What Models Are Available?
What Is a One-Stage Model?
A one-stage model fits a model to all the data in one process. If your data inputs do not have a hierarchical structure, and all model inputs are global at the same level, then fit a one-stage model.
If your data has local and global inputs, where some variables are fixed while varying others, then choose a two-stage or point-by-point model instead.
What Is a Two-Stage Model?
A two-stage model fits a model to data with a hierarchical structure. If your data has local and global inputs, where some variables are fixed while varying others, then choose a two-stage model. For example, data collected in the form of spark sweeps is suited to a two-stage model. Each test sweeps a range of spark angles, with fixed engine speed, load, and air/fuel ratio within each test.
If your data inputs do not have a hierarchical structure, and all model inputs are global, at the same level, then fit a one-stage model instead.
For two-stage models, only specify a single local variable. If you want more local inputs, use a one-stage or point-by-point model instead.
What Is a Point-by-Point Model?
Point-by-point modeling allows you to build a model at each operating point of an engine with the necessary accuracy to produce an optimal calibration. You often need point-by-point models for multiple injection diesel engines and gasoline direct-injection engines.
With point-by-point models, no predictions are available between operating points. If you need predictions between operating points, use a one-stage model instead.
Default Model Types
| Model Type | Default Model Fits | Large Data Settings |
|---|---|---|
| One-stage | Response model: Gaussian process model (GPM) | For >2000 points, uses the large data behavior for Gaussian process models from Statistics and Machine Learning Toolbox™. |
| Boundary model: Convex Hull fit to the inputs | For >2000 points, switches to pairwise convex hull (one for every pair of inputs). Switch when ≥ 8 inputs even when <2000 points. | |
| Two-stage | Local model: Quadratic Global model: Hybrid radial-basis function (RBF) | For >2000 tests, global model switches to quadratic. |
| Boundary model: Convex Hull fit to the global inputs, and a two-stage boundary model for the local input. | For >2000 tests, global boundary model switches to pairwise convex hull. Switch when ≥ 8 inputs even when <2000 points. | |
| Point-by-point | The toolbox fits these model types to each operating point and selects the best model:
| For any operating point >2000 Points or >100 operating points, switches to fitting a single GPM per operating point (no Hybrid RBF or polynomial). |
| Boundary model: Point-by-point boundary model with a single Convex Hull fit to all inputs at each operating point. | If any operating point has >2000 points, then point-by-point boundary model switches to a pairwise convex hull. Switch when ≥ 8 inputs even when <2000 points. |
If you are using a template that you created, you can override the default models when you fit the model. On the Fit Models dialog box, clear the Use default models for large data option.
You can also specify the boundary model type in the Fit Models dialog box if you want to override the default boundary model setting.
Model Types
The following table shows the model types available for one-stage and two-stage modeling.
| Model Type | One-Stage and Two-Stage Global | Two-Stage: Local |
|---|---|---|
| Linear model | Yes | Yes |
| Radial basis function (RBF) | Yes | |
| Hybrid RBF | Yes | |
| Interpolating RBF | Yes | |
| Multiple linear models | Yes | |
| Free knot spline | Yes, one factor only | Yes, one factor only |
| Neural net (requires Deep Learning Toolbox™ software) | Yes | |
| Average fit | Yes | |
| Point-by-point models* | Yes | |
| Growth models | Yes, one factor only | |
| Polynomial** | Yes, one factor only | |
| Polynomial spline** | Yes, one factor only | |
| Truncated power series | Yes, one factor only | |
| User defined# | Yes (the example is one factor only) | Yes |
| Transient# | Yes (the example is two factors only) | Yes |
* Point-by-point models give you access to global model types for your local model.
** The PEV calculation is not supported for point-by-point models using neural network models, or with greater than 500 parameters, or greater than or equal to 8 inputs.
*** Polynomial and polynomial spline are two special case linear models for local models with one input factor. You can use polynomial and polynomial spline models (with more settings) for local models with more factors by choosing Linear Models.
# User defined and transient models must be checked into the toolbox before you can use them. They are available only for the number of factors you specified. There is an example user-defined model for a single factor preregistered with the toolbox. The example transient model provided must have exactly two factors, one of which must be time.
