System performance analysis and evaluation method based on fuzzy function dependence network

Abstract

The invention discloses a system performance analysis and evaluation method based on a fuzzy function dependence network, and the method comprises the following steps: constructing a performance evaluation model based on the fuzzy function dependence network through the analysis of an equipment system, and the fuzzy dependency strength and the fuzzy dependency criticality of the dependency relationship of each pair of nodes and the autonomous efficiency value of each node are specified, and the output efficiency value of the nodes is calculated through hierarchical step-by-step recursion, so that the comprehensive evaluation of the behavior efficiency of the system is realized. According to the method, attribute parameters are processed through the triangular fuzzy number and the fuzzy logic, and the defect that values are too subjective and absolute when two parameters of dependency intensity and dependency criticality of the node dependency relationship are determined during system performance analysis and evaluation based on a traditional function dependency network is overcome. The fuzziness of manually set parameters is effectively reflected, the scientific reliability and accuracy of analysis are improved, and the system efficiency analysis and evaluation work can be scientifically, reasonably and comprehensively implemented.

Description

Technical Field

[0001] The present invention relates to the field of analysis and evaluation of equipment systems, and more particularly, to a method for analyzing and evaluating system effectiveness based on a fuzzy functional dependency network. Background Art

[0002] In order to achieve a certain goal, a combination of some independent and collaborative systems, which further manifests as a higher-level system organized together, is called a "system-of-systems (SoS)". Accurately evaluating the effectiveness of a system is an important prerequisite for improving the system structure and optimizing the action control of the system. However, the traditional effectiveness evaluation methods for single systems cannot meet the requirements, and there is an urgent need to conduct new effectiveness evaluation research based on the characteristics of the system.

[0003] The Functional Dependency Network Analysis (FDNA) method can describe the dependency relationships among the components of a system and establish a stage-linear effectiveness aggregation model. This not only limits the computational complexity of the model within an acceptable range but also represents the dependency relationships among the elements. Therefore, in the field of system simulation and evaluation, the FDNA method can quickly evaluate the system effectiveness during the system demonstration stage when the detailed information of the equipment system is not fully determined. The FDNA method introduces two key attribute parameters, the Strength Of Dependency and the Criticality Of Dependency, when studying the dependency relationships in complex systems. However, these parameters have strong subjective fuzziness, and the artificial subjective assignment method is often used to obtain their values in applications, which may lead to the scientific reliability of the parameter values being affected by subjective factors, thus potentially affecting the accuracy and credibility of the analysis.

[0004] In the existing research on the system effectiveness evaluation based on the functional dependency network analysis method, the general process is to establish a functional dependency network model, manually determine the input parameters of nodes and dependency relationships, and then calculate the output effectiveness of each node. However, the existing methods have not improved and studied the value-taking methods and strategies for the two parameters of dependency strength and dependency criticality. A method for evaluating effectiveness based on a dependency relationship network (CN115952658A) proposes a method for evaluating system effectiveness based on the internal node connection relationship of the system. However, regarding the parameters of dependency strength and dependency criticality in the calculation process, it requires experts to directly give a certain definite value, which is contrary to the fuzzy and hesitant cognitive results of the evaluation task. A method for evaluating networked system effectiveness (CN117544542A) proposes a method for evaluating system effectiveness based on various internal node connection relationships. However, the main improvement lies in the splitting of connection relationships and the modeling optimization of node effectiveness itself, and it does not solve the problem of overly strong subjectivity in the value-taking of the parameters of dependency strength and dependency criticality in the functional dependency network analysis method. Summary of the Invention

[0005] Aiming at the problem that the value-taking of the key parameters - the dependency strength SOD and dependency criticality COD of the dependency relationship - in the existing functional dependency network system effectiveness evaluation and analysis method is too subjective and absolute, the present invention provides a method for analyzing and evaluating system effectiveness based on a fuzzy functional dependency network, which processes attribute parameters through triangular fuzzy numbers and fuzzy logic, avoids strict dependence on a single value, and thus improves the scientific reliability and accuracy of the analysis.

[0006] The present invention is achieved at least by one of the following technical solutions.

[0007] A method for analyzing and evaluating system effectiveness based on a fuzzy functional dependency network includes the following steps:

[0008] S1. Construct a fuzzy functional dependency network model according to the functional dependency relationship between units in the equipment system;

[0009] S2. Set the fuzzy dependency strength and fuzzy dependency criticality values of each pair of node dependency relationships by using the expert subjective evaluation method;

[0010] S3. Analyze the effectiveness of nodes in the equipment system and set the autonomous effectiveness value of each node;

[0011] S4. Calculate the output effectiveness value of each node, including two cases:

[0012] First, for nodes without dependency relationships, the output effectiveness value is equal to the autonomous effectiveness value of the node;

[0013] Second, for nodes depending on n preceding nodes, where n is the total number of preceding nodes and is a non-zero positive integer,

[0014] is the nth pre-node, and the output efficiency value corresponding to the pre-node all determined post-nodes,

