Random Processes

Probability and statistics provide an excellent tool for understanding, modeling and communicating uncertainty in engineering systems. In many applications there is the added challenge of considering random quantities that vary over time and/or space. Examples can be found in seismic applications, financial markets, heterogeneous materials, and image processing, among many others. This course provides an introduction into some of the ways in which random processes and random fields are measured, quantified and communicated. Through video lectures, activities, and interactive content, students will learn about correlation functions, spectral density functions, local average processes and Monte Carlo simulation. There will be an emphasis on understanding each concept, estimating these quantities from data, and using this data as the basis for generating realistic sample random processes.

By the end of this course, you will be able to:

• Explain the meaning of the correlation function, the spectral density function, homogeneity, ergodicity.
• Identify parameters of a random process based on available data.
• Relate random process descriptors to reliability via maximum value distributions.
• Simulate a random process with desired correlation and/or spectral density function.