Equipment system analysis method and system based on linear constant discrete system

Abstract

The application provides a kind of equipment system analysis method and system based on linear constant discrete system, comprising: step 1, the equipment composition / communication relationship / operation flow / equipment performance integrated model of equipment system represented by linear constant discrete system state space equation G is established;Step 2, the operation capability comprehensive analysis of equipment system is carried out: including the multi-variable capability, reaction capability, task completion capability, anti-destroying capability of equipment system, the evaluation index model of calculating the above capabilities is established, and the evaluation index value of each capability is calculated based on the state motion expression of state space equation G.The problems existing in the current system can be found by analyzing the operation capability of the equipment system, which points out the direction for subsequent equipment system optimization, and can support the test and evaluation of equipment system optimization result.

Description

Technical Field

[0001] This invention relates to the field of equipment system analysis technology, specifically to an equipment system analysis method and system based on linear time-invariant discrete systems. Background Technology

[0002] With the development of information technology and equipment technology, the relationships between equipment within an equipment system have become closer and more complex. This necessitates higher-level coordination and optimization of the equipment system to enhance its operational capabilities and fully realize its effectiveness. This has significant guiding implications for equipment system construction and equipment development evaluation. Equipment system analysis, as the foundation of equipment system optimization, plays a crucial role. By analyzing the operational capabilities of the equipment system, existing problems can be identified, providing direction for subsequent optimization and supporting the verification and evaluation of optimization results. The operational capabilities of an equipment system are determined by factors at both the equipment system and equipment system levels. The equipment system level primarily involves the organization of multiple pieces of equipment, including equipment composition, communication relationships, and operational processes (reflecting the system's structural architecture). The equipment system level primarily involves the performance of each piece of equipment.

[0003] Patent document CN108489329A (application number: CN201810212580.9) discloses a weapon system analysis method based on kill chain. First, the parameters for weapon system effectiveness evaluation and analysis are input, a weapon system model based on kill chain is constructed, and then the weapon system effectiveness analysis based on kill chain is realized.

[0004] Existing system analysis methods (Li Jinjun et al., Analysis Model and Method of Operational Command System Structure Based on Complex Network Theory, Journal of System Simulation, 2008; Wang Wei et al., Analysis of Anti-Aircraft Capability of Air Defense System Based on Complex Network Theory, Command Control and Simulation, 2012; Gao Long et al., Evolution Analysis and Modeling of Equipment Support System Based on Complex Network, Journal of Armored Forces Engineering Academy, 2017) are generally based on complex network theory and use statistical characteristics of complex networks such as degree and degree distribution, average path length, and clustering coefficient for analysis. They focus on the analysis of a single dimension of system structure and are insufficient in reflecting equipment performance. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for analyzing equipment systems based on linear time-invariant discrete systems.

[0006] The equipment system analysis method based on linear time-invariant discrete systems provided by the present invention includes:

[0007] Step 1: Establish an integrated model of equipment composition, communication relationship, operation process, and equipment performance of the equipment system, represented by the state-space equation G of a linear time-invariant discrete system; where the state vector of G is x, the system matrix A of G represents the equipment composition, communication relationship, operation process, and equipment performance of the equipment system, the input variable u of G represents the external signal driving the operation of the equipment system, and the output variable y of G takes a value according to the analysis requirements.

[0008] Step 2: Conduct a comprehensive analysis of the operational capabilities of the equipment system, including its variability, responsiveness, mission completion, and survivability. By setting appropriate initial values ​​for x and u, and assigning different values ​​to the system matrix A of the state-space equation G, an evaluation index model for calculating the above capabilities is established. Based on the state motion expression of the state-space equation G, the evaluation index values ​​for each capability are calculated.

[0009] Preferably, the state-space equation G of the linear time-invariant discrete system is in the following form:

[0010]

[0011] In the formula, x is an n-dimensional column vector containing n-1 equipment states and 1 termination state, with the default termination state being the last state; A is an n×n matrix; B is an n-dimensional column vector; u is an input variable; C is an n-dimensional row vector; y is an output variable; and k is an integer not less than zero.

