Probability Computations in Civil Engineering
1st year of follow-up master's studies - full-time form

Summary: In the subject Probability Computations in Civil Engineering students learn theoretical background and practical information about probabilistic assessment of load-carrying structures. For that purpose, they should master the probability and structure reliability theories. The key feature of the probabilistic method is that it is possible to express variability of input quantities in a stochastic (probabilistic) form, for instance, by histograms. Unlike the applicable standards and procedures which are based on deterministic expression of input quantities (using a single value – a constant), the probabilistic methods provide more precise reliability assessment and improved safety for those who use the buildings and structures.

 

Materials for study - lectures
 

Topic 1

Introduction to the course: Probability calculations in civil engineering, examples of selected calculations.

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(6.0 MB)

Topic 2

Probabilistic expression of random variables: Basic concepts and principles of the theory of probability theory and mathematical statistics, random phenomenon, probability of random phenomenon, random variable, probability distribution, histogram, statistical moments, quantile.

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(3.2 MB)
Example 1
(0.2 MB)
Example 2
(0.2 MB)

Topic 3

Monte Carlo method: Inclusion of the Monte Carlo method into a list of probability methods, Monte Carlo history, Buffon's needle, the first systematic use of the Monte Carlo method. Law of large numbers, generators (pseudo) of random numbers. Numerical integration with the Monte Carlo method. An illustrative example of elemental calculation using the Monte Carlo method.

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(5.9 MB)

Example 1
(0.2 MB)

Example 2
(10.2 MB)

Example 3
(0.3 MB)

Topic 4

Simulation Based Reliability Assessment (SBRA): Insertion of the SBRA method into the overview of probability methods, SBRA simulation method, probability computation by SBRA (random quantities, computational model, reliability function analysis), illustrative examples of probability calculations by SBRA.

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(10.7 MB)
Example 1
(0.3 MB)
Table 1
(0.4 MB)

Topic 5

Parametric probability distribution of a continuous random variable: Overview of important continuous probability distribution, Gaussian probability distribution, logarithmic-normal probability distribution, coefficient of determination.

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(3.0 MB)
Example 1
(0.2 MB)
Example 2
(0.4 MB)

Topic 6

Statistical dependence of input random variables: Correlation and correlation coefficient, correlation matrix. Double and triple histogram.

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(16.0 MB)
Example 1
(0.2 MB)

Topic 7

Stratified and Advanced Simulation Methods: Incorporating stratified and advanced simulation methods into a list of probability methods. Latin Hypercube Sampling - LHS, the principle of the method and its application. Method of Importance sampling.

Approximation methods: FORM and SORM methods. Response surface method.

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(1.7 MB)

Topic 8

Direct Optimized Probabilistic Computation - DOProC: Incorporation of the Direct Optimized Probability Computation Method into the overview of probability methods, substance of the method, basic computational algorithm, DOProC method application in ProbCalc programming system, demonstration of calculation. Optimization techniques in DOProC method, theoretical principles of individual optimization techniques, examples of calculation using individual optimization procedures, recommended optimization techniques utilization in probability calculations by DOProC method.

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(9.8 MB)

Topic 9

Probabilistic calculations in practice: Demonstrations of application software using the DOProC method.

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(14.8 MB)

Topic 10

Reliability and safety of building structures: Probabilistic approach to assessment of reliability and safety of building structures, calculation of probability of failure: load effect, resistance of the structure, computational model, reliability function, reliability index, target probability. Design working life of a structure.

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(2.4 MB)
Example 1
(0.2 MB)
 

Compulsory and recommended literature:

  • Robert E. Melchers, Andre T. Beck, Structural Reliability Analysis and Prediction (3rd Edition), 528 pages, 2018, ISBN-13: 978-1119265993, ISBN-10: 1119265991. 

  • Anthony J. Hayter, Probability and Statistics for Engineers and Scientists (4th Edition), 864 pages, 2012, ISBN-13: 978-1111827045, ISBN-10: 1111827044.

Useful website and learning materials