CN109861859B - Multi-Agent system fault detection method based on side inspection comprehensive judgment - Google Patents
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Abstract
The invention discloses a multi-Agent system fault detection method based on edge detection comprehensive judgment. And detecting whether the attribute measurement of the two vertexes related to the edge is normal or not based on the inspection of the edge attribute measurement by utilizing the functional relation between the edge attribute and the attribute of the Agent vertex. And comprehensively judging the fault state of each Agent according to a maximum likelihood principle by utilizing the multi-edge detection result in the network and combining the multi-edge detection result conditional probability calculated based on the single-edge detection false alarm rate and the false alarm rate. The method is characterized in that whether the attribute measurement of each Agent is failed or not is verified by utilizing the cooperative measurement among a plurality of agents, and the failure which is difficult to detect only by the Agent self-measurement can be detected; the maximum likelihood judgment method is more accurate than simple voting; the method can ensure that the faults of any vertex with the number less than the minimum neighbor number of the vertex can be completely detected, so that the selection of the edge attribute measurement topological structure has definite basis.
Description
Technical Field
The invention relates to the technical field of multi-Agent system fault detection, in particular to a method for detecting multi-Agent system attribute measurement faults through comprehensive judgment of multilateral detection.
Background
The multi-Agent system is a unified abstract expression of various distributed systems which complete tasks through group cooperative work, and the concrete objects of the agents are different, so that the multi-Agent system has different examples, such as an unmanned aerial vehicle swarm, a satellite formation system, a robot cluster and other moving body cluster systems, and a wireless sensor network and other distributed detection systems. With the rapid development of technologies such as artificial intelligence, sensors, network communication, device miniaturization and the like, the trend of adopting a large number of micro-agents for cooperative work is already a trend, and various advantages such as performance improvement, reliability increase, adaptability enhancement, cost reduction and the like can be brought.
The measurement of the Agent to the outside or the Agent is the basic condition and the form of the cooperative work of a multi-Agent system. When the measurement of the Agent fails, the performance of group cooperative work is affected. For example, when a sensor of the wireless sensor network fails, the service quality of the system is affected, and when the moving body cluster performs positioning measurement, the system may have catastrophic consequences such as collision and damage. Therefore, the effective detection of the Agent measurement fault in the multi-Agent system is very important to the service quality, the working reliability and the robustness of the system.
Currently, for multi-Agent system fault detection, there is a method in which each Agent detects its own fault individually, and there is also a method in which Agent faults are detected by cooperation among a plurality of agents. In the field of microminiature moving bodies, GNSS (global navigation satellite system) is widely used for measuring the position of the moving body. For GNSS fault detection, current research either detects faults from GNSS positioning mechanisms using standalone measurement, or detects moving body position measurement faults by mutual verification with other measurement means of the standalone itself. In the aspect of multi-Agent cooperation fault detection, some researches detect the positioning fault of the agents by observing external scenes by using the moving body agents, and also some researches detect the position or posture measurement fault of the moving body agents based on relative measurement between the agents. In the field of wireless sensor network fault detection, some researches utilize the self-measurement of a single sensor and the time correlation thereof to detect faults, and also study utilize the spatial correlation of a plurality of sensor measurements to detect faults. The multi-Agent cooperative fault detection method is essentially mutually verified by using the measurement of different agents and the relative or cooperative measurement between the different agents, so that the fault can be only found by the cooperative detection (namely, single-side detection) between a pair of agents, but the fault source cannot be identified. In the process of identifying fault sources by utilizing the synthesis of multi-pair Agent cooperative measurement (namely, by utilizing the multi-edge detection result to comprehensively judge), the current research adopts a simple minority majority vote-obeying method, the quantitative influence of the error probability in single-edge detection on the multi-edge comprehensive judgment is not considered, the influence of a cooperative detection network topological structure on the fault detectability is not considered, and the complete detection on the faults cannot be ensured.
