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Mode: Online instructor sessions and teaching fellow sessions

The course covers the following topics: forces and moments, free body diagrams, static analyses for trusses, beams, and frames, set theory and fundamental elements of probability theory, random variables, probabilistic modeling, formulation of the reliability problem, and Monte Carlo Methods for simulations.

For high school and undergraduate students, this course provides a solid base in static analysis, applied probability and Bayesian statistics as used by engineers. It introduces them to the increasingly important topic of engineering risk analysis. For graduate students, in addition, this course provides a strong background for pursuing more advanced courses on non-deterministic methods.

Topic: Principle of statics and application to trusses

• Force and moments

• Free body diagram

• Equilibrium and determinacy

• Truss analysis

• Planar trusses

In this week, we came to know each other in this group and decided to work together. Then we shared our perspectives concerning this project and started to make schedules about what we would do in the next few weeks.

Topic: Shear and moment curves and application to beams and frames

• Shear curves

• Moment curves

• Beam analysis

• Frame analysis

In this week, we finished the lecture and our homework in time. By the way, all the contents in the lectures, mentor sessions and homework were drawn from Leet, K., Uang, C-M., and J. Lanning (2008). Fundamentals of Structural Analysis. McGraw-Hill Higher Education, New York, NY.

Two of us are juniors(Me and Atom), and Rick is about to be junior in the next term, so it is a fact that we have already learned all the contents in Week 1 and Week 2 in Mechanics of Materials and Structural Mechanics earlier. It's nothing new for us but in English 😁.

Topic: Fundamental concepts of risk and probability

• Event

• Axioms of probability

• Elementary rules of probability

• Conditional probability and statistical independence

• Bayes' rule

• Theorem of total probability

• Discrete, continuous, and mixed random variables

• Probability distributions

• Partial descriptors of a random variable

• Common distribution models

In this week, we were asked to work on our final report: a full probabilistic analysis of a structure. At first, the requirements were kind of vague for us, so we selected a complicated truss bridge for a Bayesian Network construction. But we were unsure about our selection so we asked for the mentor for advice, he said that our structure was too complicated and it was supposed to be simple enough to accomplish all calculation by hand. Finally we simplified our structure and selected a rigid frame with $2^o$ indeterminacy for our analysis.

Topic 4: Reliability analysis

• Introduction to Machine Learning

• Element of fragility analysis

• Limit-state functions

• Capacity and demand safety format

• Component vs. system reliability problems

In this week, we struggled with the promotion of our final project. At first, we were confused and quite aimless about the probabilistic analytical part of our report. And I thought I had a very deep understanding of what I've learned from the lesson Probability Theory and Mathematical Statistics when I was a first-grade college student. So I constructed a hypothetical model for our probabilistic analysis. Then I identified the distribution of our teamwork and finished the probabilistic model construction by myself.

By the way, all the contents in the lectures, mentor sessions and homework were drawn from Ang, A. H-S., and W-H Tang (2007). Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering. John Wiley, New York, NY and Alpaydin E. Introduction to machine learning. MIT press, 2020. The knowledge in probabilistic part was almost identical to what I've learned from the lesson Probability Theory and Mathematical Statistics, but it was not meant to be applied to engineer domain. Thus, I started to take the probabilistic analysis into account when thinking about structure design. The basic concepts in the lectures were nothing new but they provided me with new insight and inspired me to combined what I've learned before both in mathematics and engineering subjects.

As for the Machine Learning, I was so surprised that the professor mentioned something about ML. Compared to most of my companions, I've learned ML before both in class and after class, this subject was so attractive for me because I thought it was quite powerful and prospective. The course I've attended before was set up by school of computer science so actually I didn't possess chances to apply ML to my major, structural engineer or structural mechanics. However, I see some probability in this project, so it's highly desirable for me to apply what I've acknowledged from ML to the final report and later academic paper writing.

In this week, our group had a brief presentation of what we have done before with the professor and the mentor, and we were suggested to complicate our structure and compute the internal force step by step. Then we modified our structure and normalized the process of the internal force.

In addition to this, we were largely inspired by the work of Group 6(we are Group 3), actually they had a good understanding of the GB50009 which is a standard of PRC, and the way they processed uncertainties in both capacities and loads is quite inspiring, which allowed us to work the core problem(probability part) much more effectively.

In this week, we have made great progress. Firstly, we were smoothly converted from deterministic part to probabilistic part using unit load method, and successfully built a connection between both parts which are quite physically meaningful. I thought one reason for this may be our complete structure mechanics knowledge we've learned before and our sophisticated simplification of the structure made us process the internal forces much more easily than other groups, which left us more time and possibility to process probabilistic analysis.

Secondly, I was super inspired by Prof. Smith's paper: A Monte Carlo based method for the dynamic fragility analysis of tall buildings under turbulent wind loading. We've just learned what Monte-Carlo simulation was, but were yet unsure how to utilize it and even how to build a connection between it and engineering structures. However, we were not stuck in the beginning because this paper is definitely a classic example of Monte-Carlo simulations in engineering structures. So I got many ideas from it and through several days' MATLAB coding and visualizing via MATLAB, Origin and even Photoshop, we got satisfactory results and high recommendations from both professor and mentor, they said our project was far close to the perfect and was exactly what they expected us to achieve at the beginning of the project.

In conclusion, we make the most of what we have learned in class and achieve the final goals on the basis of our own research and independent thinking. Otherwise, we also had efficient communication with each other through online meeting almost three times a week.

In this week, we presented our work perfectly. We had an explicit division of work and demonstrated our slides clearly. The summary of our work is as follows:

This report presents a numerical algorithm for a full probabilistic analysis of a container, using Monte Carlo (MC) method. The proposed MC numerical procedure was used to compute the uncertainties in properties of the steel (e.g., the maximum bending moment the structure could sustain), and to derive the statistics of the dynamic response in the presence of uncertainty in the wind loading. The displacement method was utilized to obtain the internal forces of the container. This report also presents the computation of the structural fragility curves of the container under extreme winds.

The results of this report provide some cases about the expected losses associated with the failure of the failure of the container and related preventive measures to reduce the losses.

All the documents and codes are placed in FinalReport, all the questions and solutions are placed in Homework, and related information is shown in ProjectInfo, all the papers which gift us inspirations are placed in inspirations.

Paolo Gardoni is the Alfredo H. Ang Family Professor and an Excellence Faculty Scholar in the Department of Civil and Environmental Engineering in the Grainger College of Engineering at the University of Illinois at Urbana-Champaign. He is a Professor in the Department of Biomedical and Translational Sciences in the Carle Illinois College of Medicine, and a Fellow of the Office of Risk Management & Insurance Research in the Gies College of Business at the University of Illinois at Urbana-Champaign. Prof. Gardoni has several international courtesy appointments including at Loughborough University in the UK, and the Harbin Institute of Technology and Jianghan University both in China.

E-mail: [email protected]

Website: Paolo Gardoni