Key link identification method based on multi-modal network

Abstract

The invention relates to the technical field of communication, and particularly discloses a key link identification method based on a multi-modal network, which comprises the following steps: dividing a link into a plurality of levels, and mapping the plurality of levels into a plurality of modals; calculating a minimum path set among all source and destination node pairs, calculating transmission reliability of the network according to the minimum path set, and summarizing the transmission reliability to obtain an original transmission reliability matrix; changing the modality of the link and updating the probability distribution of the modality of the link to obtain a new transmission reliability matrix; converting the original reliability matrix into a first matrix, and converting the first matrix into a target vector; combining all the target vectors into a second matrix; calculating a weight vector of the influence of the modal change of the link on the maximum feasible traffic of different source and sink node pairs; standardizing elements in the second matrix to obtain a third matrix; and solving the maximum Minkowski distance and the minimum Minkowski distance according to the third matrix and the weight vector, and determining the importance degree of the link so as to identify the key link according to the importance degree of the link.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a key link identification method based on a multimodal network. Background Art

[0002] Modern society has continuously increased its requirements for the reliability and efficiency of power systems. As an important part of the power system, the optimization of the reliability and transmission capacity of the power communication network is particularly critical. In the power communication network, the reliability of the link is directly related to the transmission performance of the entire network. Therefore, how to effectively identify key links and improve the reliability of the network has become an urgent problem to be solved.

[0003] Traditional key link identification methods are mostly based on single parameters or static network structures, which are difficult to adapt to the actual complex environment of power communication networks. Traditional methods often cannot accurately reflect the impact of links on the overall network reliability when faced with changing link states and diversified business needs. Relying on traditional methods to identify key links is no longer sufficient to meet the needs of power communication networks, so research on key link identification in multimodal flow networks is urgent. Summary of the invention

[0004] In view of the above problems, the purpose of the present invention is to provide a critical link identification method based on a multimodal network, which can accurately and quantitatively identify the critical links of the multimodal network, and then evaluate the link importance of the links in the complex multimodal flow network.

[0005] The present invention provides a key link identification method based on a multimodal network, comprising:

[0006] Step S1, dividing the links in the power communication network into multiple levels according to the remaining bandwidth of the links, and mapping the multiple levels to multiple modes of the links in the multimodal network;

[0007] Step S2, calculating the minimum path set between all source-destination node pairs in the multimodal network by a feasible loop method, calculating the transmission reliability of the network according to the minimum path set and summarizing the transmission reliability to obtain an original transmission reliability matrix; the transmission reliability is the probability of traffic being transmitted from a source node to a destination node in the multimodal network;

[0008] Step S3, changing the mode of the link and updating the probability distribution of the mode of the link, to obtain a new transmission reliability matrix corresponding to the changed link;

[0009] Step S4, converting the original reliability matrix into a first matrix having the same number of rows and columns as the new transmission reliability matrix by a zero-padding method, and converting the first matrix into a target vector;

[0010] Step S5, traversing all links in the network to obtain the target vector corresponding to each link, and combining all the target vectors into a second matrix;

[0011] Step S6, using the objective weighting method CRITIC to calculate the weight vector of the influence of the modal change of the link on the maximum feasible flow of different source-destination node pairs;

[0012] Step S7, normalizing the elements in the second matrix to obtain a third matrix;

[0013] Step S8, solving the maximum Minkowski distance and the minimum Minkowski distance according to the third matrix and the weight vector, and determining the link importance according to the maximum Minkowski distance and the minimum Minkowski distance, so as to identify the key links in the network according to the link importance.

[0014] In a possible implementation, the S2 includes:

[0015] The transmission reliability R of the network is calculated according to the following formula: d :

[0016]

[0017] In the formula, R d is the probability that the link state vector is greater than or equal to the union of each minimum path vector, L is the number of minimum path vectors, S u is the sum of the probabilities that the link state vector is greater than or equal to any u minimum path vectors.

[0018] In a possible implementation, S3 includes:

[0019] Update the probability distribution of the link mode according to the following formula

[0020]

[0021] in, is the probability that link k is in mode number (m-θ), M * is the maximum modal value after the capacity of link k is increased, M k is the maximum value of the link k mode.

