation technique

4. An SHM approach using Machine Learning

  • Novelty detection using Mahalanobis squared distance

  • Fuzzy clustering for SHM with operational and environmental effects

  • Gaussian process regression for damage quantification

  • A Gaussian mixture model for damage detection

  • Deep learning: convolutional neural network and recurrent neural networks


  • Homework 1 - Statistical Classification using Mahalanobis Distance

  • Homework 2 - Compensation of temperature effects

  • Final Work:

The key idea is to implement a complete SHM approach to detect damage or quantify some data-driven information. The authors can use the approaches studied in the course or develop and combine other methods. It is fundamental to try to work on an original problem with suggestions to new directions.

The work can be performed individually or with two colleagues. The students are invited to use experimental data or simulated based on benchmarks to compare the performance.

It is demanded to include an in-depth performance analysis using ROC curves, confusion matrix, false-positive rate, and verification and validation of the method.

Write a detailed report with plots and all discussions about the method proposed.


  • Farrar, C.; Worden, K. Stuctural Health Monitoring: A Machine Learning, Wiley, UK, 2012.

  • Inman, D.; Farrar, C.; Lopes Jr, V; Steffen Jr, V. Damage Prognosis: For Aerospace, Civil and Mechanical Systems, Wiley, UK, 2007.

  • Paixão, J. A. S. ; da Silva, Samuel ; Figueiredo, Eloi ; Radu, L. ; Park, G. . Delamination area quantification in composite structures using Gaussian process regression and auto-regressive models. Journal of Vibration and Control, 2020.

  • da Silva, Samuel; Paixão, J. A. S. ; Rebillat, M. ; Mechbal, N.. Extrapolation of AR models using cubic splines for damage progression evaluation in composite structures. Journal of Intelligent Material Systems and Structures, 2020.

  • Cano, W.; da Silva, Samuel . Fuzzy clustering and AR models for damage detection in CFRP coupons considering loading effect. Journal of the Brazilian Society of Mechanical Sciences and Engineering, v. 42, p. 241, 2020.

  • Villani, L. G. G.; da Silva, Samuel ; Cunha, Americo ; Todd, M. D . On the detection of a nonlinear damage in an uncertain nonlinear beam using stochastic Volterra series. Structural Health Monitoring, v. 19, p. 1137-1150, 2020.

  • Villani, L. G. G.; da Silva, Samuel ; Cunha Jr A. B. . Damage detection in uncertain nonlinear systems based on stochastic Volterra series. Mechanical Systems and Signal Processing, v. 125, p. 288-310, 2019.

  • Villani, L. G. G., ; da Silva, Samuel ; Cunha Jr, A. B. ; Todd, M. D. . Damage detection in an uncertain nonlinear beam based on stochastic Volterra series: an experimental application. Mechanical Systems and Signal Processing, v. 128, p. 463-478, 2019.

  • da Silva, Samuel. Data-driven model identification of guided wave propagation in composite structures. Journal of the Brazilian Society of Mechanical Sciences and Engineering, v. 40, p. 543, 2018

  • Shiki, S. B. ; DA SILVA, S. ; Todd, M. D. . On the application of discrete-time Volterra series for the damage detection problem in initially nonlinear systems. Structural Health Monitoring, v. 16, p. 62-78, 2017.

  • Gonsalez, C. G.; da Silva, Samuel ; Brennan, M. J. ; Lopes Jr, V. Structural damage detection in an aeronautical panel using analysis of variance. Mechanical Systems and Signal Processing, v. 52-53, p. 206-216, 2015.

  • da Silva, S.; Gonsalez, C. G. ; Lopes JR, V. . Adaptive filter feature identification for structural health monitoring in an aeronautical panel. Structural Health Monitoring, v. 10, p. 481-489, 2011.

  • Silva, S.; Dias Jr, M. ; Lopes Jr, V. ; Brennan, M. J. . Structural Damage Detection By Fuzzy Clustering. Mechanical Systems and Signal Processing, 22, p. 1636-1649, 2008.

  • Silva, S.; Dias Jr, M. ; Lopes Jr, V. Structural Health Monitoring in Smart Structures Through Time Series Analysis. Structural Health Monitoring, v. 7, p. 231-244, 2008.