Topic outline

  • Assignments

    The weekly submissions will be graded from 1-5. The weekly group submissions will contribute up to 50% of the course grade. The remaining 50% of the grade is defined by the final exam or the long-learning diary that are based on individual works. The submission boxes you can find for each week by selecting from left margin the week and further the associated Group and Individual submission boxes. Late submissions will be reduced by 10% on the grade. In case you need more time for submission, ask it well before the deadline (i.e. latest few days before).   

    Individual work

    Create a long learning diary for each week according to the template found from Templates-section. Long learning diary can be used to replace the exam. Therefore it must be individual and it will be checked in the end of the course for similarity by the Turnitin software. 

    Group work

    Each week report the work done, see group report template from Templates-section. Show clearly the roles of the group members in the report (leader, algorithms, data, reporting) in table format – in case of problems this table is used to identify the source of problems. 

    Week 1, Given Sept 14th 2021, Deadline Sept 20th 2021, 23:59 – 1/12 of the course grade

    The idea of the round is to create rough overview of the treatment of random process of your engineering project. This is based on open scientific literature and data search on any projects one or some of your group members have on related subject. For example, ship in ocean waves, windmill on desert, tire of a car, airplane wing during flight etc.   

    Grade 1: Form the group of 3-5 students. Agree the meeting times. Define the roles of members for each week (report this in tabular format). Make table of weekly grades (goal vs. realization). Select the topic for engineering problem to be solved during the course where random loads are present. Give 1-2 pages description of that. 

    Grade 3: Describe the random variable associated with your engineering problem (case, location) based on related and relevant journal or conference articles (see selected articles -section for examples). Describe the expected probability distribution (both short and long term). Describe how you could define the random variable (measurements/sensors, references/literature, simulations/method) and required engineering tools and in which courses you learn to use these.

    Grade 5: Compute an average, standard deviation and autocorrelation for sinusoidal signal. Vary the signal length and discuss what happens to these mathematical properties. Extend the analysis to cover the summation of several sinusoidal component waves. 

    Week 2, Given Sept 21st 2021, Deadline Sept 27nd 2021, 23:59 – 1/12 of the course grade

    The idea of the round is to acquire confidence that we can model random processes by trigonometric functions and we learn to understand the factors that affect the results. We learn to process random event both in time and frequency domains and understand their meaning for design. 

    Grade 1: Create in Matlab a scrip that computes time signal for 1-DoF equation of motion with forced excitation and damping. Separate from there the transient and stationary parts. Extract from the stationary part the frequency and amplitude by Fast Fourier Transfrom (FFT) and assess the correctness of the result.  

    Grade 3: Create a script in MATLAB multiple sinusoidal signals in time domain and their sum. Present that in a plot. Perform Fast Fourier Transform (FFT) and assess the correctness of the result. Show both narrow and broad banded processes in time domain. Perform FFT on these and use some windowing technique to improve the results. 

    Grade 5: Create a freak event in time domain from the spectra by phase matching. Discuss in the report the likelihood of such event in practice based on open literature (journals and conferences). Also discuss the roles of time and frequency domain in the design process. 

    Week 3, Given Sept 28th 2021, Deadline Oct 4th 2021, 23:59 – 1/12 of the course grade

    The idea of the round is to learn to treat environmental loading with spectra and to understand the associated time spans and physics of stationary and developing stages. We learn to assess the response by using load spectra and response amplitude operator. We understand the difference between narrow and broad-banded processes. 

    Grade 1: Based on the 1st week report, describe the random variable formation from physical viewpoint (i.e. what causes the random nature, developing stage and stationary stage, time spans etc.). Describe the ensemble you could have for your application case. Under what circumstances you can define the random load and response for your application case using stochastic methods? Describe what kind of information is needed to estimate the magnitude of loading (e.g. meteorological) for you engineering problem. What are the random and stationary parts of the load in your application case and associated time spans? Explain what happens if time spans are changed?

    Grade 3: Describe and select the load spectrums you can use to assess the random response of your engineering problem. Justify the selection. Compute the response for random loading based on RAO from open literature. Is the response of your system narrow or broad-banded – how can you make it narrow-banded? 

    Grade 5: Describe the process to measure the random excitations and responses. What are the sensors needed? Find article (different from previous weeks) related to your engineering problem that has discussed the load spectra relevant to your selected application case. The article must be recognized by Scopus. 

    Week 4, Given Oct 5th 2021, Deadline Oct 11th 2021, 23:59 – 1/12 of the course grade

    In this round we learn to understand how we can assess probabilities from the spectra numerically. The idea is to process the time history of the random event by using different numerical techniques and to derive the probability distributions. We also compare the results to those we learned in the first week, to make sure that our physical process and associated time signal corresponds that of the open literature.  

    Grade 1: Present the load and response spectrum and RAO in one figure. Are these narrow or broad banded? Create from the load and response spectrums the time histories.  

    Grade 3: Create and test a Matlab script that numerically calculates the time average and standard deviation for random signal for load and response and extracts the probability distribution for deviation from the mean. What can you say about the mean values of these over different time spans? Do we have zero mean? In case not, manipulate the spectrum in the way that we get zero mean (clustering).

    Grade 5: Perform the Rainflow-analysis. Describe the associated probability distributions for elevation and signal height and their correspondence to those proposed in open literature (Round 1).

    Week 5, Given Oct 12th 2021, Deadline Oct 18th 2021, 23:59 – 1/12 of the course grade

    In this round we learn to understand how we can assess probabilities from the spectra directly without tedious numerical procedures by using the spectral moments. In order to do this, we must first make sure that the signal satisfies the mathematical conditions required for this approach to be valid.  

    Grade 1: What mathematical conditions must be valid in order to derive the probabilities directly from the spectrum? Compute the conditions from your load and response spectra.    

    Grade 3: Calculate the maximum load and response amplitude by using the spectral moments. Compare the results to those derived earlier with numerical techniques and/or from open scientific literature (i.e. validate the values obtained). 

    Grade 5: Discuss the reasons for agreement / disagreement between results obtained numerically or by using spectral techniques.

    Week 6, Given Oct 19th 2021, Deadline Oct 25th 2021, 23:59 – 1/12 of the course grade

    We learn to compute cycles and both short and long term estimates for the loading and responses. 

    Grade 1: Make a short term estimation of maximum amplitude of load and response based on the tools derived during this and two previous weeks. Discuss the result. 

    Grade 3: Derive a long term estimate of maximum amplitude of load and response based on sequence of short term estimates. 

    Grade 5: Discuss the associated connection between the short and long term estimates and reflect the findings to those from Round 1.


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Week 1. Mission and Case Definition