[0022] In a possible implementation, the target vector is an N×1 column vector, where N is the number of source-destination node pairs in the multimodal network; and S4 includes:

[0023] The value ΔR of the i-th row of the target vector is calculated according to the following formula i k :

[0024] ΔR ik =∑ 0≤d≤Dk d×(st i k (d)-st i 0 (d))

[0025] Where d is the number of unit flow, D k is the maximum feasible flow of the multimodal network after changing the mode of link k, st i 0 is the vector corresponding to the i-th row of the original transmission reliability matrix R0, st i k is the new transmission reliability matrix R corresponding to link k k The vector corresponding to the i-th row of .

[0026] In a possible implementation, the S6 includes:

[0027] Different source and sink nodes are regarded as different indicators, and the influence of each link on a certain source and sink node on the maximum feasible flow is regarded as the indicator value under the corresponding indicator;

[0028] The weight vector W of the influence of the modal change of the link on the maximum feasible flow of different source-destination node pairs is calculated according to the following formula:

[0029] W={w1,w2...w N}

[0030]

[0031] Among them, w n is the value in the weight vector W, n∈[1,N], E n is the amount of information contained in the nth indicator, and N is the number of source-destination node pairs in the multimodal network;

[0032] The information E contained in the nth indicator is calculated according to the following formula: n :

[0033]

[0034] Among them, ξ n is the standard deviation of the nth indicator in the link mode change, c in is the correlation coefficient between the ith indicator and the nth indicator.

[0035] In a possible implementation, the S6 further includes:

[0036] The standard deviation ξ of the nth indicator in the link mode change is calculated according to the following formula m :

[0037]

[0038] Where K is the number of links in the multimodal network, N is the number of source-destination node pairs in the multimodal network, The second matrix R * The mean of the elements in the nth row of The second matrix R * The element at row n and column i of .

[0039] In a possible implementation, S6 further includes:

[0040] The correlation coefficient c between the i-th indicator and the n-th indicator is calculated according to the following formula: in :

[0041]

[0042] Among them, ξ i is the standard deviation of the ith indicator in the link mode change, ξ n is the standard deviation of the nth indicator in the link mode change, R * i The second matrix R * The i-th row of R * n The second matrix R * The nth row of .

[0043] In a possible implementation, the S7 includes:

[0044] The second matrix R is calculated according to the following formula * The elements in are normalized:

[0045]

[0046] Among them, z ik is the element in the third matrix Z, R ik The second matrix R * The elements in , K is the number of links in the multimodal network, and k is the number of the link.

[0047] In a possible implementation, the S8 includes:

[0048] The link importance S of link k is calculated according to the following formula: k :

[0049]

[0050] in, is the maximum Minkowski distance of link k, is the minimum Minkowski distance of link k.

[0051] In a possible implementation, the S8 further includes:

[0052] The maximum Minkowski distance of link k is calculated according to the following formula

[0053]

[0054] The minimum Minkowski distance of link k is calculated according to the following formula:

[0055]

[0056] Where N is the number of source-destination node pairs in the multimodal network, w i The value of the i-th indicator in the weight vector, is the maximum value of the elements in the third matrix, is the minimum value of the elements in the third matrix, z ik is the element in the third matrix, and p is the parameter of Minkowski distance.

[0057] The key link identification method based on multimodal network provided by the present invention divides the links into multiple levels by the remaining bandwidth of the links in the power communication network, and maps them into multiple modes of the links in the multimodal flow network. By solving the minimum path set and calculating the transmission reliability, the transmission reliability set is subjected to data dimension reduction processing to obtain a matrix, and the matrix is ​​mapped to the Minkowski space after calculating the index weight. By calculating the Minkowski distance with the maximum value and the minimum value as the link importance of the link, accurate quantitative identification of the key links of the multimodal network and link importance evaluation of the links in the complex multimodal flow network are achieved, which has guiding significance for improving the reliability of the power communication network and optimizing the communication network structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A schematic diagram of a process flow of a key link identification method provided by an embodiment of the present invention;

[0059] Figure 2 A network topology diagram provided for an embodiment of the present invention;

[0060] Figure 3 A schematic diagram of link importance provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The following detailed description of the embodiments of the present invention is further described in detail in conjunction with the accompanying drawings and examples. The detailed description of the following embodiments and the accompanying drawings are used to exemplarily illustrate the principles of the present invention, but cannot be used to limit the scope of the present invention, that is, the present invention is not limited to the preferred embodiments described, and the scope of the present invention is defined by the claims.

