Single-Course Engelsk 5 ECTS

# Probabilistic Methods in Wind Energy

## Overall Course Objectives

The purpose of the course is to learn the basics of statistical modeling and data analysis in the context of wind engineering and structural engineering design applications. The students are provided with the opportunity to apply probabilistic methods and machine learning to different examples from wind energy.

See course description in Danish

Learning Objectives

• Carry out statistical analysis of measured wind speed time series and SCADA (supervisory control and data acquisition) system data.
• Apply probability distributions and random variables in structural engineering problems
• Formulate, calibrate and systematically evaluate statistical engineering models using basic machine learning tools
• Apply uncertainty quantification and propagation on commonly used probabilistic models
• Explain the concept of engineering risk and apply simple risk-based decision analysis
• Extract useful insights from data using machine learning and decision modeling tools
• Apply structural reliability analysis methods on simple design equations
• Explain how information about uncertainty and probabilistic modelling techniques can be utilized in wind turbine design
• Independently carry out the process of real-world problem solving: identifying and describing a relevant problem, finding appropriate methods, executing, and demonstrating the viability of the solution

Course Content

1) Introduction to statistics and probability theory in the context of wind engineering using hands-on applications on measured data:
– Sample statistics. Student’s T-distribution. Central limit theorem. Confidence intervals. Bootstrapping. Application on measured wind speed data.
– Probability distributions: properties, estimation of parameters. Multivariate distributions.
– Distribution of extremes. Statistical extrapolation – applications on extreme wind speeds and extreme loads.
2) Introduction to data modelling:
– Machine learning basics. Introduction to regression models with uncertainty. Estimation of model parameters: least-squares and maximum-likelihood methods. Introduction to Bayesian updating. Exercise on machine learning for training load surrogate models. Exercise on Bayesian updating and Bayesian Neural Networks.
– Data generation: design of experiments and the Monte Carlo method
– Uncertainty quantification and propagation. Variance-based sensitivity analysis.
– Wind turbine SCADA data example – filtering and data-driven analysis possibilities.
3) Structural reliability and probabilistic design
– Limit states. Concept of reliability analysis. Exercises with FORM and Monte Carlo methods.
– Structural design under uncertainty. Safety factor calibration. Exercise with probabilistic design.
– Engineering risk analysis. Decision theory and its use to evaluate the performance of machine learning applications.
4) Data science final project
– Work independently on a data science project. The project topic can be freely selected from several predefined options or a new special topic can be defined.
– Presentation of the students’ projects. Peer discussions and suggestions for improvements.

The course begins with lectures and exercises introducing the basic concepts. Students are also introduced to the requirements for the final project and are given access to student projects from previous years. During the first several weeks, the hands-on work focuses on completing a series of interconnected exercises that showcase parts in the process of probabilistic design. The results from these exercises are submitted as a short report and students will receive ongoing feedback. Afterwards, the students will begin working on a project assignment, individually or in groups of 2 to 3 students. These assignments aim at solving actual engineering challenges using data science and other tools introduced during the course. The topic of the assignment can be selected out of several predefined examples, but the students are also encouraged to specify their own topic related to the course contents. At the end of the course, the students will make a presentation of the results of their project, and submit a report containing their assignments.

Recommended prerequisites

46300, Background knowledge in statistics and probability is recommended, similar to the content of the courses 02402 and 02406. It is also assumed that the students are already familiar with basic wind energy topics as the ones taught in course 46300, and are able to use Matlab or Python programming languages. Based on these requirements, it is recommended that the course is taken during the second year of M.Sc. studies.

Teaching Method

Lectures, exercises and project work.

Faculty

Remarks

It is recommended that the course is taken during the third semester of the M.Sc. study.

See course in the course database.

## Registration

Language Engelsk 13 weeks Wind DTU Lyngby Campus 46500 Candidate Week 36 Week 49 Mon 13-17
Price 9.250,00 DKK