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CODE 98218
SEMESTER 1° Semester


The course provides the fundamentals to robust design of systems and related procedures for moitoring and diagnostics,  encompassing deterministic and stocastic approaches. Practical examples are derived from the mechanical engineering and energy system fields.



The course aims to illustrate how the design under uncertainty can help in modelling and design of the energy systems. The first part of the course will cover the necessary fundamentals of statistics. Then different uncertainty quantification methods will be presented, starting from sampling method like Monte Carlo and continuing with different approximated methods an overview of robust design will presented, focusing on the application of uncertainty quantification method in optimization problems. In the second part of the course, advanced techniques for Data Driven monitoring will be presented. Both methods will be applied to different case studies.


At the end of the course the student will be able to:

- approach and quantify the uncertainties impacting on a specific design problem

- use mathematical methods for estimating the uncertainty in the design outputs

- conduct a systematic design of experiment and treat design problems under uncertainty

- apply robust design techniques to engineering problems

- recognize the most common monitoring and diagnostic strategies

- design a monitoring system selecting the most relevant parameters

- select the most promising modelling approach on the basis of the available system information


basic analytical skills, equation handling, basic computer coding skills


Lectures and exercises on PC


Part A – Robust Design of Systems

Lecture 1 – Introduction and motivation

Course introduction, practical needs and applications of uncertainty quantification and robust design techniques.

Introduction to statistics: statistical analysis and main parameters (average, variance, probability distribution functions, etc.).

Lecture 2 – Uncertainty definition and treatment

Source and types of uncertainties (aleatory, epistemic).  Uncertainty in measurements, recommended approach in scientific publications, ASME standards.

Lecture 3 – Uncertainty estimation and Montecarlo simulation

Overview of sampling and approximate methods for uncertainty quantification - UQ (Monte Carlo, response sensitivity analysis, polynomial chaos, design of experiment, response surface methodology), backward and forward UQ analysis. The reference sampling method: MonteCarlo simulation. The concept of Mean Square Pure Error (MSPE).

Lecture 4 – Approximate methods

Fundamentals and features of approximated methods for uncertainty quantification and propagation from inputs to outputs: the Response Sensitivity Analysis - RSA, the Polynomial Chaos - PC.

Lecture 5 – Design of Experiment and Response Surface methods

Fundamentals and features of approximated methods for uncertainty quantification and propagation from inputs to outputs: Response Surface Method – RSM, Design of Experiment – DOE.

Lecture 6 – Robust design approach

Robust design: fundamentals, optimization algorithm, combination with uncertainty quantification methods. Application examples: analytical function, cantilever beam, microgas turbine, gas-gas heat exchanger, advanced fuel cell energy system.

Lecture 7 – Exercise on algebraic application

MonteCarlo simulation and RSA method in Matlab environment: the Rosenbrock function.

Lecture 8 – Exercise on engineering application

Robust Design of a gas-gas heat exchanger: optimisation algorithm and uncertainty quantification.


Part B – Monitoring and Diagnostics

Lecture 1: Overview of the monitoring and diagnostics: objective, hurdles and methods

General definitions, Maintenance Strategies, Monitoring application, Interaction between Monitoring and Control systems, Process Monitoring Design: Design of Experiment vs Monitoring

Lecture 2: Industrial approach to monitoring and diagnostics

Definitions by ISO 13372 2012: Condition monitoring and diagnostics of machines; Condition Monitoring; Diagnosis and Prognosis; Expert Systems for Monitoring and Diagnosis of Rotating Machinery

Lecture 3: Dealing with measurement error: Data Reconciliation & Gross Error Detection

Introduction to measurement errors; Comparison of data validation methods; DR and GED theory; problem formulation; Novel technique vs. traditional DR approach; VDI 2048 Exercise

Lecture 4: Exercise on Data Reconciliation

VDI 2048 Exercise solution: Linear solution with Lagrange Multiplier; Non-linear solution with Sequential Quadratic Programming.

Lecture 5: Selection of monitoring and observation + detection strategy:

First principles models and Data-Driven Models; Example of Fault detection and identification approaches; Fault simulation.

Lecture 6: Dealing with high dimension Data Base: Principal Component Analysis

PCA Theory; PCA for Dimensionality Reduction; Examples of PCA as regression model.

