Availability Analysis Method of Navigation Monitoring Network

Abstract

The present invention discloses an availability analysis method for a navigation monitoring network, and realizes a comprehensive analysis of the availability of the navigation monitoring network. The method comprises the following steps: constructing a navigation monitoring station availability model using a generalized random Petri net, isomorphizing the Markov chain state transition process, determining the differential equation of the navigation monitoring station model, and obtaining the availability of the navigation monitoring station. Determining the availability of the transmission link between the navigation monitoring stations. Determining the logical relationship between the navigation monitoring stations, and determining the logical relationship between the navigation monitoring areas, and determining the logical relationship between the state of the navigation monitoring area and the state of the navigation monitoring network. Constructing a navigation monitoring network availability model based on a Bayesian network, determining the probability of an available state, a reduced-order state, and an interruption state of the navigation monitoring network. If the navigation monitoring network is in an interruption state, solving the interruption state probability of each navigation monitoring station, sorting the interruption state probability of each navigation monitoring station from high to low, and sequentially diagnosing and troubleshooting the navigation monitoring stations.

Description

Technical Field

[0001] The invention relates to the technical field of satellite navigation system availability, and in particular to an availability analysis method for a navigation monitoring network. Background Art

[0002] The availability of the navigation monitoring network is a key parameter that characterizes the operating status of the monitoring network. It refers to the degree to which the monitoring network is in a working or usable state when it is needed and starts to perform tasks at any random moment. The above-mentioned "tasks" include: precise orbit determination and time synchronization, uplink injection of navigation information, system integrity monitoring, etc. Factors related to the availability of the navigation monitoring network include: the availability of navigation monitoring stations, the availability of transmission links between navigation monitoring stations, the logical relationship between navigation monitoring stations, the logical relationship between navigation monitoring areas, etc.

[0003] The navigation monitoring network is an important part of the satellite navigation system, responsible for the monitoring, command and control of the navigation constellation, and its operating status is related to the accuracy, availability, continuity and integrity of the satellite navigation system's service performance indicators promised to users. Engineering practice shows that the navigation monitoring network is a hardware and software integrated system, and its operating status is closely related to the short-term hardware failure, long-term hardware failure, short-term software failure, long-term software failure, hardware and software coupling failure of the navigation monitoring station, as well as the transmission link failure between navigation monitoring stations, the logical relationship between navigation monitoring stations, and the logical relationship between navigation monitoring areas.

[0004] In addition, traditional research on the availability of navigation monitoring networks mainly focuses on modeling research on hardware failures of navigation monitoring stations, with less consideration given to software failures and hardware-software coupling failures of navigation monitoring stations, and less consideration given to common cause failures of transmission link failures between navigation monitoring stations.

[0005] Therefore, there is an urgent need for a navigation monitoring network availability analysis method that can comprehensively consider the interruption status of each navigation monitoring station, the logical relationship between the transmission links between navigation monitoring stations and between navigation monitoring areas. Summary of the invention

[0006] In view of this, the present invention provides an availability analysis method for a navigation monitoring network, which can perform availability analysis on the navigation monitoring network through a modeling method, comprehensively consider the interruption status of each navigation monitoring station, the logical relationship of the transmission links between the navigation monitoring stations and between the navigation monitoring areas, and can achieve a comprehensive analysis of the availability of the navigation monitoring network. It is a quantitative analysis of the availability of the navigation monitoring network, and provides technical support and decision-making suggestions for the interruption of the navigation monitoring network.

[0007] To achieve the above object, the technical solution of the present invention comprises the following steps:

[0008] Step 1: Use generalized stochastic Petri nets to construct a navigation monitoring station availability model, isomorphize the Markov chain state transition process, determine the differential equation of the navigation monitoring station model, and then determine the availability of the navigation monitoring station.

[0009] Step 2: Determine the availability of transmission links between navigation monitoring stations.

[0010] Step 3: Determine the logical relationship between navigation monitoring stations, determine the logical relationship between navigation monitoring areas, and determine the logical relationship between the status of the navigation monitoring area and the status of the navigation monitoring network.

[0011] Step 4: Using the availability of navigation monitoring stations, the availability of transmission links between navigation monitoring stations, the logical relationship between navigation monitoring stations, and the logical relationship between navigation monitoring areas, a navigation monitoring network availability model is constructed based on the Bayesian network to determine the probability of available state, degraded state, and interrupted state of the navigation monitoring network.

[0012] Step 5. If the navigation monitoring network is in an interrupted state, use the navigation monitoring network availability model to solve the interruption state probability of each navigation monitoring station when the navigation monitoring network is in an interrupted state, sort the interruption state probability of each navigation monitoring station from high to low, and perform fault diagnosis and troubleshooting on the navigation monitoring stations in sequence according to the sorting order.

[0013] Furthermore, in step 1, the generalized random Petri net constructs the navigation monitoring station availability model including:

[0014] Overall interruption related status, including: navigation monitoring station availability status P UP (t), Navigation monitoring station interruption status P DOWN (t), hardware or software failure selection state P HOS (t).

[0015] Hardware short-term fault related status, including: hardware short-term or long-term fault selection status P SOLH (t), hardware short-term fault state P SH (t).

[0016] Hardware long-term fault related status, including: Hardware long-term fault status P LH (t), hardware spare parts selection state P SONH (t), hardware spare parts waiting state P SWH (t), hardware long-term fault repair waiting state P RWH (t).

[0017] Software short-term fault related status, including: software short-term or long-term fault selection status P SOLS (t), software and hardware failover selection state P SOHS(t), software short-term fault selection state P ROIS (t), software restart fault state P RS (t), software self-repair status P IS (t).

[0018] Software long-term fault related status, including: Software long-term fault status P LS (t).

[0019] Software and hardware coupling fault related states, including: software fault to hardware fault transfer state P STH (t).

[0020] Where t is the time variable.

[0021] Furthermore, in step 1, the differential equation of the navigation monitoring station model is determined, which is specifically:

[0022]

[0023] P UP (t)+P DOWN (t)+P SH (t)+P LH (t)+P SWH (t)+P RWN (t)+P STH (t)+P LS (t)+P RS (t)+P IS (t) = 1(2)

[0024] And f H +f s =1,f SH +f LH =1,f SPH +f NSPH =1,f SS +f LS =1,f RS +f IS =1,f STHS +f NSTHS =1where:

[0025]

[0026] They are

[0027] P UP (t), P DOWN (t), P SH (t), P LH (t), P SWH (t), P RWH (t), P STH(t), P LS (t), P RS (t), P IS The first derivative of (t).

[0028] Where: is the average interruption failure rate. OD is the average interruption detection rate. is the average short-term repair rate of hardware. is the long-term average repair rate of hardware; Average management delay rate for hardware; Average spare parts supply response rate for hardware; is the average software restart repair rate; is the average self-repair rate of the software; is the long-term average repair rate of the software; is the average failure rate of software failures propagating to hardware; f H is the average hardware failure probability; f S is the average software failure probability; f SH is the short-term average failure probability of hardware; f LH is the long-term average failure probability of hardware; f SPH is the average guarantee rate of hardware spare parts; f NSPH is the average non-guarantee rate of hardware spare parts; f SS is the short-term average failure probability of the software; f LS is the long-term average failure probability of the software; f RS is the average software restart probability; f IS is the average self-repair probability of the software; f STHS is the average probability of hardware-software coupling failure; f NSTHS is the average probability of hardware and software non-coupling failure.

