Rectifying Systematical Measurement Error Through Majority Pattern Mining and Semi-Supervised Prediction for Industrial Instrument

Systematical measurement errors in industrial sensors should be avoided or rectified, as severe discrepancies in data can impede control, operation, and evaluation. However, some systematical errors are hard to estimate or experiment with. These errors often arise due to the change in external conditions. This means the measurement errors can be ignored when the external conditions remain within the designed scope. Generally, the relationship between the external condition and the systematical error is of complex nonlinearity, which may not be analytically tractable so rectifying the error is challenging. Nonetheless, a general assumption can be made in typical industrial scenarios: most external conditions fall within the design scope so that the corresponding systematical errors are 0. This assumption holds because the sensor is generally installed and calibrated under the most common operating mode. Based on these rationales, we first propose an intermediate sample-enhanced clustering strategy to identify the majority pattern, aiding in figuring out the zero systematical measurement error points. Then, leveraging the zero systematical measurement error information and partly known labels, a semi-supervised learning method is employed for estimating the complex nonlinear mapping from the external condition and the measurement, thereby rectifying the errors. The effectiveness of our approach is demonstrated through the rectification of a density meter in a real industrial aluminum oxide process, validated by the comparison with the laboratory assay outcomes. Note to Practitioners—Measurement instruments in industrial systems are designed to meet the precision requirement under specific conditions. Once the condition x is out of scope, the measurement y will be accompanied by the systematical measurement errors which is the function of x, denoted by $f(x)$ . Thus the measurement model is $ y=y_{t}+f(x)+e$ , where $y_{t}$ is the true value and e is the random measurement error. However, for many scenarios, the errors are complex. $f(x)$ is nonlinear and even intractable. From the perspective of engineering practice, the condition x in most of the running period should remain within the design scope to ensure normal use. However, it is also common for the running status to drift from the original designed working points over time. Then, an intolerant systematical measurement error occurs, causing the instrument which can be expensive lose their function. To estimate the systematical measurement error and implement the rectification of the deviated measurement, this paper proposes a data-driven strategy when the condition x is measurable and part of the label for y is available. We demonstrated the effectiveness of the strategy using a real industrial application example.