Wireless linear sensor network system data fusion reliability analysis method

Abstract

The invention belongs to the technical field of wireless linear sensor networks, and discloses a wireless linear sensor network system data fusion reliability analysis method. Comprising the following steps that S1, a wireless linear sensor network system is constructed, the probability that the wireless linear sensor network system is in a state z is obtained, and the wireless linear sensor network system is composed of a base station N0, n sensor nodes N1, N2,..., Nn arranged on the left side of the base station N0 in a linear structure and m sensor nodes N1, N2,..., Nm arranged on the right side of the base station N0 in a linear structure; according to the method, modeling is carried out on the data fusion process in the LWSN system in a top-down mode, and new truncation, combination and reduction operations are provided to prevent unnecessary MDD nodes from being generated in the MDD model construction process, so that the required calculation amount is greatly reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless linear sensor networks, and more specifically, to a data fusion reliability analysis method for a wireless linear sensor network system. Background Art

[0002] Linear Wireless Sensor Network (LWSN) systems are widely used in various critical areas such as infrastructure and environmental monitoring. Linear wireless sensor network systems consist of sensor nodes arranged in sequence. The sensor nodes may be heterogeneous, they usually have different coverage capabilities, and correspond to more than two states. Nodes in LWSN systems usually communicate with neighboring nodes in a multi-hop communication and data fusion manner, which effectively saves energy and prolongs network lifetime. Data fusion reliability metrics are very important to help system providers or designers evaluate the ability of LWSN systems to achieve their industry goals.

[0003] However, LWSN systems often suffer from unstable data transmission due to obstacles, external interference, and signal interruptions. Compared with graph-structured WSN systems, the number of optional paths for sensor nodes to communicate with the base station in LWSN systems is very limited. If some consecutive sensor nodes fail at the same time, the LWSN system may not be able to forward all the generated information to the base station; and it is generally believed that system reliability analysis is essential to ensure reliable data support and accurate data analysis for industrial LWSN projects.

[0004] In view of this, the present invention proposes a data fusion reliability analysis method for a wireless linear sensor network system to solve the above problems. Summary of the invention

[0005] In order to overcome the above-mentioned defects of the prior art and to achieve the above-mentioned purpose, the present invention provides the following technical solution: a data fusion reliability analysis method for a wireless linear sensor network system, comprising the following steps:

[0006] S1, construct a wireless linear sensor network system, and obtain the probability that the wireless linear sensor network system is in state z, wherein the wireless linear sensor network system consists of a base station N0, n sensor nodes N1, N2, ..., N1 arranged in a linear structure on the left side of the base station N0 n And m sensor nodes N'1, N'2, ..., N' are arranged in a linear structure on the right side of the base station N0. m composition;

[0007] S2, constructing a simplified MDD model of the wireless linear sensor network system, including constructing a tree-like MDD model corresponding to the left and right LWSNs layer by layer from top to bottom, designing simplification rules, and simplifying the tree-like MDD model by using the simplification rules, thereby obtaining a simplified MDD model corresponding to the left and right LWSNs, merging the simplified MDD models corresponding to the left and right LWSNs, and finally obtaining a simplified MDD model corresponding to the entire wireless linear sensor network system;

[0008] S3, the simplified MDD model of the wireless linear sensor network system is evaluated for data fusion reliability. The evaluation method is as follows: the amount of fusion data required by the base station is preset as a threshold D, and the final fusion data vector V is evaluated by the threshold D. n+1 The data fusion reliability R is calculated based on the classification and the simplified MDD model of the wireless linear sensor network system. DF .

[0009] Further, in S1, the method of obtaining the probability that the wireless linear sensor network system is in state z includes:

[0010] The preset base station connects to the sensor node with the largest index, that is, N n and N` m , for a heterogeneous multi-state LWSN system with m+n sensor nodes, define X i is the sensor node N on the left side of N0 i The state variable, Y j is the right sensor node N` j The state variables of , and 1≤i≤n, 1≤j≤m;

[0011] Preset X i =k i Represents node N i The number of consecutive nodes that can be covered currently, the maximum value is K i ; Default Y j =k j Represents node N` j The number of consecutive nodes that can be covered currently, the maximum value is K j , preset τ i Represents node N i The generated data, and then, define K l =max{K1,K2,...,K n} and K r =max{K1,K2,...,K m} are the maximum coverage capabilities of the left and right sides respectively;

[0012] Preset X = (X1, X2, ..., X n) and Y=(Y1,Y2,...,Y m ) represent the random state vectors of the LWSN subsystems on both sides of the base station, and Z is preset to be (X1, X2, ..., X n , Y1, Y2, ..., Y m ) represents the random state vector of the entire wireless linear sensor network system, and z is preset to be (x1, x2, ..., x n , y1, y2, ..., y m ) represents a system state z, and x is assumed i Represents sensor node N i The state of y is preset j Represents sensor node Y j Status;

[0013] Furthermore, the probability that the wireless linear sensor network system is in state z is:

[0014] Pr(Z=z)=Pr left Pr right

[0015]

[0016] In the formula, Pr left Indicates that the left node of the wireless linear sensor network system is in the state (x1, x2, ..., x n ), Pr right Indicates that the right node of the wireless linear sensor network system is in the state (y1, y2, ..., y m ) probability.

[0017] Furthermore, in S1, for the sensor node N i , presupposes its discrete random state variable x i There are l different states that can be taken, and l different states can be represented as a set k l ={k1, k2, ..., k l}, and then, the distribution of the discrete random state variables of each sensor node is as follows:

[0018]

[0019]

[0020] In the formula, k l Represents sensor node N i In the first state, is the sensor node N i In state k l The probability of is the sensor node N`j In state k r probability.

