Improving Efficiency Monitoring Systems for Potentially Dangerous Objects Based on Optimization of Group Detection Sensors

This paper presented the method for improving the effectiveness detecting critical states of potentially dangerous objects on the basis of the sensors group and a joint Bayesian optimization the threshold and majority rule to detection.


Introduction
One of the main directions to reduce potential damage from potentially hazardous industrial objects (power plants, transmission facilities, hydro engineering, oil, gas and chemical objects, pipelines, etc.) is the development of electronics systems to monitor their current state and early detection of critical states of objects. The global experience of running such systems is faced with the problem of detecting the presence of errors in the critical states of dangerous objects in the form of omissions and false alarms. Due to the continuous increase in the number of potentially dangerous industrial sites in different countries, the problem of increasing the efficiency of electronics systems monitoring is becoming particularly relevant. The priority in solving this issue should be considered as reducing errors the early detection critical conditions for hazardous industrial facilities. The most constructive in this direction is the approach based on combining several primary sources of information to the group sensors. For group sensors the presence or absence of the critical state of the object shall be made on the basis of a two-step batch processing of information from the individual sensors in a group. In this regard, the need of improving effectiveness of critical states detection by means of group sensors on the one hand, and the specific conditions of monitoring for dangerous objects, that decrease the detection efficiency on the other hand, give rise to an optimization problem for a two-stage detection of group sensors. In [1] to improve the effectiveness of fire detection is proposed unification of the primary sensors in the group and application of the majority principle of processing information from a group of sensors. At the same time reducing of wrong decisions are not considered. In [2] to reduce the erroneous decisions of the group sensor is proposed to use criterion of maximum difference between the probabilities of correct and false outcome. It is shown that for a fixed threshold for the primary sensor there is a definite rule between the number of triggered sensors and the total number of sensors, using which making decision in respect of fire is optimal in terms of the selected criteria. An equation that allows choosing the optimal rule is gotten, but is not considered the question of the threshold's choice for the primary sensors and connection with rules of majority processing. The aim is to increase the efficiency of electronics system detecting critical states of potentially dangerous objects of industrial field on the basis of decreasing erroneous decisions by means of the joint optimization of the threshold in primary sensors and majority rules in group sensors. We consider the group sensor, a typical structure of which is shown in Fig. 1. Object sensors generate and transmit information about of object the states, which is exposed to influence of additive random factors ( )

Problem Definition and its Solution
In the first stage detection is carried at the sensors' level by comparing level of information signal about the critical state of object with the appropriate threshold.
The random nature of the critical state of objects, as well as confounding factors that are recorded by on-site sensors to detect the primary stage, gives rise to two types of errors: failure of the first kind -skipping in the presence of a critical state; failure of the second kind -a false alarm in the absence of a critical state. At the same time errors of the primary sensory detection will be transformed into the corresponding error detection for the group sensor. Let the error's probability of type I be the magnitude of α and the error's probability of type II -β at the time of the initial detection (at the level of sensors) for a fixed threshold. Then the error's probability α p of type I (skipping) for the group sensor, characterized by the lack of detection of the critical state for more than k n − of sensors of a group in the actual presence of it, will be determined by magnitude The error's probability of type II β p (false alarm), characterized by the detection of the critical state of not less than by k when actually it is absent, will be determined by ( Taking into account equations (1) and (2), in general, optimization of majority rules for detecting the critical state " k / n " in the second stage of detection for the sensor in the group should be carried out in accordance with the Bayesian criterion, which determines the average risk of erroneous solutions (6) In view of (6), the average risk of the Bayesian detection sensor group will be determined by functionality In general, the optimization of the sensor group in accordance with a Bayesian criterion (7) must be performed together the number n and the threshold u of sensors in the group, and the number k of sensors, which detect a critical state of the object. In practice, the total number n of sensors in the group is normally fixed. Therefore it is the joint optimization of the value k and the threshold u sensors. The threshold u is determined by current the statistical properties of the critical factors and interference Therefore, the solution of the optimization problem for the sensor group in the general case depends on the statistics of observations the critical states.
For example, key indicators of detection quality for considered test conditions for sensors group, with optimized only the number k , and for sensors group with jointly optimized number k and thresholds a u = , for total number n of sensors in a group is equal to 20 are presented in Fig. 2 a, b. On the Fig. 2 a,

Conclusions
This paper is presented the method for improving the effectiveness detecting critical states of potentially dangerous objects on the basis of the sensors group and a joint Bayesian optimization the threshold and majority rule to detection. The simulation results reveal that the threshold and majority rule to detection are not independent. This dependence has a mathematically complex representation (7). The dependence of the threshold and the detection rule is investigated in various conditions of observation. It is shown that for improve efficiency detection on the presented method the thresholds value and majority rule they must be optimized together. Quantitative assessment of expected improve detection for joint optimization of the thresholds and majority rules indicates high efficiency of the presented method for group sensors.