Lecture 7: Selection of Regression Models

Example of Regression Models; Model and Feature Selections, Technique for Data-Driven application; Evaluating the goodness of fit; Underfitting vs Overfitting;  Exercise on Data sets

Lecture 8: Real-Time Risk Management enabled by Industry 4.0

Industry 4.0; Industrial Internet of Things; Digital twin; Digital Factory; Risk Management in the Age of IIoT; State of the art of safety controls; Risk Assessment methods; Real-Time Risk Management.


  • Spiegel, M.R., Schiller, L.J.(1999), Statistics, McGraw Hill, NYC
  • Montgomery, D.C. (2000), Design and Analysis of Experiments, John Wiley & Sons, New York
  • Ralph C. Smith (2013), Uncertainty Quantification: Theory, Implementation, and Applications
  • T.J. Sullivan (2015), Introduction to Uncertainty Quantification”, Springer
  • Ghanem, Higdon, Owhadi, (2017), Handbook of Uncertainty Quantification, Springer
  • Souza de Cursi, Sampaio, (2015), Uncertainty Quantification and Stochastic Modeling with Matlab, ISTE Press – Elsevier
  • L. Eriksson, E. Johansson, N. Kettaneh-Wold, C. Wikström, and S. Wold (2001), Design of Experiments
  • Marler, R. T., and Arora, J. S., 2004 “Survey of Multi-Objective Optimization Methods for Engineering” Structural and Multidisciplinary Optimization, 26(6), pp.269.295
  • Myers, R. H., and Montgomery, D. C., 2002, “Response Surface Methodology: Process and Product Optimization Using Designed Experiments” John Wiley & Sons Inc, USA.
  • Law, A.l., Kelton, W. D., 1991, “Simulation Modeling and Analysis”, Mc Graw Hill
  • Mäkelä, M., 2017, “Experimental Design and Response Surface Methodology in Energy Applications: A Tutorial Review” Energy Conversion and Management, 151(May), pp. 630–640.
  • Kleijnen, J. P. C., 2005, “An Overview of the Design and Analysis of Simulation Experiments for Sensitivity Analysis” Eur. J. Oper. Res., 164(2), pp. 287–300.
  • Tagushi, G., Yokoyama, Y., and Wu, Y., 1993, “Taguchi Methods: Design of Experiments”
  • K. Kim, M.R. von Spakovsky, M. Wang, D.J. Nelson, 2012. “Dynamic optimization under uncertainty of the synthesis/design and operation/control of a proton exchange membrane fuel cell system, Journal of Power Sources, 205, pp. 252–263
  • Navarro, M., Witteveen, J., Blom, J., 2014. “Polynomial chaos expansion for general multivariate distributions with correlated variables”
  • Seshadri, P., Narayan, A., Mahadevan, S., 2016. “Effectively Subsampled Quadratures For Least Squares Polynomial Approximations”. ArXiv e-prints
  • Giunta, A.A., Eldred, M.S., Castro, J.P., 2004. “Uncertainty quantification using response surface approximations”, 9th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability
  • M. Cavazzuti, Optimization Methods: From Theory to Design, DOI: 10.1007/978-3-642-31187-1_3, Springer-Verlag Berlin Heidelberg, 2013.


Exam Board



ALESSANDRO SORCE (President Substitute)


Class schedule

The timetable for this course is available here: Portale EasyAcademy



The first part on robust design requires a report containing: one chapter on theoretical topic of the course, one exercise on algebric equation, one exercise on engineering application.

The second part on monitoring and diagnostics requires an oral exam.


Written and oral exam

Exam schedule

Data appello Orario Luogo Degree type Note
09/01/2024 09:30 SAVONA Orale
11/01/2024 09:30 GENOVA Orale Aula A7 / A7 Room
26/01/2024 14:30 GENOVA Orale
15/02/2024 09:30 GENOVA Orale
06/06/2024 09:30 GENOVA Orale B0 - Opera Pia, where the study area close to the bar is.
20/06/2024 09:30 GENOVA Orale A4
05/07/2024 09:30 GENOVA Orale A13
18/07/2024 09:30 GENOVA Orale
05/09/2024 09:30 GENOVA Orale A4