Disclosure of Invention
The invention aims to solve the technical problem that the prior art is not enough, and provides a multi-Agent system fault detection method based on side detection comprehensive judgment.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a multi-Agent system fault detection method based on side inspection comprehensive judgment comprises the following steps:
1) setting a topological structure of the side inspection network;
2) setting an initial value of a fault state;
3) performing single-side test on each side of the test chart G ═ V, E to obtain each side test state function value C (E)k) (ii) a Judging whether each side is normal or not; judging the top point of the normal edge in the inspection graph as normal; for the fault edge in the verification graph, i.e. all satisfy C (e)k) Edge e of 0k＝(vi，vj) If S (v)i) 1 and S (v)j) When the result is-1, let S (v)j) 0; if S (v)i) 1 and S (v)j) When 1, let S (v)i)＝0；S(vi) Is a vertex viThree value fault ofA state function; k is 1,2, …, m; 1,2, …, n; j is 1,2, …, n; v is the set of vertices in the verification graph G; e is the set of edges in the inspection graph G; v. ofiAnd vjAre two different vertices in the set of vertices of the verification graph.
After the step 3), also carrying out cluster subgraph G on the inconsistent vertexesc＝(Vc，Ec) In all vertices, where GcA connected subgraph of the inspection graph G; vcIn order to have a set of non-uniform vertices,
Ecin order to be a set of non-uniform edges,
the judgment process comprises the following steps:
4) to VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (A) and (B) are calculated according to the following formula respectivelycTotal conditional probability of occurrence of test results for all consistent normal edges associated with all vertices in the set
Wherein,
note the book
To check inconsistent vertices; omega is inconsistent vertex cluster subgraph GcThe number of the middle vertexes;
representing the conditional probability of the occurrence of the inspection results of all consistent normal edges associated with a single vertex; n isrFor checking the set V of the vertices in the graph GcThe r-th vertex in (1)
The number of the relevant normal edges which are checked to be consistent; pfaFalse alarm rate for single-side inspection; pmaThe alarm rate is the rate of missing alarm of unilateral examination;
5) to VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (A) and (B) are calculated according to the following formula respectivelycTotal conditional probability of occurrence of all consistent fail edges associated with all vertices in the set
arFor checking the set V of the vertices in the graph GcThe r-th vertex in (1)
The number of relevant fault edges which are checked to be consistent;
6) to VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (A) are calculated according to the following formulacTotal conditional probability of all edges in the test result
Wherein,
|Eci denotes EcThe total number of the middle edges is,
respectively represent inconsistent edges ek∈EcThe two vertices of (a) are,
representing the conditional probability of the occurrence of a single inconsistent edge inspection result;
7) to VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (A) and (B) are calculated according to the following formula respectivelycAre associated with clusters of inconsistent verticesTotal conditional probability P of occurrence of test results for all edges:
P(S1，S2，…，Sω)＝PN(S1，S2，…，Sω)·PA(S1，S2，…，Sω)·PF(S1，S2，…，Sω)；
8) to VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (a) and (b) find the maximum value of the conditional probability function of the test result:
taking the conditional probability P (S)1，S2，…，Sω) The value of each vertex fault state variable corresponding to the maximum value is the final judgment of the fault state of the inconsistent vertex cluster;
9) and repeating the steps 4) to 8) for other inconsistent vertex clusters in the inspection graph G until all inconsistent vertex clusters in the inspection graph G are judged again.
In step 1), the topological structure satisfies the following conditions: for a network with n vertices, when the expected maximum number of failed vertices is nfaultDesigning a side check network to make the number of neighbors of each vertex not less than nfault+1；nfault≤n-2。
The specific implementation process of the step 2) comprises the following steps: for all the vertexes viThe fault state is initially taken to be S (v)i) -1, indicating an unidentified state; for all edges ekArbitrarily set C (e)k) The initial value of (c).
And 2) respectively carrying out single-side detection on each side in the detection graph by adopting a hypothesis detection method.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a multi-Agent system fault detection method based on side inspection comprehensive judgment, which takes agents as network vertexes, takes the cooperative measurement relation among the agents as sides, and provides a method frame for detecting and identifying network vertex attribute measurement faults through side attribute inspection; the conditional probability of the multi-edge test result can be calculated based on the edge test error probability and the network graph topological structure, and the maximum likelihood judgment of the peak fault state can be made, so that the network peak fault state can be judged more scientifically than simple voting; the method can ensure the complete detectability of simultaneous faults of any vertex which is not more than a given number of vertices from the network topology structure.