[0021] Further, in the S2, a simplified MDD model of the wireless linear sensor network system is constructed, including constructing a tree-like MDD model corresponding to the LWSNs on the left and right sides layer by layer from top to bottom, designing a simplification rule, and simplifying the tree-like MDD model by the simplification rule, thereby obtaining a simplified MDD model corresponding to the LWSNs on the left and right sides, including:

[0022] The tree-like MDD model of a one-sided LWSN system with n sensor nodes is assumed to consist of n layers of decision nodes and two sink nodes labeled “0” and “1”;

[0023] At the top level i = 1 of the tree-like MDD model, there is only one root node associated with the multi-valued state variable X1, representing the empty system state z = NULL;

[0024] At the bottom layer n+1, there are two different sink nodes, which represent whether the final fused data vector is in a specific state or not;

[0025] The path from the root node to the sink node represents a specific system state z = (x1, x2, ..., x n ), where x i Represents sensor node N i coverage capability;

[0026] If the final fused data vector V corresponding to the system state z represented by the path n+1 Satisfy a certain threshold D, that is, D(V n+1 )=1, the sink node is marked as "1"; otherwise, it is marked as "0". The tree-structured MDD model has (K+1) n paths, each path encodes the state of a wireless linear sensor network system;

[0027] By simplifying the tree-like MDD model through the designed simplification rules, the simplified MDD models corresponding to the LWSNs on the left and right sides can be obtained.

[0028] Furthermore, in S2, the method of designing simplified rules includes:

[0029] When the fused data vector of the decision node at the i-th layer satisfies the threshold D, the fused data vectors derived from the i+1, i+2, ..., n+1 layers can also satisfy the threshold D;

[0030] The simplified rules include rule one, rule two and rule three;

[0031] The first rule is: if the fused data vector of the decision node at the i-th layer satisfies the threshold D, the decision node can be replaced by a sink node marked as "1";

[0032] The second rule is: the first i-1 elements in the i-th layer fusion data vector can be set to *;

[0033] The rule three is: if the decision nodes in the same layer have the same fused data vector, they have the same sub-MDD model, that is, the sub-MDD models can be merged.

[0034] Furthermore, the method of merging the simplified MDD models corresponding to the left and right LWSNs to finally obtain the simplified MDD model corresponding to the entire wireless linear sensor network system includes:

[0035] The simplified MDD models corresponding to the LWSNs on the left and right sides are preset as G=case(X,G0,G1,...,G p ) and H=case(Y,H0,H1,...,H q );

[0036] The fusion rule ⊕ is defined as:

[0037]

[0038] Where G represents the simplified MDD model corresponding to the LWSN on the left, and H represents the simplified MDD model corresponding to the LWSN on the right.

[0039] Furthermore, in S3, the amount of fusion data required by the preset base station is a threshold value D, and the final fusion data vector V is calculated by the threshold value D. n+1 The data fusion reliability R is calculated based on the classification and the simplified MDD model of the wireless linear sensor network system. DF ways, including:

[0040] Assume a sensor node N i , k i is the sensor node N i The number of consecutive nodes that can currently be covered;

[0041] The received data vector is represented as U i,ki =(U i,ki (1),U i,ki (2),...,U i,ki (n),U i,ki (n+1)), where U i,ki Indicates that all sensor nodes are from sensor node N i The received data, U i,ki(r) represents the data received by the rth sensor node, U i,ki (n+1) represents the data received by the base station;

[0042] Define the fused data vector V i =(V i (1),V i (2),...,V i (n),V i (n+1)), V i Indicates that all sensor nodes are from sensor node N i After receiving the data, the fused data is obtained, where V i (r) represents the data fused by the rth sensor node, V i (n+1) represents the data fused by the base station;

[0043] When node N i When receiving data from the forward node, node N i The fusion rule FR1 will be used to update its fusion data when node N i When generating its own data, node N i The fusion rule FR2 will be used to update its fusion data, and then the fusion data will be transmitted backward;

[0044] Use the Boolean function D to fused the final data vector V n+1 For classification, the expression is:

[0045]

[0046] In the formula, D(V n+1 ) indicates the final fused data vector V n+1 Whether the fusion data volume threshold D required by the preset base station is met;

[0047] Then, the data fusion reliability is expressed as;

[0048]

[0049] In the formula, Pr(V n+1 ) represents the final fused data vector V n+1 The probability of occurrence.

[0050] Furthermore, in S3, the data fusion reliability evaluation of the simplified MDD model of the wireless linear sensor network system can also be calculated by a recursive algorithm, and the calculation method is:

[0051] Preset p i,k Indicates that from a decision node X in the MDD model iThe probability of the kth edge starting from the node is assumed to be MDD[k], which is the probability of the kth edge starting from the node. i The sub-MDD model pointed to by the k-th edge;

[0052] Define Pr() as a function, the input is an MDD model, and the output is the probability value calculated based on the input MDD model;

[0053] The expression for data fusion reliability evaluation through recursive algorithm is:

[0054]

[0055] When the input of Pr() is the top-level MDD node of the simplified MDD model of the wireless linear sensor network system, the output of Pr() is the data fusion reliability R DF .

[0056] Technical effects and advantages of the data fusion reliability analysis method of the wireless linear sensor network system of the present invention:

[0057] 1. The data fusion process of the LWSN system is modeled by adopting a polymorphic reliability model (MDD), and a top-down method for generating the MDD model is proposed. The MDD model of the wireless linear sensor network system is used to effectively calculate the data fusion reliability of different transient times;

[0058] 2. By using the newly designed truncation, merging and restoration operations, the proposed MDD method can prevent the generation of a large number of redundant MDD nodes, thereby improving the reliability analysis efficiency of heterogeneous and multi-state LWSN systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of the data fusion reliability analysis method of the wireless linear sensor network system of the present invention;

[0060] FIG2( a ) is a schematic diagram showing a base station in the present invention dividing the system into two parts;

[0061] FIG2( b ) is a schematic diagram of a base station located at the end of a system in the present invention;

[0062] Figure 3 Schematic diagram of the MDD model of the K=2 and n=3 subsystems in the present invention;