[0062] In the description of the present invention, it should be noted that unless otherwise specified, the meaning of "a plurality of" is two or more; the terms "first", "second", etc. are only used for descriptive purposes and cannot be construed as indicating or implying relative importance; for those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0063] Figure 1 As shown in the flowchart of the key link identification method provided by the embodiment of the present invention, Figure 1 The present invention provides a key link identification method based on a multi-modal network, including:

[0064] Step S1: Divide the links in the power communication network into multiple levels according to the remaining bandwidth of the links, and map the multiple levels to multiple modes of the links in the multi-modal network;

[0065] Among them, the larger the modal number, that is, the modal value, the larger the corresponding remaining bandwidth. For link k = 1, 2, 3,..., K, where K is the number of links in the multi-modal network, the probability of link k in each mode is expressed as M k is the maximum value of the mode of link k.

[0066] Step S2: Calculate the minimum path set d-MP(s, t) between all source-destination node pairs in the multi-modal network by the feasible cycle method, calculate the transmission reliability R d (s, t) of the network according to the minimum path set, and summarize the transmission reliability to obtain the original transmission reliability matrix

[0067] Among them, the transmission reliability R d (s, t) is the probability that the traffic in the multi-modal network is transmitted from the source node to the destination node, d = 1, 2,..., D0, where D0 is the maximum feasible traffic between all source-destination node pairs under the current link state distribution. The transmission reliability set R 0 is a matrix with N rows and D0 columns, and N is the number of source-destination node pairs in the multi-modal network.

[0068] If the link state vector x satisfies the following conditions: if and for any y < x there is where y < x means that for all k, x k ≥ y k , and there is at least one link k such that x k > y k , then the link state vector x is called the minimum path vector.

[0069] Calculate all L minimum path vectors as priors, denoted as z 1 , z 2,…,z L , then the reliability R d is the probability that the link state vector x is greater than or equal to the union of each minimum path vector.

[0070] It is the structural function of a multi-state network, defined as the maximum feasible flow of the network whose state is the current link state vector x. k ,), represents the link state vector of the network, link k is in mode x k , d-MP is the minimum path vector set of the multimodal network and is called the minimum path set.

[0071] Assume E j is the event that the link state vector x is greater than or equal to every minimum path vector, that is, {x≥z j}, event E j The probability of the union of is the transmission reliability R of the network. d .

[0072] The link state vector is calculated according to the following formula The probability of being greater than or equal to the union of each minimum path vector

[0073]

[0074] Where x is the link state vector, L is the number of minimum path vectors, and z L is the minimum path vector.

[0075] The inclusion-exclusion (IE) principle is used to calculate the union probability of all given d-MPs. The IE method continuously calculates the upper and lower bounds of the joint probability of events through the Bonferroni inequality and finally converges to the exact probability value.

[0076] The probability that the link state vector is greater than or equal to the sum of any n minimum path vectors S is calculated according to the following formula: n :

[0077]

[0078] The transmission reliability R of the network is calculated according to the following formula: d :

[0079]

[0080] Among them, R d (s, t) is the reliability R of a given source-destination node pair (s, t) d , Link state vector The probability of being greater than or equal to the union of each minimum path vector, L is the number of minimum path vectors, S u is the sum of the probabilities that the link state vector is greater than or equal to any u minimum path vectors.

[0081] Step S3, changing the mode of the link and updating the probability distribution of the mode of the link to obtain a new transmission reliability matrix corresponding to the changed link;

[0082] Here, changing the mode of link k means increasing the capacity of link k.

[0083] Update the probability distribution of the link mode according to the following formula

[0084]

[0085] in, is the probability that link k is in mode number (m-θ), M * is the maximum modal value after the capacity of link k is increased, M k is the maximum value of the link k mode.

[0086] Transmission reliability set R k = {R d (s,t)|link k modal change}, d=1,2,,…,D k , D k is the maximum feasible network flow after changing the mode of link k, and the transmission reliability set R k For an N-row D k Matrix of columns.

[0087] Step S4, converting the original reliability matrix into a first matrix having the same number of rows and columns as the new transmission reliability matrix by zero padding, and converting the first matrix into a target vector; the number of rows and columns of the transmission reliability set and the matrix are the same;

[0088] In a possible implementation, the target vector is an N×1 column vector, where N is the number of source-destination node pairs in the multimodal network; S4 includes: calculating the value ΔR of the i-th row of the target vector according to the following formula: i k :

[0089]

[0090] Where d is the number of unit flow, D k is the maximum feasible flow of the multimodal network after changing the mode of link k, st i 0 is the vector corresponding to the i-th row of the original transmission reliability matrix R0, st i kis the new transmission reliability matrix R corresponding to link k k The vector corresponding to the i-th row of .

