DES verification and stochastic analysis

Due date: 11.11.2016

In this assignment you will

1. verify your FSA model by checking its execution on real data
2. compute the average return time to nominal state
3. estimate the likelihood the operations proceed without any switch failures

There is no need to do more than you're asked!! No need to write up a report, draw pictures, enclose your work in a nice binding.

Task 1: Each group is to select one of the following data files representing system execution in a 12 hour period. Coordinate with other groups to ensure that no two groups are working with the same data set.

• DaySim_01_2015.mat - Rakovcova, Myslivec, Kunes

• DaySim_02_2015.mat -Ronzka, Steinberger

• DaySim_03_2015.mat -

Verify your FSA is consistent with the data set:

1. Upload the data set into Matlab. The string of events is contained in the variable ea.
2. Import the FSA model of your controlled system (previously we called this the specification of the system beahvior) into Matlab.
3. Execute the string of events and compute the final state of your physical automaton. Submit the final state using the vector notation, e.g., (3,VN,OFF), together with the corresponding component automata, e.g., (T_switch, T_sensor, T_timer).

Note: the given string also includes events of the capacitor system. Your automata don't include these events. You may have to make some slight modifications to your automata to allow for events that are not in the set of events.

Task 2: The firing times of events in the string ea are given in tea. First, for the DES define the set of nominal states Qn. The nominal states represent normal system operation, i.e., tap changer in state 2, voltage sensor in the normal range, and timer turned off. The specification automata can be in any state. The behavior of the capacitor system can also be ignored.

For your chosen dataset,

1. Break up the string into substrings that satisfy:
   1. each substring begins and ends at nominal state.
   2. each substring does not include another substring that satisfies the previous condition.
2. Compute the time duration of each substring.
3. Compute the average duration of each substring. This is your mean return time to the nominal set of states.
4. Submit the set of substrings together with their execution times. Submit the mean return time.

Task 3: The Markov Chain model of the tap and capacitor switch system is illustrated in the attached file: MC_switchFail.pdf. In this file you will find the schematic and the actual probabilities you will use to solve Task 3. In this task, use the Markov Chain theory discussed in lecture to compute the probability pnf that the entire string executes as if no switch (tap or capacitor) failures occurred. Submit the probability pnf.

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Notes

• For the continuous time Markov Chain, recall the transition matrix Q contains the propensities off diagonal. Diagonal elements of Q are calculated form the off-diagonal elements so that each column sums to zero.