Abstract:

In engineering education field, it is essential to adequately couple the teaching of theoretical and practical knowledge. There is an increasing demand of engineers with computational skills, capable to face the design of structures and their management through the modelling of the time response and to cope with their intrinsic uncertainty. These models need to be fed with several simulations of time series that describe the inputs of the model.

There has been a huge development in the stochastic characterization and simulation techniques of vector random processes. Their underlying theories generally involve relatively complex statistical concepts which analysis and coding are out of the scope of the syllabus of specific engineering subjects. This makes it difficult to show the students a global vision of the state of the art and it results really disappointing for the students and the teacher.

MarineTools is an open-source Python package for the non-stationary (NS) statistical analysis and the simulation of vector random processes [1]. It includes functionalities to take a single time series observation as an input and to return the simulation of time series with the same probabilistic behavior. It is suitable for environmental data and has been successfully applied to a variety of time series of interest for environmental and engineering problems.

The present work shows a teaching framework developed within the subject of Risk and reliability in coastal engineering taught at the Master's Program of Environmental Hydraulics of the University of Granada (Spain). In this course of 2 ECTS, simulation techniques to obtain several realizations of vector random processes (VRPs) are included in the syllabus.

The course in simulation of VRPs is divided into three steps:
(a) a depthless description of the mathematical background of MarineTools is presented first;
(b) interface game-like activities where students play with the properties of the NS probability models (PMs) and its multivariate temporal dependency are proposed, and
(c) some short lessons are given with the aid of interactive Jupyter notebooks that combine practical exercises and allow them to go into details with small pieces of code.

Finally, students are encouraged to use the package to simulate environmental time series for a real case study such as the analysis of the damage evolution of a breakwater or the performance of an oscillating water column device.

This framework gives a step-by-step statistical background of the computational approach with the attractiveness of dealing with an open free source that the students can access and modify for its use in real engineering problems, bridging the gap between theory and application and allowing the critical analysis of results. The final paper will show the full design of the tool as well as some examples of applications.

Keywords:

Non-stationarity, probability models, stochastic approach, random vector processes.