Overcoming the Obstacle of Time-dependent Model Output for Statistical Analysis by Nonlinear Methods

Girard Sylvain, Gerrer Claire-Eleuthèriane


Modelica models represent static or dynamic systems. Their outputs can be scalar (numbers) or time-dependent (time series). The most advanced mathematical methods for the analysis of numerical models cannot cope with functional outputs. This paper aims to show an efficient method to reduce a time-dependent output to a few numbers. Principal component analysis is a well-established method for dimension reduction and can be used to tackle this issue. It relies, however, on a linear hypothesis that limits its applicability. We adapt and implement an existing method called the auto-associative model, invented by Stéphane Girard, to overcome this shortcoming. The auto-associative model generalizes PCA as it projects the data on a nonlinear (instead of linear) basis. It also provides physically interpretable data representations. The difference in efficiency between both methods is illustrated in a case study of the well-known bouncing ball model. We perform output reduction and reconstruction using both methods to compare the completeness of information kept throughout the dimension reduction process.


Doi: 10.28991/HIJ-2021-02-01-01

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Dimension Reduction; Functional Data Analysis; FMI; OtFMI; Principal Component Analysis; Auto-associative Model; Sensitivity Analysis.


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DOI: 10.28991/HIJ-2021-02-01-01


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