[0015] is the nth output efficiency value corresponding to the pre-node, and calculating the output efficiency value of the post-node includes the following steps:

[0016] (1) Calculate and update the post-node N succ and each pre-node the fuzzy dependence strength value of the dependence relationship between them;

[0017] (2) Calculate the total fuzzy dependence strength of the post-node N succ itself;

[0018] (3) Calculate and update the fuzzy dependence criticality of the dependence relationship between the post-node N succ and each pre-node take the minimum value of the fuzzy dependence criticality of all the dependence relationships existing with the post-node N succ as the fuzzy dependence criticality value of this post-node N succ ;

[0019] (4) Calculate the fuzzy output efficiency of the post-node through the total fuzzy dependence strength and the total fuzzy dependence criticality of the post-node;

[0020] (5) Defuzzify the fuzzy output efficiency of the post-node to obtain the exact value of the output efficiency value, which is the output efficiency value of the post-node;

[0021] Repeat the above steps (1) to (5) until the output efficiency of all nodes is calculated in the entire fuzzy functional dependence network, and use the final result to further evaluate the system working ability and system efficiency.

[0022] Furthermore, in step S1, the fuzzy functional dependence network model includes:

[0023] ① Nodes representing equipment units, where each node has two evaluation indicators: autonomous efficiency and output efficiency;

[0024] ② Directed edges representing the dependence relationship between equipment units point from pre-nodes to post-nodes, and each directed edge has two evaluation indicators: fuzzy dependence strength and fuzzy dependence criticality.

[0025] Furthermore, in step S2, the fuzzy dependence strength is the influence strength of the output efficiency of the pre-node on the output efficiency of the post-node. The larger the value, the greater the influence strength, and the value result is a triangular fuzzy number

[0026]

[0027] Among them l α Represents the minimum value of the dependence strength, m α represents the most likely value of the dependence strength, h α Represents the highest value of the dependence strength, and the value range satisfies 0≤l α ≤m a ≤h α ≤1;

[0028] The fuzzy dependency criticality is the upper limit of the output efficiency of the subsequent node when the previous node is completely disabled. The higher the value, the higher the dependency criticality. The value result is a triangular fuzzy number.

[0029]

[0030] Among them l β Represents the minimum value of dependency criticality, m β represents the most likely value of the dependency criticality, r β Represents the highest value of the dependency criticality, and the value range satisfies 0≤l β ≤m β ≤h β ≤100.

[0031] Furthermore, in step (1), for the dependency relationship between the post-node and each pre-node, the weighted average of the post-node autonomous efficiency and the pre-node output efficiency is calculated through the multiplication and addition rules of triangular fuzzy mathematics and the set initial fuzzy dependency strength as the weight, and the calculation result is used as the updated fuzzy dependency strength value of the dependency relationship between the post-node and each pre-node.

[0032] Furthermore, the subsequent node N succ Autonomous Efficacy and Front-End Nodes The calculation expression of the weighted average of output efficiency is:

[0033]

[0034] in Represents the previous node The output performance, Represents the subsequent node N succ and the preceding node The initial fuzzy dependency strength set by the inter-dependency relationship, SE succ Represents the subsequent node N succ The autonomous efficacy value set, The calculation result will be used as the post-node N succAnd the pre - node The updated fuzzy dependence intensity value of the dependence relationship;

[0035] Real number And triangular fuzzy number The product of them is still a triangular fuzzy number. The specific calculation formulas for the lowest value, the most likely value and the highest value are:

[0036]

[0037] Where l α , m α , h α Represent the lowest value, the most likely value and the highest value of the triangular fuzzy number respectively;

[0038] Triangular fuzzy number And the self - efficacy value SE succ Set by the post - node N succ The addition of Is still a triangular fuzzy number. The specific calculation formula is:

[0039]

[0040] Where l α , m α , h α Represent the lowest value, the most likely value and the highest value of the triangular fuzzy number respectively.

[0041] Furthermore, in step (2), for the post - node N succ And all pre - nodes The fuzzy dependence intensity Of the dependence relationship is averaged to obtain the total fuzzy dependence intensity sicc Of the post - node N itself The specific formula is:

[0042]

[0043] Where n represents the number of pre - nodes.

[0044] The above process is realized by the addition rule of triangular fuzzy numbers and the multiplication rule of triangular fuzzy numbers and real numbers.