Drawings
FIG. 1 is an exemplary diagram of inconsistent vertex clusters in an inspection diagram;
FIG. 2 is a schematic diagram of the edge inspection network and 6 Agent distribution therein.
Detailed Description
Consider the problem of fault detection for multiple Agent dynamic attribute measurements. And (3) measuring certain dynamic attribute of each Agent in real time, wherein the measurement is possible to have a fault. If for any two agents there is a variable that is functional and measurable to their property to be measured, this variable can be used to mutually verify whether the property measurements of the two agents are normal. The invention relates to a network which is formed by taking the agents in a multi-Agent system as vertexes and taking the cooperative measurement relationship between the two agents as edges.
The verification graph can be represented by an undirected graph G ═ V, E. Where V is a set of vertices, V ═ V1，v2，…，vn}，vi(i is 1,2, …, n) is the ith vertex of G, and n is the number of vertices; e is an edge set, E ═ E1，e2，…，emM is the number of edges in E, Ek(k ═ 1,2, …, m) is the kth side of G, ekCan be represented by its two vertices as ek＝(vi，vj) Wherein v isiAnd vjAre two different vertices in V.
Defining vertex-to-l-dimensional real number space R in inspection chartlA mapping p (v) representing a certain property to be detected of the vertex, such as a coordinate position; defining an edge e in a graphk＝(vi，vj) Mapping f (e) to real space Rk) The attribute value to be detected representing an edge, which has a functional relationship with the attribute to be detected of the two vertices of the edge, f (e)k)＝f(vi，vj)＝f(p(vi)，p(vj) For example, when an edge attribute is the distance between its two vertices, there is f (v)i，vj)＝||p(vi)-p(vj) L. Measure the vertex attributes as
Wherein epsiloniAnd εjTo measure random errors. The edge attribute value calculated from the vertex attribute measurements is noted as
Edge property measurements are noted
Where η is the edge property measurement random error. Judging whether the single side is normal by adopting a certain existing hypothesis test method, namely, calculating the edge attribute value obtained by the vertex attribute measured value
And edge property measurements
Whether they are consistent (k is 1,2, …, m) is called single-edge test in the present invention. And the false alarm rate of the known unilateral test is PfaLeak alarm rate is Pma。
The invention aims to solve the technical problem that the false alarm rate P of the given unilateral testfaSum and miss alarm rate PmaUnder the condition (2), the vertices v in the inspection chart are comprehensively judged by the result of the multilateral inspectioni(i-1, 2, …, n) property measurement
Whether it is faulty.
The technical scheme of the invention is that the multi-Agent system fault detection method based on side inspection comprehensive judgment provided by the invention comprehensively judges whether each network vertex, namely Agent has a fault or not based on a maximum likelihood principle by utilizing each single-side inspection result and single-side inspection false alarm rate and missing alarm rate information in a side inspection network. Specifically, the method comprises the following steps:
(1) the topology of the edge checking network is set. To ensure complete detectability of all failed vertices of the network, for a network with n vertices, when the maximum number of failed vertices is expected to be nfault(nfaultN-2) or less, designing the side check network to make the neighbor number of each vertex not less than nfault+1, it can ensure that the number of the fault vertices is not more than nfaultCan be fully detected.
(2) And (6) fault detection initialization.
Defining a binary one-sided test state function C (e)k) ( k 1,2, …, m), if side ekIs checked as normal, then C (e)k) 1, otherwise C (e)k) 0. Let ek＝(vi，vj) For convenience, C (e) will be mentionedk) Equivalently denoted as C (v)i，vj) Or simply CijAnd C (e)k)＝C(vi，vj)＝Cij＝C(vj，vi)＝Cji。
Defining a three-valued fault state function S (v) for a vertexi) (i is 1,2, …, n), if the vertex v is determinediIs normal, then S (v)i) 1 is ═ 1; if the vertex v is determinediIs failure, then S (v)i) 0; if the vertex v isiIf the fault is unknown, let S (v)i)＝-1。
At the beginning of the algorithm, all the vertexes v are processedi(i is 1,2, …, n), and the failure state is initially S (v)i) The expression "1" indicates an unidentified state. For all edges ek(k is 1,2, …, m), and C (e) can be arbitrarily setk) The initial value of (c).
