Mathematical model of pulse scanning of pressure along a piezo-electro-luminescent fiber-optical sensor

The mathematical model is developed aimed at locating pressure non-uniformity along a fiber optic-piezo-electro-luminescent sensor using the location scanning electrical video pulse with a step by step change of its value. The algorithm of finding the function of pressure distribution along a local section and the whole length of the sensor is developed based on the results of the intensity of light proceeding from a fiber optic phase measured on the edge section of the sensor for a case of nonlinear “luminescence function”, which is a dependence between the intensity of light and voltage acting on the luminescent element. The problem is reduced to the solution of the Fredholm integral equation of the 1st kind with the differential kernel depending on the operating and informative transfer coefficients of the sensor and on the set luminescence function of the element. Analytical solutions for the pressure distribution functions along the sensor are obtained for special cases, when the kernel or the function of distribution density is expressed via delta function, and the Fredholm integral equation becomes algebraic. Domains of admissible values of the operating voltage for various modes of diagnostics of pressure distribution are defined. Results of numerical solutions of direct and reverse problems for non-uniform distribution of pressure by means of “pointed” scanning of this pressure are presented by an extremely narrow impulse of the operating voltage. Luminescence functions at the exit from the optical fiber at various time points and values of the impulse of the operating voltage taking into account the set luminescence function of an electroluminescent element are found in the direct problem. The distribution of pressure depending on the values of the luminescence intensity function at various time points is found in the reverse problem.