[0029] The Runge-Kutta method is used to solve equations (1) and (2) to obtain the available status P of the navigation monitoring station: UP The transient solution of (t) is When time t→∞, the navigation monitoring station is available in state P UP The transient solution of (t) The steady-state solution to the available state of the navigation monitoring station is

[0030] Furthermore, in step 2, determining the availability of the transmission link between the navigation monitoring stations specifically includes the following steps:

[0031] S201. The reliability of optical fiber between navigation monitoring stations is:

[0032] Where m is the shape parameter of the optical fiber and η is the scale parameter of the optical fiber.

[0033] S202, the average optical fiber repair time is T OF (t), then the availability of the transmission link between navigation monitoring stations is:

[0034]

[0035] Furthermore, in step 3, the logical relationship between navigation monitoring stations and the logical relationship between navigation monitoring areas are determined, including the following specific contents:

[0036] The navigation monitoring network is divided into five navigation monitoring areas, namely: southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, northwest navigation monitoring area, to determine the logical relationship between navigation monitoring stations and between navigation monitoring areas:

[0037] The states of the navigation monitoring area include available state, degraded state and interrupted state.

[0038] The availability of a single navigation monitoring area is given by the k / n relationship; where n is the total number of navigation monitoring stations in the current navigation monitoring area, and k is the number of navigation monitoring stations in the current navigation monitoring area that are available.

[0039] If a single navigation monitoring area is interrupted, the navigation monitoring network is in a degraded state.

[0040] If any two or more navigation monitoring areas are interrupted, the navigation monitoring network will be in an interrupted state.

[0041] Furthermore, in step 4, a navigation monitoring network availability model is constructed based on the Bayesian network, wherein the state S(t) of the navigation monitoring network includes three states, namely, an available state O, a degraded state D, and an interrupted state F.

[0042] Then the probability of the navigation monitoring network being in an available state is P(S(t)=0), the probability of the navigation monitoring network being in a degraded state is P(S(t)=D), and the probability of the navigation monitoring network being in an interrupted state is P(S(t)=F):

[0043] P(S(t)=O)

[0044] =P(A N (t)=O,R SE (t),R NE (t),R CE (t),R SW (t),R NW (t),M SE1 (t),...,M NWn (t),T SE (t),...,T NW (t))

[0045] =P(A N (t) = OR SE (t),R NE (t),R CE (t),R SW (t),R NW (t))·P(R SE (t) M SE1 (t),...,M SEn (t),T SE (t))

[0046] P(R NE (t) M NE1 (t),...,M NEn (t),T NE (t))·P(R CE (t) M CE1 (t),...,M CEn (t),T CE (t))

[0047] P(R SW (t) M SW1 (t),...,M SWn (t),T SW (t))·P(R NW (t) M NW1 (t),...,M NWn (t),T NW (t))

[0048] P(M SE1 (t))·P(M SE2 (t))...·P(M NWn (t))·P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t))

[0049] Where: P(S(t)=0) represents the probability of the navigation monitoring network being available.

[0050] A N (t) represents the navigation monitoring network.

[0051] R SE (t), R NE (t), R CE (t), R SW (t), R NW(t) represent the southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, and northwest navigation monitoring area respectively.

[0052] M SE1 (t),...,M SEn (t) represent the 1st to nth navigation monitoring stations in the southeast navigation monitoring area respectively.

[0053] M NE1 (t),...,M NEn (t) represent the 1st to nth navigation monitoring stations in the northeast navigation monitoring area respectively.

[0054] M CE1 (t),...,M CEn (t) represent the 1st to nth navigation monitoring stations in the central navigation monitoring area respectively.

[0055] M SW1 (t),...,M SWn (t) represent the 1st to nth navigation monitoring stations in the southwest navigation monitoring area respectively.

[0056] M NW1 (t),...,M NWn (t) represent the 1st to nth navigation monitoring stations in the northwest navigation monitoring area respectively.

[0057] T SE (t), T NE (t), T CE (t), T SW (t), T NW (t) respectively represent the transmission link between navigation monitoring stations in the southeast navigation monitoring area, the transmission link between navigation monitoring stations in the northeast navigation monitoring area, the transmission link between navigation monitoring stations in the central navigation monitoring area, the transmission link between navigation monitoring stations in the southwest navigation monitoring area, and the transmission link between navigation monitoring stations in the northwest navigation monitoring area.

[0058] P(A N (t) = OR SE (t),R NE (t),R CE (t),R SW (t),R NW (t)) represents the combined logical relationship function of each navigation monitoring area when the navigation monitoring network is in an available state.

[0059] P(R SE (t) M SE1 (t),...,M SEn (t),T SE(t)) represents the combined logical relationship function of the navigation monitoring stations and the inter-station transmission links in the southeast navigation monitoring area when the southeast monitoring area is in an available, degraded or interrupted state.

[0060] P(R NE (t) M NE1 (t),...,M NEn (t),T NE (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the Northeast navigation monitoring area when the Northeast monitoring area is in an available, degraded or interrupted state.

[0061] P(R CE (t) M CE1 (t),...,M CEn (t),T CE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the central navigation monitoring area when the central monitoring area is in an available, degraded or interrupted state.

[0062] P(R SW (t) M SW1 (t),...,M SWn (t),T SW (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the southwest navigation monitoring area when the southwest monitoring area is in an available, degraded or interrupted state.

[0063] P(R NW (t) M NW1 (t),...,M NWn (t),T NW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northwest navigation monitoring area when the northwest monitoring area is in an available, degraded or interrupted state.

[0064] P(M SE1 (t)), P(M SE2 (t))..., P(M NWn (t)) represents the probability of each navigation monitoring station being available or interrupted.

[0065] P(T SE (t)), P(T NE (t)), P(T CE (t)), P(T SW (t)), P(T NW (t)) represent the probability that the transmission link between navigation monitoring stations is available or interrupted.

[0066] P(S(t)=D)

[0067] =P(A N (t)=D,R SE (t),R NE (t),R CE (t),R SW (t),R NW (t),M SE1 (t),...,M NWn (t),T SE (t),...,T NW (t))

[0068] =P(A N (t)=D|R SE (t),R NE (t),R CE (t),R SW (t),R NW (t))·P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t))·

[0069] P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t))·P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t))·

[0070] P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t))·P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t))·

[0071] P(M SE1 (t))·P(M SE2 (t))...·P(M NWn (t))·P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t))

[0072] Where: P(S(t)=D) represents the probability of the navigation monitoring network being in a degraded state.

[0073] A N (t) represents the navigation monitoring network.

[0074] R SE (t), R NE (t), R CE (t), R SW (t), R NW (t) represent the southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, and northwest navigation monitoring area respectively.

[0075] M SE1 (t),...,M SEn (t) represent the navigation monitoring stations in the southeast navigation monitoring area.

[0076] M NE1 (t),...,M NEn (t) represent the navigation monitoring stations in the northeast navigation monitoring area.

[0077] M CE1 (t),...,M CEn (t) represent the navigation monitoring stations in the central navigation monitoring area.

[0078] M SW1 (t),...,M SWn (t) represent the navigation monitoring stations in the southwest navigation monitoring area.

[0079] M NW1 (t),...,M NWn (t) represent the navigation monitoring stations in the northwest navigation monitoring area.

