In this paper, a novel algorithm based on sparse identification, subsampling and co-teaching is developed to mitigate the problems of highly noisy data from sensor measurements in modeling of nonlinear systems. Specifically, sparse identification is combined with subsampling, a method where a fraction of the data set is randomly sampled and used for model identification, as well as co-teaching, a method that mixes noise-free data from first-principles simulations with the noisy measurements to provide a mixed data set that is less corrupted with noise for model training. The proposed method is bench-marked against sparse identification without subsampling as well as subsampling but without co-teaching using two examples, a predator-prey system and a chemical process, both of which are modeled as nonlinear systems of ordinary differential equations. It was shown that the proposed method yields better models in terms of prediction accuracy in the presence of high noise levels.

在本文中，开发了一种基于稀疏识别、子采样和协同教学的新算法，以减轻非线性系统建模中传感器测量数据的高噪声问题。具体来说，稀疏识别与子采样相结合，这是一种随机采样数据集的一部分并用于模型识别的方法，以及联合教学，一种将第一性原理模拟中的无噪声数据与噪声混合的方法。为模型训练提供较少受噪声破坏的混合数据集。所提出的方法针对不带子采样的稀疏识别和不带子采样但不协同教学的稀疏识别进行了基准测试，使用两个例子，一个捕食者-猎物系统和一个化学过程，这两个例子都被建模为常微分方程的非线性系统。