SCAP-1D : A Spatial Correlation Assessment Procedure from unidimensional discrete data

Highlights: • Exposes hypotheses for mathematically rigorous assessment of spatial variability. • Develops method for spatial variability estimation of 1D non-stationary random field. • Presents execution time improvements. • Illustrates method on numerical data : piecewise-constant and piecewise-linear mean. • Uses empirical data from reinforced concrete marine bridge inspection for validation. -- Abstract: Optimal placement of Non-destructive Testing sensors is essential for structure diagnosis as it allows to get maximum information about degradation at minimum cost. Latest optimization methods consider spatial variability of quantities of interest and thus strongly rely on correlation lengths assessment. However, this assessment is usually done with straightforward techniques on raw data, which may not satisfy the required hypotheses of stationarity and ergodicity and induce important mis-estimations. In this paper, we propose a Spatial Correlation Assessment Procedure (SCAP-1D) which allows to rigorously assess correlation length of a quantity of interest modeled as a piecewise-trend-stationary Gaussian-Random-Field (GRF). The procedure is applicable to unidimensional limited data and comprises two steps. First, the correlation length is assessed through an iterative algorithm including mean changepoints detection. Then, stationarity, ergodicity, and normality are tested to validate both the model and estimations. In numerical studies, we demonstrate the ability of our procedure to accurately estimate correlation length of a GRF in the cases of constant, stepped and bilinear mean, with performance ranges assessment. Applications to experimental Half-Cell Potential measurements with effective mean and slope steps validate the capacity of our method to precisely determine mean changepoints and correlation length on real data.