MapleSim[Analysis]
MonteCarlo
perform a Monte Carlo analysis of a MapleSim model
Calling Sequence
Parameters
Options
Description
Examples
MonteCarlo(C, params, options)
C
-
module; output of GetCompiledProc
params
set or list of equations; model parameters to vary
options
(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
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
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
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
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
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
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.
withMapleSim:-Analysis:
withStatistics:
Assign model the filename of the MapleSim model we want to analyze.
model≔catkerneloptstoolboxdir=MapleSim,/data/examples/RLCcircuit.msim:
Use MapleSim[LinkModel] to link to the MapleSim model.
A≔MapleSim:-LinkModelfilename=model:
Inspect the available parameters.
A:-GetParametersallparams
C=1,L=1,T=600320,R1_alpha=0,R=1,S1_amplitude=1,S1_f=1,S1_offset=0,S1_phase=0
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.
C1≔A:-GetCompiledProcparams=L=4,C=5:
Assign a simple procedure that generates a random variable uniformly distributed around a nominal value.
rv≔nom,tol↦RandomVariableUniformDistributionnom⋅1−tol,nom⋅tol+1:
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.
results≔MonteCarloC1,C=rv5,0.1,L=rv4,0.1,C_opts=ds=0.01,tf=1,include_nominal,num_sims=100:
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.
results1:-params
C=5.,L=4.
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.
results[1]:-data[-2..-1,..];
0.990000000000001−0.006408918431351991.−0.00647314869227591
The first column is the time, the remaining column(s) corresponds to the output(s) of C1:
C1:-GetOutputs
Voutt
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)]):
HistogramX
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; M; end proc):
Run a MonteCarlo analysis with the squared output.
results2≔MonteCarloC1,C=rv5,0.1,L=rv4,0.1,C_opts=ds=0.01,tf=1,include_nominal:
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.
results3≔MonteCarloC1,C=rv5,0.1,L=rv4,0.1,C_opts=ds=0.01,tf=1,include_nominal,ret_record:
Compute the range over which the peak value varied.
evalf2min..maxresults3:-data
0.0031..0.0038
See Also
MapleSim
MapleSim[Analysis][ParameterSweep]
MapleSim[LinkModel]
Download Help Document