[0091] Step S5, traversing all links in the network to obtain the target vector corresponding to each link, and combining all the target vectors into a second matrix;

[0092] In a possible implementation, according to the target vector ΔR corresponding to all links in the multimodal network k , combined into the second matrix R with N rows and K columns * .

[0093] Step S6, using an objective weighting method (Criteria Importance Through Intercriteria Correlation, CRITIC) to calculate the weight vector of the impact of the link mode change on the maximum feasible flow of different source-destination node pairs;

[0094] In a possible implementation, different source and sink nodes are regarded as different indicators, and the influence of each link on a certain source and sink node on the maximum feasible flow is regarded as the indicator value under the corresponding indicator; that is, each row of the second matrix corresponds to the indicator value under each indicator;

[0095] The weight vector W of the impact of the link mode change on the maximum feasible flow of different source and sink node (s, t) pairs is calculated according to the following formula:

[0096] W={w1,w2…w N}

[0097]

[0098] Among them, w n is the value in the weight vector W, n∈[1,N], E n is the amount of information contained in the nth indicator, and N is the number of source-destination node pairs in the multimodal network;

[0099] The information E contained in the nth indicator is calculated according to the following formula: n :

[0100]

[0101] Among them, ξ n is the standard deviation of the nth indicator in the link mode change, c in is the correlation coefficient between the ith indicator and the nth indicator.

[0102] The standard deviation ξ of the nth indicator in the link mode change is calculated according to the following formula n :

[0103]

[0104] Where K is the number of links in the multimodal network, N is the number of source-destination node pairs in the multimodal network, The second matrix R * The mean of the elements in the nth row of The second matrix R * The element at row n and column i of .

[0105] The correlation coefficient c between the i-th indicator and the n-th indicator is calculated according to the following formula: in :

[0106]

[0107] Among them, ξ i is the standard deviation of the ith indicator in the link mode change, ξ n is the standard deviation of the nth indicator in the link mode change, R * i The second matrix R * The i-th row of R * n The second matrix R * The nth row of .

[0108] Step S7, normalizing the elements in the second matrix to obtain a third matrix;

[0109] In a possible implementation, S7 includes:

[0110] The second matrix R is calculated according to the following formula * The elements in are normalized:

[0111]

[0112] Among them, z ik is the element in the third matrix Z, R ik The second matrix R * The elements in , K is the number of links in the multimodal network, and k is the number of the link.

[0113] Define the maximum value Z + The following formula:

[0114] Z + ={max(z 11 ,z 12 ,…,z 1K ),max(z 21 ,z 22 ,…,z 2K ),…,max(z N1 ,z N2,…,z NK )

[0115] Define the minimum value Z - The following formula:

[0116] Z - ={min(z 11 ,z 12 ,…,z 1K ),min(z 21 ,z 22 ,…,z 2K ),…,min(z N1 ,z N2 ,…,z NK )

[0117] Step S8, solving the maximum Minkowski distance and the minimum Minkowski distance according to the third matrix and the weight vector, and determining the link importance according to the maximum Minkowski distance and the minimum Minkowski distance, so as to identify the key links in the network according to the link importance.

[0118] In one possible implementation, the maximum Minkowski distance of link k is calculated according to the following formula:

[0119]

[0120] The minimum Minkowski distance of link k is calculated according to the following formula:

[0121]

[0122] Where N is the number of source-destination node pairs in the multimodal network, w i The value of the i-th indicator in the weight vector, is the maximum value of the elements in the third matrix, is the minimum value of the elements in the third matrix, z ik is the element in the third matrix, and p is the parameter of Minkowski distance.

[0123] The link importance S of link k is calculated according to the following formula: k :

[0124]

[0125] in, is the maximum Minkowski distance of link k, is the minimum Minkowski distance of link k.

[0126] The following further illustrates the method of the present invention by applying it to a local network of a provincial power communication network.

[0127] Figure 2 The network topology diagram provided for the embodiment of the present invention includes 14 nodes and 16 links, and the nodes (1, 2, 5, 7, 13) in the diagram are source-destination node pairs in the multimodal network.

[0128] Step 1: According to the remaining bandwidth of the 16 links in the power communication network, the links are divided into three levels and mapped into three modes of the links in the multimodal flow network. The probability distribution of the probability of each link being in each mode is the same, that is, p k =(0.2,0.4,0.4|k=1,2,3,…,16).

