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ProperOrthogonalDecompositionOptions

Options for model order reduction with proper orthogonal decomposition

Since R2024b

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    Description

    This object contains model order reduction options of proper orthogonal decomposition (POD) and is contained in the Options property of a ProperOrthogonalDecomposition object R created using reducespec. To configure these options, use dot notation, for example, R.Options.Excitation = "prbs".

    Properties

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    Proper orthogonal decomposition algorithm, specified as one of the following.

    • "balanced" — This algorithm preserves the input-output response and considers both the input-to-state and state-to-output maps.

    • "galerkin" — This algorithm focuses on dominant mode shapes and only considers input-to-state map.

    • "compress" — This algorithm is a variant of the balanced algorithm and is typically faster when you have tall or wide models (few inputs, many outputs or many inputs, few outputs).

    Frequency range of interest in rad/s, specified as a vector of form [fmix,fmax]. Use this option to specify a range where the POD approximation must be most accurate. The software ignores this option when you use custom POD data.

    Excitation signal for simulation, specified as "impulse", "chirp", or "prbs". The software ignores this option when you use custom POD data.

    • "impulse" — Use Dirac impulse δ(t) in continuous time and a unit pulse in discrete time. This is the same notion as simulation using impulse.

    • "chirp" — Use a chirp pulse covering about one decade.

    • "prbs" — Use a pseudorandom binary sequence (see [1]).

    Static input and output weights, specified as matrices of size compatible with model inputs and outputs. Use these weights for input and output scaling in MIMO models, or to implicitly reduce the input-output size in large MIMO models. The software applies POD to the smaller model Wy(sys)Wu to obtain the model order reduction projectors. Here, Wy is the output weight and Wu is the input weight. The reduced model has the same input-output size as the original model.

    Custom POD data to approximate the Gramian factor Lr, specified as an incrementalPOD object. Use this option when you have obtained state data by running custom simulations on the model you are reducing. For available workflows, see incrementalPOD. The algorithm uses this data as is and does not run additional simulations.

    Custom POD data to approximate the Gramian factor Lo, specified as an incrementalPOD object. Use this option when you have obtained state data by running custom simulations on the adjoint of the model you are reducing. For available workflows, see incrementalPOD. The algorithm uses this data as is and does not run additional simulations. Leave this option empty for symmetric (self-adjoint) models or when R.Options.Algorithm = "galerkin".

    Set Center to true to subtract the mean state value from the POD data. Use this option when you have custom POD data with a strong bias.

    Biases typically only affect the largest HSV and have limited impact on the quality of the approximation except for a tendency to emphasize low frequency. The main impact of biases is to skew the Error and Loss values, making it harder to select the order.

    Relative rank tolerance, specified as a scalar value between 0 and 1. This tolerance controls how many principal components (state dimensions) to retain in the POD and is used for SVD truncation during the POD process.

    Relative tolerance for input-output compression, specified as a scalar value between 0 and 1. This option controls the amount of output or input compression in the "compress" algorithm.

    Number of steps per simulation, specified as a positive scalar value. Use this option to specify how many fixed steps to take in the continuous- time simulations. The default value is usually sufficient for well-damped systems. You may require more steps for undamped or poorly damped systems. The software ignores this options in discrete time and when providing custom POD data.

    References

    [1] Pintelon, R., and J. Schoukens. System Identification: A Frequency Domain Approach, p 157. 2nd ed. Hoboken, N.J: John Wiley & Sons Inc, 2012.

    Version History

    Introduced in R2024b

    See Also

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