[0045] Furthermore, for the post - node N succ And all pre - nodes The sum of the fuzzy dependence intensities of the dependence relationship Is still a triangular fuzzy number. The specific calculation is realized by the following steps:

[0046] First, define the operation rule for adding triangular fuzzy numbers: Let the minimum value, the most likely value, and the maximum value of the first triangular fuzzy number be \(l_1\), \(m_1\), and \(h_1\) respectively, and the minimum value, the most likely value, and the maximum value of the second triangular fuzzy number be \(l_2\), \(m_2\), and \(h_2\) respectively. Then the result of adding the two numbers is still a triangular fuzzy number, and its value is

[0047] \(<l_1,m_1,h_1> + <l_2,m_2,h_2> = <\min(l_1 + m_2, l_2 + m_1), m_1 + m_2, \min(m_1 + h_2, m_2 + h_1)>\)

[0048] That is, for the added triangular fuzzy number, the minimum value is \(\min(l_1 + m_2, l_2 + m_1)\), the most likely value is \(m_1 + m_2\), and the maximum value is \(\min(m_1 + h_2, m_2 + h_1)\);

[0049] Calculate the initial sum Specifically, let the triangular fuzzy number be denoted as and the triangular fuzzy number be denoted as

[0050]

[0051] The initial sum \(S_2\) represents the result of adding the first 2 triangular fuzzy numbers in , and it is also a triangular fuzzy number; and represent the minimum value, the most likely value, and the maximum value of the triangular fuzzy number respectively; and represent the minimum value, the most likely value, and the maximum value of the triangular fuzzy number respectively;

[0052] Let the sum of the first \(k\) numbers in in step (2) be denoted as \(S\) k , that is

[0053]

[0054] Then for \(k = 3, 4, \cdots, n\), calculate the values of \(S_3\), \(S_4\), \(\cdots\), \(S\) n one by one through an iterative method, that is, \(S\) k = \(S\) k-1 + where the calculation of each step follows the operation rule defined for adding triangular fuzzy numbers. Specifically, let the value of \(S\) k-1 calculated in the previous iteration be denoted as \(\lt l\) k-1 , \(m\)k-1 ,h k-1 >, The value of but

[0055]

[0056] Where l k-1 、m k-1 and h k-1 Denote the triangular fuzzy number S k-1 the minimum, most likely and maximum values ​​of ; and They represent triangular fuzzy numbers the minimum, most likely and maximum values ​​of ;

[0057] Finally, the iteration reaches the situation where k=n is calculated, and the calculation result is The sum of

[0058] Furthermore, in step (3), the total fuzzy dependency criticality COD is calculated i When the post-node N succ And each predecessor node Fuzzy dependency criticality of dependency relationship between The specific steps for taking the minimum value are as follows:

[0059] Fuzzy dependency criticality for all dependencies By comparing two by two, we can get the possibility matrix P = (p ij ) n×n , where the matrix element p ij Represents the fuzzy dependency criticality of the i-th dependency and the fuzzy dependency criticality of the j-th dependency The triangular fuzzy number sorting function is used to obtain Possibility

[0060] Calculate the sorting vector λ = (λ1,λ2,…,λ n ) T ,in λ i The bigger, the Fuzzy dependency criticality in all dependencies The larger the ranking in;

[0061] Sort the whole set of fuzzy numbers according to the size of the sorting vector, and take the minimum value as the fuzzy dependency criticality value of the post-node;

[0062] Finally, compare the total fuzzy dependence strength and the fuzzy dependence criticality of the post - node, and take the minimum value as the fuzzy output efficiency of the post - node.

[0063] Further, in step (5), for the fuzzy output efficiency value perform defuzzification to obtain the real - number output efficiency value O i The formula is:

[0064] Let Then

[0065] Where represents the fuzzy output efficiency obtained in step (4), l succ , m succ , h succ respectively represent the minimum value, the most likely value, and the maximum value of, and the output efficiency value represents the ability level of the equipment node in the system. The higher the efficiency value, the stronger the ability of the equipment in the system.

[0066] A computer device of the present invention includes: a memory, a processor, and a computer program stored on the memory. When the computer program is executed on the processor, the method for analyzing and evaluating the system efficiency based on the fuzzy functional dependence network as described above is implemented.

[0067] Compared with the disadvantages and deficiencies of the prior art, the present invention has the following beneficial effects:

[0068] The present invention introduces the processing of attribute parameters through triangular fuzzy numbers and fuzzy logic, and solves the defect that the values of the two parameters of the dependence strength and the dependence criticality for determining the node dependence relationship are too subjective and absolute when analyzing and evaluating the system efficiency based on the traditional functional dependence network. It effectively reflects the fuzziness of the artificially set parameters, improves the scientific reliability and accuracy of the analysis, and can scientifically, reasonably, and comprehensively implement the analysis and evaluation work of the system efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a schematic flow chart of the method for analyzing and evaluating the system efficiency based on the fuzzy functional dependence network of the present invention;

[0070] Figure 2 is a schematic diagram of the functional dependence network model constructed in the embodiment;

[0071] Figure 3 is a schematic diagram of the calculation process of the embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0072] In order to make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0073] As Figure 1 shown, a system effectiveness analysis and evaluation method based on a fuzzy functional dependence network in this embodiment includes the following steps:

[0074] S1. Analyze the equipment system, and construct a fuzzy functional dependence network model according to the dependence relationship between units in the equipment system. For the nodes representing equipment units, and for the equipment units with a functional dependence relationship, add a directed edge between the corresponding nodes, with the directed edge pointing from the dependent node to the dependent node.

