CN113055230B - Network reconstruction method and system for information physical system - Google Patents

Abstract

The invention discloses a network reconstruction method and system oriented to an information physical system. The PC algorithm is used to preliminarily construct the causal relationship of each node in the network, and the connection edges reconstructed from the PC algorithm are screened in combination with the MCI algorithm. Improve the authenticity and reliability of the reconstructed network.

Description

A cyber-physical system-oriented network reconfiguration method and system

technical field

The invention belongs to the technical field of network analysis and reconstruction, and relates to a network inference and reconstruction method oriented to an information physical system.

Background technique

Cyber physical systems (CPS) are next-generation intelligent systems that integrate computing, communication and control. Since the system realizes the interaction with the physical process through the human-computer interaction interface, people can use the networked space to remotely control various physical entities in the system in real time and safely and reliably. CPS is usually composed of three subsystems: autonomous data acquisition and diagnosis system - for the self-control of physical entities, global information interaction experiment system - for the development of human-computer interaction interfaces, and intelligent logic analysis system - for physical entities and Analysis of data networks between human-computer interaction interfaces. Among them, the intelligent logic analysis subsystem is a key part to realize the remote control of the system. It integrates the global information flow and logic chain of the CPS system to infer the causal relationship, and can build a complete causal graph of the data network, and establish a multi-dimensional system based on big data statistics. The intelligent body algorithm model provides scientific decision-making tools for the development and design of intelligent algorithms and control chips. Therefore, the scientific and rational realization of the reconfiguration of the CPS system network is an important guarantee for the reliability of the system's operation.

Aiming at the problem of network reconstruction, domestic and foreign researchers have done in-depth research on it, and proposed many methods. The correlation method proposed by Mantegna can use the Pearson correlation coefficient to build a spanning tree structure between variables according to the changing relationship between variables, so as to divide and reorganize the variable structure, but this method can only build an undirected graph structure, so it cannot Infer the causality between network nodes; in order to reconstruct the causal network, Granger proposed a Granger causality test method, which uses the statistical significance of "the sequence of two events" to conduct causal inference, but this method only It can be used in linear systems, but cannot analyze the nonlinear relationship ubiquitous in actual systems; the convergent cross-mapping method proposed by Sugihara can solve the problem of network reconstruction in nonlinear systems, but for high-dimensional (the number of network nodes is relatively small) A large amount of computation is required for reconstruction problems with multiple), and the solution efficiency needs to be improved.

As an emerging causal network inference algorithm in recent years, PC algorithm can effectively solve the problem of high-dimensional network reconstruction. The idea is: first treat the network as a fully connected graph, then for any node, through the conditional independence test in the iterative process to continuously eliminate the edges of irrelevant (separate) nodes, and finally when the termination condition is satisfied, it can be simultaneously Construct the complete causal network of the node. This method effectively improves the computational efficiency of network reconstruction because there is no need to compare pairs of nodes one by one.

In general, network reconstruction methods (including PC algorithms) inevitably reconstruct spurious, that is, connections that do not actually exist. The transient conditional independence (MCI) test algorithm can further verify the reconstructed edges by identifying spurious edges caused by indirect effects or common driving factors, and eliminating them, thereby further Improve the performance and reliability of network reconfiguration.

In view of the characteristics and limitations of the above methods, a more effective causal inference method is urgently needed for the network reconstruction of the CPS system, so as to truly restore the interaction structure between the unmanned and autonomous agents in the CPS system.

SUMMARY OF THE INVENTION

In view of the above-mentioned defects of the prior art, the present invention proposes a PCMCI method, which uses the PC algorithm to initially construct the causal relationship of each node in the network, and combines the MCI algorithm to screen the reconstructed edges in the PC algorithm, thereby improving the performance of the network. Reconstruct the authenticity and reliability of the network.

