Numerical simulation and manifold learning for the vibration of molten steel draining from a ladle

To ensure the purity of molten steel and maintain the continuity of casting, the slag detection utilizing vibration signals has been widely applied in the continuous casting. Due to the non-stationary and non-linear flow behavior of molten steel, it is hard to construct a reliable criterion to identify the slag entrapment from the vibration signals. In this paper, a numerical simulation model is built to reveal the flow process of molten steel draining from a ladle. By the analysis of the volume fraction, path line and velocity field, the flow state at the moment of slag outflowing is captured. According to the simulated results, a method based on the manifold learning is proposed to deal with the vibration signals. Firstly, the non-stationary vibration signals are decomposed into sub-bands by the continuous wavelet transform and the energy of the signal component at each wavelet scale is calculated to constitute the high dimensional feature space. Then, a manifold learning algorithm called local target space alignment (LTSA) is employed to extract the non-linear principal manifold of the feature space. Finally, the abnormal spectral energy distribution caused by slag entrapment is indicated by the one-dimensional principal manifold. The proposed method is evaluated by the vibration acceleration signals acquired from a steel ladle of 60 tons. Results show that the slag entrapment is exactly and timely identified

A surrogate modelling approach based on nonlinear dimension reduction for uncertainty quantification in groundwater flow models

In this paper, we develop a surrogate modelling approach for capturing the output field (e.g., the pressure head) from groundwater flow models involving a stochastic input field (e.g., the hy- draulic conductivity). We use a Karhunen-Lo`eve expansion for a log-normally distributed input field, and apply manifold learning (local tangent space alignment) to perform Gaussian process Bayesian inference using Hamiltonian Monte Carlo in an abstract feature space, yielding outputs for arbitrary unseen inputs. We also develop a framework for forward uncertainty quantification in such problems, including analytical approximations of the mean of the marginalized distri- bution (with respect to the inputs). To sample from the distribution we present Monte Carlo approach. Two examples are presented to demonstrate the accuracy of our approach: a Darcy flow model with contaminant transport in 2-d and a Richards equation model in 3-d