[0075] Among them, the nodes representing equipment units, where each node has two evaluation indicators: autonomous effectiveness and output effectiveness; the directed edges representing the dependence relationship between equipment units, pointing from the pre-node to the post-node, and each directed edge has two evaluation indicators: fuzzy dependence strength and fuzzy dependence criticality.

[0076] S2. According to the expert subjective evaluation method, set the values of the fuzzy dependence strength and fuzzy dependence criticality of each pair of node dependence relationships, which specifically includes the following steps:

[0077] S21. According to historical data, expert experience, and actual situations, determine the maximum value h α of the dependence strength of each node dependence relationship, α the most likely value m α and the minimum value l α such that the value range satisfies 0 ≤ l α ≤ m α ≤ h α ≤ 1, and form the fuzzy dependence strength

[0078] of each dependence relationship.

[0079]

[0080] On this basis, assuming that the entire fuzzy functional dependence network model has K node-to-node dependence relationships, the obtained fuzzy dependence strengths are respectively: where is the fuzzy dependence strength of the Kth node-to-node dependence relationship,

[0081] S22. According to historical data, expert experience, and actual situations, determine the maximum value h β of the fuzzy dependence criticality of each node dependence relationship, β the most likely value mand the minimum value l β , the value range satisfies 0≤l β ≤m β ≤h β ≤100, forming the fuzzy dependency criticality of each dependency

[0082] On this basis, there are n inter-node dependencies, and the fuzzy dependency criticalities are:

[0083]

[0084] in is the fuzzy dependency criticality of the nth inter-node dependency relationship, l βn ,m βn ,h βn They are respectively the maximum value, most likely value and minimum value of the fuzzy dependency criticality of the nth node dependency.

[0085] S3. Analyze the performance of nodes in the equipment system and set the autonomous performance value of each node. For example, suppose there are p nodes N1, N2, ..., N p , then we need to analyze N1, N2, …, N p The performance of the equipment system node is obtained by SE p is the autonomous effectiveness value of the pth node.

[0086] S4. Calculate the output efficiency value of each node. The output efficiency value of the node includes the following two cases:

[0087] Case 1: For nodes that do not have a dependent relationship, set their output performance value equal to their autonomous performance value. Specifically, suppose there are p nodes N1, N2, ..., N p There is a node N without any dependencies. m (m∈{1,2,…,p}), then:

[0088] O m =SE m (1);

[0089] Among them, m Representative node N m Output efficiency value, SE m Representative node N m autonomous efficacy value.

[0090] Case 2: For n preceding nodes Dependency, n is a non-zero positive integer and the output performance value corresponding to all predecessor nodes All confirmed post-nodes Nsucc , calculate N through the following steps succ 's output performance value:

[0091] First, calculate and update N through the following formula succ and the fuzzy dependence strength value of the dependence relationship between each predecessor node and the successor node N:

[0092]

[0093] where n is the total number of predecessor nodes, a non-zero positive integer, represents the i-th predecessor node among the n predecessor nodes after update and the fuzzy dependence strength value of the dependence relationship between the successor node N ; succ represents the initial fuzzy dependence strength set for the dependence relationship between N and succ ; represents the output performance value of the predecessor node , SE ; succ represents the autonomous performance value of the successor node N succ .

[0094] In formula (2), is a triangular fuzzy number, and SE succ are real numbers. Therefore, the calculation of involves the multiplication of a triangular fuzzy number and a real number, and the calculation of involves the addition of a triangular fuzzy number and a real number. The specific rules are as follows:

[0095] The product of the real number and the triangular fuzzy number is still a triangular fuzzy number. The specific calculation formulas for the lowest value, the most likely value, and the highest value of the triangular fuzzy number are:

[0096]

[0097] where l α , m α , h α represent the lowest value, the most likely value, and the highest value of the triangular fuzzy number respectively;

[0098] The addition of the triangular fuzzy number and the autonomous performance value SE succ set by the successor node N succ , It is still a triangular fuzzy number, and the specific calculation formula is as follows:

[0099]

[0100] where l α , m α , h α represent the minimum value, the most likely value, and the maximum value of the triangular fuzzy number respectively.

[0101] For the post node N succ , after updating the fuzzy dependence strength of the dependence relationship between N succ and each pre node , the average value is taken as the total fuzzy dependence strength succ of the post node N itself

[0102]

[0103] Here represents the fuzzy dependence strength between the post node N succ calculated by formula (2) and the pre node , and n represents the number of pre nodes.