[0063] Figure 4 A schematic diagram of the top-down MDD construction process in the present invention;

[0064] Figure 5 It is a schematic diagram of the combination of the left and right MDD models in the present invention;

[0065] Figure 6 A schematic diagram of a simplified MDD model of a LWSN subsystem with m=2, K=3 and D=4 in the present invention;

[0066] Figure 7 Schematic diagram of equivalent MDD models of two LWSN subsystems in the present invention;

[0067] Figure 8 It is a schematic diagram of the system MDD model of the entire LWSN system in the present invention;

[0068] Fig. 9 Schematic diagram of the final compact system MDD model of the LWSN example system in the present invention. DETAILED DESCRIPTION

[0069] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] Example 1

[0071] See also Figures 1 to 9 As shown, the wireless linear sensor network system data fusion reliability analysis method described in this embodiment includes the following steps:

[0072] S1, construct a wireless linear sensor network system, and obtain the probability that the wireless linear sensor network system is in state z, wherein the wireless linear sensor network system consists of a base station N0, n sensor nodes N1, N2, ..., N1 arranged in a linear structure on the left side of the base station N0 n And m sensor nodes N'1, N'2, ..., N' are arranged in a linear structure on the right side of the base station N0. m composition;

[0073] S2, constructing a simplified MDD model of the wireless linear sensor network system, including constructing a tree-like MDD model corresponding to the left and right LWSNs layer by layer from top to bottom, designing simplification rules, and simplifying the tree-like MDD model by using the simplification rules, thereby obtaining a simplified MDD model corresponding to the left and right LWSNs, merging the simplified MDD models corresponding to the left and right LWSNs, and finally obtaining a simplified MDD model corresponding to the entire wireless linear sensor network system;

[0074] S3, the simplified MDD model of the wireless linear sensor network system is evaluated for data fusion reliability. The evaluation method is as follows: the amount of fusion data required by the base station is preset as a threshold D, and the final fusion data vector V is evaluated by the threshold D. n+1 The data fusion reliability R is calculated based on the classification and the simplified MDD model of the wireless linear sensor network system. DF .

[0075] Further, in S1, the method of obtaining the probability that the wireless linear sensor network system is in state z includes:

[0076] The sensor nodes in the preset LWSN system receive data from their neighboring nodes and then transmit the fused data to the base station along a linear path. Specifically, the node fuses the received data with its own data to form a new data packet of the same size as the original data, and then transmits the new data packet to the neighboring nodes. This process continues until the data is finally received and fused by the base station. The base station will store the fused data in the database, and users can query the occurrence of specific scenes or specific events in the database;

[0077] Figure 2(a) shows the overall structure of the heterogeneous multi-state LWSN system considered in this paper. The wireless linear sensor network system consists of m+n sensor nodes N1, N2, ..., N n , N`1, N`2, ..., N` m and base station N0. When m=0, the structure of the LWSN system is shown in Figure 2(b). The maximum signal transmission distance of the heterogeneous sensor node Ni can cover the continuous Ki nodes. The coverage capability of the node is affected by factors such as residual power and interference, which leads to different transmission radius. Therefore, the coverage capability of the sensor node is a random variable; Figure 2(a) indicates that the base station divides the system into two parts, and Figure 2(b) indicates that the base station is located at the end of the system;

[0078] The preset base station connection index is the largest sensor node, that is, N n and N` m For a heterogeneous multi-state LWSN (LWSN refers to LinearWSN, i.e. wireless linear sensor network) system with m+n sensor nodes, define X i is the sensor node N on the left side of N0 i The state variable, Y j is the right sensor node N` j The state variables of , and 1≤i≤n, 1≤j≤m;

[0079] Preset X i =k i (or Yj =k j ) represents node N i (or N` j ) The number of consecutive nodes that can be covered at present, the maximum value is K i (or K j ), preset τ i Represents node N i The generated data, and then, define K l =max{K1,K2,...,K n} and Kr=max{K1,K2,...,K m} are the maximum coverage capabilities of the left and right sides respectively;

[0080] Preset X = (X1, X2, ..., X n ) and Y=(Y1,Y2,...,Y m ) represents the random state vector of the LWSN subsystems on both sides of the base station, and Z is preset to be (X1, X2, ..., X n , Y1, Y2, ..., Y m ) represents the random system state vector of the entire LWSN system, and z is preset to be (x1, x2, ..., x n , y1, y2, ..., y m ) represents the system state z, and x is preset i or j Represents sensor node N i or Y j Status;

[0081] Furthermore, the probability that the wireless linear sensor network system is in state z is:

[0082] Pr(Z=z)=Pr left Pr right

[0083]

[0084] In the formula, Pr left Indicates that the left node of the wireless linear sensor network system is in the state (x1, x2, ..., x n ), Pr right Indicates that the right node of the wireless linear sensor network system is in the state (y1, y2, ..., y m ) probability.

[0085] Furthermore, in S1, for the sensor node N i , presupposes its discrete random state variable x i There are l different states that can be taken, and l different states can be represented as a set kl ={k1, k2, ..., k l}, and then, the distribution of the discrete random state variables of each sensor node is as follows:

[0086]

[0087]

[0088] In the formula, k l Represents sensor node N i In the first state, is the sensor node N i In state k l The probability of, similarly, is the sensor node N` j In state k r probability.

[0089] Further, in the S2, a simplified MDD model of the wireless linear sensor network system is constructed, including constructing a tree-like MDD model corresponding to the LWSNs on the left and right sides layer by layer from top to bottom, designing a simplification rule, and simplifying the tree-like MDD model by the simplification rule, thereby obtaining a simplified MDD model corresponding to the LWSNs on the left and right sides, including:

[0090] The LWSN system configuration shown in Figure 2(b) consists of n sensor nodes N1, N2, ..., N n It is composed of a base station N0 and arranged in a linear structure; each node fuses the received data with its own data, and then transmits the fused data to the next node. This process continues until the data is finally fused by the base station. The data fusion reliability of the LWSN system refers to the probability that the data fused by the base station is greater than a given threshold D.

