The Reliability Model of Artificial Monitoring on the Anomalous Event in Expressway Tunnels and Monte Carlo Simulation

Artificial monitoring remains to be a major way to detect anomalous events in expressway tunnels. To estimate the reliability of artificial monitoring on anomalous events in expressway tunnels, the video surveillance and mobile inspection based reliability models of artificial monitoring on the anomalous event in the expressway tunnel were built, and Monte Carlo method was applied to calculate the probability and mean time to detect the anomalous event at the specific time. The results showed that the Monte Carlo method could simulate video surveillance and mobile inspection, and obtain the probability distribution and mean time of detecting anomalous events. The mean time to spot the anomalous event was in reverse relation with the number of inspectors, the time of mobile inspection, and the reliability probability of the monitoring pre-warning system in tunnels and was in positive relationships with the departure interval. Combined with the actual operation cost, the model serves as a basis for the artificial monitoring package.


Introduction
As more and more people own a car and the expressway networks are improved in China, the number of expressway tunnels in the mountainous areas rises, ushering in increasingly convenient transportation. Meanwhile, accidents in expressway tunnels accounting for a large part of traffic accidents have a wide-ranging impact with serious consequence, extensive traffic jams and difficulty in rescue and evacuate, which causes "chain reaction", "radiation reaction" and so forth in the neighborhood (Jia, 2009). Therefore, based on the existing equipment and safety management of expressway tunnels, it is essential to enhance the monitoring pre-warning of traffic incidents in tunnels so that they could be discovered and dealt with in the shortest time possible (Wang & Yang, 2009).
The literature studied the monitoring pre-warning system in tunnels in aspects including the construction framework (Xu, 2009;Zeng, 2008), the design plan of the monitoring system (Mohammadi, 2008;Ma, 2001;Zeng, 2004;Song, 2000), the automatic detection algorithm of the anomalous event (Liu, 1998) and so forth. Zeng Sheng et al. discussed the design of the tunnel monitoring system by categorizing the components of the system and defining the functions of the sub-systems (Zeng, 2004). Relevant studies categorized the automatic detection methods based on detection strategies, the detected cross section, and the monitoring equipment (Yan, 2006). Most studies just offered the theories of the monitoring pre-warning system in the tunnel while seldom touched its application (Xiong, 2012). However, the artificial detection method is widely applied in detecting the anomalous event, which is the core of the monitoring pre-warning system. Therefore, the artificial detection method mainly composed of a video surveillance system or artificial inspection is necessary for the safe operation of the tunnels.
In view of the above, the paper combined video surveillance in the tunnels and artificial inspection to build the reliability probability model of monitoring anomalous events in tunnels and use the Monte Carlo method for simulation. The study has theoretical significance and could be applied to popularize the monitoring pre-warning system, pinpoint its usage plan, improve the safety management of tunnel operation, and reduce traffic accidents.

Video Surveillance Model
Surveillance cameras are usually installed in the expressway tunnel at intervals. The visual information inside the tunnel collected by several cameras is then transmitted to the monitors on the television wall in the monitor room. The whole tunnel is under around the clock surveillance without interruption by switching the real-time pictures from a few monitors.  single person to switch is  per minute. The inspection route is shown in Figure 1. as a horizontal Z.
The frequency to switch is 6 0 m a  per minute.

Figure 1. The Inspection Route
Assume the lens of camera n shows the anomalous event ( ) n m  at a specific time when the staff is inspecting screen (1, ) X U m  , the probability ( ) P Q for a single person to detect it within h seconds is: respectively. The probability ( ) P Q for the anomalous event to be discovered within h seconds is: Among them: It could be then inferred that for k inspectors, the inspection frequencies are i A is the zone where the anomalous event takes place and the probability ( ) P Q for the anomalous event to be discovered within h seconds is:

Mobile Inspection Model
There are q tunnels on a certain section of the expressway ( 1,2,3 ) i q   , the staff inspect the tunnels assigned to him in the patrol car repeatedly at a frequency of  per minute. The inspection route is shown in Figure 2.