[0012] The element in the i-th row and j-th column of matrix A is a ij When i≠n, j≠n and a ij When ≠0, it means that the i-th and j-th equipment are included in the equipment system, and there is a communication relationship between them. The operation process is from the j-th equipment to the i-th equipment, a ij The specific values ​​are related to equipment performance and are set according to the analysis and evaluation requirements in step 2. When i = n, j ≠ n and a ij When ≠0, it means that the system operation process terminates after the j-th equipment finishes running, that is, the j-th equipment is the terminal equipment of the operation process; matrix B makes the input variable u act on the state corresponding to the starting equipment of the operation process; matrix C makes the output variable y take the termination state in x.

[0013] Preferably, the state motion expression x(k) and the corresponding output y(k) of the state-space equation G are as follows:

[0014]

[0015] To establish a model for evaluating variability, responsiveness, task completion ability, and resilience, the initial state vector x(0) is taken as the zero vector, and the input variable u(k) is taken as the unit impulse signal, i.e.:

[0016]

[0017] Substituting equation (3) into equation (2), we get:

[0018] y(k)=CA k-1 B…………(4)

[0019] Construct a variable capability evaluation index model, denoted as an n×n dimensional matrix A. v The element a in the i-th row and j-th column vij It is 1 or 0, when i≠n, j≠n and a vij When = 1, it means selecting the j-th equipment and the i-th equipment to include in the equipment system and establishing their communication relationship. The operation flow is from the j-th equipment to the i-th equipment. When i ≠ n, j ≠ n and a vij When = 0, it means that the j-th equipment and the i-th equipment have no communication relationship and no operational flow relationship; when i = n, j ≠ n and a vij =1 indicates that the system operation process terminates after the j-th equipment finishes operation, meaning the j-th equipment is the terminal equipment in the operation process; take the matrix A = A of the state-space equation G. v According to equation (4):

[0020]

[0021] Then the variable ability evaluation index I v for:

[0022]

[0023] According to equation (4), calculate the integer k that makes y(k) > 0, and then sum all y(k) greater than zero to obtain I. v I v The larger the value, the more ways the equipment system can complete its operation and reach the final state, and the stronger its versatility.

[0024] Construct a survivability evaluation index model. Based on the variable capability evaluation index model, establish a survivability evaluation index model, and use matrix A. v The first n-1 columns are set to zero, representing that a piece of equipment in the system or the communication link related to that equipment has been attacked, damaged, or failed. The corresponding variable capability evaluation index I is then calculated. v , if I v The minimum value is 0, then the damage resistance evaluation index I r =0, meaning there is a possibility that an attack on a piece of equipment or its associated communication link could prevent the system from completing its operational process; if I v If the minimum value is greater than 0, then take I. v In the smallest case, let A be... vSet the remaining n - 2 columns in the first n - 1 columns to zero respectively, and calculate the corresponding variable capacity evaluation index I v , until I v The minimum value is 0, then the anti - destruction ability evaluation index I r = A v The number of zero - set columns - 1; The larger the value of I r , the fewer the number of necessary equipment in the equipment system to ensure the completion of the task, that is, the larger the number of equipment losses that can be tolerated, and the stronger the anti - destruction ability.

[0025] Preferably, construct a reaction ability evaluation index model, set as an n×n - dimensional matrix A t :

[0026] A t = A v *T…………(7)

[0027] In the formula, T is an n×n - dimensional matrix, and its element in the i - th row and j - th column is σ tij , σ is a constant greater than zero, t ij is the time consumed by the j - th equipment in the operation process, j < n, and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension; Take the matrix A = A t of the state - space equation G, and according to formula (4), there is:

[0028]

[0029] Refer to formula (6), calculate the integer k that makes y[[ID=3८]] t (k)>0, and then sum all y t (k) that are greater than zero, and organize them into the following form:

[0030] [[ID=५6]]:

[0031] In the formula, t c represents the time consumed by the c - th way for the equipment system to complete the operation process, c = 1,2,...,I v ]|END]], and the reaction ability evaluation index I t is:

[0032]

[0033] The reaction ability is evaluated by the mean value of the time - exponential function for the equipment system to complete the operation process and reach the termination state. The smaller I t , the stronger the reaction ability.

