sdo.GriddedSpace
Description
Use sdo.GriddedSpace to generate samples of parameter values over
a grid of values for sensitivity analysis. Where sdo.ParameterSpace allows you to draw random samples of parameter values from
probability distributions, sdo.GriddedSpace allows you to generate uniform or
nonuniform grids of parameter values at which to evaluate your cost function or design
objectives. You can generate gridded samples of continuous or discrete parameters obtained
from a Simulink® model using sdo.getParameterFromModel. You can also create
composite spaces such that sdo.sample samples some parameters across a
grid and generates random samples of other parameters.
Use the sdo.GriddedSpace object as an input to the
sdo.sample command to generate values of model parameters across the
grid. Then, use sdo.evaluate to analyze how the model parameters
influence the design objectives.
Creation
Description
gs = sdo.GriddedSpace(p)param.Continuous and
param.Discrete parameters specified in p. The grid
values for each parameter are set as follows:
Continuous parameter with nonzero nominal value —
{nom-10%,nom,nom+10%}, wherenomis the nominal value.Continuous parameter with
nom = 0—{-1,0,1}.Discrete parameter — The
ValueSetproperty of the discrete parameter.
This syntax is most useful when p contains discrete parameters.
For continuous parameters, use the parameterValues input argument to
specify the grid of values.
gs = sdo.GriddedSpace(p,parameterValues)p.
Input Arguments
Properties
Object Functions
sdo.sample | Generate parameter samples for sensitivity analysis |
combine | Combine parameter spaces defined for sensitivity analysis |
addParameter | Add parameter to sdo.ParameterSpace or
sdo.GriddedSpace object |
removeParameter | Remove parameter from sdo.ParameterSpace or
sdo.GriddedSpace object |
Examples
This example uses the sdoCSTR model discussed in detail in Design Exploration Using Parameter Sampling (Code). Among the parameters in this model are the reactor cylinder area A and height h. Suppose that you want to test the sensitivity of your design objectives over a grid of values for these parameters. To start, open the model and create param.Continuous objects to represent the two parameters.
mdl = "sdoCSTR"; open_system(mdl); p = sdo.getParameterFromModel(mdl,{'A','h'});
Specify the grid of values for each parameter by placing the values in a cell array. The grids in this example are uniformly spaced, but you can also use nonuniformly spaced values.
Avals = {0.2 0.6 1.0 1.4 1.8 2.2};
hvals = {0.5 1.5 2.5 3.5};Define the gridded parameter space using this grid.
gp = sdo.GriddedSpace(p,{Avals,hvals});Sample the parameter space to generate all the combinations to use for sensitivity analysis. By default, sdo.sample generates an exhaustive list of all possible combinations in the parameter space, (Avals,hvals) = (0.2,0.5), (0.6,0.5), (1.0,0.5), ..., (1.4,3.5), (1.8,3.5), (2.2,3.5). Thus, the sampled values make up a table of 24 rows.
values = sdo.sample(gp)
values=24×2 table
A h
___ ___
0.2 0.5
0.6 0.5
1 0.5
1.4 0.5
1.8 0.5
2.2 0.5
0.2 1.5
0.6 1.5
1 1.5
1.4 1.5
1.8 1.5
2.2 1.5
0.2 2.5
0.6 2.5
1 2.5
1.4 2.5
⋮
You can visualize the sampled values for a view of the distribution of samples.
sdo.scatterPlot(values)
Use values with sdo.evaluate to evaluate your design objectives at the sampled parameter values. For instance, if you have defined a cost function design.m to capture your design objectives, you can use values in a call to sdo.evaluate as follows.
[yR,infoR] = sdo.evaluate(@design,p,values);
The example Exhaustive Sampling Across a Grid of Parameter Values shows how to create exhaustive grids of parameter values. Suppose instead that you want to create a set of specified pairs of parameter values (A1,h1), (A2,h2), and so on. To do so, use the sequential method of sampling the gridded parameter space. Open the model and create param.Continuous objects to represent the two parameters.
mdl = "sdoCSTR"; open_system(mdl); p = sdo.getParameterFromModel(mdl,{'A','h'});
Specify the values (A1, A2, ...) and (h1, h2, ...). For sequential sampling, use the same number of values for each parameter.