Figure 2. The Sketch Map of the Artificial Inspection Route
Assume an anomalous event occurs in tunnel n ( n q  ) at a specific time when tunnel ' (1,q) X U  is under inspection. There is situation A and B.
Situation A: tunnel n where the anomalous event occurs is in the same direction as the inspected tunnel ' X , namely Then the probability ( ) P Q for the anomalous event to be spotted within ' h seconds is: Situation B: tunnel n where the anomalous event occurs is in the opposite direction as the inspected tunnel ' X , and the patrol car needs to turn around. This takes t  seconds, namely: ∈ 1, , ∈ 1, or ∈ 1, , ∈ 1, Then the probability ( ) P Q for the anomalous event to be spotted within ' h seconds is:

Simulation Objective
Monte Carlo simulation is a calculation method based on the random number. The method estimates and counts the parameters by generating time sequences repeatedly in random settings to study its distribution characteristics.
Based on Monte Carlo simulation, the Matlab platform was chosen. Simulations were made according to the reliability probability models of closed-circuit television and artificial inspection monitoring to predict the shortest time for the anomalous event to be spotted once it occurred in the tunnel and obtain the probability distribution for it to be spotted within the required time.

The Simulation
Take the video monitoring pre-warning system as an example to illustrate the simulation. Create

Background
The road is 40.1km with 36 tunnels where 84 cameras are installed. Among them, a camera is installed every 125m in a tunnel on average. There are 48 monitors on the television wall in the monitor center.
All the pictures are inspected by switching.

Video Monitor Simulation
It takes 5s for one staff to inspect a picture and the frequency is 1 7 per minute. The frequencies for two staffs are the same and each is 2 7 per minute. For several staffs ( 1,2,3 ) i k   , the frequency is 7 k per minute for each. The above formulas lead to the probability curve for different numbers of inspectors to spot the anomalous event at different inspection times, as shown in Figure 4. When one staff inspects for 7 minutes, the probability to spot the anomalous event is 100%, namely, the anomalous event is sure to be spotted within 7 minutes. For two inspectors, the anomalous event is sure to be spotted within 3.5 minutes. The probability to spot the anomalous event rises with the inspection time and the number of inspectors. However, for the safe management of the tunnel, 1-4 inspectors are necessary. A working plan is proposed based on the practical situation while taking economic costs such as the salary for the inspectors into consideration.   The time and location for the anomalous event to occur are random. Two monitoring personnel inspect 84 pictures in total, and each inspects 42 pictures. Thus the mean time for the anomalous event to be spotted is 1.67 minutes. Figure 5 shows the time distribution sequence and expectation for 2 inspectors to spot the anomalous event.  When the number of inspectors increases from 1 to 2, the expected value of time will drop from 3.04 minutes to 1.67 minutes. When the number of inspectors increases from 2 to 3 or 4, the expected time will fall slowly. Therefore, it is necessary to increase the number of monitoring personnel from 1 to 2 under the assumption, and the actual cost should be considered for personnel enlargement.

Mobile Inspection Simulation
There are 36 tunnels for inspection in total. When the patrol car is dispatched every 1 hour to every 6h, the daily inspection ranges from 4 to 24, and the inspection frequency ranges from 1 360 per minute to 1 60 per minute. Thus probability curves to spot the anomalous event for different departure frequencies at different inspection times are calculated, as shown in Figure 7. It is sure to spot the anomalous event within 6 hours when the inspection takes place every 6 hours. It is certain to spot the anomalous event within 1 hour when the tunnels are inspected every hour. It is obvious that the probability to spot the tunnel anomaly at short time increases as the departure interval shortens and the inspection frequency increases.

Conclusions
The paper systematically studied the reliability of the monitoring pre-warning system in expressway tunnels. The probability models of the reliability for closed-circuit television and artificial inspection were established respectively. The Monte Carlo simulation method was applied to obtain the final simulation results. The main conclusions were as follows.
The probability model could judge the probabilities to spot the anomalous event in the tunnel on the same road in different monitoring plans. The simulation results lead to the probability distribution and the mean time to spot the anomalous event.
In the video surveillance pre-warning system, the probability to spot the anomalous event increases with the inspection time, and the number of inspectors. In the artificial monitoring pre-warning system, the probability to spot the tunnel anomaly at short time increases as the departure interval shortens and the inspection frequency increases.
The mean time to spot the anomalous event serves as a major index to assess the monitoring pre-warning system. Therefore, if possible, the tunnel administration could adjust the monitoring plan appropriately so that the anomalous event in the tunnel could be spotted as soon as possible, guaranteeing the cost-saving, safe operation of the tunnels.