Probabilistic-Mathematical Models for Formation of Information Flows in Aircraft Fire Alarm System

摘要

The article deals with solving the problem urgent for aviation practice which consists in providing the aircraft crew with reliable information from primary sources of information (sensors of controlled parameters) in normal and special flight situations. To solve this problem we have developed the probabilistic-physical model of processes of information flows formation in aircraft fire alarm system and showed geometric probabilistic characteristics: the probabilities of correct fire detection, non-detection and false alarm. The article has proved mathematically the conditions ensuring simultaneously equal degree of reducing the probabilities of non-detection and false alarm so that they would be simultaneously equal and minimum. It is proposed to consider the fire extinguishing system using the structural diagram of the state graph of the information-redundant system. The analysis of formation and creation of the control flows in the fire alarm system has been carried out and it has been proved that the system probabilities form a complete group of events that can be afterwards considered by the mathematical and probabilistic analysis methods to predict the state of the fire alarm system. The mathematical formulas for comparing the probabilities of non-detection and false alarm are obtained and their graphical dependences with respect to probability of correct detection and the number of sensors in the system are shown. We have obtained the mathematical dependence of growth coefficient of probability of correct fire detection compared with the false alarm probability considering the number of sensors. It is proved that with the increased number of sensors the growth coefficient increases in exponential function. Therefore in special conditions it makes sense to desensitize the sensors raising the actuation threshold and in so doing maintaining conditions ensuring the minimum values of probabilities of non-detection and false alarm of fire alarm system.