On Data-Driven Self-Calibration for IoT-Based Gas Concentration Monitoring Systems

Abstract

In this article, data-driven self-calibration algorithms for the Internet of Things-based gas concentration monitoring systems embedded with low-cost gas sensors are designed. The measurement errors are assumed to be caused by imperfect compensation for the variation of sensor component behavior. Specifically, the calibration procedure for the nondispersive infrared <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$CO_{2}$ </tex-math></inline-formula> sensors is developed, for which the temperature dependency is the most dominant drift source. For a single sensor, the hidden Markov model is used to characterize the statistical relationship between different quantities introduced by the physical model that builds on the Beer–Lambert law. For the calibration in the Internet of Things-based system, sensors first transmit their belief functions of the true gas concentration level to the cloud. Then, the cloud fusion center computes a fused belief function according to certain rules. This belief function is then used as reference for calibrating the sensors. To deal with the case where belief functions highly conflict with each other, a Wasserstein distance-based weighted average belief function fusion approach is first proposed as a networked calibration algorithm. To achieve more long-term stable calibration results, the networked calibration problem is further formulated as a partially observed Markov decision process (MDP) problem, and the calibration strategies are derived in a sequential manner. Correspondingly, the deep <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -network approach is applied as a computationally efficient method to solve the proposed MDP problem. The performance of practical designs of the proposed self-calibration algorithms is finally illustrated in numerical experiments utilizing real data.