[0091] Let f:{0,1,2,...,K} n →{0,1} represents a multi-valued variable vector x=(x1,x2,...,x n ) is a multi-valued logic function. The variable x i The Shannon decomposition of ∈x is defined as follows:

[0092]

[0093] variable x i The case format used in MDD operations is concisely expressed as:

[0094]

[0095] For the state variable X in the MDD model iThe corresponding decision nodes are displayed, representing sensor nodes N i The state space of each decision node has K+1 outgoing edges: X i =0 means N i The signal of X cannot cover any subsequent nodes. i =1 means N i The signal transmission distance only covers one subsequent node N i+1 ,X i =K represents N i The signal transmission distance covers K consecutive nodes, that is, N i+1 , ..., N i+K The kth (0≤k≤K) outgoing edge is connected to an MDD decision node, representing the multi-valued logic function f xi＝k . Therefore, each decision node in the MDD model encodes a case structure;

[0096] The MDD model of the LWSN system with n sensor nodes is assumed to consist of n layers of decision nodes and two sink nodes labeled “0” and “1”;

[0097] At the top level of the MDD model, i = 1, there is only one root node associated with the multi-valued state variable X1, representing the empty system state z = NULL;

[0098] At the bottom layer (n+1), there are two different sink nodes, which represent whether the final fused data vector is in or not in a specific state;

[0099] The path from the root node to the sink node represents a specific system state z = (x1, x2, ..., x n ), where x i Represents sensor node N i coverage capability;

[0100] If the final fused data vector corresponding to the system state z represented by the path satisfies a certain threshold D, that is, D(V n+1 )=1, the sink node is marked as "1"; otherwise, it is marked as "0". The tree-structured MDD model has (K+1) n paths, each path encodes the state of a wireless linear sensor network system;

[0101] The common MDD model of LWSN system is a tree structure with decision nodes. Figure 3 The tree-like MDD structure of the LWSN system with K = 2 and n = 3 is illustrated. The MDD model has 13 decision nodes (represented by circles), and each decision node has 3 outgoing edges;

[0102] The data fusion process of the LWSN system is modeled using the top-down MDD model generation method. Here, we take the LWSN system with n = 3 and K = 3 as an example to illustrate the generation of the MDD model. The data generated by the three sensor nodes are 4, 2, and 6 respectively;

[0103] Taking the MDD tree of the WSN system as an example, at the top level, the highest decision node is X1, and the initial fusion data vector is V0 = (, *, *,).

[0104] In the second layer, there is a fused data vector (*, *, *) on the 0 edge from the decision node X1, indicating that the sensor nodes N2, N3 and the base station have not received the data; there is a fused data vector (*, 4, *, *) on the 1 edge, indicating that only the sensor node N2 has received the data of 4; there is a fused data vector (*, 4, 4, *) on the 2 edge, indicating that all sensor nodes N2 and N3 have received the data of 4; there is a fused data vector (*, 4, 4, 4) on the 3 edge, indicating that all sensor nodes and the base station have received the data of 4.

[0105] In the third layer, the fused data vector (*, 4, 3, *) indicates that the base station has no fused data, while the fused data of sensor nodes N2 and N3 are 4 and 3 respectively; (*, 4, 4, 3) indicates that the fused data of sensor nodes N2 and N3 are both 4, while the fused data of the base station is 3; (*, 4, 4, 4) indicates that the fused data of sensor nodes N2, N3 and the base station are all 4.

[0106] In the 4th layer, the fused data vector (*, *, 6) indicates that the fused data of the base station is 6; (*, 4, 3, 3) indicates that the fused data of the base station and sensor node N3 is 3, and the fused data of sensor node N2 is 4;

[0107] In this embodiment, if the data fused by the base station is greater than the threshold 4 (ie, D = 4), the LWSN system is considered to be reliable. All decision nodes in the 4th layer will be connected to two sink nodes "0" and "1", indicating that the data fused by the base station does not meet such constraints (ie, D (V n+1 )=0) or the data fused by the base station meets the given threshold (i.e. D(V n+1 )=1);

[0108] The tree-structured MDD model has (K+1) from the root node to the sink node. n paths, each path encodes a system state. Therefore, the tree-structured MDD model has the same complexity as the state space-based enumeration method. Now, we will try to design servo simplification rules, that is, merge decision nodes with the same subtrees and perform subtree truncation to significantly reduce model complexity and improve analysis efficiency;

[0109] By examining the MDD tree of the WSN system (existing public technology), we can find that when the fused data vector of the decision node at the i-th layer meets the threshold D, the fused data vectors derived from the i+1, i+2, ..., n+1 layers can also meet the threshold D;

[0110] By simplifying the MDD model according to the set simplification rules, the MDD model of the wireless linear sensor network system can be obtained.

[0111] Furthermore, in S2, the method of designing simplified rules includes:

[0112] When the fused data vector of the decision node at the i-th layer satisfies the threshold D, the fused data vectors derived from the i+1, i+2, ..., n+1 layers can also satisfy the threshold D;

[0113] In the MDD tree of the WSN system, the simplified rule includes rule one, rule two and rule three;

[0114] The first rule is: if the fused data vector of the decision node at the i-th layer satisfies the threshold D, the decision node can be replaced by a sink node marked as "1";

[0115] Specifically, in the layer-by-layer evolution of the fused data vector, the calculation of the fused data vector of the i-th layer can be divided into two parts. One part is the first i-1 elements, whose values ​​will not change in subsequent iterations and have no effect on the data fusion of the base station. Therefore, this part can be deleted from the subsequent evolution. The other part is the remaining ni elements, which will be updated in the subsequent evolution. This discovery leads to the following simplified rules;

[0116] The second rule is: the first i-1 elements in the i-th layer fusion data vector can be set to *;

[0117] Specifically, if two different decision MDD nodes are given in the same layer, they have the same fused data vector, then for all possible later evolutionary trajectories, they will have the same evolution tree. This finding leads to the following merging rule;

[0118] The third rule is: if the decision nodes in the same layer have the same fusion data vector, they have the same sub-MDD model, that is, they can be merged;

[0119] Specifically, by applying the above three simplification rules in the process of generating the MDD model from top to bottom, the MDD tree of the WSN system can be avoided and a simplified MDD model of the LWSN system can be generated.