[0034] Preferably, construct a task - completion ability evaluation index model, set as an n×n - dimensional matrix A p :

[0035] A p = Av *P…………(11)

[0036] In the formula, P is an n×n dimensional matrix, and the element in the i-th row and j-th column is p. ij p ij Let A be the success rate of the j-th equipment in completing its mission during the operation process. The operator * represents the element-wise multiplication of two matrices of the same dimension. Let A = A be the matrix of the state-space equation G. p According to equation (4):

[0037]

[0038] Referring to equation (6), calculate y p (k) is an integer k greater than 0, and then all y values ​​greater than zero are... p (k) Sum and rearrange to form the following form:

[0039]

[0040] In the formula, p c The success rate of the c-th path for the equipment system to complete its operational process and reach the termination state, where c = 1, 2, ..., I v Evaluation index I for task completion ability p Defined as:

[0041]

[0042] The ability to complete a mission is evaluated by the average success rate of the equipment system in completing the operational process through all possible means. p The larger the size, the stronger the ability to complete tasks.

[0043] The equipment system analysis system based on linear time-invariant discrete systems provided by the present invention includes:

[0044] Module M1 establishes an integrated model of equipment composition, communication relationships, operation process, and equipment performance of the equipment system, represented by the state-space equation G of a linear time-invariant discrete system. Here, the state vector of G is x, the system matrix A of G represents the equipment composition, communication relationships, operation process, and equipment performance of the equipment system, the input variable u of G represents the external signal driving the operation of the equipment system, and the output variable y of G takes a value according to the analysis requirements.

[0045] Module M2 conducts a comprehensive analysis of the operational capabilities of the equipment system, including its variability, responsiveness, mission completion, and survivability. By setting appropriate initial values ​​for x and u, and assigning different values ​​to the system matrix A of the state-space equation G, an evaluation index model for calculating the above capabilities is established. Based on the state motion expression of the state-space equation G, the evaluation index values ​​for each capability are calculated.

[0046] Preferably, the state-space equation G of the linear time-invariant discrete system is in the following form:

[0047]

[0048] In the formula, x is an n-dimensional column vector containing n-1 equipment states and 1 termination state, with the default termination state being the last state; A is an n×n matrix; B is an n-dimensional column vector; u is an input variable; C is an n-dimensional row vector; y is an output variable; and k is an integer not less than zero.

[0049] The element in the i-th row and j-th column of matrix A is a ij When i≠n, j≠n and a ij When ≠0, it means that the i-th and j-th equipment are included in the equipment system, and there is a communication relationship between them. The operation process is from the j-th equipment to the i-th equipment, a ij The specific values ​​are related to equipment performance and are set according to the analysis and evaluation requirements in module M2. When i = n, j ≠ n and a ij When ≠0, it means that the system operation process terminates after the j-th equipment finishes running, that is, the j-th equipment is the terminal equipment of the operation process; matrix B makes the input variable u act on the state corresponding to the starting equipment of the operation process; matrix C makes the output variable y take the termination state in x.

[0050] Preferably, the state motion expression x(k) and the corresponding output y(k) of the state-space equation G are as follows:

[0051]

[0052] To establish a model for evaluating variability, responsiveness, task completion ability, and resilience, the initial state vector x(0) is taken as the zero vector, and the input variable u(k) is taken as the unit impulse signal, i.e.:

[0053]

[0054] Substituting equation (3) into equation (2), we get:

[0055] y(k)=CA k-1 B…………(4)