[0080] T SE (t), T NE (t), T CE (t), T SW (t), T NW (t) respectively represent the transmission link between navigation monitoring stations in the southeast navigation monitoring area, the transmission link between navigation monitoring stations in the northeast navigation monitoring area, the transmission link between navigation monitoring stations in the central navigation monitoring area, the transmission link between navigation monitoring stations in the southwest navigation monitoring area, and the transmission link between navigation monitoring stations in the northwest navigation monitoring area.

[0081] P(A N (t) = DR SE (t),R NE (t),R CE (t),RSW (t),R NW (t)) represents the combined logical relationship function of each navigation monitoring area when the navigation monitoring network is in a degraded state.

[0082] P(R SE (t)M SE1 (t),...,M SEn (t),T SE (t)) represents the combined logical relationship function of the navigation monitoring stations and the inter-station transmission links in the southeast navigation monitoring area when the southeast monitoring area is in an available, degraded or interrupted state.

[0083] P(R NE (t)M NE1 (t),...,M NEn (t),T NE (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the Northeast navigation monitoring area when the Northeast monitoring area is in an available, degraded or interrupted state.

[0084] P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the central navigation monitoring area when the central monitoring area is in an available, degraded or interrupted state.

[0085] P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the southwest navigation monitoring area when the southwest monitoring area is in an available, degraded or interrupted state.

[0086] P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northwest navigation monitoring area when the northwest monitoring area is in an available, degraded or interrupted state.

[0087] P(M SE1 (t)), P(M SE2 (t))..., P(M NWn (t)) represents the probability of each navigation monitoring station being available or interrupted.

[0088] P(T SE(t)), P(T NE (t)), P(T CE (t)), P(T SW (t)), P(T NW (t)) represents the probability that the transmission link between navigation monitoring stations is available or interrupted.

[0089] P(S(t)=F)

[0090] =P(A N (t)=F,R SE (t),R NE (t),R CE (t),R SW (t),R NW (t),M SE1 (t),...,M NWn (t),T SE (t),...,T NW (t))

[0091] =P(A N (t) = F | R SE (t),R NE (t),R CE (t),R SW (t),R NW (t))·P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t))

[0092] P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t))·P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t))

[0093] P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t))·P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t))

[0094] P(M SE1(t))·P(M SE2 (t))...·P(M NWn (t))·P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t))

[0095] Where: P(S(t)=F) represents the probability of interruption of the navigation monitoring network.

[0096] A N (t) represents the navigation monitoring network.

[0097] R SE (t), R NE (t), R CE (t), R SW (t), R NW (t) represent the southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, and northwest navigation monitoring area respectively.

[0098] M SE1 (t),...,M SEn (t) represent the navigation monitoring stations in the southeast navigation monitoring area.

[0099] M NE1 (t),...,M NEn (t) represent the navigation monitoring stations in the northeast navigation monitoring area.

[0100] M CE1 (t),...,M CEn (t) represent the navigation monitoring stations in the central navigation monitoring area.

[0101] M SW1 (t),...,M SWn (t) represent the navigation monitoring stations in the southwest navigation monitoring area.

[0102] M NW1 (t),...,M NWn (t) represent the navigation monitoring stations in the northwest navigation monitoring area.

[0103] T SE (t), T NE (t), T CE (t), T SW (t), T NW(t) respectively represent the transmission link between navigation monitoring stations in the southeast navigation monitoring area, the transmission link between navigation monitoring stations in the northeast navigation monitoring area, the transmission link between navigation monitoring stations in the central navigation monitoring area, the transmission link between navigation monitoring stations in the southwest navigation monitoring area, and the transmission link between navigation monitoring stations in the northwest navigation monitoring area.

[0104] P(A N (t) = F | R SE (t),R NE (t),R CE (t),R SW (t),R NW (t)) represents the combined logical relationship function of each navigation monitoring area when the navigation monitoring network is in an interrupted state.

[0105] P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t)) represents the combined logical relationship function of the navigation monitoring stations and the inter-station transmission links in the southeast navigation monitoring area when the southeast monitoring area is in an available, degraded or interrupted state.

[0106] P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the Northeast navigation monitoring area when the Northeast monitoring area is in an available, degraded or interrupted state.

[0107] P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the central navigation monitoring area when the central monitoring area is in an available, degraded or interrupted state.

[0108] P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the southwest navigation monitoring area when the southwest monitoring area is in an available, degraded or interrupted state.

[0109] P(R NW (t)|M NW1 (t),...,M NWn (t),T NW(t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northwest navigation monitoring area when the northwest monitoring area is in an available, degraded or interrupted state.

[0110] P(M SE1 (t)), P(M SE2 (t))..., P(M NWn (t)) represents the probability of each navigation monitoring station being available or interrupted.

[0111] P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t)) represents the probability that the transmission link between navigation monitoring stations is available or interrupted.

[0112] Further, in step 5, when the navigation monitoring network status A N When (t) is in interruption state F, the interruption state probability of each navigation monitoring station is solved as:

[0113]

[0114] Where: M i is the status of navigation monitoring station i,

[0115] i=SE,...,SEn,NE1,...,NEn,CE1,...,CEn,SW1,...,SWn,NW1,...,NWn.

[0116] Beneficial effects:

[0117] 1. A method for modeling and analyzing the availability of a navigation monitoring network of the present invention comprehensively considers various factors such as short-term hardware failures, long-term hardware failures, short-term software failures, long-term software failures, hardware-software coupling failures, transmission link failures between navigation monitoring stations, logical relationships between navigation monitoring stations, and logical relationships between navigation monitoring areas of navigation monitoring stations, uses generalized random Petri nets to build a navigation monitoring station availability model, uses Bayesian networks to build a navigation monitoring network availability model, determines the probability of available states, reduced-order states, and interrupted states of the navigation monitoring network, identifies weak links, and can achieve availability modeling and analysis of the navigation monitoring network; thereby achieving a comprehensive analysis of the availability of the navigation monitoring network, providing a quantitative basis for the availability analysis of the navigation monitoring network, and providing technical support and decision-making suggestions for navigation monitoring network interruptions.

[0118] 2. The present invention integrates multiple reliability, maintainability and security indicators of navigation monitoring stations, such as average interruption interval time, average interruption detection time, short-term average hardware repair time, long-term average hardware repair time, average hardware management delay time, average hardware spare parts supply response time, average software restart repair time, average software self-repair time, long-term average software repair time, and average time for software faults to propagate to hardware, into a unified framework, thereby realizing the interaction between the reliability, maintainability and security indicators of navigation monitoring stations, the availability indicators of transmission links between navigation monitoring stations and the availability indicators of the navigation monitoring network. BRIEF DESCRIPTION OF THE DRAWINGS

[0119] Figure 1 is a flow chart of a method for analyzing the availability of a navigation monitoring network provided by an embodiment of the present invention;

[0120] Figure 2 It is a schematic diagram of the availability model of navigation monitoring stations based on generalized random Petri nets;

[0121] Figure 3 It is a schematic diagram of the transition of various stable states of the navigation monitoring station;

[0122] Figure 4 It is a navigation monitoring station Availability diagram during 5 years of operation;

[0123] Figure 5 It is a schematic diagram of the reliability of the transmission link between navigation monitoring stations during the 5-year operation period;

[0124] Figure 6 It is a schematic diagram of the availability of the transmission link between navigation monitoring stations during the 5-year operation period;

[0125] Figure 7 It is a schematic diagram of the navigation monitoring network availability model based on Bayesian network;

[0126] Figure 8 It is a schematic diagram of the probability of availability of the navigation monitoring network during the 5-year operation period;

[0127] Fig. 9 It is a schematic diagram of the probability of degraded state during the 5-year operation of the navigation monitoring network;

[0128] Fig.10 It is a schematic diagram of the probability of each navigation monitoring station being in an interrupted state when the navigation monitoring network is in an interrupted state;

[0129] Fig.11 It is a schematic diagram of the probability of each navigation monitoring station being in an interrupted state based on a combination of multiple evidences. DETAILED DESCRIPTION

[0130] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0131] The present invention provides a method for modeling and analyzing the availability of a navigation monitoring network of the present invention, the steps are as follows: Figure 1 As shown, the following steps are included:

[0132] Step 1: Use generalized stochastic Petri nets to construct a navigation monitoring station availability model, isomorphize the Markov chain state transition process, determine the differential equation of the navigation monitoring station model, and then determine the availability of the navigation monitoring station.

