100 Z.Wu et al. Fig. 13.1 Illustrated IGL algorithm with global and local FE models of miter gate uses the 3D shell elements. The global displacement around local boundary solving from global model is imposed as the boundary conditions of the local model, and the local force along the boundary solving from the local model is applied back as a reaction to the global model. The IGL algorithm finds an accurate representation of the physics by iteratively updating the interaction between the coupled global and local models. Stress intensity factor (SIF) as the key parameter of fatigue crack growth modelling indicates the crack growth pattern. For each step, the range of SIF values ΔKin a loading cycle at the crack front tip along with the crack length are extracted through stress analysis. In this paper, the Paris’ law is adopted as a commonly used crack growth model, da/dN =c(ΔK)m where c and mare the material coefficients of Paris’ law, da is the crack length change at each time step, and da/dN is the fatigue crack growth for a load cycle N. To increase the computational efficiency for the IGL method, a surrogate model using Gaussian Process Regression (GPR) [1, 2] is constructed to replace the non-linear behavior of the local domain. Image-Based Measurements Although FE analysis can capture the displacement for visualization, such computational-expensive model poses challenges to probabilistic analysis for diagnostics and prognostics. Given that the model needs to be executed thousands of times, an auxiliary surrogate model that is built to produce image-based observations, shown in Fig. 13.2. The images that come from a camera are consist of uniform square-like pixels, where the resolution of the images is determined by the side length of the pixels. By interpolating the Abaqus results into a uniform mapping, the function of “camera” can be fully learned. Online Diagnosis and Prognosis The diagnosis of the structures aims to detect and quantify the potential damage, which provides essential information on the current health state. Damage prognosis, in the meanwhile, extends the gathered information to predict the impact and the evolution of the damage, i.e., the remaining useful life (RUL) of the objective structures. Figure 13.3 illustrates the Bayesian network for online diagnosis where the hup and hdown represents the upstream and downstream hydrostatic pressure applied on the global domain of the miter gate. The filtering process is composed of the crack evolution equation from IGL algorithm and observations from the auxiliary surrogate model that links the generated image-based measurements with the true system
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