(3) Each side in the network checks independently. Adopting the existing hypothesis testing method to testPerforming single-side inspection on each side in the graph respectively, judging whether each side is normal or not, and obtaining a function value C (e) of inspection state of each sidek)(k＝1，2，…，m)。
(4) And judging the state of the vertex of the normal edge. And judging the vertexes of all normal edges in the inspection graph as normal. I.e. find all C (e) in the verification mapk) Edge of 1 for ek＝(vi，vj) Let S (v)i)＝S(vj)＝1。
(5) And judging the state of the vertex of the fault edge. For each fault edge in the inspection graph, namely all C (e) is satisfiedk) Edge e of 0k＝(vi，vj) If S (v)i) 1 and S (v)j) When the result is-1, let S (v)j) 0; if S (v)i) 1 and S (v)j) When 1, let S (v)i)＝0。
(6) And (5) correcting inconsistent judgment of the vertex and the edge.
Due to the fact that false alarm and missed alarm exist in single-side detection, whether a certain vertex has faults or not can be judged according to different detection sides to be inconsistent. If the inspection result of a certain edge in the inspection graph is a fault and the two related vertexes are judged to be normal, the edge is called as an edge for inspecting inconsistency, and is called as an inconsistent edge for short, and the two related vertexes are called as vertexes for inspecting inconsistency, and are called as inconsistent vertexes for short. In the algorithm, the correction of the inconsistent judgment of the top point and the edge is the reintegrated judgment of the top point fault state associated with the inconsistent edge.
For a plurality of test inconsistent vertexes which are communicated by inconsistent edges in the test graph, the test inconsistent vertexes are referred to as forming an inconsistent vertex cluster. Fig. 1 shows an example of an inconsistent vertex cluster, in which circles represent vertices, lines between the circles represent edges, numbers in the circles are used for judging the current failure state of the vertices, and numbers marked by the edges beside each edge represent the edge inspection result. V in FIG. 1i、vjAnd vkThree vertices are connected by two non-uniform edges, and vi、vjAnd vkThere are no inconsistent edges with other vertices in the inspection map, so vi、vjAnd vkForm aClusters of inconsistent vertices. Note that the neutral of the drawing is vi、vjAnd vkOther vertices adjacent to v are possiblei、vjAnd vkTwo or three of which are simultaneously adjacent, a relationship is not shown in the figure because it does not affect the method and results.
For a certain inconsistent vertex cluster in the verification graph G ═ V, E), all vertex sets are recorded as
And is
To check for inconsistent vertices. The set of all the inconsistent edges between the vertexes of the inconsistent vertex cluster is recorded as EcAnd satisfies the following conditions:
to pair
ekFor testing non-uniform edges, and having vi∈Vc，vj∈Vc(ii) a To pair
If it is
To check for inconsistent edges, it is necessary to have V ∈ VcAnd
thus, set V of inconsistent verticescAnd inconsistent edge set EcA connected subgraph G constituting the test graph Gc＝(Vc，Ec) Called the inconsistent vertex cluster subgraph. For set of vertices VcThe r-th vertex in (1)
Suppose that a is associated with it in the verification graph GrPersonal examinationCheck a consistent fault edge with nrNormal edge with check consistency, and number of edge with check inconsistency w associated therewithrIs equal to it is in GcNumber of neighbors in
The failure state of all failed vertices in a cluster of inconsistent vertices in the verification graph must be re-determined in their entirety. Clustering subgraph G for inconsistent verticescThe specific steps for re-judging the fault states of all the vertexes are as follows:
(6.1) for VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (A) and (B) are calculated according to the following formula respectivelycTotal conditional probability P of occurrence of test results for all consistent normal edges associated with all vertices in the setN：
Wherein
Representing the conditional probability of the occurrence of the test result for all consistent normal edges associated with a single vertex.
