Hidden Markov Model Based Data-driven Calibration of Non-dispersive Infrared Gas Sensor

Abstract

Non-dispersive infrared gas sensing is one of the best gas measurement method for air quality monitoring. However, sensors drift over time due to sensor aging and environmental factors, which makes calibration necessary. In this paper, we propose a hidden Markov model approach for sensor selfcalibration, which builds on the physical model of gas sensors based on the Beer-Lambert law. We focus on the statistical dependency between a calibration coefficient and the temperature change. Supervised and unsupervised learning algorithms to learn the stochastic paramentes of the hidden Markov model are derived and numerically tested. The true calibration coefficient at each time instant is estimated using the Viterbi algorithm. The numerical experiments using CO2 sensor data show excellent initial results which confirms that data-driven calibration of non-dispersive infrared gas sensors is possible. Meanwhile, the challenge in the practical design is to find an appropriate quantization scheme to keep the computation burden reasonable while achieving a good performance. Index Terms-Non-dispersive infrared gas sensor, drift, self calibration, data-driven modeling, hidden Markov model, statistical inference. This research project has received funding from the European Unions Horizon 2020 research and innovation programme under grant agreement No 825272 (ULISSES). We would also like to acknowlegde Henrik Rödjegård and Hans Martin from SenseAir for the helpful technical discussions and for providing us the sensor data used in this work.

Time-Adaptive Expectation Maximization Learning Framework for HMM Based Data-Driven Gas Sensor Calibration

“…The general operation principle of an NDIR sensor is illustrated Fig. 1, more details can be found in previous works [15] and [28]. In this work, we focus on the CO 2 NDIR sensors for which the temperature dependency is the most dominant effect on the sensor components behavior [7].…”

“…We use the same HMM framework as proposed in [15] and [28] to jointly model the statistical relationship between observed sensor measurements sequence, observed environmental temperature sequences, and the sequence of true calibration parameter. This stochastic model is designed to capture the aforementioned dependency between the behavior of the sensor components and the temperature.…”

“…In the following, we call the normalizing factor r as calibration parameter, and we call the calibration parameter that perfectly compensates the imperfect model f as true calibration parameter. 1 To calibrate NDIR sensors with the above sensing model, previous work [15] proposes to build a hidden Markov model (HMM) between observed sensor measurements sequence, observed environmental factor sequences, and the sequence of the true calibration parameter. The true calibration parameter is later estimated by using statistical inference tools from the standard HMM framework.…”

“…Since a reference measurement is usually not available, expectation maximization (EM) based unsupervised learning approach is further proposed to deal with the unlabelled dataset, where only the sensor measurements and the environmental factors can be observed while the values of true calibration parameter are missing. However, the HMM proposed in [15] is a deterministic model that is trained by using a dataset collected from a short term. This model can only guarantee its prediction accuracy within a short period instead of a long term, since the dependency between the behavior of the sensor components and the environmental factors varies as time evolves.…”

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

“…In the following, we briefly outline the supervised approach on learning these HMM parameters. For the details of the unsupervised approach and its corresponding experiments, see our previous work [38] for more details.…”