Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create residuals for fault diagnosis applications. While recurrent neural network models have been shown capable of modeling complex non-linear dynamic systems, they are limited to fixed steps discrete-time simulation. Modeling using neural ordinary differential equations, however, make it possible to evaluate the state variables at specific times, compute gradients when training the model and use standard numerical solvers to explicitly model the underlying dynamic of the time-series data. Here, the effect of solver selection on the performance of neural ordinary differential equation residuals during training and evaluation is investigated. The paper includes a case study of a heavy-duty truck's after-treatment system to highlight the potential of these techniques for improving fault diagnosis performance.

翻译：数据驱动建模与机器学习被广泛应用于描述动态系统的行为特性。其中一项重要应用为技术系统的残差评估：通过比较模型预测值与实际测量数据生成残差，进而开展故障诊断。尽管循环神经网络模型已被证明能够有效建模复杂非线性动态系统，但其受限于固定步长的离散时间仿真。相比之下，基于神经常微分方程的建模方法不仅能够在特定时间点评估状态变量、计算模型训练过程中的梯度，还能利用标准数值求解器显式建模时间序列数据的内在动态特性。本文重点研究求解器选择对神经常微分方程残差在训练与评估阶段性能的影响。为凸显这些技术在提升故障诊断性能方面的潜力，论文以重型卡车后处理系统为例进行案例研究。