Avals = {0.2 0.6 1.0 1.4 1.8};
hvals = {0.5 1.0 1.5 2.0 2.5};Define the gridded parameter space using this grid.
gp = sdo.GriddedSpace(p,{Avals,hvals});Specify sequential sampling using the Method property of the Options property of gp.
gp.Options.Method = 'sequential';Finally, sample the parameter space to generate the parameter samples (Avals,hvals) = (0.2,0.5), (0.6,1.0), ..., (1.8,2.5).
values = sdo.sample(gp)
values=5×2 table
A h
___ ___
0.2 0.5
0.6 1
1 1.5
1.4 2
1.8 2.5
You can visualize the sampled values for a view of the set of samples.
sdo.scatterPlot(values)
Use values with sdo.evaluate to evaluate your design objectives at the sampled parameter values. For instance, if you have defined a cost function design.m to capture your design objectives, you can use values in a call to sdo.evaluate as follows.
[yR,infoR] = sdo.evaluate(@design,p,values);
You can sample discrete parameters across their full grid of allowed values or across a subset of those values. As with continuous parameters, sampling can be exhaustive or sequential.
The sdoMotorPosition model includes a resistor network containing resistors R1, R2, R3, and R4. Open the model, and create a vector of param.Discrete objects to represent the resistor values.
mdl = "sdoMotorPosition"; open_system(mdl) params = sdo.getParameterFromModel(mdl,[],{'R1','R2','R3','R4'});
Specify sets of allowed values and current values for these parameters,
% R1 values params(1).ValueSet = [39 43 47 51 56]; params(1).Value = 47; % R2 values params(2).ValueSet = [150 160 180 200 220]; params(2).Value = 180; % R3 values params(3).ValueSet = [8.2 9.1 10 11 12]; params(3).Value = 10; % R4 values params(4).ValueSet = [8.2 9.1 10 11 12]; params(4).Value = 10;
To generate samples using the full set of allowed values, create the gridded parameter space without specifying any values.
gspace = sdo.GriddedSpace(params)
gspace =
GriddedSpace with properties:
ParameterValues: {{1×5 cell} {1×5 cell} {1×5 cell} {1×5 cell}}
Notes: []
Spaces: {1×0 cell}
ParameterNames: {'R1' 'R2' 'R3' 'R4'}
Options: [1×1 sdo.GriddingOptions]
Generate a sequential sample set, (R1_1, R2_1, R3_1, R4_1), ..., (R1_5, R2_5, R3_5, R4_5), by setting the sampling method of gspace.
gspace.Options.Method = 'sequential';
svalues = sdo.sample(gspace)svalues=5×4 table
R1 R2 R3 R4
__ ___ ___ ___
39 150 8.2 8.2
43 160 9.1 9.1
47 180 10 10
51 200 11 11
56 220 12 12
To draw samples from a subset of the allowed parameter values, reset the values in gspace using setValues. Alternatively, specify the subsets when you create the gridded parameter space. The values you specify must be subsets of the ValueSet property of params and must include the current value of each parameter.
gsubspace = sdo.GriddedSpace(params,...
{{39 43 47},{150 160 180},{8.2 9.1 10},{8.2 9.1 10}});Suppose that you want an exhaustive of every possible combination of R1, R2, R3, and R4 values in these subsets. Use sdo.sample to obtain these samples.
gsubspace.Options.Method = 'exhaustive';
evalues = sdo.sample(gsubspace)evalues=81×4 table
R1 R2 R3 R4
__ ___ ___ ___
39 150 8.2 8.2
43 150 8.2 8.2
47 150 8.2 8.2
39 160 8.2 8.2
43 160 8.2 8.2
47 160 8.2 8.2
39 180 8.2 8.2
43 180 8.2 8.2
47 180 8.2 8.2
39 150 9.1 8.2
43 150 9.1 8.2
47 150 9.1 8.2
39 160 9.1 8.2
43 160 9.1 8.2
47 160 9.1 8.2
39 180 9.1 8.2
⋮
Version History
Introduced in R2023a
See Also
sdo.ParameterSpace | sdo.sample | combine | sdo.getParameterFromModel | addParameter | removeParameter | setValues
