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perform a Monte Carlo analysis of a MapleSim model


Calling Sequence





Calling Sequence

MonteCarlo(C, params, options)




module; output of GetCompiledProc



set or list of equations; model parameters to vary



(optional) equation(s) of the form option = value; specify options for MonteCarlo


The options parameters are optional parameters of the form option = value, where option is one of the names listed below. These are keyword parameters; the left side of the equation is the keyword and the right side is the value. Each keyword parameter has a default value that is assigned if the parameter is not passed.



C_opts = set or list of equations


Options passed to C.  The available options depend on C; see GetCompiledProc for details. The default is an empty set.



include_nominal = true or false


True means include, as the first data record, the result of using the nominal values of the random variables. Depending on use_mean, the nominal value of a parameter is either retrieved from the model or computed from the random variable using Statistics[Mean]. The default is false.



num_sims = positive integer


The number of simulations. Does not include the simulation using nominal values; see include_nominal. The default is 10.



ret_record = true or false


True means return a record with the following fields:


data: a list of Matrices, these are the simulation results;


params : a list of the parameter names;


values : a Matrix of the parameter values. The k-th column contains the values for the k-th name in the params field.


errors : a list of strings of the errors that occurred during the corresponding simulation. This field is present only if the C module was generated with the witherror option to GetCompiledProc.


False means return a list of records, one for each simulation. Each record has the following fields:


data: the Matrix that is the simulation result; the first column is the time samples, the remaining columns are the values of the outputs of C.


params: the set of equations specifying the value of each parameter.


errors: a string corresponding to an error that occurred during the simulation; the empty string indicates no error occurred. This field is present only if the C module was generated with the witherror option to GetCompiledProc.


The default is false.



use_mean = true or false


True means use Statistics[Mean] to compute the nominal value of the parameters, otherwise use the values assigned by the model. This option is used with include_nominal. The default is false.



use_threads = true or false


True means use the Threads package to compute the results in parallel. The default is true.



The MonteCarlo command performs a Monte Carlo analysis of a MapleSim model. A MapleSim model is repeatedly simulated with selected model parameters varied using specified random variables.


The C parameter is a module, the output of GetCompiledProc. See the Advanced Usage section in the Examples for further details.


The params parameter specifies the model parameters that are varied. It is either a set or list of equations. The left side of each equation is the name of the parameter, the right side is a random variable.


By default, the result is a list of records, one for each simulation. If the include_nominal option is set to true, the first record corresponds to the output of the model with nominal parameter values.  Each record has the following fields:


params: the set of equations specifying the value of each parameter;


data: the Matrix whose first column is the time samples of a simulation and whose remaining columns are the values of the outputs of C.


errors : a string corresponding to an error that occurred during the simulation; the empty string indicates no error occurred. This field is present only if the C module was generated with the witherror option to GetCompiledProc.




Assign model the filename of the MapleSim model we want to analyze.


Use MapleSim[LinkModel] to link to the MapleSim model.


Inspect the available parameters.




Use the GetCompiledProc export of A to assign the module that will be passed to MonteCarlo. Assign nominal values for the two model parameters of interest.


Assign a simple procedure that generates a random variable uniformly distributed around a nominal value.


Call MonteCarlo, using C1 and assigning random variables for the L and C model parameters. The C_opts option specifies that the final time of the simulation is 0.5 seconds. The include_nominal option means the first simulation corresponds to the given nominal values of the model parameters. The num_sims option specifies that 100 randomized simulations are made.


Verify that the values of the parameters for the first simulation are the nominal values. The subexpression results[1] accesses the first element of the list results. That element is a record.  The full expression results[1]:-params specifies the params field of that record.  The params field, as seen below, is a set of equations that express the sampled values of the parameters.




Display the data for the final two sample times for the first (nominal) simulation. The notation results[1] accesses the first record stored in the list results; results[1]:-data references the data field (a Matrix) in that record; the [-2..-1,..] indices extract a sub-block of the Matrix (the last two rows, all columns), see rtable_indexing.




The first column is the time, the remaining column(s) corresponds to the output(s) of C1:




Plot the output versus time for all records. To do that, generate a set of two-column matrices, the first column being the time, the second being the output of interest. The seq command is used to sequentially access the Matrices in results. The expression rec:-data[..,[1,2]] corresponds to the appropriate sub-block of the Matrix in the data field; in this case, all rows (..) and the first and second columns, ([1,2]). Because each Matrix is already two-columns, we could have used the simpler notation rec:-data, however, if the system has more than one output (probe), we would then use the notation rec:-data[..,[1,k]], where k is the column of interest.

plot({seq(rec:-data[..,[1,2]], rec=results)});

Generate a histogram of the final output point by creating a Vector of the data and passing it to Statistics[Histogram]. The expression rec:-data[-1,2] evaluates to the final row (-1), second column, of the data Matrix of a record in the results list.

X := Vector([seq(rec:-data[-1,2], rec=results)]):


Assigning an Objective Procedure


The module returned by GetCompiledProc has a SetObjective export that uses a provided procedure to manipulate the output. Here we pass it a procedure to square the output (column two of the matrix).

C1:-SetObjective( proc(M)
                  local i;
                      for i to upperbound(M,1) do
                          M[i,2] := M[i,2]^2;
                      end do;
                  end proc):


Run a MonteCarlo analysis with the squared output.


plot({seq(rec:-data[..,[1,2]], rec=results2)});


The objective procedure is not limited to modifying the matrix of simulation data, it can also compute a value from the matrix and return that. Here we assign a procedure that returns the peak of the squared result.

C1:-SetObjective(proc(M) max(map(x->x^2, M[..,2])) end proc):


Run a MonteCarlo analysis; use the ret_record option to return a record.



Compute the range over which the peak value varied.




See Also