In order to achieve the above object, the present invention provides, in a first aspect, a cyber-physical system-oriented network reconfiguration method, comprising the steps of:

According to the collected timing state information of nodes in the network, construct a fully connected timing network diagram;

For any node, the nodes that are not related to the node are eliminated;

Carry out an iterative process, update the test conditions in each iteration process, and continuously eliminate other nodes independent of the node according to the conditional independence test algorithm;

Jump out of the iterative process when the termination condition is met;

Each connected edge is evaluated according to a transient conditional independence test algorithm and spurious connections are removed.

Further, the following specific steps are included:

(1) Initialize the parameters of the PC algorithm: set the input state time series X=(X ¹ , X ² ,..., X ^N ), the maximum causal lag time τ _max , the maximum number of parent nodes that can have a causal relationship (maximum iteration number of rounds) N _c,mac , number of conditional independence tests N _CI and termination condition threshold α _PC ;

进行因果关系重构：选取某一节点

进行初始化，设置其父节点

为所有其他节点，设置其与任意其他节点

间的独立检验统计量

设置初始迭代轮数N_c＝0；(2) Arbitrarily select a node

Perform causal reconstruction: pick a node

Initialize, set its parent node

For all other nodes, set it to be the same as any other node

independent test statistic between

Set the initial iteration round number N _c =0;

中选取一个在本轮迭代过程中未进行CI检测的节点

对

在条件

下进行CI检验，其中

且满足

得到假设检验的P值与独立性大小分别记为(p,I)；(3) Perform the N- _th round of iteration: from

Select a node that has not undergone CI detection in this round of iterations

right

in condition

The CI test is carried out under the

and satisfy

The P value and independence of the hypothesis test are recorded as (p, I) respectively;

中剔除

的节点，并根据

给

进行降序排序；否则返回步骤(3)；(4) If p>α _PC , then from

medium culling

node, and according to

Give

Sort in descending order; otherwise, return to step (3);

则节点

的因果关系重构完成；否则令N_c＝N_c+1，并返回执行步骤(3)进行新一轮迭代；(5) If

then the node

The reconstruction of the causal relationship is completed; otherwise, let N _c =N _c +1, and return to step (3) for a new round of iteration;

(6) Judging whether the causal relationship of all nodes has been reconstructed, if completed, enter step (7); otherwise, return to step (2);

(7) MCI test is performed on the reconstructed causal network, and false connections are eliminated.

Further, in step (3), the Gaussian process regression and the distance correlation coefficient are used to carry out the independence test, and the specific process is as follows:

分别进行回归分析，并计算其P值，其模型如下式所示：(3a) Using a Bayesian nonparametric regression model to

Regression analysis was carried out respectively, and its P value was calculated, and its model was as follows:

的残差为：(3b) Calculated under this model

The residuals are:

和

两者间的独立性可通过

与

来计算，若I＝0则表示两变量是独立的：(3c) For

and

The independence between the two can be achieved by

and

To calculate, if I=0, it means that the two variables are independent:

的定义分别如下：in

are defined as follows:

where d _u and d _v represent the dimensions of the vectors u and v, respectively;

(3d) Update

的连边检验具体过程如下：Further, in step (7), to any node

The specific process of the edge connection test is as follows:

计算

(7a) For any node

calculate

定义

为

的前p_X个节点构成的集合；(7b) Select any node

definition

for

The set consisting of the first p _X nodes of ;

在条件

下进行CI检验，其过程同第三步中所述方法；(7c) Yes

in condition

The CI test is carried out below, and its process is the same as that described in the third step;

(7d) According to the CI test result, remove the false connection;

(7f) Select other nodes and repeat steps (7b) to (7d). If all nodes have completed the MCI check, the final PCMCI-reconstructed causal network is obtained.

In a second aspect, the present invention provides a cyber-physical system-oriented network reconfiguration system, comprising:

The timing network diagram building module is used to construct a fully connected timing network diagram according to the collected timing state information of the nodes in the network;

The causal network reconstruction module is used to eliminate any node that is not related to the node; iterative process is performed, the test conditions are updated in each iteration process, and the node is continuously eliminated according to the conditional independence test algorithm Other nodes that are independent of each other; jump out of the iterative process when the termination condition is met;

The causal network checking module is used to evaluate each connected edge according to the transient conditional independence test algorithm and remove false connected edges.