[0129] Step 2: Calculate the minimum path set d-MP between the specified source node s and the destination node t for transmitting d unit flows by using the feasible round-robin method. (s,t ), and then calculate the corresponding transmission reliability R d (s, t). Traverse all source-destination node pairs in the network to obtain the original transmission reliability matrix of the network Original transmission reliability set R 0 is a matrix with 10 rows and 4 columns, where the number of source-destination node pairs in the network is 10, and the maximum feasible flow between all source-destination node pairs under the current link state distribution is 4, that is, d is at most 4.

[0130] Step 3: Increase the capacity of link k, that is, change the mode of link k in the multimodal network, and update the probability distribution of the mode of link k, and get 10 rows of D k The maximum modal value of link k after the capacity increase is 3.

[0131] Step 4: Use the zero-filling method to obtain a 10×1 column target vector ΔR k .

[0132] Step 5: traverse all the links in the network and obtain the target vector ΔR corresponding to all the links in the network according to steps 3 and 4. k , which is combined into a second matrix R with 10 rows and 16 columns * , R * (i,k) represents the ΔR of the i-th source-destination node pair after the mode change of link k i k .

[0133] Step 6: Use the CRITIC method to calculate the weight vector W = (4.273, 0.912, 0.523, 1..192, 0.738, 0.340, 3.934, 2.838, 0.405, 0.213) of the impact of link mode change on the maximum feasible flow of different source and sink node pairs (s,,t)

[0134] Step 7: Calculate the matrix R according to the following formula * The third matrix Z is obtained by normalizing the elements in .

[0135] The maximum value Z in the normalized matrix Z + :

[0136] Z +

[0137] Normalize the minimum value Z in the matrix Z - :

[0138] Z - =(1.61,0.37,0.35,0.41,0,1.69,0.41,0.83,0.35,0.70,0.64,0.70,0.83,0.37,0.37,0)

[0139] Step 8, solving the maximum Minkowski distance and the minimum Minkowski distance according to the third matrix and the weight vector, and determining the link importance according to the maximum Minkowski distance and the minimum Minkowski distance, so as to identify the key links in the network according to the link importance.

[0140] In this embodiment, the parameter p of the Minkowski distance is 3. The link importance S of link k k The following formula:

[0141]

[0142] Figure 3 This is a schematic diagram of link importance provided by an embodiment of the present invention, so that key links can be clearly seen.

[0143] In summary, the key link identification method based on multimodal network provided by the present invention first divides the links into multiple levels according to the remaining bandwidth of the links in the power communication network, and maps them into multiple modes of the links in the multimodal flow network. Then, the minimum path set is calculated by the feasible loop method, and then the corresponding transmission reliability R is calculated. d (s, t), traverse all source-destination node pairs in the network and obtain the network original transmission reliability matrix R 0 . Change the mode of the link in the multimodal network and transform the original transmission reliability matrix R 0 Transformed into the first matrix R with the same number of rows and columns as the new transmission reliability set k , and converted into the target vector ΔR k Traverse all the links in the network and obtain the target vector ΔR corresponding to all links k , which is combined into the second matrix R *Subsequently, the CRI TIC method is used to calculate the weight vector of the impact of link mode changes on the maximum feasible flow of different source and sink nodes, and the link importance of the link is obtained through normalization processing and calculation of Minkowski distance. Finally, according to the link importance of the link, the key links in the network are identified as edge 1 and edge 6.

[0144] The method of the present invention changes the link mode in the multimodal flow network and comprehensively considers the impact of different source-destination node pairs on the maximum feasible flow, thereby solving the problem that traditional methods cannot accurately quantify and identify the key links of the multimodal network. It can achieve accurate quantification and identification of the key links of the multimodal network and link importance evaluation of the links in the complex multimodal flow network, which has guiding significance for improving the reliability of the power communication network and optimizing the communication network structure.

