22 Nov 2021
22 Nov 2021
Status: a revised version of this preprint is currently under review for the journal GI.

Response time correction of slow response sensor data by deconvolution of the growth-law equation

Knut Ola Dølven1, Juha Vierinen2, Roberto Grilli3, Jack Triest4, and Bénédicte Ferré1 Knut Ola Dølven et al.
  • 1Centre for Arctic Gas Hydrate, Environment, and Climate,UiT The Arctic University of Norway, Tromsø, Norway
  • 2Institute for Physics and Technology, UiT The Arctic University of Norway, Tromsø, Norway
  • 3CNRS, University of Grenoble Alpes, IRD, Grenoble INP, 38000 Grenoble, France
  • 44H-JENA engineering GmbH Wischhofstrasse 1-3, 24148 Kiel, Germany

Abstract. Accurate, high resolution measurements are essential to improve our understanding of environmental processes. Several chemical sensors relying on membrane separation extraction techniques have slow response times due to a dependence on equilibrium partitioning across the membrane separating the measured medium (i.e., a measuring chamber) and the medium of interest (i.e., a solvent). We present a new technique for deconvolving slow sensor response signals using statistical inverse theory; applying a weighted linear least squares estimator with the growth-law as measurement model. The solution is regularized using model sparsity, assuming changes in the measured quantity occurs with a certain time-step, which can be selected based on domain-specific knowledge or L-curve analysis. The advantage of this method is that it: 1) models error propagation, providing an explicit uncertainty estimate of the response time corrected signal, 2) enables evaluation of the solutions self consistency, and 3) only requires instrument accuracy, response time, and data as input parameters. Functionality of the technique is demonstrated using simulated, laboratory, and field measurements. In the field experiment, the coefficient of determination (R2) of a slow response methane sensor in comparison with an alternative, fast response sensor, significantly improved from 0.18 to 0.91 after signal deconvolution. This shows how the proposed method can open up a considerably wider set of applications for sensors and methods suffering from slow response times due to a reliance on the efficacy of diffusion processes.

Knut Ola Dølven et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gi-2021-28', Anonymous Referee #1, 13 Dec 2021
    • AC3: 'Reply on RC1', Knut Ola Dølven, 08 Apr 2022
  • RC2: 'Comment on gi-2021-28', Anonymous Referee #2, 03 Feb 2022
    • AC1: 'Reply on RC2', Knut Ola Dølven, 08 Apr 2022

Knut Ola Dølven et al.

Knut Ola Dølven et al.


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Short summary
Sensors capable of measuring rapid fluctuations are important to improve our understanding of environmental processes. Many sensors are unable to do this, due to their reliance on the transfer of the measured property, for instance a gas, across a semi-permeable barrier. We have developed a mathematical tool which enables the retrieval of fast response signals from sensors with this type of sensor design.