Further, the timing network diagram building block is configured to perform the following steps:

(1) Receive parameter settings for initializing the PC algorithm: state time series X=(X ¹ , X ² ,..., X ^N ), maximum causal lag time τ _max , maximum number of parent nodes that can have causal relationships (maximum iteration number of rounds) N _c,max , number of conditional independence tests N _CI and termination condition threshold α _PC ;

The causal network reconstruction module is set up to perform the following steps:

进行因果关系重构：选取某一节点

进行初始化，设置其父节点

为所有其他节点，设置其与任意其他节点

间的独立检验统计量

设置初始迭代轮数N_c＝0；(2) Arbitrarily select a node

Perform causal reconstruction: pick a node

Initialize, set its parent node

For all other nodes, set it to be the same as any other node

independent test statistic between

Set the initial iteration round number N _c =0;

中选取一个在本轮迭代过程中未进行CI检测的节点

对

在条件

下进行CI检验，其中

且满足

得到假设检验的P值与独立性大小分别记为(p,I)；(3) Perform the N- _th round of iteration: from

Select a node that has not undergone CI detection in this round of iterations

right

in condition

The CI test is carried out under the

and satisfy

The P value and independence of the hypothesis test are recorded as (p, I) respectively;

中剔除

的节点，并根据

给

进行降序排序；否则返回步骤(3)；(4) If p>α _PC , then from

medium culling

node, and according to

Give

Sort in descending order; otherwise, return to step (3);

则节点

的因果关系重构完成；否则令N_c＝N_c+1，并返回执行步骤(3)进行新一轮迭代；(5) If

then the node

The reconstruction of the causal relationship is completed; otherwise, let N _c =N _c +1, and return to step (3) for a new round of iteration;

(6) Judging whether the causal relationship of all nodes has been reconstructed, if completed, enter step (7); otherwise, return to step (2);

The causal network inspection module is set up to perform the following steps:

(7) MCI test is performed on the reconstructed causal network, and false connections are eliminated.

Further, the causal network reconstruction module is set to use Gaussian process regression and distance correlation coefficient to carry out the independence test when performing step (3), and the specific process is as follows:

分别进行回归分析，并计算其P值，其模型如下式所示：(3a) Using a Bayesian nonparametric regression model to

Regression analysis was carried out respectively, and its P value was calculated, and its model was as follows:

的残差为：(3b) Calculated under this model

The residuals are:

和

两者间的独立性可通过

与

来计算，若I＝0则表示两变量是独立的：(3c) For

and

The independence between the two can be achieved by

and

To calculate, if I=0, it means that the two variables are independent:

的定义分别如下：in

are defined as follows:

where d _u and d _v represent the dimensions of the vectors u and v, respectively;

(3d) Update

的连边检验具体过程如下：Further, the causal network checking module is set to perform step (7), for any node

The specific process of the edge connection test is as follows:

计算

(7a) For any node

calculate

定义

为

的前p_X个节点构成的集合；(7b) Select any node

definition

for

The set consisting of the first p _X nodes of ;

在条件

下进行CI检验，其过程同第三步中所述方法；(7c) Yes

in condition

The CI test is carried out below, and its process is the same as that described in the third step;

(7d) According to the CI test result, remove the false connection;

(7f) Select other nodes and repeat steps (7b) to (7d). If all nodes have completed the MCI check, the final PCMCI-reconstructed causal network is obtained.

The present invention designs a causal network inference method based on the PCMCI algorithm for the situation that the number of unmanned autonomous nodes is large and the network complexity is high in the CPS system. This method can not only solve the problem of causal network reconstruction of nonlinear systems, but also has certain computational speed advantages in high-dimensional network scenarios. Aiming at the dilemma often faced in network reconstruction problems - the number of false connections is generally proportional to the number of reconstructed true causal relationships, in order to ensure that the true causal network is reconstructed as completely as possible to reduce the number of false connections. The invention adopts MCI test to further eliminate false connection edges, which makes up for the defect of PC algorithm that there are many false connection edges, and solves the problem of complex network reconstruction of CPS system. The method is also portable and suitable for causal inference problems in other network scenarios.