[0133] In the embodiment of the present invention, step one includes the following steps:

[0134] (1.1) According to the interruption characteristics and reasons of the navigation monitoring station, the operating status and interruption status of the navigation monitoring station are determined. The interruption of the navigation monitoring station is divided into overall interruption, short-term hardware failure, long-term hardware failure, short-term software failure, long-term software failure, and hardware-software coupling failure, and the relevant status parameters of each type of interruption are determined.

[0135] in:

[0136] The overall interruption-related status includes: navigation monitoring station availability status P UP (t), Navigation monitoring station interruption status P DOWN (t), hardware or software failure selection state P HOS (t).

[0137] Hardware short-term fault related states include: Hardware short-term or long-term fault selection state P SOLH (t), hardware short-term fault state P SH (t).

[0138] The hardware long-term failure related states include: Hardware long-term failure state P LH (t), hardware spare parts selection state P SONH (t), hardware spare parts waiting state P SWH (t), hardware long-term fault repair waiting state P RWH (t).

[0139] Software short-term fault related states include: Software short-term or long-term fault selection state P SOLS (t), software and hardware failover selection state P SOHS (t), software short-term fault selection state P ROIS (t), software restart fault state P RS (t), software self-repair status P IS (t).

[0140] The software long-term fault related states include: software long-term fault state P LS (t).

[0141] The states related to software-hardware coupling faults include: software fault to hardware fault transfer state P STH (t).

[0142] The overall interruption stable state includes: navigation monitoring station available state P UP (t), Navigation monitoring station interruption status P DOWN (t).

[0143] The stable state of hardware short-term fault includes: hardware short-term fault state P SH (t).

[0144] The stable state of hardware long-term failure includes: hardware long-term failure state P LH (t), hardware spare parts waiting state P SWH (t), hardware long-term fault repair waiting state P RWH (t).

[0145] The software short-term fault stable state includes: software restart fault state P RS (t), software self-repair status P IS (t).

[0146] The stable state of software long-term fault includes: Software long-term fault state P LS (t).

[0147] The stable state of software-hardware coupling fault includes: the state P of software fault transferring to hardware fault STH (t).

[0148] (1.2) According to the above-mentioned related states, an availability model of the navigation monitoring station based on generalized random Petri nets is constructed.

[0149] (1.3) According to the generalized stochastic Petri net isomorphic Markov chain, the differential equation of the navigation monitoring station model is determined, and then the availability of the navigation monitoring station is determined The differential equation is

[0150]

[0151] P UP +P DOWN +P SH +P LH +P SWH +P RWN +P STH +P LS +P RS +P IS =1 (2)

[0152] Where:

[0153] is the average interruption failure rate ( MTBO M is the average interruption interval).

[0154] λ OD is the average interruption detection rate (λ OD =1 / T OD , T OD is the average interruption detection time).

[0155] is the average short-term hardware repair rate ( MTTR SH is the short-term mean time to repair of hardware).

[0156] is the long-term average repair rate of hardware ( MTTR LH is the long-term mean time to repair of the hardware).

[0157] is the average hardware management delay rate ( MADT LH is the average hardware management delay time).

[0158] is the average spare parts supply response rate for hardware ( MSRT LH Mean spare parts supply response time for hardware).

[0159] is the average software restart repair rate ( MTTR RS is the average software restart repair time).

[0160] is the average self-repair rate of software ( MTTR IS is the mean self-repair time of the software).

[0161] is the long-term average software repair rate ( MTTR LS is the long-term mean time to repair of the software).

[0162] is the average failure rate of software failures propagating to hardware ( T STH is the average time it takes for a software fault to propagate to hardware).

[0163] f H is the average probability of hardware failure. S is the average software failure probability; fSH is the short-term average failure probability of hardware; f LH is the long-term average failure probability of hardware; f SPH is the average guarantee rate of hardware spare parts; f NSPH is the average non-guarantee rate of hardware spare parts; f SS is the short-term average failure probability of the software; f LS is the long-term average failure probability of the software; f RS is the average software restart probability; f IS is the average self-repair probability of the software; f STHS is the average probability of hardware-software coupling failure; f NSTHS is the average probability of hardware and software non-coupling failure.

[0164] Furthermore, f H +f s =1,f SH +f LH =1,f SPH +f NSPH =1,f SS +f LS =1,f RS +f IS =1,f STHS +f NSTHS =1.

[0165] (1.4) The Runge-Kutta method is used to solve equations (1) and (2) to obtain the available status P of the navigation monitoring station: UP The transient solution of (t) is When time t→∞, the navigation monitoring station is available in state P UP The transient solution of (t) The steady-state solution to the available state of the navigation monitoring station is

[0166] In the embodiment of the present invention, when time t→∞, the transient solution of the navigation monitoring station availability becomes the steady-state solution of the navigation monitoring station availability: From the Markov chain we get:

[0167]

[0168] Where:

[0169]

[0170]

[0171]

[0172]

[0173]

[0174]

[0175]

[0176]

[0177]

[0178]

[0179] Step 2: Determine the availability of transmission links between navigation monitoring stations.

[0180] S201. According to the failure mechanism of optical fiber communication, the main factors affecting the reliability of optical fiber include: crack formation, stress corrosion, zero stress aging, and coating effect. The reliability of optical fiber is determined as follows:

[0181]

[0182] S202, assuming that the average optical fiber repair time is T OF (t) Determine the availability of the transmission link between navigation monitoring stations as:

[0183]

[0184] Step 3: Determine the logical relationship between navigation monitoring stations, determine the logical relationship between navigation monitoring areas, and determine the logical relationship between the status of the navigation monitoring area and the status of the navigation monitoring network.

[0185] The navigation monitoring network is divided into the southeast navigation monitoring area, the northeast navigation monitoring area, the central navigation monitoring area, the southwest navigation monitoring area, and the northwest navigation monitoring area. The logical relationship between navigation monitoring stations and the logical relationship between navigation monitoring areas are determined in the following manner:

[0186] A. The availability of a single navigation monitoring area is given by the number of navigation monitoring stations in the monitoring area and the outage situation according to the k / n relationship (n: total number of monitoring stations in the area, k: number of available monitoring stations).

[0187] B. When all navigation monitoring areas are available, the navigation monitoring network is in an available state.

[0188] C. When any navigation monitoring area is interrupted, the navigation monitoring network is in a degraded state.