(6.2) for VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (A) and (B) are calculated according to the following formula respectivelycTotal conditional probability P of occurrence of the inspection results of all consistent fault edges associated with all vertices in the setA：
(6.3) for VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (A) are calculated according to the following formulacAll ofTotal conditional probability P of edge inspection result occurrenceF：
Wherein | EcI denotes EcThe total number of the middle edges is,
respectively represent inconsistent edges ek∈EcThe two vertices of (a) are,
representing the conditional probability of the occurrence of a single inconsistent edge check result.
(6.4) for VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (A) and (B) are calculated according to the following formula respectivelycThe total conditional probability P of the test results of all edges associated with the cluster of inconsistent vertices:
P(S1，S2，…，Sω)＝PN(S1，S2，…，Sω)·PA(S1，S2，…，Sω)·PF(S1，S2，…，Sω) (4)
(6.5) for VcFault state variable S of each vertex1，S2，…，SωAll the different value combinations of (a) and (b) find the maximum value of the conditional probability function of the test result:
then the conditional probability P (S) is taken according to the maximum likelihood principle1，S2，…，Sω) The value of each vertex fault state variable corresponding to the maximum value is the final judgment of the fault state of the inconsistent vertex cluster.
And (6.6) repeating the re-determination processes from (6.1) to (6.5) on other inconsistent vertex clusters in the inspection graph G until all inconsistent vertex clusters in the inspection graph G are re-determined.
The method steps of the invention end here.
The fault detection effect of the method is verified by using a multi-Agent system to locate the fault detection problem.
Taking six Agent networks distributed in a regular hexagon as an example, the side length of the regular hexagon in which each Agent is distributed is 1000m, as shown in fig. 2. In order to detect the self position measurement fault of each Agent, a mutual distance measurement method among the agents is adopted, and the fault state of the agents in the network is determined based on distance measurement side detection and comprehensive judgment. The self position measurement of each Agent is designed to adopt a satellite navigation positioning system, the distance measurement between each Agent can adopt the modes of laser ranging, radio ranging and the like, and the ranging precision is much higher than that of the position measurement, so that the ranging error is ignored. And verifying the network vertex fault detection algorithm based on edge inspection through Monte Carlo simulation. Evaluating algorithm performance by statistical failure Detection accuracy CDR (correct Detection rate), wherein CDR is NC/NSIn which N isCRepresenting the number of simulations that can correctly determine the fault status of all vertices, NSRepresenting the total number of monte carlo simulations. Each simulation was based on a random sampling of each Agent's position measurements for fault detection. The failure mode is mean value failure, the mean value deviation delta is respectively different given values, and the direction of the mean value deviation vector is sampled according to random uniform distribution. Setting the standard deviation of the normal position measurement error of each Agent as sigma0The single-side detection method adopts the existing single-side distance detection method based on non-central chi-square distribution, the confidence coefficient of the single-side detection is alpha is 0.02, and the single-side false alarm rate is PfaThe single-edge leak alarm rate of this distance test method has been obtained by simulation and is shown in table 1, where d represents the actual distance between agents.
TABLE 1 unilateral leak detection alarm Rate statistics
The method is characterized in that three faults including that No. 6 Agent has faults, No. 4 Agent and No. 6 Agent have faults simultaneously, and No. 2 Agent, No. 4 Agent and No. 6 Agent have faults simultaneously are set, and Monte Carlo simulation results are listed in a table 2. The number of Monte Carlo simulations per computational example was 10000.
TABLE 2 Fault detection accuracy of each fault scenario
According to the results in table 2, it can be seen that the fault determination method of the present invention can achieve a high fault detection accuracy when the single-side detection leak alarm rate is low. The invention provides the comprehensive correction based on the maximum likelihood principle for testing inconsistency, which has obvious improvement effect on the algorithm detection accuracy, and the accuracy improvement brought by the correction is more obvious when the unilateral leakage alarm rate is higher. This is because the higher the single-sided leak alarm rate, the higher the probability of the occurrence of a case where the multilateral test is inconsistent.
