(Invited) Strategies for Calibration Cost Reduction in Heterogeneous Chemical Sensor Arrays
Authors: Fonollosa Jordi 
Published: July 2021

Introduction

Heterogeneous gas sensor arrays coupled with machine learning algorithms have been proposed for a wide range of applications. However, inherent sensor variability degrades the performance of calibration models when directly transferred to new replicates of the original system [1]. As a result, in order to fulfill industry requirements, very often, calibration needs to be performed individually for each unit, limiting mass-deployment [2]. Recently, calibration methodologies have been proposed to reduce calibration costs and extend lifetime of the models. Briefly, these strategies make use of calibration models built for a primary system, incorporate new information to the calibration model, or take advantage of nearby units.

Calibration Transfer

Calibration transfer relies on a primary unit, for which a calibration model is built using a full set of calibration samples. Then, the sensor space of the secondary unit is mapped to the space of the primary unit using a set of transfer samples. Finally, using the transfer function, the calibration model built for the primary can be used with the secondary instrument. Hence, the cost reduction can be estimated from the ratio between the full set of calibration measurements and the transfer samples.
Different methodologies have been proposed to obtain the transfer function, with different assumptions. For example, Single Signal Standardization assumes that the differences between units are linear, with no shifts in the signal. On the contrary, Direct Standardization (DS) constructs the mapping between all signals and can capture shifts in the signal. DS, however, may incorporate unwanted sources of variability and may face highly underdetermined systems [3]. Piecewise Direct Standardization (PDS) operates locally and can overcome the computational limitations of DS. The mentioned techniques have been tested on heterogeneous MOX gas sensor arrays [4,5]. Results showed that variations in sensor operating temperature can be corrected by means of calibration transfer techniques. Moreover, aging and sensor drift can be also alleviated with calibration transfer methods [6].

Calibration Update

Calibration update, instead, enriches the calibration dataset with new calibration examples (update samples). The model incorporates the update samples using a hyperparameter that controls the weight of the new samples. It can also be combined with system regularization, in which case the regularization parameter needs to be selected for each task. The method showed successful results when applied to potentiometric chemical sensors [7,8]. Nevertheless, the regularization parameter and the weight of the new samples significantly changed between calibration updates. After some time, new samples dominate the calibration model such that the original calibration dataset contributes scarcely to the model. Although calibration update was designed to adapt the calibration model of a sensing unit affected by drift, it can also be applied to other sensing units since, after some time, any sensing unit behaves like another unit.

In-the-field calibration

A background mismatch between laboratory calibration and in-the-field operation may render calibration models inefficient. In-the-field calibration takes advantage of on-site reference instrumentation to perform calibration and ensure same background during calibration phase and deployment. Usually, linear models are built, which can include additional terms to account for temperature, humidity and time effects [9]. Collocation, however, requires the installation of the sensing unit next to the reference instrumentation, time during which the system is not operational.
Multi-hop calibration enables node-to-node calibration such that data stream is not interrupted (see Figure). This strategy is particularly appropriate in scenarios with moving units that encounter each other regularly. It provided higher accuracy than single collocation when implemented in public vehicles equipped with electrochemical sensors [10]. However, as the number of hops increases, the resulting calibration becomes less reliable. It has been suggested that a node redundancy of about 30% can keep calibration error contained [11].

Conclusions

Very different methodologies have been proposed to reduce calibration costs and increase lifetime of heterogeneous chemical systems. However, the suitability of each method depends on the sensor technology and the required task. Further benchmark is still required to elucidate the methods that provide best results and under which conditions and environments. This work provides a discussion on the calibration methodologies that aim at reducing calibration costs and encourages researchers to share datasets for the benchmark of the different calibration strategies.

References

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Figure 1