Training Course on System Identification and Parameter Estimation

Course Title: Training Course on System Identification and Parameter Estimation

Executive Summary

This intensive two-week course provides a comprehensive introduction to system identification and parameter estimation techniques. Participants will learn to build mathematical models of dynamic systems from experimental data. The course covers both time-domain and frequency-domain methods, including least squares, maximum likelihood, and subspace identification. Hands-on exercises and real-world case studies will enable participants to apply these techniques to a variety of engineering and scientific problems. By the end of the course, participants will be able to design experiments, collect data, estimate model parameters, validate models, and use them for prediction, control, and optimization. The course blends theoretical foundations with practical implementation using industry-standard software.

Introduction

System identification and parameter estimation are essential tools for modeling dynamic systems in engineering, science, and economics. This course provides a comprehensive introduction to these techniques, enabling participants to build mathematical models of systems from experimental data. The course emphasizes the practical application of system identification methods to real-world problems. Participants will learn how to design experiments, collect data, estimate model parameters, validate models, and use them for prediction, control, and optimization. The course covers both time-domain and frequency-domain methods, including least squares, maximum likelihood, and subspace identification. Hands-on exercises and case studies will be used throughout the course to reinforce the theoretical concepts and provide practical experience. The course is designed for engineers, scientists, and other professionals who need to model dynamic systems from data. Participants will gain a solid foundation in system identification and parameter estimation, enabling them to apply these techniques to a wide range of problems.

Course Outcomes

• Understand the basic principles of system identification and parameter estimation.
• Design experiments for effective data collection.
• Apply various parameter estimation techniques, including least squares and maximum likelihood.
• Validate and assess the quality of identified models.
• Use identified models for prediction, control, and optimization.
• Implement system identification techniques using industry-standard software.
• Analyze real-world case studies and apply system identification to practical problems.

Training Methodologies

• Interactive lectures and discussions.
• Hands-on computer exercises using industry-standard software.
• Case study analysis of real-world applications.
• Group projects and presentations.
• Individual assignments and problem-solving.
• Guest lectures from industry experts.
• Q&A sessions and open forum discussions.

Benefits to Participants

• Gain a comprehensive understanding of system identification and parameter estimation.
• Develop practical skills in designing experiments and collecting data.
• Learn to apply various parameter estimation techniques.
• Improve model validation and assessment skills.
• Enhance ability to use models for prediction, control, and optimization.
• Become proficient in using industry-standard software for system identification.
• Expand problem-solving skills through case study analysis.

Benefits to Sending Organization

• Improved ability to model and control dynamic systems.
• Enhanced product development and optimization capabilities.
• Better decision-making based on data-driven models.
• Increased efficiency in process monitoring and control.
• Reduced costs through improved system performance.
• Greater insight into system behavior and dynamics.
• Enhanced innovation and competitiveness.

Target Participants

• Control engineers
• Process engineers
• Mechanical engineers
• Electrical engineers
• Aerospace engineers
• Data scientists
• Researchers in related fields

Week 1: Fundamentals and Time-Domain Methods

Module 1: Introduction to System Identification

1. Overview of system identification and parameter estimation.
2. Types of models: black-box, grey-box, and white-box.
3. Model structures: linear vs. nonlinear, parametric vs. non-parametric.
4. The system identification process: experiment design, data collection, model estimation, model validation.
5. Applications of system identification in engineering and science.
6. Introduction to software tools for system identification.
7. Case study: Introduction to a real-world system identification problem.

Module 2: Experiment Design and Data Acquisition

1. Planning experiments for system identification.
2. Input signal design: PRBS, step, impulse, and random signals.
3. Sampling rate selection and anti-aliasing filters.
4. Data pre-processing: filtering, detrending, and normalization.
5. Dealing with noise and outliers in data.
6. Practical considerations for data acquisition.
7. Hands-on exercise: Designing an experiment for a given system.

Module 3: Least Squares Estimation

1. Introduction to least squares estimation.
2. Linear regression and the normal equations.
3. Ordinary least squares (OLS) and weighted least squares (WLS).
4. Recursive least squares (RLS) algorithm.
5. Properties of least squares estimators.
6. Model order selection using information criteria (AIC, BIC).
7. Hands-on exercise: Implementing least squares estimation in software.

Module 4: Model Validation and Assessment

1. Model validation techniques: residual analysis, cross-validation.
2. Goodness-of-fit measures: R-squared, RMSE, and NMSE.
3. Statistical tests for model validation.
4. Bias and variance analysis.
5. Model structure validation.
6. Using simulation for model validation.
7. Case study: Validating a model of a dynamic system.

Module 5: Time-Domain Model Structures

1. Introduction to time-domain model structures.
2. ARX, ARMAX, OE, and BJ models.
3. Model structure selection criteria.
4. Parameter estimation for time-domain models.
5. Model order selection for time-domain models.
6. Practical considerations for using time-domain models.
7. Hands-on exercise: Estimating parameters of different time-domain models.

Week 2: Frequency-Domain Methods and Advanced Topics

Module 6: Frequency-Domain Analysis

1. Introduction to frequency-domain analysis.
2. Fourier transform and frequency response.
3. Bode plots and Nyquist plots.
4. Frequency-domain system identification.
5. Spectral analysis and coherence functions.
6. Practical considerations for frequency-domain analysis.
7. Hands-on exercise: Analyzing the frequency response of a system.

Module 7: Frequency-Domain Model Structures

1. Introduction to frequency-domain model structures.
2. Non-parametric frequency response estimation.
3. Parametric frequency response estimation.
4. Model order selection for frequency-domain models.
5. Practical considerations for using frequency-domain models.
6. Hands-on exercise: Estimating parameters of a frequency-domain model.

Module 8: Maximum Likelihood Estimation

1. Introduction to maximum likelihood estimation (MLE).
2. Likelihood functions and optimization.
3. Properties of maximum likelihood estimators.
4. MLE for linear and nonlinear systems.
5. Dealing with non-Gaussian noise.
6. Practical considerations for MLE.
7. Hands-on exercise: Implementing maximum likelihood estimation in software.

Module 9: Subspace Identification Methods

1. Introduction to subspace identification methods.
2. State-space models and realization theory.
3. N4SID and MOESP algorithms.
4. Model order selection for subspace identification.
5. Practical considerations for using subspace identification.
6. Hands-on exercise: Implementing subspace identification in software.
7. Case study: Applying subspace identification to a real-world system.

Module 10: Advanced Topics and Case Studies

1. Identification of nonlinear systems.
2. Identification of time-varying systems.
3. Adaptive system identification.
4. Applications of system identification in control, signal processing, and other fields.
5. Real-world case studies.
6. Future trends in system identification.
7. Project presentations and course wrap-up.

Action Plan for Implementation

1. Identify a specific system in your organization that could benefit from system identification.
2. Design an experiment to collect data from the system.
3. Use the techniques learned in the course to estimate a model of the system.
4. Validate the model and assess its performance.
5. Use the model to improve the performance of the system.
6. Document your findings and share them with your colleagues.
7. Continue to explore and apply system identification techniques in your work.