Full-field stress estimation of offshore structures using modal expansion and principal component analysis

It is important to capture the quasi-static response accurately in virtual sensing of offshore structures, as the contribution of this part is essential to the total fatigue damage. The quasi-static response from wave excitation challenges virtual sensing methods, as it cannot be easily captured by a limited set of dynamic modes due to its spatial and temporal variability from the changing sea elevations. The common solution is to apply Ritz vectors, which require that the excitation has a set of time-invariant spatial distributions. Irregular waves, however, result in a time-varying spatial distribution; as such, Ritz vectors represent a simplified wave excitation. This paper proposes an alternative method for calculating deflection shapes in wave-induced quasi-static responses, where the shapes constitute the best low-rank approximation of the quasi-static response. Furthermore, the paper demonstrates the implementation of these deflection shapes within modal expansion for enhanced virtual sensing. By leveraging principal component analysis (PCA), which reduces dimensionality and extracts dominant components from noisy data, the proposed method captures the quasi-static behaviour of the system. The method uses training data from wave model simulations under sea conditions with similar statistical characteristics as the measurement period, allowing for the estimation of deflection shapes through PCA. A numerical study tests the applicability of the method on an offshore structure, which is simulated in a setting with additive noise on the acceleration response to emulate realistic sensor imperfections. Under these conditions, the PCA-based method provides more accurate stress estimates than traditional methods that rely on dynamic modes and/or Ritz pseudo-modes.