Gaussian Process Regression and Classification for Probabilistic Damage Assessment of Spatially Distributed Systems

We illustrate how methods for non-parametric regression and classification based on Gaussian Processes can be adapted for inferring the condition state of infrastructure components under spatially distributed stressors. When the stressor is modeled by a random field, observations collected in one location can reduce the uncertainty about the stressor intensity also in other locations. Exact inference is possible when the field is Gaussian and observations are perfect or affected by Gaussian noise. However, often the available observations are binary, as those related to the failure or survival of components, and indicate whether the local field is above or below a threshold whose value may also be uncertain. While no efficient scheme for exact inference is available in that setting, we can perform efficient approximate inference when the field is Gaussian and so is the uncertainty on the threshold value. The mathematical formulation for this problem is analogous to that of classification in machine learning, that can be based on latent Gaussian processes. We show how to formulate the problem and how to adapt deterministic methods, as Laplace’s method and Expectation Propagation, and methods based on random number generation, as Monte Carlo uniform sampling and importance sampling, to perform approximate inference. Our illustrative application is the condition assessment of assets exposed to a seismic event. Under specific assumptions, the seismic demand can be modeled as a Gaussian random field, and measures about the demand and about the survival and failure of assets can be processed globally, to update the risk assessment. Specifically, we evaluate methods for approximate inference and discuss their merits.