The present invention focuses on the causal network inference problem of the CPS system, and starts from the nonlinear system and the high-dimensional network structure, and conducts research on the network reconstruction method. This method has important practical significance for causal inference and reconstruction of complex networks.

The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings, so as to fully understand the purpose, characteristics and effects of the present invention.

Description of drawings

1 is an example of a causal network graph model diagram in the prior art;

Fig. 2 is an example of a causal network sequence diagram adopted by the present invention;

Fig. 3 is the sequence diagram after causal network reconstruction in a preferred embodiment of the present invention;

FIG. 4 is a flow chart of a PCMCI method in a preferred embodiment of the present invention.

Detailed ways

The following describes several preferred embodiments of the present invention with reference to the accompanying drawings, so as to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned herein.

Description of each symbol below:

X: state time series collection;

X ⁱ : Unmanned autonomous body;

无人自主体在时序图中对应的节点；

The node corresponding to the unmanned autonomous body in the sequence diagram;

时序图中t时刻之前的所有时序节点集合；

The set of all timing nodes before time t in the timing diagram;

对

存在“因”关系的父节点；

right

There is a parent node with a "cause"relationship;

I: independent test statistic;

I ^min ( ): the minimum value of the independent test statistic;

独立检验条件；

independent inspection conditions;

p: independent test P value;

α _PC : independent test significance threshold;

τ _max : maximum causal lag time;

N _c,max : the maximum number of parent nodes;

N _CI : the number of conditional independence tests;

N _c : the number of iteration rounds;

The invention provides a network inference and reconstruction method oriented to an information physical system. In this method, firstly, a fully connected time sequence network diagram is constructed according to the collected time sequence state information of unmanned autonomous entities (nodes in the network); secondly, for any node, the nodes that are not related to the node are eliminated; Next, the iterative process is carried out, the test conditions are updated in each iteration process, and other nodes independent of the node are continuously eliminated according to the conditional independence test algorithm; when the termination conditions are met, the iterative process is jumped out, and the remaining edges are initially connected. The causal relationship network between the node and other nodes is formed; finally, each connection is evaluated according to the transient conditional independence test algorithm, and the false connection is deleted to complete a more reliable causal network reconstruction.

The causal network inference method based on PCMCI includes the following specific steps:

Step 1: Initialize the parameters of the PC algorithm, set the input state time series X=(X ¹ , X ² ,..., X ^N ), the maximum causal lag time τ _max , the maximum number of parent nodes that can have causal relationships (maximum iteration number of rounds) N _c,max , number of conditional independence tests N _CI and termination condition threshold α _PC .

进行初始化，设置其父节点

为所有其他节点，设置其与任意其他节点

间的独立检验统计量

设置初始迭代轮数N_c＝0。Step 2: Select a node

Initialize, set its parent node

For all other nodes, set it to be the same as any other node

independent test statistic between

Set the initial iteration round number N _c =0.

在不同的

条件下进行条件独立性检验。Step 3: N _c round of iteration. According to the PC ₁ algorithm, the

in different

Conditional independence tests were performed.

独立的

从其父节点

中进行剔除。Step 4: According to the significance level of the hypothesis test, compare the

independent

from its parent node

removed in.

则执行步骤6；否则返回步骤3进行一轮迭代。Step 5: If

Then go to step 6; otherwise, return to step 3 for one round of iteration.

Step 6: If the causal relationship of all nodes has been reconstructed, go to Step 7; otherwise, return to Step 2.

Step 7: Check the transient conditional independence between nodes through MCI, remove false connections due to indirect influences or common driving factors, and obtain the final reconstructed causal network.