[0189] D. When any two or more navigation monitoring areas are interrupted, the navigation monitoring network is in an interrupted state.

[0190] Step 4: Using the availability of navigation monitoring stations, the availability of transmission links between navigation monitoring stations, the logical relationship between navigation monitoring stations, and the logical relationship between navigation monitoring areas, a navigation monitoring network availability model is constructed based on the Bayesian network to determine the probability of available state, degraded state, and interrupted state of the navigation monitoring network.

[0191] (4.1) Determine the probability of the navigation monitoring network being available P(S(t)=O) as:

[0192] P(S(t)=O)

[0193] =P(A N (t)=O,R SE (t),R NE (t),R CE (t),R SW (t),R NW (t),M SE1 (t),...,M NWn (t),T SE (t),...,T NW (t))

[0194] =P(A N (t)=O|R SE (t),R NE (t),R CE (t),R SW (t),R NW (t))·P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t))

[0195] P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t))·P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t))

[0196] P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t))·P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t))

[0197] P(M SE1 (t))·P(M SE2 (t))...·P(M NWn (t))·P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t))

[0198] Where: P(S(t)=O) represents the probability of the navigation monitoring network being available; A N (t) represents the navigation monitoring network;

[0199] R SE (t), R NE (t), R CE (t), R SW (t), R NW (t) represent the southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, and northwest navigation monitoring area respectively;

[0200] M SE1 (t),...,M SEn (t) represent the navigation monitoring stations in the southeast navigation monitoring area.

[0201] M NE1 (t),...,M NEn (t) represent the navigation monitoring stations in the northeast navigation monitoring area.

[0202] M CE1 (t),...,M CEn (t) represent the navigation monitoring stations in the central navigation monitoring area.

[0203] M SW1 (t),...,M SWn (t) represent the navigation monitoring stations in the southwest navigation monitoring area.

[0204] M NW1 (t),...,M NWn (t) represent the navigation monitoring stations in the northwest navigation monitoring area.

[0205] T SE (t), T NE (t), T CE (t), T SW (t), T NW(t) respectively represent the transmission link between navigation monitoring stations in the southeast navigation monitoring area, the transmission link between navigation monitoring stations in the northeast navigation monitoring area, the transmission link between navigation monitoring stations in the central navigation monitoring area, the transmission link between navigation monitoring stations in the southwest navigation monitoring area, and the transmission link between navigation monitoring stations in the northwest navigation monitoring area.

[0206] P(A N (t)=O|R SE (t),R NE (t),R CE (t),R SW (t),R NW (t)) represents the combined logical relationship function of each navigation monitoring area when the navigation monitoring network is in an available state.

[0207] in

[0208] P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t)) represents the combined logical relationship function of the navigation monitoring stations and the inter-station transmission links in the southeast navigation monitoring area when the southeast monitoring area is in an available, degraded or interrupted state.

[0209] in

[0210] P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the Northeast navigation monitoring area when the Northeast monitoring area is in an available, degraded or interrupted state.

[0211] in

[0212] P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the central navigation monitoring area when the central monitoring area is in an available, degraded or interrupted state.

[0213] in

[0214] P(R SW (t)|M SW1 (t),...,M SWn (t),TSW (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the southwest navigation monitoring area when the southwest monitoring area is in an available, degraded or interrupted state.

[0215] in

[0216] P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northwest navigation monitoring area when the northwest monitoring area is in an available, degraded or interrupted state.

[0217] in

[0218] P(M SE1 (t)), P(M SE2 (t))..., P(M NWn (t)) represents the probability of each navigation monitoring station being available or interrupted.

[0219] P(T SE (t)), P(T NE (t)), P(T CE (t)), P(T SW (t)), P(T NW (t)) represent the probability of the transmission link between each navigation monitoring station being available or interrupted;

[0220] (4.2) Determine the probability of the navigation monitoring network degraded state P(S(t)=D) as:

[0221] P(S(t)=D)

[0222] =P(A N (t)=D,R SE (t),R NE (t),R CE (t),R SW (t),R NW (t),M SE1 (t),...,M NWn (t),T SE (t),...,T NW (t))

[0223] =P(A N (t) = D | R SE (t),R NE (t),R CE (t),RSW (t),R NW (t))·P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t))·P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t))·P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t))·P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t))·P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t))·P(M SE1 (t))·P(M SE2 (t))...·P(M NWn (t))·P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t))

[0224] Where: P(S(t)=D) represents the probability of navigation monitoring network degradation; A N (t) represents the navigation monitoring network;

[0225] R SE (t), R NE (t), R CE (t), R SW (t), R NW (t) represent the southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, and northwest navigation monitoring area respectively.

[0226] M SE1 (t),...,M SEn (t) represent the navigation monitoring stations in the southeast navigation monitoring area.

[0227] M NE1 (t),...,M NEn(t) represent the navigation monitoring stations in the northeast navigation monitoring area.

[0228] M CE1 (t),...,M CEn (t) represent the navigation monitoring stations in the central navigation monitoring area.

[0229] M SW1 (t),...,M SWn (t) represent the navigation monitoring stations in the southwest navigation monitoring area.

[0230] M NW1 (t),...,M NWn (t) represent the navigation monitoring stations in the northwest navigation monitoring area.

[0231] T SE (t), T NE (t), T CE (t), T SW (t), T NW (t) respectively represent the transmission link between navigation monitoring stations in the southeast navigation monitoring area, the transmission link between navigation monitoring stations in the northeast navigation monitoring area, the transmission link between navigation monitoring stations in the central navigation monitoring area, the transmission link between navigation monitoring stations in the southwest navigation monitoring area, and the transmission link between navigation monitoring stations in the northwest navigation monitoring area.

[0232] P(A N (t) = D | R SE (t),R NE (t),R CE (t),R SW (t),R NW (t)) represents the combined logical relationship function of each navigation monitoring area when the navigation monitoring network is in a degraded state.

[0233] in

[0234] P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t)) represents the combined logical relationship function of the navigation monitoring stations and the inter-station transmission links in the southeast navigation monitoring area when the southeast monitoring area is in an available, degraded or interrupted state.

[0235] in

[0236] P(R NE (t)|M NE1 (t),...,M NEn (t),T NE(t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the Northeast navigation monitoring area when the Northeast monitoring area is in an available, degraded or interrupted state.

[0237] in

[0238] P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the central navigation monitoring area when the central monitoring area is in an available, degraded or interrupted state.

[0239] in

[0240] P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the southwest navigation monitoring area when the southwest monitoring area is in an available, degraded or interrupted state.

[0241] in

[0242] P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northwest navigation monitoring area when the northwest monitoring area is in an available, degraded or interrupted state.

[0243] in

[0244] P(M SE1 (t)), P(M SE2 (t))..., P(M NWn (t)) represents the probability of each navigation monitoring station being available or interrupted.

[0245] P(T SE (t)), P(T NE (t)), P(T CE (t)), P(T SW (t)), P(T NW (t)) represents the probability that the transmission link between navigation monitoring stations is available or interrupted;

[0246] (4.3) Determine the probability P(S(t)=F) of the navigation monitoring network interruption status as follows:

[0247] P(S(t)=F)

[0248] =P(A N (t)=F,R SE (t),R NE (t),R CE (t),R SW (t),R NW (t),M SE1 (t),...,M NWn (t),T SE (t),...,T NW (t))

[0249] =P(A N (t)=F|R SE (t),R NE (t),R CE (t),R SW (t),R NW (t))·P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t))·P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t))·P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t))·P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t))·P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t))·P(M SE1 (t))·P(M SE2 (t))...·P(M NWn (t))·P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t))

[0250] Where: P(S(t)=F) represents the probability of interruption of navigation monitoring network; A N (t) represents the navigation monitoring network.

