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The purpose of this exercise is to practice basic Markov chain calculations.
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The purpose of this exercise is to practice basic Markov chain calculations for a discrete time, discrete state, finite state example. The Markov chain is a stochastic representation of the distribution grid where the events have the following physical meaning (ve = voltage error; f0 = voltage back to norm without intervention; s1 = first transformer switch; f1 = voltage back to norm following first switch; s2 = second transformer switch; f2 = voltage back to norm following second switch).
  
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Step 1: Consider the Markov Chain in Figure 1. Is the Markov chain ergodic?
  
Step 1: Consider the Markov Chain in Figure 1.  
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Step 2: In Matlab, define the 1-step probability matrix P.
  
[[File:Exercise3_MC.png|thumb|Figure 1: Markov Chain]]
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Step 3: Find the stationary distribution of this Markov chain.
  
Step 2: create the component FSA models
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Step 4: Calculate the expected number of steps required to return back to norm following a voltage error.
* Download The Case study component graphs - [http://ccy.zcu.cz/files/MS2_2014/MS2_RS_automata_components_2.pdf FSA schematics].
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* Build the finite state machines by following the file format here: [https://www.eecs.umich.edu/umdes/projects/lib/formats.html#fsm FSM file format]
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* note 1: the file extension is not important
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* note 2: place the files in a separate directory
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Step 3: test the accessibility of the constructed FSA
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* copy and paste the UMDES executables "acc" and "co_acc", which compute the accessible and co-accessible parts of your FSAs, into the FSA folder
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* execute the commands
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* the acc and co_acc operations must work and must not delete any states
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step 4: download the following Matlab files and import some FSMs into Matlab
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* [http://ccy.zcu.cz/files/MS2_2014/MATLAB2UMDES.m MATLAB2UMDES.m]
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* [http://ccy.zcu.cz/files/MS2_2014/UMDES2MATLAB.m UMDES2MATLAB.m]
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* [http://ccy.zcu.cz/files/MS2_2014/setEvents.m setEvents.m]
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* [http://ccy.zcu.cz/files/MS2_2014/executeEvents.m executeEvents.m]
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* follow the instructions in UMDES2MATLAB.m to import an automata into Matlab
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step 5: test whether your automata accept the following strings, verify the final states are correct
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* T_sensor: s1 = {'vm' 'vn' 'vp' 'vm' 'vp'}, s2 = {'vm' 'vn' 'vm' 'vp' 'vp'}
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* T_switch: s1 = {'tp' 'tf' 'tm' 'tf' 'tm' 'tf' 'tm'}, s2 = {'tm' 'tf' 'tm' 'tp' 'tf' 'tp' 'tf'}
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Revision as of 21:48, 12 November 2020

The purpose of this exercise is to practice basic Markov chain calculations for a discrete time, discrete state, finite state example. The Markov chain is a stochastic representation of the distribution grid where the events have the following physical meaning (ve = voltage error; f0 = voltage back to norm without intervention; s1 = first transformer switch; f1 = voltage back to norm following first switch; s2 = second transformer switch; f2 = voltage back to norm following second switch).

Step 1: Consider the Markov Chain in Figure 1. Is the Markov chain ergodic?

Step 2: In Matlab, define the 1-step probability matrix P.

Step 3: Find the stationary distribution of this Markov chain.

Step 4: Calculate the expected number of steps required to return back to norm following a voltage error.