A Method for Reliability Analysis of Aircraft Power Distribution System Based on Petri Net

The variety of electrical equipment on modern aircraft is increasing, the power consumption is increasing, and strict requirements are imposed on the capacity, power supply quality and reliability of the airborne power supply. With the continuous application of advanced technology on the aircraft, the requirements for the reliability of the aircraft power supply system are getting higher and higher. Aircraft power distribution systems are an important part of the power supply system, so it is important to study the reliability of the power distribution system. Existing reliability analysis methods include minimum path method, minimum cut set method, fault tree analysis method, and failure mode consequence analysis method. Although these reliability analysis methods can calculate the reliability index of the power distribution system more effectively, in practical application, in the qualitative analysis process of large complex systems, the calculation amount is very large, and even the NP difficulty problem may be formed.
Petri is a system description, simulation math and graphical analysis tool that expresses the static structure and dynamics of a system. Therefore, this paper proposes a reliability analysis method for aircraft power distribution system based on Petri net.

1 Petri Net Overview
As a special directed network, Petri nets use the library and transition as nodes, and indicate the propagation relationship of system faults in the direction of the arc. The state of the system is represented by a place, and events that change state are represented by a transition. In the Petri net graphic description, "○" is used to represent the library, "|" is used to represent the transition, and the directed arc "→" is used to represent the sequence, and thus constitutes a graphical representation of the Petri net. If the weight of all directed arcs of a Petri net is 1, then this network is called the specification network. Only the situation of the specification network is considered here.
The hexad N=(P, T, I, O, M, Mo) is called a Petri net if the following conditions are satisfied.
1) P = {P1, P2..., Pn} is a finite set of libraries, n is the number of libraries, n> 0;
2) T={T1, T2..., Tm} is a finite set of transitions, m is the number of transitions, m>0, P∩T=empty set;
3) I: PxT → N is an input function that defines a set of directed arc repetitions or weights from P to T, where N = {0, 1...} is a set of non-negative integers;
4) I: TxP → N is an input function that defines a set of directed arc repetitions or weights from T to P;
5) M: P → N is the distribution of the identifiers in each library;
6) MO: P → N is the initial identification distribution in each library.
The application of Petri net to analyze system faults is to use the undesired events of the system as the top library, and to find out all the possible factors that cause this event as the intermediate and bottom libraries. Using the basic elements of the Petri net - the different connections of the library and the transition can represent the logical relationship of the fault tree model, and the graph theory method can be fully utilized to solve the diagnostic inference problem of the fault model. The top event, intermediate event, and bottom event in the fault tree are represented by the library, transition, and arc in the Petri net, as shown in Figure 1.

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2 Reliability analysis based on Petri net
2.1 Qualitative analysis The
Petri net model simplifies the various logical connection relationships of the fault tree into a network consisting only of the library and the transition, with the directed arc as the connected edge, making the fault model of the system simple and easy to understand, and the fault propagation. The relationship is clear at a glance. At present, many scholars have proposed many methods to apply Petri nets to minimize the cut set, such as path search method and library matrix method. This paper mainly introduces a new algorithm for applying the Petri net's association matrix to find the minimum cut set. This algorithm derives the cut set directly from the correlation matrix according to the input and output relations expressed in the specified association matrix, which is easy to implement computer programs, and It is simpler and more intuitive to find a cut set with a repetitive event Petri net model.
The structure of the Petri net can be represented by a matrix. If the input function from the library P to t takes a non-negative integer w, denoted as I(P,t)=w, it is represented by a directed arc from P to t and a side note w; The output function of t to P takes a non-negative integer w, denoted as O(P,t)=w, and is represented by a directed arc from t to P and a sidenote w. In particular, if w=1, it is not necessary to label; if I(P, t)=0 or O(P,t)=0, it is not necessary to draw an arc. Both I and O can be represented as nxm non-negative integer matrices, and the difference between O and I, A=OI, is called an associative matrix. For the specification network, w=1. The following is an example of the method steps for the association matrix to find the minimum cut set.


The correlation matrix is ​​obtained from the Petri net model in Figure 2:

It can be seen that in this correlation matrix, -1 indicates that the directed arc is changed by the library, and the library is the input library of the transition; 1 indicates that the directed arc is changed to the library by the transition, and the library is the output of the transition. Library. According to the above correlation matrix, the steps of finding the minimum cut set of the Petri net are as follows:
1) Find the row with only 1 and 0 and no -1 in the correlation matrix, then the row corresponds to the top library (only the input library, there is no output library), so the library starts to search (in this association matrix) For the last line).
2) Starting from the row 1 corresponding to the top library, look for -1 by column. The library represented by the row corresponding to -1 is an input library of the top library. If there are multiple -1 in the column, the corresponding There are multiple input libraries for the same transition, and the input library is a "phase-to-peer" relationship.
3) The -l found by step 2) finds 1 by row. If there is 1 indicating that the library is the intermediate library, it will cycle through the steps 2) until the row does not have 1; if there is no 1, the library is explained Is a bottom library; if the row has more than 1, it means that the library corresponding to these 1 should be a "phase or" relationship.
4) Continue to search by step 2) and step 3) until the bottom library is found.
5) According to the previous "phase" and "phase" relationship, the bottom library is expanded, and all the cut sets are obtained.
6) Obtain the minimum cut set according to the Boolean absorption law or the prime number method.
Follow the steps above to write:
P7=P6+P5=P3xP4+P5=(P1+P2)×P4+P5=P1×P4+P2×P4+P5
It can be seen that the minimum cut set is {P1, P4}, {P2, P4}, {P5}.
2.2 Quantitative calculation After all the minimum cut sets of the fault tree are obtained, the probability of the top event occurring can be obtained by the minimum cut set. The probability of occurrence of the top event is P(T), C1={P1, P4}, C2={P2, P4}, C3={P5}. then:


3 Reliability Analysis of Aircraft Power Distribution System Based on Petri Nets Figure 3 is a simplified schematic diagram of a distributed distributed distribution system of aircraft. It uses the no-channel automatic relay protection technology of distribution lines to control the on/off of circuit breakers and ring switches. In order to achieve fault isolation and fault-tolerant power supply.


3.1 Establishing a Fault Tree Figure 4 is a fault tree model diagram. In the figure, Fn represents the fault of the nth generator, and Kn represents the fault of the nth ring switch.


3.2 Transforming the fault tree model into a Petri net model Figure 5 shows the Petri net model map, and Pn represents the corresponding events in the fault tree of Figure 4.


3.3 Applying the correlation matrix of the Petri net to find the minimum cut set According to the above steps of finding the minimum cut set:
P14=P13+P12=P10+P11+P12=P7+P8+P9+P11+P12=P1P2+P1P3P4P5+P1P3P4P6+P11+P12
Thus, the minimum cut set is obtained: C1={P1, P2}, C2={P1, P3, P4, P5}, C3={P1, P3, P4, P6}, C4={P12}. C5={P12}. Similarly, the above quantitative calculation method can be used to obtain the probability of occurrence of the top event.

4 Conclusion Fault tree analysis method is often used in the reliability analysis of aircraft power distribution system. Although the reliability analysis problem of power distribution system is better solved, the practical application shows the disadvantages of complicated analysis and large calculation, which is not conducive to The distribution system is quickly and efficiently evaluated. Transforming the fault tree model into a Petri net model for analysis and calculation can greatly simplify the calculation in the fault tree analysis and make up for the shortcomings of the traditional fault tree analysis method.

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