Midpoint-radii principal component analysis -based EWMA and application to air quality monitoring network

Abstract

Monitoring air quality is crucial for the safety of humans and the environment. Moreover, real world data collected from air quality network is often affected by different types of errors as measurement noise and variability of pollutant concentrations. The uncertainty in the data, which is strictly connected to the above errors, may be treated by considering interval-valued data analysis. In practical cases of measured data, the true value cannot be measured and the collected data on a process are only approximations given by sensors, and are thus imprecise. This is due mainly to the uncertainties induced by measurement errors or determined by specific experimental conditions. Thus, the main aim of this paper is to develop an enhanced monitoring of air quality network by taking into account the uncertainties on the data. To do that, we develop a new monitoring technique that merges the advantages of Midpoint-radii PCA (MRPCA) method with exponentially weighted moving average (EWMA) chart, in order to enhance sensor fault detection technique of air quality monitoring process. MRPCA is the most popular interval multivariate statistical method, able to tackle the issue of uncertainties on the models and one way to improve the fault detection abilities. On the other hand, the EWMA statistic allows an exponential weighted average to successive observations and able to detect small and moderate faults. The developed MRPCA-based EWMA method relies on using MRPCA as a modeling framework for fault detection and EWMA as a detection chart. The proposed MRPCA-based EWMA scheme is illustrated using a simulation example and applied for sensor fault detection of an air quality monitoring network. The monitoring performances of the developed technique are compared to the classical monitoring techniques. MRPCA model performances are compared with the interval PCA models: complete-information principal component analysis (CIPCA) and Centers PCA (CPCA). The MRPCA-based EWMA monitoring performances are compared to MRPCA-based Shewhart, generalized likelihood ratio test (GLRT) and squared prediction error (SPE) techniques.