[0120] Furthermore, the method of merging the simplified MDD models corresponding to the left and right LWSNs to finally obtain the simplified MDD model corresponding to the entire wireless linear sensor network system includes:

[0121] Consider the LWSN system configuration shown in Figure 2(a), where the base station is not placed at the end of the system as a terminal node; in other words, the LWSN system consists of two LWSN subsystems separated by the base station, which is different from the LWSN system shown in Figure 2(b). In this case, one more step should be performed to combine the two MDD models encoding the two LWSN subsystems on the left and right sides of the base station to generate the final system MDD model;

[0122] The case formats of the default left and right MDD models are recorded as G = case (X, G0, G1, ..., G p ) and H=case(Y,H0,H1,...,H q ):

[0123] The fusion rule ⊕ is used to further fuse the two fusion data of both parties, and ⊕=add is used as an illustration. Then, the fusion rule ⊕ for generating the final system MDD model according to G and H is defined as:

[0124]

[0125] In the formula, G represents the simplified MDD model corresponding to the LWSN on the left, and H represents the simplified MDD model corresponding to the LWSN on the right;

[0126] like Figure 5 As shown, the combination of the left and right MDD models is as follows;

[0127] As an example, a LWSN system is given. The subsystem on the left is the same as the subsystem in the MDD tree of the WSN system, n = 3, K l =3; the configuration of the right subsystem is m=2, K r =2; the MDD model of the left subsystem is shown in the simplified MDD model of the LWSN system (existing technology), and the MDD model of the right subsystem can also be generated by a similar method. The simplified MDD model is shown in Figure 6 As shown, Figure 8 A simplified MDD model of an LWSN system with m=2, K=3 and D=4 LWSN subsystem;

[0128] By looking at the simplified MDD model of the LWSN system and Figure 8 , we can find that the base station will obtain seven different fusion data from the right subsystem and four different fusion data from the left subsystem. Therefore, we can get the equivalent MDD model of each LWSN subsystem, as Figure 7 As shown in Figure 2. The final fusion data can be generated by using the ⊕ operation. The system MDD model of the entire LWSN system is shown in Figure 2. Figure 8 As shown;

[0129] In addition, we can also merge the identical subgraphs involved in the system MDD model through a reduction process. This reduction process will generate a most compact MDD model in a bottom-up manner. Specifically, a hash table is used to record unique MDD nodes and their graph properties, such as the child MDD nodes pointed to by all their outgoing edges. Each node in the compact system MDD model has an entry in the hash table. Before adding a new node to the compact system MDD model, a lookup in the hash table determines whether the same node already exists to avoid generating the same subgraph. Therefore, by "merging isomorphic subtrees" and "deleting useless nodes", we can generate the following: Fig. 9 The final compact system MDD model is shown. It can be found that with the complexity (K l +1) n .(K r +1) m Compared with the traditional state space method, the MDD modeling method we proposed greatly alleviates the problem of state space explosion.

[0130] Furthermore, in S3, the amount of fusion data required by the base station is preset as a threshold D, and the final fusion data vector V is calculated by the threshold D. n+1 The data fusion reliability R is calculated based on the classification and the simplified MDD model of the wireless linear sensor network system. DF ways, including:

[0131] Assume a sensor node N i (1≤i≤n),k i is the sensor node N i The number of consecutive nodes that can currently be covered;

[0132] The received data vector is represented as U i,ki =(U i,ki (1),U i,ki (2),...,U i,ki (n),U i,ki (n+1)), where U i,ki Indicates that all sensor nodes are from sensor node N i The received data, U i,ki (r) represents the data received by the rth sensor node, U i,ki (n+1) represents the data received by the base station;

[0133] Define the fused data vector V i =(Vi (1),V i (2),...,V i (n),V i (n+1)), V i Indicates that all sensor nodes are from sensor node N i After receiving the data, the fused data is obtained, where V i (r) represents the data fused by the rth sensor node, V i (n+1) represents the data fused by the base station;

[0134] Assume a sensor node N i (1≤i≤n), when node N i When receiving data from the forward node, node N i The fusion rule FR1 will be used to update its fusion data when node N i When generating its own data, node N i The fusion rule FR2 will be used to update its fusion data, and then the fusion data will be transmitted backward;

[0135] Among them, the fusion rules FR1 and FR2 can be implemented in many ways, such as addition, multiplication, average, maximum, minimum, etc.; FR1 = max and FR2 = mean can be used as an illustration. For example, consider a system of 4 sensor nodes LWSN. We set the initial fused data vector V0 = (*, *, *); when the first sensor node N1 generates data τ1 = 4, it will use the fusion rule mean to update its initial fused data *, that is, mean(4, *) = 4. Please note that we set the result of * fusion with other data to be d for any fusion rule. Then, node N1 sends the newly fused data 4 to the two backward sensor nodes N2 and N3, and the received data vector is U1 = (*, 4, 4, *). When sensor node N2 receives data 4, it will use the fusion rule max to update its fused data max(*, 4) = 4. When sensor node N3 receives data 4, it will use the fusion rule max to update its fused data max(*, 4) = 4. Here, we will get a new fused data vector V1 = (*, 4, 4, *);

[0136] When sensor node N2 generates its own data τ2=2, it will use the fusion rule average to update its fused data average (4, 2)=3, and then send the fused data 3 to the two backward sensor nodes N3 and N4. Here, the received data vector will be U2=(*, *, 3, 3). When sensor node N3 receives data 3, it will use the fusion rule max to update its fused data max(4, 3)=4. When sensor node N4 receives data 3, it will use the fusion rule max to update its fused data max(*, 3)=3. Here, we will get a new fused data vector V2=(*, 4, 4, 3);

[0137] When sensor node N3 generates its own data τ3=6, it will use the fusion rule average to update its fused data average (4, 6)=5, and then send the fused data 5 to the two backward sensor nodes N4. Here, the received data vector is U2=(*, *, *, 5). After receiving data 5, sensor node N4 will use the fusion rule max to update its fused data max(3, 5)=5. Here, we will get a new fused data vector V3=(*, 4, 4, 5).

