Application of the least square method for processing the signal obtained by the tuneable diode laser absorption spectroscopy method in the range 4860–4880 cm⁻¹for the problem of measuring¹³CO₂content in exhaled air

Abstract

The 1st, 2nd and 3rd order least square method (LSM-1, LSM-2 and LSM-3) is applied to smooth the experimental absorption signal of 13 CO 2 and 12 CO 2 obtained by the tuneable diode laser absorption spectroscopy method in the 4860-4880 cm −1 frequency range of a tuneable diode laser. It has been shown clearly that using LSM-2 with a filter window N ~ 100 allows the 13 CO 2 content in exhaled air to be measured at an error level of 0.28%, which meets breathing tests requirements.

High-precision concentration detection of CO2 in flue gas based on BO-LSTM and variational mode decomposition

“…where, o t represents the output gate of the current time step; W o and U o are the corresponding weight matrices; and b o is the bias matrix of the output gate. The memory state of the LSTM can be updated using equation ( 10) (10) where, C t represents the memory state of the current time step, and ⊙ represents the multiplication of two vector elements. g t represents the memory state of the current time-step.…”

“…Existing regression fitting models include linear fitting, least squares method, back propagation neural networks (BP), radial basis function (RBF), support vector machine, convolutional neural networks (CNN), and long short-term memory (LSTM) neural networks Based on TDLAS technology, curve fitting of CH 4 concentration under rain and fog conditions was performed by Yang et al The results indicate that the proposed method exhibits good accuracy [9]. Kireev et al used the least squares method to detect the specific concentration of CO 2 in exhaled air, and the final result met the requirements of the breathing experiment [10]. However, when linear fitting and the least squares method are interfered with by the outside world, the linear relation will decrease, and the error will inevitably increase.…”