Specifically, the present invention provides a cyber-physical system (CPS)-oriented network inference and reconstruction method. The problem to be considered is: in the CPS system, while ensuring the reconstruction of the actual causal relationship between unmanned and autonomous entities , to reduce the existence of false connections/false relationships as much as possible. Figure 1 shows a schematic diagram of the causal relationship that may exist between unmanned and autonomous agents in a CPS. Unmanned and autonomous agents are represented in the form of nodes, and their states are denoted as X ⁱ , and the causal relationship between nodes is represented by solid lines with arrows. And if there is an arrow pointing from X ⁱ to X ^j , then we call unmanned subject i the "cause" of unmanned subject j. In the actual physical system, the transmission of signals takes time, so the causal relationship between nodes is also linked to time information. The graph model in Figure 1 cannot express the time lag effect of the causal relationship. Therefore, in this method, we use the sequence diagram as shown in Figure 2 to describe it. Unlike the graph model, the sequence diagram includes both node information and time information. , so the causal relationship of the network can be described more completely.

The first step is to initialize the parameters of the PC algorithm, including the following points: 1. The total number N of unmanned autonomous entities (nodes) in the network; 2. The state time series X=(X ¹ , X ² ,...,X ^N ), that is, the observed time-series state information of each node; 3. The maximum causal lag time τ _max , that is, the maximum transfer time required for the physical influencing factors emitted by a node to have an effect on another node; 4. The maximum can exist The number of parent nodes of the causal relationship (maximum number of iteration rounds) N _c,max , that is, the number of nodes that can theoretically affect a node at most, in this method, it is set as the total number of nodes included in the network N; 5. Conditions The number of tests of independence (conditional independence, CI) N _CI , that is, the number of conditions that need to be tested for conditional independence test in each iteration process, is set to 1 in this method, indicating that only one CI test needs to be performed in each iteration 6. Termination condition threshold α _PC , that is, the significance threshold of conditional independence hypothesis test.

进行因果关系重构。首先对其进行初始化，设置其父节点为所有其他节点(全连通)，即满足下式：The second step is to arbitrarily select a node

Reconstruct causality. First initialize it, set its parent node to all other nodes (fully connected), that is, to satisfy the following formula:

表示节点

的父节点，

表示当前时刻t之前时刻的所有时序状态节点的集合，由于实际的物理信息传递需要时间，因此本方法认为同时刻下的其他节点

与节点

间无因果关系。in

represents a node

the parent node of ,

Represents the set of all timing state nodes before the current time t. Since the actual physical information transmission takes time, this method considers other nodes at the same time

with node

There is no causal relationship between them.

与任意其他节点

间的独立检验统计量为一个足够大的量，即：At the same time, initialize the node

with any other node

The independent test statistic between is a large enough quantity, namely:

Finally, the current iteration number N _c =0 is initialized.

中选取一个在本轮迭代过程中未进行CI检测的节点

对

在条件

下进行CI检验，其中

且满足

得到假设检验的P值与独立性大小分别记为(p,I)。在本方法中，采用高斯过程回归(Gaussian process regression,GPR)与距离相关系数(distance correlation,DC)来进行独立性检验，其具体过程如下：The third step is to perform the N _c round of iterations. from

Select a node that has not undergone CI detection in this round of iterations

right

in condition

The CI test is carried out under the

and satisfy

The P value and the degree of independence of the hypothesis test were obtained as (p, I), respectively. In this method, Gaussian process regression (GPR) and distance correlation coefficient (distance correlation, DC) are used to test independence. The specific process is as follows:

分别进行回归分析，并计算其P值，其模型如下式所示：1. Use a Bayesian nonparametric regression model to

Regression analysis was carried out respectively, and its P value was calculated, and its model was as follows:

的残差为：2. Calculated under this model

The residuals are:

和

两者间的独立性可通过

与

来计算，若I＝0则表示两变量是独立的：3. For

and

The independence between the two can be achieved by

and

To calculate, if I=0, it means that the two variables are independent:

的定义分别如下：in

are defined as follows:

where d _u and d _v represent the dimensions of the vectors u and v, respectively.

4. Update

中剔除

的节点，并根据

给

进行降序排序；否则返回执行第三步。The fourth step, if p > α _PC , then from

medium culling

node, and according to

Give

Sort in descending order; otherwise, return to the third step.