[0104] Among them, for the total fuzzy dependence strength succ of the dependence relationship between the post node N and all pre nodes is still a triangular fuzzy number, and the specific calculation is implemented by the following steps: First, define the operation rule for adding a triangular fuzzy number to a triangular fuzzy number: Let the minimum value, the most likely value, and the maximum value of the first triangular fuzzy number be l1, m1, and h1 respectively, and the minimum value, the most likely value, and the maximum value of the second triangular fuzzy number be l2, m2, and h2 respectively. Then, the result of adding the two numbers is still a triangular fuzzy number, and the value is

[0105] <l1,m1,h1>+<l2,m2,h2> = <min(l1 + m2, l2 + m1), m1 + m2, min(m1 + h2, m2 + h1)>

[0106] That is, for the added triangular fuzzy number, the minimum value is min(l1 + m2, l2 + m1), the most likely value is m1 + m2, and the maximum value is min(m1 + h2, m2 + h1);

[0107] Then, calculate the initial sum according to the above definition Specifically, let the value of the triangular fuzzy number be denoted as and the value of be denoted as

[0108]

[0109] Here, the initial value and S2 represent the result after adding the first two triangular fuzzy numbers in step (2), which is also a triangular fuzzy number; and and represent the minimum value, the most likely value, and the maximum value of the triangular fuzzy number respectively; and represent the minimum value, the most likely value, and the maximum value of the triangular fuzzy number respectively;

[0110] Subsequently, let the sum of the first k numbers in step (2) be denoted as S k , that is

[0111]

[0112] Then for k = 3, 4,..., n, the values of S3, S4,..., S n are calculated one by one through an iterative method, that is where the calculation of each step follows the operation rule definition for adding triangular fuzzy numbers. Specifically, assume that the value of S k-1 calculated in the previous iteration is denoted as <l k-1 , m k-1 , h k-1 >, and the value of is denoted as

[0113]

[0114] where l k-1 , m k-1 , and h k-1 represent the minimum value, the most likely value, and the maximum value of the triangular fuzzy number S k-1 respectively; and represent the minimum value, the most likely value, and the maximum value of the triangular fuzzy number respectively;

[0115] Finally, when iterating to the case of k = n, the calculation result is the sum of which is

[0116] As an example, for those that meet the requirements of Case 2 and are dependent on one or more preceding nodes and the output efficiency value corresponding to the preceding node All determined post - nodes N succ , calculate and update N by the following formula succ and each pre - node the fuzzy - dependence criticality of the dependence relationship between

[0117]

[0118] where represents, after update, the i - th pre - node among n pre - nodes and the post - node N the fuzzy - dependence criticality of the dependence relationship between succ ; represents N succ and the initial fuzzy - dependence criticality of the dependence relationship set at step S2; represents the output efficiency value of the pre - node .

[0119] For all the fuzzy - dependence criticalities of the dependence relationships stored with the post - node N succ , take the minimum value as the fuzzy - dependence criticality of this post - node N succ : The value of:

[0120]

[0121] Here represents the fuzzy - dependence criticality of the dependence relationship between the post - node N succ calculated by formula (7) and the pre - node

[0122] , n represents the number of pre - nodes of the post - node N succ .

[0123] For the calculation of the minimum value of multiple fuzzy - dependence criticality values , it includes the following steps:

[0124] 1), pairwise compare using the following formula to obtain the possibility degree of sorting for every two triangular fuzzy numbers:

[0125] Let the triangular fuzzy numbers Let a ≤ d,

[0126] then:

[0127]

[0128] where and represent The two triangular fuzzy numbers to be compared; a, b, and c respectively represent the minimum value, the most likely value, and the maximum value; d, e, and f respectively represent the minimum value, the most likely value, and the maximum value.

[0129] 2), According to the results of pairwise comparison, obtain the sorting possibility matrix P = (p ij ) n×n :

[0130] where

[0131] where (p ij ) n×n indicates that P is an n×n matrix, and n is the number of precursor nodes; p ij is the element in the i-th row and j-th column of the matrix, representing the i-th number and the j-th number when sorting, the possibility size; and

[0132] 3), Based on the sorting possibility matrix, calculate the sorting vector λ of this group of triangular fuzzy numbers:

[0133] λ = (λ1, λ2, …, λ n ) T , where

[0134] where λ i represents the sorting value of the i-th number in this group of triangular fuzzy numbers. The larger λ i is, the larger the sorting of the triangular fuzzy number in this group;

[0135] 4), According to the sorting vector λ, obtain the minimum value of this group of triangular fuzzy numbers:

[0136] If min(λ1, λ2, …, λ n ) T = λ k , then

[0137] That is, λ k represents the minimum value among λ1, λ2, …, λ n , then the corresponding triangular fuzzy number is also the minimum value of this group of triangular fuzzy numbers ;

[0138] Final result That is, as the post - node N succ The total fuzzy - dependence criticality

[0139] Through formula (13), for the post - node N i The total fuzzy - dependence intensity And the total fuzzy - dependence criticality Take the minimum value as the fuzzy output effectiveness of the post - node

[0140]

[0141] Defuzzify the fuzzy output effectiveness of the post - node N i Using the following formula to obtain the real - number output effectiveness value of the post - node N i Suppose Then:

[0142]

[0143] Where Represents the fuzzy output effectiveness obtained in formula (13), l succ , m succ , h succ Represent respectively The minimum value, the most - likely value, and the maximum value. The output effectiveness value represents the ability level of the equipment node in the system. The higher the effectiveness value, the stronger the ability of the equipment in the system.

