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

• Main Authors: Girard Sylvain, Gerrer Claire-Eleuthèriane
• Format: Article
• Language: English
• Published: Ital Publication 2021-03-01
• Series: HighTech and Innovation Journal
• Subjects: dimension reduction; functional data analysis; fmi; otfmi; principal component analysis; auto-associative model; sensitivity analysis.
• Online Access: https://hightechjournal.org/index.php/HIJ/article/view/79

Modelica models represent static or dynamic systems. Their outputs can be scalar (numbers) or time-dependent (time series). Most advanced mathematical methods for the analysis of numerical models cannot cope with functional outputs. This paper aims at showing an efficient method to reduce a time-dependent output to a few numbers. The 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, 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 Full Text: PDF