则节点

的因果关系重构完成；否则令N_c＝N_c+1，并返回执行第三步进行新一轮迭代。The fifth step, if

then the node

The reconstruction of the causal relationship is completed; otherwise, let N _c =N _c +1, and return to the third step for a new round of iteration.

The sixth step is to judge whether the causal relationship of all nodes has been reconstructed, and if so, execute the seventh step; otherwise, return to the second step.

)示意图如附图3所示，其中黑色实线表示对于

实际存在因果关系的连边，灰色实线表示对于

实际不存在因果关系的连边，不同深度颜色的点分别表示不同迭代轮数中被剔除的点，颜色越深表示越晚被剔除，而黑色的点表示最终保留下来的点。可以看到被倒三角符号标识的点并不是实际与

存在因果关系的点，因此需要通过MCI对其进行识别与剔除。针对任意一个节点

的连边甄别具体过程如下：The seventh step is to perform MCI test on the reconstructed causal network. The reconstructed network part (for nodes

) schematic diagram as shown in Figure 3, wherein the black solid line represents for

There is actually a causal connection, and the gray solid line indicates that for

There is actually no causal connection. Points with different depth colors represent points that are removed in different iteration rounds. The darker the color, the later the points are removed, and the black points represent the points that are finally retained. It can be seen that the point identified by the inverted triangle symbol is not actually related to the

There is a causal relationship, so it needs to be identified and eliminated by MCI. for any node

The specific process of edge screening is as follows:

计算

1. For any node

calculate

定义

为

的前p_X个节点构成的集合；2. Select any node

definition

for

The set consisting of the first p _X nodes of ;

在条件

下进行CI检验，其过程同第三步中所述方法；3. Yes

in condition

The CI test is carried out below, and its process is the same as that described in the third step;

4. According to the CI test results, eliminate false connections;

5. Select other nodes and repeat steps 2-4. If all nodes have completed the MCI check, the final PCMCI-reconstructed causal network is obtained.

The entire inventive method can be illustrated by the flowchart of FIG. 4 .

The preferred embodiments of the present invention have been described in detail above. It should be understood that many modifications and changes can be made according to the concept of the present invention by those skilled in the art without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art through logical analysis, reasoning or limited experiments on the basis of the prior art according to the concept of the present invention shall fall within the protection scope determined by the claims.

Claims (6)

1. a cyber-physical system-oriented network reconstruction method, is characterized in that, comprises the steps: According to the collected timing state information of nodes in the network, construct a fully connected timing network diagram; For any node, the nodes that are not related to the node are eliminated; Carry out an iterative process, update the test conditions in each iteration process, and continuously eliminate other nodes independent of the node according to the conditional independence test algorithm; Jump out of the iterative process when the termination condition is met; Evaluate each connected edge according to the transient conditional independence test algorithm, and delete false connections; Among them, the following specific steps are included: (1) _Initialize the parameters of the PC algorithm: set the input state time series X ⁼ (X ¹ , X ² , . number of rounds) N _{c , max} , number of conditional independence tests N _CI and termination condition threshold α _PC ; (2) Arbitrarily select a node

Perform causal reconstruction: pick a node

Initialize, set its parent node

For all other nodes, set it to be the same as any other node

independent test statistic between

Set the initial iteration round number N _c =0; (3) Perform the N- _th round of iteration: from

Select a node that has not undergone CI detection in this round of iterations

right

in condition

The CI test is carried out under the

and satisfy

The P value and independence of the hypothesis test are recorded as (p, I) respectively; (4) If p>α _PC , then from

medium culling

node, and according to

Give

Sort in descending order; otherwise, return to step (3); (5) If

then the node

The reconstruction of the causal relationship is completed; otherwise, let N _c =N _c +1, and return to step (3) for a new round of iteration; (6) Judging whether the causal relationship of all nodes has been reconstructed, if completed, enter step (7); otherwise, return to step (2); (7) MCI test is performed on the reconstructed causal network, and false connections are eliminated. 2. the network reconstruction method for cyber-physical systems as claimed in claim 1, wherein, in step (3), adopt Gaussian process regression and distance correlation coefficient to carry out independence test, and its concrete process is as follows: (3a) Using a Bayesian nonparametric regression model to