[0251] R SE (t), R NE (t), R CE (t), R SW (t), R NW (t) represent the southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, and northwest navigation monitoring area respectively.

[0252] M SE1 (t),...,M SEn (t) represent the navigation monitoring stations in the southeast navigation monitoring area.

[0253] M NE1 (t),...,M NEn (t) represent the navigation monitoring stations in the northeast navigation monitoring area.

[0254] M CE1 (t),...,M CEn (t) represent the navigation monitoring stations in the central navigation monitoring area.

[0255] M SW1 (t),...,M SWn (t) represent the navigation monitoring stations in the southwest navigation monitoring area.

[0256] M NW1 (t),...,M NWn (t) represent the navigation monitoring stations in the northwest navigation monitoring area.

[0257] T SE (t), T NE (t), T CE (t), T SW (t), T NW (t) respectively represent the transmission link between navigation monitoring stations in the southeast navigation monitoring area, the transmission link between navigation monitoring stations in the northeast navigation monitoring area, the transmission link between navigation monitoring stations in the central navigation monitoring area, the transmission link between navigation monitoring stations in the southwest navigation monitoring area, and the transmission link between navigation monitoring stations in the northwest navigation monitoring area.

[0258] P(A N (t) = FR SE (t),R NE (t),R CE (t),R SW (t),R NW(t)) represents the combined logical relationship function of each navigation monitoring area when the navigation monitoring network is in an interrupted state.

[0259] in

[0260] P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t)) represents the combined logical relationship function of the navigation monitoring stations and the inter-station transmission links in the southeast navigation monitoring area when the southeast monitoring area is in an available, degraded or interrupted state.

[0261] in

[0262] P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the Northeast navigation monitoring area when the Northeast monitoring area is in an available, degraded or interrupted state.

[0263] in

[0264] P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the central navigation monitoring area when the central monitoring area is in an available, degraded or interrupted state.

[0265] in

[0266] P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t)) represents the combined logical relationship function of the navigation monitoring stations and inter-station transmission links in the southwest navigation monitoring area when the southwest monitoring area is in an available, degraded or interrupted state.

[0267] in

[0268] P(R NW (t)|M NW1 (t),...,M NWn (t),T NW(t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northwest navigation monitoring area when the northwest monitoring area is in an available, degraded or interrupted state.

[0269] in

[0270] P(M SE1 (t)), P(M SE2 (t))..., P(M NWn (t)) represents the probability of each navigation monitoring station being available or interrupted.

[0271] P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t)) represents the probability that the transmission link between navigation monitoring stations is available or interrupted.

[0272] Step 5. If the navigation monitoring network is in an interrupted state, use the navigation monitoring network availability model to solve the interruption state probability of each navigation monitoring station when the navigation monitoring network is in an interrupted state, sort the interruption state probability of each navigation monitoring station from high to low, and perform fault diagnosis and troubleshooting on the navigation monitoring stations in sequence according to the sorting order.

[0273] In the embodiment of the present invention, when the navigation monitoring network is interrupted, the probability that each navigation monitoring station is in an interrupted state is:

[0274]

[0275] Where: i = SE1, SE2, ..., NWn.

[0276] In addition, by adding observation evidence, fault diagnosis can be performed under multiple evidence combinations. When the navigation monitoring network is interrupted and the transmission link between the navigation monitoring stations in the southeast region is available, the probability that each navigation monitoring station is in a degraded state is:

[0277]

[0278] Where: i = SE1, SE2, ..., NWn.

[0279] Implementation example:

[0280] Construct a navigation monitoring network with a total of 25 monitoring stations.

[0281] (a) Determine the availability of navigation monitoring stations. According to step (1), construct the navigation monitoring station availability model, such as Figure 2As shown; the isomorphism corresponds to the Markov chain state transfer process, as Figure 3 shown. Figure 4 It is a navigation monitoring station (A MSE1 ) Availability during the 5-year operation period. As can be seen from the figure, the availability of the navigation monitoring station decreases rapidly in the initial 0-0.5 years, and then remains stable during the 0.5-5 years. The steady-state availability is A MSE1 (∞)=0.9867.

[0282] (b) Determine the availability of the transmission link between navigation monitoring stations. According to step (2), determine the reliability of the optical fiber, assuming that the optical fiber shape parameter m = 2.99 and the scale parameter η = 6a, Figure 5 The figure shows the reliability of the transmission link between navigation monitoring stations during 5 years of operation. Assume that the average optical fiber repair time is T OF =10h, Figure 6 Shown is the availability of the transmission links between navigation monitoring stations during a five-year operation.

[0283] (c) Determine the logical relationship between navigation monitoring stations and the logical relationship between navigation monitoring areas. According to step (3), the navigation monitoring network is divided into the southeast navigation monitoring area, the northeast navigation monitoring area, the central navigation monitoring area, the southwest navigation monitoring area, and the northwest navigation monitoring area; determine the logical relationship between navigation monitoring stations and the logical relationship between navigation monitoring areas:

[0284] The availability of a single navigation monitoring area is given by the number of monitoring stations and the interruption situation in the monitoring area according to the 3 / 5 relationship (5: total number of monitoring stations in the area, 3: number of available monitoring stations); when all navigation monitoring areas are available, the navigation monitoring network is in an available state; if any one of the navigation monitoring areas is interrupted, the navigation monitoring network is in a degraded state; if any two or more navigation monitoring areas are interrupted, the navigation monitoring network is in an interrupted state.

[0285] (4) Determine the probability of each state of the navigation monitoring network. According to step (4), a navigation monitoring network availability model based on the Bayesian network is constructed, such as Figure 7 As shown; determine the probability of availability of the navigation monitoring network during the 5-year operation period, as Figure 8 As shown in the figure, the availability of the navigation monitoring network decreases significantly over time from 0 to 0.5 years, and the availability drops to A in the 0.5 year. N (0.5a) = 0.9994. The availability then gradually decreases from 0.5 to 5 years, and drops to A in the third year. N (3a) = 0.9992, the availability in the fifth year is A N (5a) = 0.9989; Determine the probability of a degraded state during the 5-year operation of the navigation monitoring network, such as Fig. 9 shown.

[0286] (5) Navigation monitoring network fault diagnosis. According to step (5), determine the probability that each navigation monitoring station is in an interrupted state when the navigation monitoring network is interrupted, such as Fig.10 As shown in the figure, the fault diagnosis of the navigation monitoring network under different combinations of observation evidence is carried out. For example, when the navigation monitoring network is interrupted, and it is observed that the monitoring stations in the southeast and northwest navigation monitoring areas are available and the transmission links between the navigation monitoring stations in each monitoring area are available, the probability of the monitoring stations in the central, southwest and northwest navigation monitoring areas being in an interrupted state is analyzed, as shown in the figure. Fig.11 As shown in the figure, it can be seen that the additional evidence will significantly affect the probability of each monitoring station being in an interrupted state. Under the above evidence, the monitoring stations in the southwest, northeast, and central monitoring areas can be troubleshooted in turn.

