Reconstruct Phase Space

Reconstruct phase space of a uniformly sampled signal in the Live Editor

Description

The Reconstruct Phase Space task lets you interactively reconstruct phase space of a uniformly sampled signal. The task automatically generates MATLAB^® code for your live script. For more information about Live Editor tasks generally, see Add Interactive Tasks to a Live Script.

Phase space reconstruction is useful to verify the system order and reconstruct all dynamic system variables, while preserving system properties. Reconstructing the phase space is performed when limited data is available, or when the phase space dimension and lag values are unknown. Also, the nonlinear features approximateEntropy, correlationDimension, and lyapunovExponent use phase space reconstruction as the first step of the computation. For more information about phase space reconstruction, see phaseSpaceReconstruction.

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Open the Task

To add the Reconstruct Phase Space task to a live script in the MATLAB Editor:

• On the Live Editor tab, select Task > Reconstruct Phase Space.

• In a code block in your script, type a relevant keyword, such as phase or phase space. Select Reconstruct Phase Space from the suggested command completions.

Examples

Reconstruct Phase Space in the Live Editor

Use the Reconstruct Phase Space task in the Live Editor to interactively reconstruct the phase space of a uniformly sampled signal. Experiment with different values for lag, embedding dimension, histogram bins and distance threshold. The task automatically generates code reflecting your selections. Open this example to see a preconfigured script containing the Reconstruct Phase Space task.

For this example, consider 'uavPositionData.mat' which contains signal xv which is the x-component of a 3-D path traversed by an unmanned aerial vehicle (UAV). The x, y, and z coordinates define a circle of 2-m radius at 0.75-m altitude.

load('uavPositionData.mat','xv')

To reconstruct the phase space of the signal xv, open the Reconstruct Phase Space task in the Live Editor. On the Live Editor tab, select Task > Reconstruct Phase Space. In the task, select signal xv.

Clear the Time Lag check box if you want to use your own values in the Maximum Lag and Histogram Bins fields. For this example, leave the box checked to calculate the lag using Average Mutual Information (AMI). Since dimension is known, clear the Embedding Dimension field and specify dimension as 3.

Evaluate whether the reconstructed phase space preserves the system dynamics with the assigned values by observing the output plots. You can toggle between the display type by choosing between Individual or All in the Output Plot dropdown menu.

The task generates code in your live script. The generated code reflects the parameters and options you select, and includes code to generate the type of plot you specify. To see the generated code, click at the bottom of the task parameter area. The task expands to display the generated code.

By default, the generated code uses phaseSpace as the name of the output variable. To specify a different output variable name, enter a new name in the summary line at the top of the task. For instance, change the name to pSpace.

The task updates the generated code to reflect the new variable name, and the new variable pSpace appears in the MATLAB workspace. You can use the reconstructed phase space to identify condition indicators like Lyapunov exponent or correlation dimension.

Related Examples

• Reconstruct Phase Space and Estimate Condition Indicators Using Live Editor Tasks

Parameters

Select Signal

Signal — Uniformly sampled time-domain signal

array | timetable

Select a uniformly sampled time-domain signal in array or timetable format.

Specify Phase Space Parameters

Time Lag — Check to use Average Mutual Information (AMI) algorithm to compute time lag

on (default) | off

Check to use Average Mutual Information (AMI) algorithm to compute time lag. Clear to try your own value of Maximum Lag and Histogram Bins. If the time delay is too small, random noise is introduced in the states. In contrast, if the lag is too large, the reconstructed dynamics do not represent the true dynamics of the time series.

Maximum Lag — Maximum value of lags used in the lag estimation

positive scalar

Maximum value of lag used to estimate the time delay using the Average Mutual Information (AMI) algorithm.

Histogram Bins — Number of bins for discretization when computing the average mutual information

positive scalar

Number of bins for discretization to compute lag using the AMI algorithm. Set the value of Histogram Bins based on the length of your signal.

Embedding Dimension — Check to use Percent False Neighbors (PFN) algorithm to compute embedding dimension

on (default) | off

Check to use Percent False Neighbors (PFN) algorithm to automatically compute embedding dimension.

Maximum Dimension — Maximum value of embedding dimension used in the dimension estimation

positive scalar

Maximum value of embedding dimension used in the dimension estimation with Percent False Neighbors (PFN) algorithm.

Distance Threshold — Distance ratio threshold for determining two points as false neighbors

scalar

Distance ratio threshold for determining two points as false neighbors using Percent False Neighbors (PFN) algorithm. For more information, see phaseSpaceReconstruction.

Percent False Neighbors — Percent false neighbors threshold for detecting embedding dimension

scalar

Percent false neighbors threshold for detecting embedding dimension using PFN algorithm. To specify percent false neighbors, check the Embedding Dimension check box. For more information, see phaseSpaceReconstruction.

Visualize Results

Output Plot — Number of output plots to display

Individual (default) | All | None

Number of output plots to display. To toggle between the reconstructed plot and the histogram plot, and to go through each plot, select Individual. To display both plots in the Live Editor, select All. To hide plots, select None.

Version History

Introduced in R2019b