Uncertainties of Data-Driven Models: Theory and Application to Condition Monitoring

Abnormal operational conditions often induce intrinsic uncertainties, making them valuable for health monitoring of the underlying system. However, assessing intrinsic uncertainties for online condition monitoring of manufacturing and process engineering, especially when various practical working loads are applied, has proven a challenging problem. The present study strives to address this problem by quantifying intrinsic uncertainties through system identification and nonlinear frequency analysis. First, the concerned system is represented by data-driven Nonlinear Auto-Regressive with eXogenous input (NARX) models accounting uncertainties in model coefficients. This is achieved by using a newly developed Bayesian linear regression-based orthogonal least squares (BLROLSs) algorithm from the system input and output measurements. The BLROLS algorithm is transparent and auto-tuned to ensure the NARX model has stable long-term predictions. After that, nonlinear frequency response functions (NOFRFs) features are derived from the NARX models to quantify system intrinsic uncertainties for condition monitoring. The concept of NOFRFs is an extension of the frequency response function (FRF) for linear systems to nonlinear cases, which have been proven as powerful physically interpretable indicators that are independent of working loads and sensitive to faulty conditions. Finally, an experimental study on the online monitoring of machining cutting tools was conducted, demonstrating the effectiveness of the proposed approach in addressing engineering problems.