Regression analysis was carried out respectively, and its P value was calculated, and its model was as follows:

(3b) Calculated under this model

The residuals are:

(3c) For

and

The independence between the two can be achieved by

and

To calculate, if I=0, it means that the two variables are independent:

in

are defined as follows:

where d _u and d _v represent the dimensions of the vectors u and v, respectively; (3d) Update

3. The cyber-physical system-oriented network reconfiguration method as claimed in claim 2, wherein, in step (7), to any node

The specific process of the edge connection test is as follows: (7a) For any node

calculate

(7b) Select any node

definition

for

The set of the first pX nodes of ; (7c) Yes

in condition

The CI test is carried out below, and its process is the same as that described in the third step; (7d) According to the CI test result, remove the false connection; (7f) Select other nodes and repeat steps (7b) to (7d). If all nodes have completed the MCI check, the final PCMCI-reconstructed causal network is obtained. 4. A cyber-physical system-oriented network reconfiguration system is characterized in that, comprising The timing network diagram building module is used to construct a fully connected timing network diagram according to the collected timing state information of the nodes in the network; The causal network reconstruction module is used to eliminate any node that is not related to the node; iterative process is performed, the test conditions are updated in each iteration process, and the node is continuously eliminated according to the conditional independence test algorithm Other nodes that are independent of each other; jump out of the iterative process when the termination condition is met; The causal network test module is used to evaluate each connection according to the transient conditional independence test algorithm, and delete the false connection; where the timing network diagram building block is set up to perform the following steps: (1) Receive parameter _settings for initializing the PC algorithm: state time series X ⁼ ((X ¹ , X ² , . The number of iteration rounds) N _{c, max} , the number of conditional independence tests N _CI and the termination condition threshold αPC; The causal network reconstruction module is set up to perform the following steps: (2) Arbitrarily select a node

Perform causal reconstruction: pick a node

Initialize, set its parent node

For all other nodes, set it to be the same as any other node

independent test statistic between

Set the initial iteration round number N _c =0; (3) Perform the N- _th round of iteration: from

Select a node that has not undergone CI detection in this round of iterations

right

in condition

The CI test is carried out under the

and satisfy

The P value and independence of the hypothesis test are recorded as (p, I) respectively; (4) If p>α _PC , then from

medium culling

node, and according to

Give

Sort in descending order; otherwise, return to step (3); (5) If

then the node

The reconstruction of the causal relationship is completed; otherwise, let N _c =N _c +1, and return to step (3) for a new round of iteration; (6) Judging whether the causal relationship of all nodes has been reconstructed, if completed, enter step (7); otherwise, return to step (2); The causal network inspection module is set up to perform the following steps: (7) MCI test is performed on the reconstructed causal network, and false connections are eliminated. 5. The cyber-physical system-oriented network reconstruction system as claimed in claim 4, wherein the causal network reconstruction module is set to perform independence test by using Gaussian process regression and distance correlation coefficient when performing step (3). , the specific process is as follows: (3a) Using a Bayesian nonparametric regression model to

Regression analysis was carried out respectively, and its P value was calculated, and its model was as follows:

(3b) Calculated under this model

The residuals are:

(3c) For

and

The independence between the two can be achieved by

and

To calculate, if I=0, it means that the two variables are independent:

in

are defined as follows:

where d _u and d _v represent the dimensions of the vectors u and v, respectively; (3d) Update

6. The cyber-physical system-oriented network reconfiguration system as claimed in claim 5, wherein the causal network checking module is set to when performing step (7), and the specific process of checking the connection of any node is as follows: (7a) For any node

calculate

(7b) Select any node

definition

for

The set of the first pX nodes of ; (7c) Yes

in condition

The CI test is carried out below, and the process is the same as the method in the third step; (7d) According to the CI test result, remove the false connection; (7f) Select other nodes and repeat steps (7b) to (7d). If all nodes have completed the MCI check, the final PCMCI-reconstructed causal network is obtained.

Images