David G. Barker and Dr. Matthew R. Jones, Mechanical Engineering
Advances in the area of Optical Fiber Thermometry (OFT) are leading to more accurate temperature measurements in high-temperature environments. A typical OFT application is when the tip of an optical fiber is inserted into an environment where the temperature is to be measured. The other end of the fiber is attached to an optical system where light from the fiber is measured (see Figure 1). From the light emission measurements, the temperature at the heated tip of the fiber can be inferred.1
The standard method of OFT works well when the tip of the fiber is the only part exposed to the high temperature environment. If the length of the optical fiber is also exposed to high temperatures, error is introduced to the inferred temperatures. This error is due to emission by the heated length of the optical fiber. It has been shown that this can cause the temperature measurement to be significantly erroneous.2
One possible solution to this problem is to use a genetic algorithm to account for the emission by the fiber and retrieve an accurate tip temperature. A genetic algorithm uses principles of natural selection to arrive at the best temperature profile from a given population. It has been shown that this technique is very effective at finding an accurate tip temperature and reconstructing an estimation of the temperature profile along the OFT.3 A genetic algorithm is, however, very computationally costly.
This research led to the development of an alternative approach to finding the temperature at the tip of the OFT and reconstructing an estimate of the temperature profile along the optical fiber. Based on the discussion by Öziºik and Orlande4, a conjugate gradient algorithm (CGA) was developed. One of the main differences between a conjugate gradient algorithm and a genetic algorithm is that it uses mathematical techniques to arrive at the best estimate of the temperature profile; the genetic algorithm, on the other hand, uses a random-search technique. This difference allows the CGA to converge on a solution nearly 45 times faster than the genetic algorithm. Table 1 shows a comparison between the two approaches, and Figure 2 shows a simulated temperature reconstruction using the CGA.5
It is evident that the CGA improves significantly on the genetic algorithm. One problem, however, with the CGA is that it is sensitive to the initial guess. For example, with a flat initial guess at 500K, the CGA did not converge; the genetic algorithm did converge in this situation, although the computation time was significantly higher than shown in Table 1. Taking into account the computation time required for the genetic algorithm, it would still be more feasible to run the CGA several times with different initial guesses than to run the genetic algorithm once. This makes the CGA as potentially robust as the genetic algorithm with considerably improved accuracy.
This research has been documented in greater detail and with further developments in professional publications.5,6
__________________________
1 Dils, R. R., “High-temperature optical fiber thermometer,” Journal of Applied Physics, Vol. 54 No. 3, pp. 1198 – 1201, 1983.
2 Jones, M. R., Farmer, J. T., and Breeding, S. P., Evaluation of the Use of Optical Fiber Thermometers for Thermal Control of the Quench Module Insert, Proceedings of the Thermal & Fluids Analysis Workshop, 1999.
3 Jones, M. R., and Barker, D. G., Use of Blackbody Optical Fiber Thermometers in High Temperature Environments, J. Thermophysics and Heat Transfer, Vol. 16, No.3, 2002.
4 Öziºik, M. N., and Orlande, H. R. B., Inverse Heat Transfer, Taylor & Francis, New York, 2000.
5 Barker, D. G. and Jones, M. R., “A Hybrid-Inverse Method for Predicting the Temperature Profile Along a Blackbody Optical Fiber Thermometer,” Proceedings of IMECE: 2002 International Mechanical Engineering Congress and Exposition, Nov. 17-22, New Orleans, LA.
6 Barker D. G., and Jones, M. R., “Inversion of Spectral Emission Measurements to Reconstruct the Temperature Profile along a Blackbody Optical Fiber Thermometer,” Submitted to Inverse Problems in Engineering, 2002.