Information on the course:

Oct 27, 2000/TA

System and Load Identification

- a graduate course from Solid Mechanics


Course outline and duration

A course plan is given in the table below. Dates and times, exept for the first lecture, may be subject to change. They will be discussed and specified during the introductory lecture. The course will end before this years end.

The course will be given in the form of seminars. Each course participant give one seminar (also the two teachers). The distribution of topics for the seminars will be given at the start of the course.

# Content

Date/seminar holder

0 Course start. Oct 27, 10:15
1 Time-Invariant Linear Systems. Simulation and Prediction. Models of Time-Invariant Systems. System Identification in Practice  (Chapters 1-4 and 17 in LL's book). 100pp

Read on own. Omit appendices and chapters denoted (*) in the book.

2 Parameter Estimation Methods (Chapter 7 in LL's book). Guiding principles behind parameter estimation methods. Minimizing prediction errors. Linear regressions and least-squares method. A statistical framework for parameter estimation and the maximum likelihood method. Correlating prediction errors with past data.  26pp

Friday Nov 3, 13:15-15:00

/Thomas  Abrahamsson

3 Asymptotic Distribution of Parameter Estimates (Chapter 9 in LL's book). The prediction error approach: basic theorem. Expressions for the asymptotic variance.  The correlation approach.  Use and relevance of asymptotic variance expressions. 21pp

Friday Nov 10, 13:15-15:00

/Patrik Nordberg

4 Computing the Estimate (Chapter 10 in LL's book). Linear regression and least squares. Numerical solution by iterative search methods. Computing gradients. Two-stage and multistage methods. Local solutions and initial values. 24pp

Tuesday Nov 21, 13:15-15:00

/Lars Nordström

5 Options and Objectives. Experiment Design. Preprocessing Data. (Chapters 12-14 in LL's book). Options. Objectives. Bias and variance. Som general [experimental] considerations. Informative experiments. Input design for open loop experiments. Choice of sampling interval and presampling filters. Drifts and detrending. Outliers and missing data. Prefiltering. 46pp

Friday Nov 24, 13:15-15:00

/Andreas Linderholt

6 Choice of Identification Criterion. Model Structure Selection and Model Validation (Chapters 15-16 in LL's book). General aspects [on identification criterion]. Choice of norms: robustness. General aspects of the choice of model structure. A priori considerations. Model structure selection based on preliminary data analysis. Comparing model structures. Model validation. Residual analysis. 34pp Friday Dec 1, 13:15-15:00

/Hoang Nam

7 Dynamic Programming. The Inverse Structural Dynamics Problem (Chapters 1 and 5 in DT&HB's book). Dynamic programming. Generalized cross-validation. L-curve analysis. Inverse structural dynamics problems. 67pp

Tuesday Dec 5, 13:15-15:00

/Peter Möller

8 Input Force Estimation Using an Inverse Structural Filter. Article Friday Dec 8, 13:15-15:00

/Thomas Abrahamsson


Course literature and fee

The lectures will be based on the books ’System Identification - Theory for the User’, by L. Ljung, Prentice Hall 1999, and 'Practical Inverse Analysis in Engineering', D. Trujillo and H Busby, CRC Press, 1997. Some articles will supplement the books.

The course will be free of charge for Chalmers affiliated students. The fee for non-chalmers students is SEK 3000.

Course responsible and teachers

Responsible: Prof. Thomas Abrahamsson,  e-mail:, tel +46-31-772 1506, fax +46-31-772 3827

Teachers: Dr. Peter Möller and Prof. Thomas Abrahamason

Registration and examination

Registration shall be made to Thomas Abrahamsson before w0043.

The examination consists of given seminars (one seminar per participant), implementation of methods for system and load identification with the solutions to problems that will be given during the course. The implementation will require programming in MATLAB or any other programming language of choice. A passed examination will give 3 or 5 credit points in the graduate course program for graduate students at Solid Mechanics. To receive 5 credit points, more extensive implementations and problem solutions have to be made.

Course language and miscellaneous

The lectures will be given in english. The course will be held in the seminar room at the department of Solid Mechanics, Chalmers University of Technology, Hörsalsvägen 7.

Course assignments

The course assignments can be found here. The two last assignments are for the extended course only.