Co-Kriging strategy for structural health monitoring of bridges

Computational models are crucial in applied science and engineering, offering valuable insights on the behavior of strutures and mechanical systems. However, their effectiveness is often hindered by complexity and substantial time required for execution. Metamodeling, or surrogate modeling, is a practical strategy to optimize computational time and resources. This approach involves substituting a complex model with a metamodel, that is, a simplified function that mimics the behavior of the original model, thereby significantly expediting the evaluation process. One widely utilized method is Gaussian Process Regression (GPR), also known as Kriging, which has demonstrated effectiveness in numerous structural health monitoring (SHM) applications. However, achieving accurate predictions for a target variable (e.g., damage-sensitive feature) often requires a significant amount of past data or well-calibrated models of the structure under analysis, presenting challenges and high costs. Therefore, the innovation presented in this article is applying a co-Kriging method, a multivariate extension of ordinary Kriging that leverages the covariance between two or more related datasets. This is an efficient decision-making process in various fields, especially when the co-variable is more cost-effective to measure than the target variable. Three distinct applications are presented here, showcasing the efficacy of the co-Kriging methodology. Two of these applications focus on generic mathematical functions. The third pertains to a real-world scenario involving the correlation of the natural frequencies of a concrete bridge under varying thermal conditions. Across all three scenarios, co-Kriging emerges as a robust method, consistently yielding superior results compared to ordinary Kriging.