User's guide

This user's guide demonstrates the features of the Optimal Experimental Design Toolbox and their application.

Contents

Specify the model

The first step to optimizing of model parameters or corresponding measurement conditions with the Optimal Experimental Design Toolbox is to specify the model function. This is done by providing an object that implements the model interface, which prescribes methods for the model function and its first and second derivative with respect to the model parameters.

model_object = model_class();

If the model function is given in an explicit form you can use the model_explicit class. The necessary function values and derivatives will then be calculated automatically.

model_object = model_explicit(model_function, parameter_variables, experimental_design_variables);

If the model function is given as an initial value problem you can use the model_ivp class. There only the initial value problem must be specified. The necessary function values and derivatives will then be calculated automatically.

model_object = model_ivp(differential_equation, parameter_variables, ...
    independent_variable, initial_value, dependent_variable, integration_interval);

If you are using the model_ivp class you can obtain a speedup by calculating the necessary derivations of the model in parallel. To achieve that you only have to open a matlabpool before the calulations.

matlabpool open number_of_cores

If you have an arbitrary implementation of the model function without the derivatives with respect to the parameters you can implement the model_fd interface instead of the model interface. This provides the first and second derivatives with respect to the parameters by finite differences approximations.

Create and configure an solver object

The next step is to create and configure an solver object. First of all you have to create an solver object via the constructor.

solver_object = solver(model_object, ...
    parameter_estimation, measurement_points, corresponding_variances);

Then you have to pass the previously created model object presenting your model function to your solver object. This can be done via the constructor or the set_model method.

solver_object.set_model(model_object);

Further an approximation of the parameter values must be specified via the constructor or the set_initial_parameter_estimation method. This can arise for example from experience or previous measurements.

solver_object.set_initial_parameter_estimation(parameter_estimation);

Next you have to specify selectable measurements and there corresponding variances of the measurement errors. This can be done via the constructor and the set_selectable_measurements method.

solver_object.set_selectable_measurements(measurement_points, ...
    corresponding_variances);

If you already have done previous measurements, this can be included. The measurements and there corresponding variances of the measurement errors can be set via the set_accomplished_measurements method.

solver_object.set_accomplished_measurements(measurement_points, ...
    corresponding_variances, measurement_results);

Optimize measurements

Now you can calculate the optimal measurements by using the get_optimized_weights method of your solver object. The result of the get_optimized_weights method is a weight 0 or 1 for each measurements. 1 means the measurement has been chosen and 0 means the measurement has not been chosen. You can pass linear constraints to the measurements. Thereby, for example, a restriction to the cost of the measurements can be achieved.

weights = solver_object.get_optimized_weights(A, b);

A common case is that the number of selected measurements should be restricted. This can be achieved directly as follows.

weights = solver_object.get_optimized_weights(maximal);

Quality of measurements

You can also calculate the quality of a set of measurements with the get_quality method. This allows, for example, to calculate the quality resulting by omitting some measurements.

quality = solver_object.get_quality(weights);

Optimize model parameters

If you have done previous measurements you can optimize the model parameters with your measurement results. For that you can use the get_optimal_parameters method.

parameter = solver_object.get_optimal_parameters(lower_bound, upper_bound);

Change options

Several options are available to configure the optimization of the experimental designs and model parameters according to your needs. You can set your desired option with the set_option method of your solver object.

solver_object.set_option('option1', value1);
solver_object.set_option('option2', value2);

The possible options are

Published with MATLAB® R2014a