[0144] S5. Repeat the above steps until the output effectiveness of all nodes in the entire fuzzy functional - dependence network is calculated. Use the final result to further evaluate the system working ability and system effectiveness.

[0145] As a specific embodiment, this embodiment performs corresponding operations according to the steps of the above - mentioned method for analyzing and evaluating system effectiveness based on a fuzzy functional - dependence network. Specifically:

[0146] In step S1, construct a functional - dependence network model based on a fuzzy functional - dependence network according to the functional - dependence relationship between units in the equipment system.

[0147] In this example, take the system structure of a certain unmanned surface vehicle as an example. Suppose the equipment system has 5 equipment units, namely 2 controlled unmanned surface vehicles, 1 command unmanned surface vehicle, 1 land - based command node, and 1 detection satellite. Initialize the nodes of the functional - dependence network model as N1, N2, N3, N4, N5. Among them, N1 and N2 represent 2 controlled unmanned surface vehicles; N3 represents the command unmanned surface vehicle; N4 represents the detection satellite; N5 represents the land - based command node.

[0148] For the nodes representing equipment units, each node has two evaluation indicators: autonomous efficiency and output efficiency.

[0149] For the directed edges representing the dependency relationships between equipment units, which are directed from the pre - decessor nodes to the successor nodes, each directed edge has two evaluation indicators: fuzzy dependency strength and fuzzy dependency criticality.

[0150] For equipment units with dependency relationships, add directed edges between the corresponding nodes, directed from the dependent nodes to the dependent - upon nodes.

[0151] In this example, 2 controlled unmanned boats receive instructions sent by 1 command unmanned boat. The command unmanned boat receives work instructions from the on - land command node, and the on - land command node receives intelligence information from the detection satellite. Therefore, the directed edges with dependency relationships include N1→N3, N2→N3, N3→N5, N4→N5.

[0152] Finally, the functional dependency network model constructed in this effect embodiment is as Figure 2 shown.

[0153] In step S2, set the values of fuzzy dependency strength and fuzzy dependency criticality for each pair of node dependency relationships. The results are shown in Table 1 and Table 2:

[0154] Table 1 Fuzzy Dependency Strength of Dependency Relationships between Nodes

[0155]

[0156] Table 2 Fuzzy Dependency Criticality of Dependency Relationships between Nodes

[0157]

[0158]

[0159] In step S3, set the autonomous efficiency value SE of each node i , where i = 1, 2, 3, 4, 5. The specific data is shown in Table 3:

[0160] Table 3 Autonomous Efficiency Values of Nodes

[0161] Node <![CDATA[Self - efficiency value SE i > <![CDATA[N1]]> 10 <![CDATA[N2]]> 20 <![CDATA[N3]]> 30 <![CDATA[N4]]> 40 <![CDATA[N5]]> 50

[0162] Based on Equation (1), calculate the output efficiency value O for the pre - decessor nodes without dependency - upon relationships i . The results of the output efficiency values of nodes N1, N2, and N4 are shown in Table 4:

[0163] Table 4 Output Efficiency Values of Nodes

[0164] Node <![CDATA[Output efficiency value O i > <![CDATA[N1]]> 10 <![CDATA[N2]]> 20 <![CDATA[N4]]> 40

[0165] Calculate through equations (2), (3) and (4) and Then calculate the total fuzzy dependence strength of the post - node N3 through equation (5) Obtain:

[0166]

[0167] Where and represent the updated fuzzy dependence strengths of the dependence relationships N1→N3 and N2→N3 between the command unmanned boat node N3 and the two controlled unmanned boat nodes N1 and N2; and represent the initially set fuzzy dependence strengths of the dependence relationships N1→N3 and N2→N3; O1 and O2 represent the output efficiency values of the two controlled unmanned boat nodes N1 and N2; SE3 represents the autonomous efficiency value set for the command unmanned boat node N3.

[0168] Calculate through equations (7), (8) and (9) and Calculate the total fuzzy dependence criticality of the post - node N3 Obtain:

[0169]

[0170] Where and represent the updated fuzzy dependence criticalities of the dependence relationships N1→N3 and N2→N3 between the command unmanned boat node N3 and the two controlled unmanned boat nodes N1 and N2; and represent the initially set fuzzy dependence criticalities of the dependence relationships N1→N3 and N2→N3; O1 and O2 represent the output efficiency values of the two controlled unmanned boat nodes N1 and N2;

[0171] Calculate the total fuzzy dependence strength and the total fuzzy dependence criticality The fuzzy output efficiency of node N3 can be determined through equation (13)

[0172]

[0173] Based on the output efficiency values of nodes N1, N2, N3, N4, repeat the above calculation of the fuzzy output efficiency value of node N5, and we can get

[0174] Based on equation (14), finally give the defuzzified real - number output efficiency values of nodes N3 and N5, and the output efficiency values of the entire fuzzy functional dependence network are shown in Table 5:

[0175] Table 5 Output Efficiency Values of Nodes in the Fuzzy Functional Dependence Network

[0176] Node <![CDATA[Real output performance value O i > <![CDATA[N1]]> 10 <![CDATA[N2]]> 20 <![CDATA[N3]]> 27.35 <![CDATA[N4]]> 40 <![CDATA[N5]]> 46.55

[0177] The overall calculation process of this specific embodiment is summarized as Figure 3 shown. It can be seen that the calculation results of the output efficiency values of the fuzzy functional dependence network are consistent with the analysis and calculation results of the functional dependence network.

