Feasibility study of Neural Networks interpolation applied to Synthetic Aperture Radar Deformations
Authors: Dumoulin Jean , Renier-Robin Alexis , Reale Diego , Toullier Thibaud , Verde Simona , Soldovieri Francesco 
Published: February 2023

After the collapse of the Genoa Bridge in August 2018, a renewed interest in permanent monitoring of the structural behavior of civil infrastructures [2] was observed. Such monitoring has to encompass the need to survey a very large number of structures that reach critical age but also new structures. In addition, recent technological advances have helped to make the installation and operation of continuous monitoring systems more practical and economical. In parallel, monitoring approaches based on the use of data acquired by satellite Synthetic Aperture Radar (SAR) may complete and enlarge the observation scale of such ground based monitoring systems, to enhance Structural Health Monitoring (SHM) performances.Monitoring of civil structures is frequently based on vibration analysis. Anyway, one limitation to the use of SHM algorithms based on modal parameter analysis is its sensitivity to environmental effects and not to damage. Among them, the subsidence around and at structure&#8217;s foundation level is a factor that has a great influence on natural frequencies.In this study, we address quasi-periodic monitoring and subsidence characterization using surface deformation measurements achieved through the Differential Interferometric SAR (DInSAR) technology [1]. Peculiarities of DInSAR have to be taken into account with reference to the application to structures monitoring:Robustness of estimated ground deformation obtained throught the combination of the Line-of-sight (LOS) deformation measurements carried out by the processing of complementary ascending and descending orbits data, for which the measurements points and date of acquisition could be different;
Sparse, or absence of, measurements points on some areas induced by strong decorrelation phenomena;
Limited range of the actual structure deformation that could reach the accuracy of the DInSAR technology.
Bibliographic study showed that it could be di&#64256;icult to exploit the DInSAR data directly for the SHM because of the problems mentioned above. The proposed procedure aims at reconstructing the deformations over an area of interest using a regularly spaced grid whose deformations would be interpolated on the available sparse measurements dataset. The interpolation is carried out on each orbit trajectory and for each acquisition date. This allows both to:Estimate measurements point on the same, possibly regular, grid for different orbits;
Estimate deformation in areas lacking of measurement points;
Inspired from research works of Chen et al. [3] we implemented and studied a neural network (NN) kriging based interpolation (introducing the spatial dimension inside the NN). It allows the modelisation of the points correlation (variograms) directly from the data instead of predefined functions.An overview of the studied method and developed software applied on 2 use-cases will be presented and analysed. Perspectives towards improvements of such approach will be also discussed.References[1] Antonio Pepe and Fabiana Cal&#242;. &#8220;A Review of Interferometric Synthetic Aperture RADAR (InSAR) Multi-Track Approaches for the Retrieval of Earth&#8217;s Surface Displacements&#8221;. In: Applied Sciences 7.12 (2017). doi: 10.3390/app7121264.&#160;[2] Riccardo Lanari et al. &#8220;Comment on &#8220;Pre-Collapse Space Geodetic Observations of Critical Infrastructure: The Morandi Bridge, Genoa, Italy&#8221; by Milillo et al. (2019)&#8221;. In: Remote Sensing 12.24 (2020). doi:10.3390/rs12244011.[3] Wanfang Chen et al. &#8220;DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction&#8221;. In: arXiv:2007.11972 (May 23, 2022).