[0145] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A key link identification method based on a multimodal network, characterized in that: include:: Step S1, dividing the links in the power communication network into multiple levels according to the remaining bandwidth of the links, and mapping the multiple levels to multiple modes of the links in the multimodal network; Step S2, calculating the minimum path set between all source-destination node pairs in the multimodal network by a feasible loop method, calculating the transmission reliability of the network according to the minimum path set and summarizing the transmission reliability to obtain an original transmission reliability matrix; The transmission reliability is the probability of traffic being transmitted from a source node to a sink node in a multimodal network; Step S3, changing the mode of the link and updating the probability distribution of the mode of the link to obtain a new transmission reliability matrix corresponding to the changed link; Step S4, converting the original reliability matrix into a first matrix having the same number of rows and columns as the new transmission reliability matrix by a zero-padding method, and converting the first matrix into a target vector; Step S5, traversing all links in the network to obtain the target vector corresponding to each link, and combining all the target vectors into a second matrix; Step S6, using the objective weighting method CRITIC to calculate the weight vector of the influence of the modal change of the link on the maximum feasible flow of different source-destination node pairs; Step S7, normalizing the elements in the second matrix to obtain a third matrix; Step S8, solving the maximum Minkowski distance and the minimum Minkowski distance according to the third matrix and the weight vector, and determining the link importance according to the maximum Minkowski distance and the minimum Minkowski distance, so as to identify the key links in the network according to the link importance.

2. The key link identification method according to claim 1, characterized in that: The S2 includes: The transmission reliability R of the network is calculated according to the following formula: d : In the formula, R d is the probability that the link state vector is greater than or equal to the union of each minimum path vector, L is the number of minimum path vectors, S u is the sum of the probabilities that the link state vector is greater than or equal to any u minimum path vectors.

3. The key link identification method according to claim 1, characterized in that: The S3 includes: Update the probability distribution of the link mode according to the following formula in, is the probability that link k is in mode number (m-θ), M * is the maximum modal value after the capacity of link k is increased, M k is the maximum value of the link k mode.

4. The key link identification method according to claim 1, characterized in that: The target vector is an N×1 column vector, where N is the number of source-destination node pairs in the multimodal network; S4 includes: The value ΔR of the i-th row of the target vector is calculated according to the following formula i k : Where d is the number of unit flow, D k is the maximum feasible flow of the multimodal network after changing the mode of link k, st i 0 is the vector corresponding to the i-th row of the original transmission reliability matrix R0, st i k is the new transmission reliability matrix R corresponding to link k k The vector corresponding to the i-th row of .

5. The key link identification method according to claim 1, characterized in that: The S6 includes: Different source and sink nodes are regarded as different indicators, and the influence of each link on a certain source and sink node on the maximum feasible flow is regarded as the indicator value under the corresponding indicator; The weight vector W of the influence of the modal change of the link on the maximum feasible flow of different source-destination node pairs is calculated according to the following formula: W={w1,w2...w N } Among them, w n is the value in the weight vector W, n∈[1,N], E n is the amount of information contained in the nth indicator, and N is the number of source-destination node pairs in the multimodal network; The information E contained in the nth indicator is calculated according to the following formula: n : Among them, ξ n is the standard deviation of the nth indicator in the link mode change, c in is the correlation coefficient between the ith indicator and the nth indicator.

6. The key link identification method according to claim 5, characterized in that: The S6 further includes: The standard deviation ξ of the nth indicator in the link mode change is calculated according to the following formula n : Where K is the number of links in the multimodal network, N is the number of source-destination node pairs in the multimodal network, The second matrix R * The mean of the elements in the nth row of The second matrix R * The element at row n and column i of .

7. The key link identification method according to claim 5, characterized in that: The S6 further includes: The correlation coefficient c between the i-th indicator and the n-th indicator is calculated according to the following formula: in : Among them, ξ i is the standard deviation of the ith indicator in the link mode change, ξ n is the standard deviation of the nth indicator in the link mode change, R * i The second matrix R * The i-th row of R * n The second matrix R * The nth row of .

8. The key link identification method according to claim 1, characterized in that: The S7 includes: The second matrix R is calculated according to the following formula * The elements in are normalized: Among them, z ik is the element in the third matrix Z, R ik The second matrix R * The elements in , K is the number of links in the multimodal network, and k is the number of the link.

9. The key link identification method according to claim 1, characterized in that: The S8 includes: The link importance S of link k is calculated according to the following formula: k : in, is the maximum Minkowski distance of link k, is the minimum Minkowski distance of link k.

10. The key link identification method according to claim 9, characterized in that: The S8 further comprises: The maximum Minkowski distance of link k is calculated according to the following formula The minimum Minkowski distance of link k is calculated according to the following formula: Where N is the number of source-destination node pairs in the multimodal network, w i The value of the i-th indicator in the weight vector, is the maximum value of the elements in the third matrix, is the minimum value of the elements in the third matrix, z ik is the element in the third matrix, and p is the parameter of Minkowski distance.

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