[0287] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for analyzing the availability of a navigation monitoring network, characterized in that: The steps include: Step 1: Use generalized stochastic Petri nets to construct a navigation monitoring station availability model, isomorphize the Markov chain state transition process, determine the differential equation of the navigation monitoring station model, and then determine the availability of the navigation monitoring station; Step 2: Determine the availability of transmission links between navigation monitoring stations; Step 3: determine the logical relationship between navigation monitoring stations, determine the logical relationship between navigation monitoring areas, and determine the logical relationship between the status of the navigation monitoring area and the status of the navigation monitoring network; Step 4: using the availability of the navigation monitoring stations, the availability of the transmission links between the navigation monitoring stations, the logical relationship between the navigation monitoring stations, and the logical relationship between the navigation monitoring areas, a navigation monitoring network availability model is constructed based on a Bayesian network to determine the probability of an available state, a probability of a degraded state, and a probability of an interrupted state of the navigation monitoring network; Step 5: If the navigation monitoring network is in an interrupted state, the navigation monitoring network availability model is used to solve the interruption state probability of each navigation monitoring station when the navigation monitoring network is in an interrupted state, and the interruption state probability of each navigation monitoring station is sorted from high to low, and the navigation monitoring stations are diagnosed and checked in sequence according to the sorting order; In the step 2, determining the availability of the transmission link between the navigation monitoring stations specifically includes the following steps: S201. The reliability of optical fiber between navigation monitoring stations is: Where m is the shape parameter of the optical fiber, and η is the scale parameter of the optical fiber; S202, the average optical fiber repair time is T OF (t), then the availability of the transmission link between navigation monitoring stations is: In the step 3, determining the logical relationship between navigation monitoring stations and determining the logical relationship between navigation monitoring areas includes the following specific contents: The navigation monitoring network is divided into five navigation monitoring areas, namely: southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, northwest navigation monitoring area, to determine the logical relationship between navigation monitoring stations and between navigation monitoring areas: The state of the navigation monitoring area includes an available state, a degraded state and an interrupted state; The availability of a single navigation monitoring area is given by the relationship k / n; n is the total number of navigation monitoring stations in the current navigation monitoring area, and k is the number of navigation monitoring stations in the current navigation monitoring area that are available; If a single navigation monitoring area is interrupted, the navigation monitoring network is in a degraded state; If any two or more navigation monitoring areas are interrupted, the navigation monitoring network will be in an interrupted state.

2. The method according to claim 1, characterized in that In the step 1, the generalized random Petri net constructs the navigation monitoring station availability model including: Overall interruption related status, including: navigation monitoring station availability status P UP (t), Navigation monitoring station interruption status P DOWN (t), hardware or software failure selection state P HOS (t); Hardware short-term fault related status, including: hardware short-term or long-term fault selection status P SOLH (t), hardware short-term fault state P SH (t); Hardware long-term fault related status, including: Hardware long-term fault status P LH (t), hardware spare parts selection state P SONH (t), hardware spare parts waiting state P SWH (t), hardware long-term fault repair waiting state P RWH (t); Software short-term fault related status, including: software short-term or long-term fault selection status P SOLS (t), software and hardware failover selection state P SOHS (t), software short-term fault selection state P ROIS (t), software restart fault state P RS (t), software self-repair status P IS (t); Software long-term fault related status, including: Software long-term fault status P LS (t); Software and hardware coupling fault related states, including: software fault to hardware fault transfer state P STH (t); Where t is the time variable.