[0178] However, since triangular fuzzy numbers are introduced to represent the dependence intensity and dependence criticality of the dependence relationship between nodes, the problem of over - absoluteness in the subjective value - taking of experts can be effectively avoided.

[0179] The above - mentioned are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A system performance analysis and evaluation method based on fuzzy functional dependency network, characterized in that: The following steps are involved: S1. Construct a fuzzy functional dependency network model based on the functional dependency relationship between units in the equipment system; S2, using the expert subjective evaluation method to set the fuzzy dependency strength and fuzzy dependency criticality values ​​of each pair of node dependencies; S3. Analyze the performance of nodes in the equipment system and set the autonomous performance value of each node; S4. Calculate the output performance value of each node, including two cases:

1. For a node that does not have a dependent relationship, the output performance value is equal to the node's autonomous performance value; 2. For n preceding nodes Dependency, n is the total number of predecessor nodes, which is a non-zero positive integer. is the nth predecessor node, and the output performance value corresponding to the predecessor node All determined post nodes, Calculating the output performance value of the subsequent node for the nth output performance value corresponding to the preceding node includes the following steps: (1) Calculate and update the post-node N succ And each predecessor node The fuzzy dependency strength value of the dependency relationship between i=1, 2, ..., n; (2) Calculate the post-node N succ Its total fuzzy dependency strength; (3) Calculate and update the post-node N succ And each predecessor node The fuzzy dependency criticality of the dependency relationship between all nodes N succ The fuzzy dependency criticality of the dependency relationship takes the minimum value as the post-node N succ The fuzzy dependency criticality value of (4) Calculate the fuzzy output efficiency of the post-node by the total fuzzy dependency strength and total fuzzy dependency criticality of the post-node; (5) Defuzzify the fuzzy output efficiency of the post-node to obtain the exact value of the output efficiency value, which is the output efficiency value of the post-node; Repeat the above steps (1) to (5) until the output performance of all nodes in the entire fuzzy functional dependency network is calculated, and use the final result to further evaluate the system working ability and system performance.

2. The system performance analysis and evaluation method based on fuzzy functional dependency network according to claim 1 is characterized in that: In step S1, the fuzzy functional dependency network model includes: ①Nodes representing equipment units, each of which has two evaluation indicators: autonomous effectiveness and output effectiveness; ② The directed edges representing the dependency relationship between equipment units point from the preceding node to the succeeding node, and each directed edge has two evaluation indicators: fuzzy dependency strength and fuzzy dependency criticality.

3. The system performance analysis and evaluation method based on fuzzy functional dependency network according to claim 1 is characterized in that: In step S2, the fuzzy dependency strength is the influence strength of the output performance of the preceding node on the output performance of the following node. The larger the value, the greater the influence strength. The value result is a triangular fuzzy number. Among them l α Represents the minimum value of the dependence strength, m α represents the most likely value of the dependence strength, h α Represents the highest value of the dependence strength, and the value range satisfies 0≤l α ≤m α ≤h α ≤1; The fuzzy dependency criticality is the upper limit of the output efficiency of the subsequent node when the previous node is completely disabled. The higher the value, the higher the dependency criticality. The value result is a triangular fuzzy number. Among them l β Represents the minimum value of dependency criticality, m β represents the most likely value of the dependency criticality, r β Represents the highest value of the dependency criticality, and the value range satisfies 0≤l β ≤m β ≤h β ≤100.

4. The system performance analysis and evaluation method based on fuzzy functional dependency network according to claim 1 is characterized in that: In step (1), for the dependency relationship between the post-node and each pre-node, the weighted average of the post-node autonomous efficiency and the pre-node output efficiency is calculated through the multiplication and addition rules of triangular fuzzy mathematics and the set initial fuzzy dependency strength as the weight, and the calculation result is used as the fuzzy dependency strength value after the dependency relationship between the post-node and each pre-node is updated.

