The new principle is presented related to construction of the multipoint optoelectronic flame detection system based on the sum-total of non-coordinate optoelectronic sensors located in a special way at the protected technogenic object. The system allows to detect the flame and determine its spatial coordinates throughout the volume of the protected premises of complex geometric shape. The analysis was conducted concerning the methods for solving the problem of determining the flame spatial coordinates: multifactorial polynomial regression; regression by neural networks; numerical methods for solving nonlinear equations.

Optimal approach for determination of flame spatial coordinates is proposed, which is based on obtaining the polynomial regression function of the output signals of non-coordinate of the optoelectronic sensors. As a result, the calculation process is simplified, high speed is ensured while maintaining the required error even in dustiness of atmosphere of the protected object. The method was developed for adapting flame detection for the protected object of complex geometric shape, which allows to determine the optimal number of non-coordinate optoelectronic sensors, their spatial location and orientation. For this, the numerical methods were used for searching the minimum target function in order to detect the flame and determine its spatial coordinates with a given error over the entire volume of the protected technogenic object. The task of minimizing the target function is solved by the method of coordinate descent or the gradient method with step breaking. The results are shown related to the adaptation of the system to the conditions of the test objects in the form of rectangular conjunction of the coal mine workings. The required error of flame coordinates  determination when using fourth-order polynoms for conjugating in the form of the direct intersection is ensured through the use of nine sensors for conjugating in the form of a direct branch — eight sensors, for conjugating in the form of a junction of  the working  at  right angle — seven sensors.