[0138] We consider the amount of fused data required by the base station as a threshold D specified by the designer, which can be obtained by applying a Boolean function D to the final fused data vector V defined as n+1 For classification, the expression is:

[0139]

[0140] In the formula, D(V n+1 ) indicates the final fused data vector V n+1 Whether the fusion data volume threshold D required by the preset base station is met;

[0141] Then, the data fusion reliability R DF , that is, the probability that the base station has at least D fused data, which is expressed as;

[0142]

[0143] In the formula, Pr(V n+1 ) represents the final fused data vector V n+1 Probability of occurrence.

[0144] Furthermore, in S3, the data fusion reliability evaluation of the simplified MDD model of the wireless linear sensor network system can also be calculated by a recursive algorithm, and the calculation method is:

[0145] The data fusion reliability related to the lower limit D can be calculated as the sum of the occurrence probabilities of all system states that satisfy the lower limit D. According to the construction process of the MDD model, we can know that it encodes the entire system state space; in fact, the path from the MDD root node to the sink node "1" encodes all system states that satisfy the lower limit D;

[0146] In this embodiment, the data fusion reliability R of the LWSN system is obtained by evaluating the constructed MDD model. DF , specifically, R DF It can be calculated by summing the probabilities of all paths from the root node to the sink node "1", where the probability of each path can be determined by multiplying the probabilities of all node states on the path.

[0147] In software implementation, MDD model evaluation can be expressed by a recursive algorithm, as shown in the following expression, which is more concise; i,k (t) represents the number of nodes from decision node X i The probability of the kth edge at the beginning, that is, at time t, k = 1, 2, ..., K, the sensor node N i In state k (sensor node N i can cover k nodes backward); MDD.Branch[k] is the node of decision node X i The sub-MDD model pointed to by the k-th edge; Pr() is a function, the input is an MDD model, and the output is the probability value calculated based on the input MDD model;

[0148] Preset p i,k (t) represents the number of nodes from decision node X i The probability of occurrence of the kth edge at the beginning, assuming that MDD.Branch[k] is the decision node X i The sub-MDD model pointed to by the k-th edge of , defines Pr() as a function, the input is an MDD model, and the output is the probability value calculated based on the input MDD model;

[0149] Then, the expression for calculating the data fusion reliability of the wireless linear sensor network system through a recursive algorithm is:

[0150]

[0151] Can also be:

[0152] When the input of Pr() is the top-level MDD node of the simplified MDD model of the wireless linear sensor network system, the output of Pr() is the data fusion reliability R DF ;

[0153] The recursive MDD model evaluation algorithm is shown in Table 1. Through this evaluation algorithm, the data fusion reliability R DF The computational probability of being the root MDD node can be calculated; the complexity of this recursive evaluation algorithm is linear with the number of decision nodes in the compact system MDD model.

[0154] Table 1. R DF MDD Model Evaluation Algorithm

[0155]

[0156] In this embodiment, the data fusion process of the LWSN system is modeled by adopting a polymorphic reliability model (i.e., MDD), and a top-down method for generating the MDD model is proposed. The constructed MDD model of the wireless linear sensor network system is used to effectively calculate the data fusion reliability of different transient times. By using the newly designed truncation, merging and restoration operations, the proposed MDD method can prevent the generation of a large number of redundant MDD nodes, thereby improving the reliability analysis efficiency of heterogeneous and multi-state LWSN systems.

[0157] Example 2

[0158] The wireless linear sensor network system data fusion reliability analysis method described in this embodiment is as follows:

[0159] Consider a heterogeneous multi-state sensor chain in a cluster-chain WSN system with subchain lengths of n = 3 and m = 2. The data perception capability of each sensor node is given in Table 2, and the fault parameters are shown in Table 3. Assume that the life time of all sensor nodes follows the parameter λ i The exponential distribution of the cumulative distribution function is F(t) = 1-exp(-λ i t). The state transition process of each sensor node corresponds to a continuous-time Markov random process. Assume that the sensor node can only transfer from a high performance level to a low performance level, and is only allowed to transfer from the previous performance level to the next performance level, but cannot jump to perform state transition.

[0160] Table 2. Parameter configuration of each sensor node

[0161]

[0162] Table 3. Parameter configuration of each sensor node state occupancy time

[0163]

[0164] In theory, the finite state space I = {0, 1, ..., n} and the infinitesimal generator matrix Q = [q ij] As shown in the following formula, it is used to define CTMC. The transition rate of CTMC from state i to state j is q ij It means that in a finite state space, The Kolmogorov backward equation shown below can be solved for the conditional transient probability at any time t, using p ij (t) represents all conditional probabilities. All conditional probabilities are represented by the conditional transient probability matrix P(t) = [p ij (t)] collection.

[0165]

[0166]

[0167] The initial probability distribution of CTMC is represented by {p j (0),j∈I}. The transient probability distribution is denoted as {p j (t),j∈I},p j (t) can be calculated by the following formula. Table 4 provides the transient probability distribution of each sensor node at t = 1000h.