5. The system performance analysis and evaluation method based on fuzzy functional dependency network according to claim 4 is characterized in that: Post node N succ Autonomous Efficacy and Front-End Nodes The calculation expression of the weighted average of output efficiency is: in Represents the previous node The output performance, Represents the subsequent node N succ and the preceding node The initial fuzzy dependency strength set by the inter-dependency relationship, SE succ Represents the subsequent node N succ The autonomous efficacy value set, The calculation result will be used as the post-node N succ and the preceding node The fuzzy dependency strength value after the dependency relationship is updated; Real Numbers and triangular fuzzy numbers The product of is still a triangular fuzzy number. The calculation formula for the specific minimum value, most likely value and maximum value of the triangular fuzzy number is: Among them l α 、m α 、h α Represent triangular fuzzy numbers the minimum, most likely and maximum values ​​of ; Triangular fuzzy numbers With the subsequent node N succ Set the autonomous effectiveness value sE succ Add It is still a triangular fuzzy number, and the specific calculation formula is: Among them l α 、m α 、h α Represent triangular fuzzy numbers The lowest, most likely, and highest values ​​of .

6. The system performance analysis and evaluation method based on fuzzy functional dependency network according to claim 1 is characterized in that: In step (2), for the subsequent node N succ With all predecessor nodes The fuzzy dependency strength of the dependency relationship Take the average value as the post-node N succ Total fuzzy dependency strength The specific formula is: Where n represents the number of front-end nodes.

7. The system performance analysis and evaluation method based on fuzzy functional dependency network according to claim 6 is characterized in that: For the subsequent node N succ With all predecessor nodes The sum of the fuzzy dependency strengths of the dependency relations It is still a triangular fuzzy number, and the specific calculation is implemented using the following steps: First, define the operation rules for adding triangular fuzzy numbers: let the minimum value, most likely value and maximum value of the first triangular fuzzy number be l1, m1 and h1 respectively, and the minimum value, most likely value and maximum value of the second triangular fuzzy number be l2, m2 and h2 respectively, then the result of adding the two numbers is still a triangular fuzzy number, and its value is <l1,m1,h1> +<l2,m2,h2> =<min(l1+m2, l2+m1), m1+m2, min(m1+h2, m2+h1)> That is, the triangular fuzzy number after addition has a minimum value of min(l1+m2, l2+m1), a most likely value of m1+m2, and a maximum value of min(m1+h2, m2+h1); Calculate the initial sum Specifically, let the triangular fuzzy number The value of The value of but Initial and S2 represent the The result of adding the first two triangular fuzzy numbers in is also a triangular fuzzy number; and They represent triangular fuzzy numbers the minimum, most likely and maximum values ​​of ; and They represent triangular fuzzy numbers the minimum, most likely and maximum values ​​of ; Assume that in step (2) The sum of the first k numbers is recorded as S k ,Right now Then for k = 3, 4, ..., n, S3, S4, ..., S4 are calculated one by one in an iterative manner. n The value of The calculation of each step follows the definition of the operation rule of adding triangular fuzzy numbers. Specifically, suppose S is calculated in the previous iteration. k-1 The value of is recorded as <l k-1 , m k-1 ,h k-1 >, The value of but Where l k-1 、m k-1 and h k-1 Denote the triangular fuzzy number S k-1 the minimum, most likely and maximum values ​​of ; and They represent triangular fuzzy numbers the minimum, most likely and maximum values ​​of ; Finally, the iteration reaches the situation where k=n is calculated, and the calculation result is The sum of 8. The system performance analysis and evaluation method based on fuzzy functional dependency network according to claim 1 is characterized in that: In step (3), the total fuzzy dependency criticality COD is calculated i When the post-node N succ And each predecessor node Fuzzy dependency criticality of dependency relationship between The specific steps for taking the minimum value are as follows: Fuzzy dependency criticality for all dependencies By comparing two by two, we can get the possibility matrix P = (p ij ) n×n , where the matrix element p ij Represents the fuzzy dependency criticality of the i-th dependency and the fuzzy dependency criticality of the j-th dependency The triangular fuzzy number sorting function is used to obtain Possibility Calculate the sorting vector λ = (λ1, λ2, ..., λ n ) T ,in λ i The bigger, the Fuzzy dependency criticality in all dependencies The larger the ranking in; Sort the whole set of fuzzy numbers according to the size of the sorting vector, and take the minimum value as the fuzzy dependency criticality value of the post-node; Finally, the total fuzzy dependency strength and fuzzy dependency criticality of the post-node are compared, and the minimum value is taken as the fuzzy output efficiency of the post-node.

9. The system performance analysis and evaluation method based on fuzzy functional dependency network according to claim 1 is characterized in that: In step (5), the fuzzy output performance value Defuzzification is performed to obtain the real output efficiency value O i The formula is: set up but in represents the fuzzy output efficiency obtained in step (4), l succ , m succ ,h succ Respectively represent The minimum, most likely and maximum values ​​of the output efficiency value represent the capability level of the equipment node in the system. The higher the efficiency value, the stronger the capability of the equipment in the system.

10. A computer device, characterized in that: include: A memory, a processor and a computer program stored in the memory, when the computer program is executed on the processor, implements a system performance analysis and evaluation method based on a fuzzy functional dependency network as described in any one of claims 1 to 9.

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