[0056] Construct a variable capability evaluation index model, denoted as an n×n dimensional matrix A. v The element a in the i-th row and j-th column vij It is 1 or 0, when i≠n, j≠n and a vij When = 1, it means selecting the j-th equipment and the i-th equipment to include in the equipment system and establishing their communication relationship. The operation flow is from the j-th equipment to the i-th equipment. When i ≠ n, j ≠ n and a vijWhen = 0, it means that the j-th equipment and the i-th equipment have no communication relationship and no operational flow relationship; when i = n, j ≠ n and a vij =1 indicates that the system operation process terminates after the j-th equipment finishes operation, meaning the j-th equipment is the terminal equipment in the operation process; take the matrix A = A of the state-space equation G. v According to equation (4):

[0057]

[0058] Then the variable ability evaluation index I v for:

[0059]

[0060] According to equation (4), calculate the integer k that makes y(k) > 0, and then sum all y(k) greater than zero to obtain I. v I v The larger the value, the more ways the equipment system can complete its operation and reach the final state, and the stronger its versatility.

[0061] Construct a survivability evaluation index model. Based on the variable capability evaluation index model, establish a survivability evaluation index model, and use matrix A. v The first n-1 columns are set to zero, representing that a piece of equipment in the system or the communication link related to that equipment has been attacked, damaged, or failed. The corresponding variable capability evaluation index I is then calculated. v , if I v The minimum value is 0, then the damage resistance evaluation index I r =0, meaning there is a possibility that an attack on a piece of equipment or its associated communication link could prevent the system from completing its operational process; if I v If the minimum value is greater than 0, then take I. v In the smallest case, let A be... v Set the remaining n-2 columns of the first n-1 columns to zero, and calculate the corresponding variable capability evaluation index I. v until I v The minimum value is 0, then the damage resistance evaluation index I r =A v Set the number of columns to zero by 1; I r The larger the value, the fewer pieces of equipment are required in the equipment system to ensure the completion of the mission, meaning that the greater the amount of equipment loss that can be tolerated, and the stronger the resilience.

[0062] Preferably, a reaction capability evaluation index model is constructed, denoted as an n×n dimensional matrix A. t :

[0063] A t =A v*T…………(7)

[0064] Where T is an n×n dimensional matrix, and the element in its i-th row and j-th column is σ tij , σ is a constant greater than zero, t ij is the time consumed by the j-th equipment in the operation process, j < n, and the operator * represents the multiplication of corresponding elements of two matrices of the same dimension; take the matrix A of the state space equation G as A t , according to Equation (4), we have:

[0065]

[0066] Referring to Equation (6), calculate the integer k that makes y t (k)>0, and then sum all y t (k) that are greater than zero, and organize them into the following form:

[0067]

[0068] Where t c represents the time consumed by the c-th way for the equipment system to complete the operation process, c = 1, 2,..., I v , and the reaction ability evaluation index I t is:

[0069]

[0070] The reaction ability is evaluated by the mean value of the time exponential function for the equipment system to complete the operation process and reach the termination state. The smaller I t , the stronger the reaction ability.

[0071] Preferably, construct a task completion ability evaluation index model, denoted as an n×n dimensional matrix A p :

[0072] A p = A v *P…………(11)

[0073] Where P is an n×n dimensional matrix, and the element in its i-th row and j-th column is p ij , p ij is the success rate of the j-th equipment to complete its task in the operation process. The operator * represents the multiplication of corresponding elements of two matrices of the same dimension. Take the matrix A of the state space equation G as A p , according to Equation (4), we have:

[0074]

[0075] Referring to Equation (6), calculate the integer k that makes y p (k)>0, and then sum all y p(k) Sum and rearrange to form the following form:

[0076]

[0077] In the formula, p c The success rate of the c-th path for the equipment system to complete its operational process and reach the termination state, where c = 1, 2, ..., I v Evaluation index I for task completion ability p Defined as:

[0078]

[0079] The ability to complete a mission is evaluated by the average success rate of the equipment system in completing the operational process through all possible means. p The larger the size, the stronger the ability to complete tasks.

