Estimation of Temperature and Associated Uncertainty from Fiber-Optic Raman-Spectrum Distributed Temperature Sensing

Abstract

Distributed temperature sensing (DTS) systems can be used to estimate the temperature along optic fibers of several kilometers at a sub-meter interval. DTS systems function by shooting laser pulses through a fiber and measuring its backscatter intensity at two distinct wavelengths in the Raman spectrum. The scattering-loss coefficients for these wavelengths are temperature-dependent, so that the temperature along the fiber can be estimated using calibration to fiber sections with a known temperature. A new calibration approach is developed that allows for an estimate of the uncertainty of the estimated temperature, which varies along the fiber and with time. The uncertainty is a result of the noise from the detectors and the uncertainty in the calibrated parameters that relate the backscatter intensity to temperature. Estimation of the confidence interval of the temperature requires an estimate of the distribution of the noise from the detectors and an estimate of the multi-variate distribution of the parameters. Both distributions are propagated with Monte Carlo sampling to approximate the probability density function of the estimated temperature, which is different at each point along the fiber and varies over time. Various summarizing statistics are computed from the approximate probability density function, such as the confidence intervals and the standard uncertainty (the estimated standard deviation) of the estimated temperature. An example is presented to demonstrate the approach and to assess the reasonableness of the estimated confidence intervals. The approach is implemented in the open-source Python package "dtscalibration".Sensors 2020, 20, 2235 2 of 21 scattering), but a small fraction has different wavelengths (Raman scattering). The detectors in DTS systems measure the intensity of the backscatter at two distinct wavelengths: Stokes (-Raman) and anti-Stokes (-Raman) scatter. The temperature at the point of reflection is estimated from these two types of scatter. Stokes scatter has a longer wavelength than the laser and its intensity does not vary much with temperature, while anti-Stokes scatter has a shorter wavelength than the laser and its intensity varies significantly with temperature. The location of the measurement along the fiber is estimated from the time between sending the laser pulse and receiving the scatter. Temperature along the fiber is estimated from the measured intensities of the Stokes and anti-Stokes scatter by calibrating to reference sections with a known temperature. In practice, these fiber sections are submerged in water baths of which the temperature is continuously measured with a separate temperature sensor. The water can be mixed with small pumps in an attempt to equalize the temperature of the water in the baths. Sequential temperature measurements require continuous calibration due to varying gains and losses in the DTS system. Detailed calibration procedures are available in the literature [11][12][13][14]. The uncertainty in the temperature estimates is strongly aff...

Thermodynamics of a fast-moving Greenlandic outlet glacier revealed by fiber-optic distributed temperature sensing

“…We used the open source Python “dtscalibration” package ( 63 ) to calculate a temperature time series, T (K), with uncertainty bounds at time t (s) and depth z (m), which builds on the standard DTS equation P S and P aS are the Stokes and anti-Stokes power and ζ is the sensitivity of (anti-)Stokes scattering to temperature which is dependent on fiber material and does not vary in time. C is a dimensionless function of the alignment and sensitivity of the optical system, connectors, and splices that can vary with interrogator temperature and movement.…”

“…A full description of the dtscalibration package can be found within des Tombe et al . ( 63 ) and accompanying GitHub documentation. The spatial temperature change within the absolute 95% confidence intervals produced with this method ( Fig.…”

Revisiting wind speed measurements using actively heated fiber optics: a wind tunnel study

“…3, an approximately 20 % additional bias in calculating the wind speed was created. By using a more recent version for calculating the empirical Nusselt number (Cengel and Ghajar, 2014), the bias in our study is reduced to ∼ 5 %. Therefore, Eq.…”

Decoupling of a Douglas fir canopy: a look into the subcanopy with continuous vertical temperature profiles

“…Calibration was performed using the Python package 'dtscalibration' (des Tombe and des Tombe et al, 2020).…”