A probabilistic neural network for uncertainty prediction with applications to manufacturing process monitoring

Modeling the uncertainty from data is an essential quest in the learning of neural network models but has not been well addressed. A probabilistic neural network with Gaussian-mixture distributed parameters is developed in this work to provide an efficient and high-fidelity solution for learning multimodal uncertainties in neural networks. An adaptive Gaussian mixture scheme is adopted to refine the Gaussian mixture probability distributions and ensure the fidelity of uncertainty propagation in both linear and nonlinear transformations through the network. As its predictive distribution can be inferred analytically, this probabilistic network can be trained efficiently using a backpropagation method based on gradient descent. The proposed network not only achieves a state-of-the-art performance when benchmarked on a series of public datasets but also improves the accuracy and uncertainty quantification quality in two manufacturing process monitoring schemes. In a tool wear monitoring scheme for machining, it reduced the root mean square error (RMSE) by 44% and narrowed the confidence intervals of tool wear prediction by 35% compared to a neuro-fuzzy model. In a porosity monitoring system for additive manufacturing, the proposed network improved the porosity detection accuracy by 2% to 93.6% and quantified confidence intervals that were not available in conventional deep learning models. All these successes prove that the proposed probabilistic neural network can be a promising solution to address practical problems subject to significant uncertainties.