Resonant diagnostics of temperature distribution by the piezo-electro-luminescent fiber-optical sensor according to the solution of the Fredholm integral equation

The mathematical model of the resonant diagnostics of the non-uniform temperature field using the piezo-electro-luminescent fiber-optical sensor is developed. The sensor is an optical fiber with electroluminescent and piezoelectric layers. The sensor’s first thin cylindrical photo passing electrode is located between the optical fiber and the electroluminescent layer, and the second electrode is located on an external cylindrical surface of the piezoelectric layer. The mechanoluminescent effect is a result of the interaction between the electroluminescent and piezoelectric layers in case of axisymmetric forced vibrations of the sensor. In case of vibrations, the electroluminescent glow penetrates through an inner electrode into the optical fiber and reaches the receiver-analyzer of light intensity on the output of the optical fiber. The model is based on the amplitude-frequency characteristic for the stationary electroelastic axisymmetric forced vibrations of a local section of the sensor. The forced oscillations are caused by the harmonious part of the control voltage on the electrodes of the sensor; the constant part of the control voltage is necessary for the setup of the sensor for an operating mode in the considered range of temperatures. When heating a local section of the sensor, the diagram of its amplitude-frequency characteristic displaces along the frequency axis (at a value of resonance frequency’s change), proportionally to the temperature change of this section. As a result, the problem of finding the required function of temperature distribution density along the sensor is reduced to the solution of the Fredholm integral equation of the 1-st kind, based on the results of the measured values of a derivative of amplitude of the luminescence intensity at the output of the optical fiber. Fredholm's kernel is calculated using the known amplitude-frequency characteristic of the sensor and the dependence of the resonant frequency on temperature. The numerical modeling results are presented and the influence on amplitude of the luminescence intensity at output of the sensor’s optical fiber are studied for various models and real laws of distribution of the diagnosed temperatures on a sensor ‘s length.