[0168]

[0169] Table 4 State occupancy probability distribution of each sensor node at t = 1000h

[0170]

[0171] We tested nine cases with thresholds D ranging from 3 to 8.5. For each case, a compact MDD model was first built using the MDD model generation method described in Section 3. The probabilities in Table 4 were then used as the edge probabilities of the decision nodes in the constructed MDD model. Finally, the data fusion reliability R was calculated using the reliability evaluation algorithm (Table 1). DF Table 5 lists the MDD size and data fusion reliability results for each threshold D. In addition, Table 6 also gives the data fusion reliability results for different transient times when the threshold D=4 is selected.

[0172] Table 5. MDD size and reliability results

[0173]

[0174] Table 6. Reliability at different times when the system threshold is 4

[0175]

[0176] Example 3

[0177] The wireless linear sensor network system data fusion reliability analysis method described in this embodiment is as follows:

[0178] Consider another heterogeneous multi-state LWSN system, n = 10, K l =6; m=5, K r =4. Tables 7 and 8 list the parameter configurations of all sensor nodes. Table 9 gives the state occupancy probability distribution of each sensor node in the LWSN system at t = 1000h.

[0179] Table 7. Parameter configuration of the ten sensor nodes on the left

[0180]

[0181] Table 8. Parameter configuration of the ten sensor nodes on the right

[0182]

[0183] Table 9. State occupancy probability distribution of the ten sensor nodes on the left at t = 1000h

[0184]

[0185] Table 10. State occupancy probability distribution of the ten sensor nodes on the right at t = 1000h

[0186]

[0187] Table 11. MDD size and reliability results for different thresholds D

[0188]

[0189] To verify the efficiency of the proposed MDD-based approach, a benchmark study is conducted. Consider a larger heterogeneous multi-state LWSN system with n = 10 and m = 10. Table 12 provides the data generated by each sensor node, and Table 13 provides the maximum coverage capability of each sensor node. The CTMC model has a one-to-one mapping relationship between the CTMC states and the system states. Therefore, the number of CTMC states in the CTMC model is For this benchmark system, the total number of CTMC states is 4670854. Therefore, even for this moderately sized benchmark system, an exhaustive approach based on all system states is very time-consuming.

[0190] Table 12. Data generated by each sensor node

[0191]

[0192] Table 13. Maximum coverage capability parameters for each sensor node

[0193]

[0194] The benchmark study explored the reliability of data fusion under different thresholds D (from 4 to 8). Table 14 shows the results obtained during the construction of the benchmark system MDD model, where the column “MDD size” represents the number of decision nodes in the compact MDD model constructed under different thresholds. The remaining three columns provide detailed information on the MDD construction process: “Truncation operation” according to rule 1, “Merge operation” according to rule 3, and “Reduction operation” represents the number of MDD nodes reduced during the system MDD combination process.

[0195] Table 14. Results of the MDD model construction process for different thresholds D

[0196]

[0197]

[0198] In addition, we also studied five LWSN systems of different sizes, with parameter pairs (m,n) of (10,10), (15,10), (15,15), (15,20) and (20,20). Table 15 shows the number of truncation, merging and reduction operations performed by the proposed MDD-based method under the condition of threshold D = 4, as well as the size of the final system MDD model.

[0199] All these results indicate that our MDD-based approach can generate smaller MDD models than traditional CTMC models by performing a large number of truncation, merging, and reduction operations, thus improving computational efficiency and reducing storage requirements.

[0200] Table 15. Results of the MDD model building process for different LWSN system sizes

[0201]

[0202] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0203] In the several embodiments provided by the present invention, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic, for example, the division of the units is only one, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0204] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

[0205] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit 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 reliability of data fusion in a wireless linear sensor network system, characterized in that: The following steps are involved: S1, construct a wireless linear sensor network system, and obtain the probability that the wireless linear sensor network system is in state z, wherein the wireless linear sensor network system consists of a base station N0, n sensor nodes N1, N2, ..., N1 arranged in a linear structure on the left side of the base station N0 n And m sensor nodes N'1, N'2, ..., N' are arranged in a linear structure on the right side of the base station N0. m composition; S2, constructing a simplified MDD model of the wireless linear sensor network system, including constructing a tree-like MDD model corresponding to the left and right LWSNs layer by layer from top to bottom, designing simplification rules, and simplifying the tree-like MDD model by using the simplification rules, thereby obtaining a simplified MDD model corresponding to the left and right LWSNs, merging the simplified MDD models corresponding to the left and right LWSNs, and finally obtaining a simplified MDD model corresponding to the entire wireless linear sensor network system; S3, the simplified MDD model of the wireless linear sensor network system is evaluated for data fusion reliability. The evaluation method is as follows: the amount of fusion data required by the base station is preset as a threshold D, and the final fusion data vector V is evaluated by the threshold D. n+1 The data fusion reliability R is calculated based on the classification and the simplified MDD model of the wireless linear sensor network system. DF .

2. The wireless linear sensor network system data fusion reliability analysis method according to claim 1 is characterized in that: In S1, the method of obtaining the probability that the wireless linear sensor network system is in state z includes: The preset base station connects to the sensor node with the largest index, that is, N n and N` m , for a heterogeneous multi-state LWSN system with m+n sensor nodes, define X i is the sensor node N on the left side of N0 i The state variable, Y j is the right sensor node N` j The state variables of , and 1≤i≤n, 1≤j≤m; Preset X i =k i Represents node N i The maximum number of consecutive nodes that can be covered is K i ; Default Y j =k j Represents node N` j The maximum number of consecutive nodes that can be covered is K j , preset τ i Represents node N i The generated data, and then, define K l =max{K1,K2,...,K n } and K r =max{K1,K2,...,K m } are the maximum coverage capabilities of the left and right sides respectively; Preset X = (X1, X2, ..., X n ) and Y=(Y1,Y2,...,Y m ) represent the random state vectors of the LWSN subsystems on both sides of the base station, and Z is preset to be (X1, X2, ..., X n , Y1, Y2, ..., Y m ) represents the random state vector of the entire wireless linear sensor network system, and z is preset to be (x1, x2, ..., x n , y1, y2, ..., y m ) represents a system state z, and x is assumed i Represents sensor node N i The state of y is preset j Represents sensor node Y j Status; Furthermore, the probability that the wireless linear sensor network system is in state z is: In the formula, Pr left Indicates that the left node of the wireless linear sensor network system is in the state (x1, x2, ..., x n ), Pr right Indicates that the right node of the wireless linear sensor network system is in the state (y1, y2, ..., y m ) probability.

