Fault Detection and Control

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

This course concerns theory of model-based automatic detection of failures like sensor failures etc. The material is largely based on probability theory and system theory and the lecture comprises fundamentals of these. Some knowledge from system identification will be an advantage. The material comprises basics of hypotheses testing, sequential statistics, large-sample approximations (likelihood scores), analysis of variance, Bayesian approach and multiple models.

Requirements:

Presentation of the seminary work and a hardcopy of the technical report.

Syllabus of lectures:

1. Problem formulation and examples

2. Application of probability theory and mathematical statistics to the problem of detection

3. Likelihood, conditional probability, maximum likelihood and likelihood ratio

4. Stochastic games, statistical decisions and Bayes risk function

5. Linear regression and test of linear hypotheses via Bayes risk and Fisher's criterion

6. Review of models: state space, ARX, ARMAX, transfer function and additive/non-aditive changes of these

7. Multiple-model approach, hybrid models, bank of Kalman filters

8. Sequential statistical analysis, GLR and CUSUM tests

9. Local approach and differential approximation of the likelihood function

10. Geometric approach, changes of signal direction and eigenstructure, unknown input observer.

11. Numerical methods of detection

12. Estimates and test on unobserved signal covariance matrices

13. Fault detection in non-linear systems using modified linear algorithms and approximations

14. Implementation and robustness issues

Syllabus of tutorials:

1. Risk function minimization, analytic and numeric optimization, examples in MATLAB

2. Probability density functions used in statistic, examples of application, graphs in MATLAB, Seminary work set

3. Likelihood calculation, conditioned probability distribution, conditioned mean

4. Simple and composed hypotheses tests, GRL - Generalized likelihood tests, power of the test and other characteristics

5. Asymptotic behaviour of statistical decisiions, asymtotics for their characteristics

6. Linear hypotheses tests and variance analysis - practical examples, Principal component analysis PCA

7. Geometric approach, parity checks,analytic redundancy

8. Hybrid and paralel models, sequential tests, CUSUM

9. Unknown Input Observer a Dedicated Observer Scheme

10. Individual seminary work, consultations

11. Proposed solution for the individual work presented and corrected

12. Individual seminary work, consultations

13. Individual seminary work, consultations

14. Presentations of the individual seminary works

Study Objective:

Study materials:

1. Basseville, Nikiforov. Detection of abrupt changes.Prentice Hall, 1993.

2. Borovkov. Matematičeskaja statistika - Ocenka parametrov i proverka gipotez. Nauka Moskva, 1984.

3. Drain. Statistical methods for industrial process

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements - Control Engineering- structured studies (compulsory elective course)
• Cybernetics and Measurements - Artificial Intelligence- structured studies (compulsory elective course)
• Cybernetics and Measurements - Measurement and Instrumentation Systems- structured studies (compulsory elective course)
• Cybernetics and Measurements - Aeronautical Engineering and Control Systems- structured studies (compulsory elective course)