Deep neural networks (DNNs) are often coupled with physics-based models or data-driven surrogate models to perform fault detection and health monitoring of systems in the low data regime. These models serve as digital twins to generate large quantities of data to train DNNs which would otherwise be difficult to obtain from the real-life system. However, such models can exhibit parametric uncertainty that propagates to the generated data. In addition, DNNs exhibit uncertainty in the parameters learnt during training. In such a scenario, the performance of the DNN model will be influenced by the uncertainty in the physics-based model as well as the parameters of the DNN. In this article, we quantify the impact of both these sources of uncertainty on the performance of the DNN. We perform explicit propagation of uncertainty in input data through all layers of the DNN, as well as implicit prediction of output uncertainty to capture the former. Furthermore, we adopt Monte Carlo dropout to capture uncertainty in DNN parameters. We demonstrate the approach for fault detection of power lines with a physics-based model, two types of input data and three different neural network architectures. We compare the performance of such uncertainty-aware probabilistic models with their deterministic counterparts. The results show that the probabilistic models provide important information regarding the confidence of predictions, while also delivering an improvement in performance over deterministic models.

翻译：深度神经网络（DNNs）常与基于物理的模型或数据驱动的代理模型相结合，以在低数据条件下执行系统的故障检测与健康监控。这些模型作为数字孪生体生成大量数据来训练DNNs，而这类数据若依赖真实系统则难以获取。然而，此类模型可能存在参数不确定性，并传播至生成的数据中。此外，DNNs在训练过程中习得的参数本身也具有不确定性。在此情境下，DNN模型的性能将同时受到基于物理模型的不确定性与自身参数不确定性的影响。本文量化了这两种不确定性来源对DNN性能的影响：一方面通过显式地将输入数据的不确定性经DNN所有层进行传播，并隐式预测输出不确定性以捕捉前者；另一方面采用蒙特卡洛 dropout（Monte Carlo dropout）来捕捉DNN参数的不确定性。我们以电力线路故障检测为例，基于一个物理模型、两种输入数据类型及三种不同神经网络架构演示了该方法，并将此类不确定性感知概率模型与确定性模型的性能进行了对比。结果表明，概率模型不仅提供了关于预测置信度的重要信息，还比确定性模型展现了更优的性能表现。