3. The wireless linear sensor network system data fusion reliability analysis method according to claim 2 is characterized in that: In S1, for sensor node N i , presupposes its discrete random state variable x i There are l different states that can be taken, and l different states can be represented as a set k l ={k1, k2, ..., k l }, and then, the distribution of the discrete random state variables of each sensor node is as follows: In the formula, k l Represents sensor node N i In the first state, is the sensor node N i In state k l The probability of is the sensor node N` j In state k r probability.

4. The wireless linear sensor network system data fusion reliability analysis method according to claim 1, characterized in that: In the S2, a simplified MDD model of the wireless linear sensor network system is constructed, including constructing a tree-like MDD model corresponding to the LWSNs on the left and right sides layer by layer from top to bottom, designing a simplification rule, and simplifying the tree-like MDD model by the simplification rule, thereby obtaining a simplified MDD model corresponding to the LWSNs on the left and right sides, including: The tree-like MDD model of a one-sided LWSN system with n sensor nodes is assumed to consist of n layers of decision nodes and two sink nodes labeled “0” and “1”; At the top level i = 1 of the tree-like MDD model, there is only one root node associated with the multi-valued state variable X1, representing the empty system state z = NULL; At the bottom layer n+1, there are two different sink nodes, which represent whether the final fused data vector is in a specific state or not; The path from the root node to the sink node represents a specific system state z = (x1, x2, ..., x n ), where x i Represents sensor node N i coverage capability; If the final fused data vector V corresponding to the system state z represented by the path n+1 Satisfy a certain threshold D, that is, D(V n+1 )=1, the sink node is marked as "1"; otherwise, it is marked as "0". The tree-structured MDD model has (K+1) n paths, each path encodes the state of a wireless linear sensor network system; By simplifying the tree-like MDD model through the designed simplification rules, the simplified MDD models corresponding to the LWSNs on the left and right sides can be obtained.

5. The wireless linear sensor network system data fusion reliability analysis method according to claim 4 is characterized in that: In S2, a method of simplifying rules is designed, including: When the fused data vector of the decision node at the i-th layer satisfies the threshold D, the fused data vectors derived from the i+1, i+2, ..., n+1 layers can also satisfy the threshold D; The simplified rules include rule one, rule two and rule three; The first rule is: if the fused data vector of the decision node at the i-th layer satisfies the threshold D, the decision node can be replaced by a sink node marked as "1"; The second rule is: the first i-1 elements in the i-th layer fusion data vector can be set to *; The rule three is: if the decision nodes in the same layer have the same fusion data vector, they have the same sub-MDD model, that is, the sub-MDD models can be merged.

6. The wireless linear sensor network system data fusion reliability analysis method according to claim 5, characterized in that: The method of merging the simplified MDD models corresponding to the left and right LWSNs to finally obtain the simplified MDD model corresponding to the entire wireless linear sensor network system includes: The simplified MDD models corresponding to the LWSNs on the left and right sides are preset as G=case(X,G0,G1,...,G p ) and H=case(Y,H0,H1,...,H q ); Fusion Rules Defined as: Where G represents the simplified MDD model corresponding to the LWSN on the left, and H represents the simplified MDD model corresponding to the LWSN on the right.

7. The wireless linear sensor network system data fusion reliability analysis method according to claim 6, characterized in that: In S3, the amount of fusion data required by the preset base station is a threshold value D, and the final fusion data vector V is calculated by the threshold value D. n+1 The data fusion reliability R is calculated based on the classification and the simplified MDD model of the wireless linear sensor network system. DF ways, including: Assume a sensor node N i , k i is the sensor node N i The number of consecutive nodes that can currently be covered; The received data vector is represented as U i,ki =(U i,ki (1),U i,ki (2),...,U i,ki (n),U i,ki (n+1)), where U i,ki Indicates that all sensor nodes are from sensor node N i The received data, U i,ki (r) represents the data received by the rth sensor node, U i,ki (n+1) represents the data received by the base station; Define the fused data vector V i =(V i (1),V i (2),...,V i (n),V i (n+1)), V i Indicates that all sensor nodes are from sensor node N i After receiving the data, the fused data is obtained, where V i (r) represents the data fused by the rth sensor node, V i (n+1) represents the data fused by the base station; When node N i When receiving data from the forward node, node N i The fusion rule FR1 will be used to update its fusion data when node N i When generating its own data, node N i The fusion rule FR2 will be used to update its fusion data, and then the fusion data will be transmitted backward; Use the Boolean function D to fused the final data vector V n+1 For classification, the expression is: In the formula, D(V n+1 ) indicates the final fused data vector V n+1 Whether the fusion data volume threshold D required by the preset base station is met; Then, the data fusion reliability is expressed as; In the formula, Pr(V n+1 ) represents the final fused data vector V n+1 The probability of occurrence.

8. The wireless linear sensor network system data fusion reliability analysis method according to claim 7, characterized in that: In S3, the data fusion reliability evaluation of the simplified MDD model of the wireless linear sensor network system can also be calculated by a recursive algorithm, and the calculation method is: Preset p i,k Indicates that from a decision node X in the MDD model i The probability of the kth edge starting from the node is assumed to be MDD[k], which is the probability of the kth edge starting from the node. i The sub-MDD model pointed to by the k-th edge; Define Pr() as a function, the input is an MDD model, and the output is the probability value calculated based on the input MDD model; The expression for data fusion reliability evaluation through recursive algorithm is: When the input of Pr() is the top-level MDD node of the simplified MDD model of the wireless linear sensor network system, the output of Pr() is the data fusion reliability R DF .

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