3. The method according to claim 2, characterized in that In the step 1, the differential equation of the navigation monitoring station model is determined, specifically: P UP (t)+P DOWN (t)+P SH (t)+P LH (t)+P SWH (t)+P RWN (t)+P STH (t)+P LS (t)+P RS (t)+P IS (t)=1(2) And f H +f s =1,f SH +f LH =1,f SPH +f NSPH =1,f SS +f LS =1,f RS +f IS =1,f STHS +f NSTHS =1where: P UP (t), P DOWN (t), P SH (t), P LH (t), P SWH (t), P RWH (t), P STH (t), P LS (t), P RS (t), P IS The first derivative of (t); Where: is the average interruption failure rate; OD is the average interruption detection rate; is the average short-term repair rate of hardware; is the long-term average repair rate of hardware; Average management delay rate for hardware; Average spare parts supply response rate for hardware; is the average software restart repair rate; is the average self-repair rate of the software; is the long-term average repair rate of the software; is the average failure rate of software failures propagating to hardware; f H is the average hardware failure probability; f S is the average software failure probability; f SH is the short-term average failure probability of hardware; f LH is the long-term average failure probability of hardware; f SPH is the average guarantee rate of hardware spare parts; f NSPH is the average non-guarantee rate of hardware spare parts; f SS is the short-term average failure probability of the software; f LS is the long-term average failure probability of the software; f RS is the average software restart probability; f IS is the average self-repair probability of the software; f STHS is the average probability of hardware-software coupling failure; f NSTHS is the average probability of hardware-software non-coupling failure; The Runge-Kutta method is used to solve equations (1) and (2) to obtain the available status P of the navigation monitoring station: UP The transient solution of (t) is A Mi (t); When time t→∞, the navigation monitoring station is available in the state P UP The transient solution of (t) The steady-state solution to the available state of the navigation monitoring station is 4. The method according to claim 1, characterized in that In the step 4, the navigation monitoring network availability model is constructed based on the Bayesian network, wherein the state S(t) of the navigation monitoring network includes three states, namely, an available state O, a degraded state D, and an interrupted state F; Then the probability of the navigation monitoring network being in an available state is P(S(t)=0), the probability of the navigation monitoring network being in a degraded state is P(S(t)=D), and the probability of the navigation monitoring network being in an interrupted state is P(S(t)=F): P(S(t)=O) =P(A N (t)=O,R SE (t),R NE (t),R CE (t),R SW (t),R NW (t),M SE1 (t),...,M NWn (t),T SE (t),...,T NW (t)) =P(A N (t)=O|R SE (t),R NE (t),R CE (t),R SW (t),R NW (t))·P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t))· P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t))·P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t))· P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t))·P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t))· P(M SE1 (t))·P(M SE2 (t))...·P(M NWn (t))·P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t)) Where: P(S(t)=0) represents the probability of the navigation monitoring network being available; A N (t) represents the navigation monitoring network; R SE (t), R NE (t), R CE (t), R SW (t), R NW (t) represent the southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, and northwest navigation monitoring area respectively; M SE1 (t),...,M SEn (t) represent the 1st to the nth navigation monitoring stations in the southeast navigation monitoring area respectively; M NE1 (t),...,M NEn (t) respectively represent the 1st to the nth navigation monitoring stations in the northeast navigation monitoring area; M CE1 (t),...,M CEn (t) respectively represent the 1st to the nth navigation monitoring stations in the central navigation monitoring area; M SW1 (t),...,M SWn (t) respectively represent the 1st to the nth navigation monitoring stations in the southwest navigation monitoring area; M NW1 (t),...,M NWn (t) respectively represent the 1st to the nth navigation monitoring stations in the northwest navigation monitoring area; T SE (t), T NE (t), T CE (t), T SW (t), T NW (t) represent the transmission link between navigation monitoring stations in the southeast navigation monitoring area, the transmission link between navigation monitoring stations in the northeast navigation monitoring area, the transmission link between navigation monitoring stations in the central navigation monitoring area, the transmission link between navigation monitoring stations in the southwest navigation monitoring area, and the transmission link between navigation monitoring stations in the northwest navigation monitoring area respectively; P(A N (t) = O | R SE (t),R NE (t),R CE (t),R SW (t),R NW (t)) represents the combined logical relationship function of each navigation monitoring area when the navigation monitoring network is in an available state; P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the southeast navigation monitoring area when the southeast monitoring area is in an available, degraded or interrupted state; P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northeastern navigation monitoring area when the northeastern monitoring area is in an available, degraded or interrupted state; P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the central navigation monitoring area when the central monitoring area is in an available, degraded or interrupted state; P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the southwest navigation monitoring area when the southwest monitoring area is in an available, degraded or interrupted state; P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northwest navigation monitoring area when the northwest monitoring area is in an available, degraded or interrupted state; P(M SE1 (t)), P(M SE2 (t))..., P(M NWn (t)) represents the probability of each navigation monitoring station being available or interrupted; P(T SE (t)), P(T NE (t)), P(T CE (t)), P(T SW (t)), P(T NW (t)) represent the probability of the transmission link between each navigation monitoring station being available or interrupted; P(S(t)=D) =P(A N (t)=D,R SE (t),R NE (t),R CE (t),R SW (t),R NW (t),M SE1 (t),...,M NWn (t),T SE (t),...,T NW (t)) =P(A N (t)=D|R SE (t),R NE (t),R CE (t),R SW (t),R NW (t))·P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t))· P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t))·P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t))· P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t))·P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t))· P(M SE1 (t))·P(M SE2 (t))...·P(M NWn (t))·P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t)) where: P(S(t) = D) represents the probability of the navigation monitoring network being in a degraded state; A N (t) represents the navigation monitoring network; R SE (t), R NE (t), R CE (t), R SW (t), R NW (t) represent the southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, and northwest navigation monitoring area respectively; M SE1 (t),...,M SEn (t) represent the navigation monitoring stations in the southeast navigation monitoring area respectively; M NE1 (t),...,M NEn (t) represent the navigation monitoring stations in the northeast navigation monitoring area; M CE1 (t),...,M CEn (t) represent the navigation monitoring stations in the central navigation monitoring area respectively; M SW1 (t),...,M SWn (t) represent the navigation monitoring stations in the southwest navigation monitoring area respectively; M NW1 (t),...,M NWn (t) represent the navigation monitoring stations in the northwest navigation monitoring area respectively; T SE (t), T NE (t), T CE (t), T SW (t), T NW (t) represent the transmission link between navigation monitoring stations in the southeast navigation monitoring area, the transmission link between navigation monitoring stations in the northeast navigation monitoring area, the transmission link between navigation monitoring stations in the central navigation monitoring area, the transmission link between navigation monitoring stations in the southwest navigation monitoring area, and the transmission link between navigation monitoring stations in the northwest navigation monitoring area respectively; P(A N (t) = D | R SE (t),R NE (t),R CE (t),R SW (t),R NW (t)) represents the combined logical relationship function of each navigation monitoring area when the navigation monitoring network is in a degraded state; P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the southeast navigation monitoring area when the southeast monitoring area is in an available, degraded or interrupted state; P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northeastern navigation monitoring area when the northeastern monitoring area is in an available, degraded or interrupted state; P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the central navigation monitoring area when the central monitoring area is in an available, degraded or interrupted state; P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the southwest navigation monitoring area when the southwest monitoring area is in an available, degraded or interrupted state; P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northwest navigation monitoring area when the northwest monitoring area is in an available, degraded or interrupted state; P(M SE1 (t)), P(M SE2 (t))..., P(M NWn (t)) represents the probability of each navigation monitoring station being available or interrupted; P(T SE (t)), P(T NE (t)), P(T CE (t)), P(T SW (t)), P(T NW (t)) represents the probability that the transmission link between navigation monitoring stations is available or interrupted; P(S(t)=F) =P(A N (t)=F,R SE (t),R NE (t),R CE (t),R SW (t),R NW (t),M SE1 (t),...,M NWn (t),T SE (t),...,T NW (t)) =P(A N (t)=F|R SE (t),R NE (t),R CE (t),R SW (t),R NW (t))·P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t))· P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t))·P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t))· P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t))·P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t))· P(M SE1 (t))·P(M SE2 (t))...·P(M NWn (t))·P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t)) where: P(S(t) = F) represents the probability of interruption of the navigation monitoring network; A N (t) represents the navigation monitoring network; R SE (t), R NE (t), R CE (t), R SW (t), R NW (t) represent the southeast navigation monitoring area, northeast navigation monitoring area, central navigation monitoring area, southwest navigation monitoring area, and northwest navigation monitoring area respectively; M SE1 (t),...,M SEn (t) represent the navigation monitoring stations in the southeast navigation monitoring area respectively; M NE1 (t),...,M NEn (t) represent the navigation monitoring stations in the northeast navigation monitoring area; M CE1 (t),...,M CEn (t) represent the navigation monitoring stations in the central navigation monitoring area respectively; M SW1 (t),...,M SWn (t) represent the navigation monitoring stations in the southwest navigation monitoring area respectively; M NW1 (t),...,M NWn (t) represent the navigation monitoring stations in the northwest navigation monitoring area respectively; T SE (t), T NE (t), T CE (t), T SW (t), T NW (t) represent the transmission link between navigation monitoring stations in the southeast navigation monitoring area, the transmission link between navigation monitoring stations in the northeast navigation monitoring area, the transmission link between navigation monitoring stations in the central navigation monitoring area, the transmission link between navigation monitoring stations in the southwest navigation monitoring area, and the transmission link between navigation monitoring stations in the northwest navigation monitoring area respectively; P(A N (t) = F | R SE (t),R NE (t),R CE (t),R SW (t),R NW (t)) represents the combined logical relationship function of each navigation monitoring area when the navigation monitoring network is in an interrupted state; P(R SE (t)|M SE1 (t),...,M SEn (t),T SE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the southeast navigation monitoring area when the southeast monitoring area is in an available, degraded or interrupted state; P(R NE (t)|M NE1 (t),...,M NEn (t),T NE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northeastern navigation monitoring area when the northeastern monitoring area is in an available, degraded or interrupted state; P(R CE (t)|M CE1 (t),...,M CEn (t),T CE (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the central navigation monitoring area when the central monitoring area is in an available, degraded or interrupted state; P(R SW (t)|M SW1 (t),...,M SWn (t),T SW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the southwest navigation monitoring area when the southwest monitoring area is in an available, degraded or interrupted state; P(R NW (t)|M NW1 (t),...,M NWn (t),T NW (t)) represents the combined logical relationship function of the navigation monitoring stations and the transmission links between stations in the northwest navigation monitoring area when the northwest monitoring area is in an available, degraded or interrupted state; P(M SE1 (t)), P(M SE2 (t))..., P(M NWn (t)) represents the probability of each navigation monitoring station being available or interrupted; P(T SE (t))·P(T NE (t))·P(T CE (t))·P(T SW (t))·P(T NW (t)) represents the probability that the transmission link between navigation monitoring stations is available or interrupted.

5. The method according to claim 4, characterized in that In step 5, when the navigation monitoring network status A N When (t) is in interruption state F, the interruption state probability of each navigation monitoring station is solved as: Where: M i is the status of navigation monitoring station i, i = SE,..., SEn, NE1,..., NEn, CE1,..., CEn, SW1,..., SWn, NW1,..., NWn.

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