Claims (4)
1. A multi-Agent system fault detection method based on side inspection comprehensive judgment is characterized by comprising the following steps:
1) setting a topological structure of the side inspection network;
2) setting an initial value of a fault state;
3) performing single-side test on each side of the test chart G ═ V, E to obtain each side test state function value C (E)k) (ii) a Judging whether each side is normal or not; judging the top point of the normal edge in the inspection graph as normal; for the fault edge in the verification graph, i.e. all satisfy C (e)k) Edge e of 0k＝(vi,vj) If S (v)i) 1 and S (v)j) When the result is-1, let S (v)j) 0; if S (v)i) 1 and S (v)j) When 1, let S (v)i)＝0；S(vi) Is a vertex viA three-valued fault status function of; k is 1,2, …, m; 1,2, …, n; j is 1,2, …, n; v is the vertex in the inspection chart GA set of (a); e is the set of edges in the inspection graph G; v. ofiAnd vjIs two different vertices in the set of vertices of the verification graph;
after the step 3), also carrying out cluster subgraph G on the inconsistent vertexesc＝(Vc,Ec) In all vertices, where GcA connected subgraph of the inspection graph G; vcIn order to have a set of non-uniform vertices,
Ecin order to be a set of non-uniform edges,
the judgment process comprises the following steps:
4) to VcFault state variable S of each vertex1,S2,…,SωAll the different value combinations of (A) and (B) are calculated according to the following formula respectivelycTotal conditional probability P of occurrence of test results for all consistent normal edges associated with all vertices in the setN：
Wherein,
note the book
To check inconsistent vertices; omega is inconsistent vertex cluster subgraph GcThe number of the middle vertexes;
representing the conditional probability of the occurrence of the inspection results of all consistent normal edges associated with a single vertex; n isrFor checking the set V of the vertices in the graph GcThe r-th vertex in (1)
Verification of associationsThe number of the consistent normal edges; pfaFalse alarm rate for single-side inspection; pmaThe alarm rate is the rate of missing alarm of unilateral examination;
5) to VcFault state variable S of each vertex1,S2,…,SωAll the different value combinations of (A) and (B) are calculated according to the following formula respectivelycTotal conditional probability P of occurrence of the inspection results of all consistent fault edges associated with all vertices in the setA：
arFor checking the set V of the vertices in the graph GcThe r-th vertex in (1)
The number of relevant fault edges which are checked to be consistent;
6) to VcFault state variable S of each vertex1,S2,…,SωAll the different value combinations of (A) are calculated according to the following formulacTotal conditional probability P of all edges in the test resultF：
Wherein,
|Eci denotes EcThe total number of the middle edges is,
respectively represent inconsistent edges ek∈EcThe two vertices of (a) are,
representing the conditional probability of the occurrence of a single inconsistent edge inspection result;
7) to VcFault state variable S of each vertex1,S2,…,SωAll the different value combinations of (1) are pressed down respectivelyFormula calculation in inspection chart G and GcThe total conditional probability P of the test results of all edges associated with the cluster of inconsistent vertices:
P(S1,S2,…,Sω)＝PN(S1,S2,…,Sω)·PA(S1,S2,…,Sω)·PF(S1,S2,…,Sω)；
8) to VcFault state variable S of each vertex1,S2,…,SωAll the different value combinations of (a) and (b) find the maximum value of the conditional probability function of the test result:
taking the conditional probability P (S)1,S2,…,Sω) The value of each vertex fault state variable corresponding to the maximum value is the final judgment of the fault state of the inconsistent vertex cluster;
9) and repeating the steps 4) to 8) for other inconsistent vertex clusters in the inspection graph G until all inconsistent vertex clusters in the inspection graph G are judged again.
2. The multi-Agent system fault detection method based on edge inspection comprehensive judgment according to claim 1, wherein in the step 1), the topological structure meets the following conditions: for a network with n vertices, when the expected maximum number of failed vertices is nfaultDesigning a side check network to make the number of neighbors of each vertex not less than nfault+1；nfault≤n-2。
3. The multi-Agent system fault detection method based on edge inspection comprehensive judgment according to claim 1, wherein the specific implementation process of the step 2) comprises the following steps: for all the vertexes viThe fault state is initially taken to be S (v)i) -1, indicating an unidentified state; for all edges ekArbitrarily set C (e)k) The initial value of (c).
4. The method for detecting the faults of the multi-Agent system based on the edge inspection comprehensive judgment according to claim 1, wherein in the step 2), a hypothesis testing method is adopted to respectively carry out single-edge inspection on each edge in the inspection chart.
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