[0080] Compared with the prior art, the present invention has the following beneficial effects:

[0081] (1) This invention improves the system's operational capabilities and fully leverages its effectiveness, providing important guidance for equipment system construction and equipment development demonstration;

[0082] (2) By analyzing the operational capabilities of the equipment system, this invention can identify the problems existing in the current system, point out the direction for subsequent equipment system optimization, and support the verification and evaluation of the equipment system optimization results.

[0083] (3) This invention proposes an equipment system analysis method based on linear time-invariant discrete systems, which solves the problem of analyzing the comprehensive impact of equipment composition, communication relationship, operation process and equipment performance on the system operation capability. Attached Figure Description

[0084] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0085] Figure 1 This is a flowchart of the implementation steps of the equipment system analysis method based on linear time-invariant discrete systems proposed in this invention;

[0086] Figure 2 This is a schematic diagram of the communication connection and operation process of equipment system 1 in an embodiment of the equipment system analysis method based on linear time-invariant discrete systems proposed in this invention;

[0087] Figure 3 This is a schematic diagram of the communication connection and operation process of equipment system 2 in an embodiment of the equipment system analysis method based on linear time-invariant discrete systems proposed in this invention. Detailed Implementation

[0088] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0089] Example:

[0090] like Figure 1 This invention proposes a method for analyzing equipment systems based on linear time-invariant discrete systems, including:

[0091] Assume an equipment system (referred to as Equipment System 1) consisting of 8 types of equipment: S1, S2, Z1, Z2, G1, G2, F1, and F2. S1 and S2 are the starting equipment in the operational process, as are F1 and F2. The communication connections and operational flow of the equipment system are as follows: Figure 2 As shown, Figure 2 The circle and its number represent equipment (S1, S2, Z1, Z2, G1, G2, F1, F2) or termination status (T). The solid line with arrows represents the communication relationship between equipment and the arrow indicates the operation process. The dashed line with arrows indicates the process from the end of the operation of the starting equipment to the termination status.

[0092] Step 1: Model an integrated system encompassing equipment composition, communication relationships, operational processes, and equipment performance. Figure 2 For the equipment system shown, an integrated model of equipment composition, communication relationships, operation process, and equipment performance is established, represented by the state-space equation G of a linear time-invariant discrete system. The form of the state-space equation G of the linear time-invariant discrete system is as follows.

[0093]

[0094] In the formula, x is a 9-dimensional column vector, whose 1st to 8th elements (states) correspond to the equipment states S1, S2, Z1, Z2, G1, G2, F1, and F2, respectively, and whose 9th element (state) is the termination state; A is a 9×9 matrix, B is a 9-dimensional column vector, u is an input variable, C is a 9-dimensional row vector, y is an output variable, and k is an integer not less than zero; the specific forms of matrices A, B, and C are as follows:

[0095]

[0096] C = [0 0 0 0 0 0 0 0 1]

[0097] a 31 The element in the 3rd row and 1st column;

[0098] Step 2: Comprehensive analysis of the operational capability of the equipment system. Let the initial value of vector x(0) be the zero vector, and the input variable u(k) be a unit impulse signal. The expression is:

[0099]

[0100] Establish evaluation index models for variable capability, responsiveness, task completion capability, and damage resistance respectively:

[0101] (1) Evaluation index model and analysis of variable ability

[0102] Based on matrix A in G, take matrix A. v for:

[0103]

[0104] According to the variable ability evaluation index I v Calculation formula:

[0105]

[0106] y v Let matrix A v The output variable.

[0107] Multivariable Ability Evaluation Index I v =2 indicates that there are two paths for the equipment system to complete its operational process and reach the termination state, such as... Figure 2 It can be seen that S1→Z1→G1→F1→T and S2→Z2→G2→F2→T;

[0108] (2) Evaluation index model and analysis of responsiveness

[0109] Based on the time consumption performance of the equipment in the operation process, the values ​​of matrix T are as follows (Note: If there is no flow relationship in the operation process between two pieces of equipment, the corresponding element in matrix T is zero, which does not affect the capability analysis), matrix A t The calculation is as follows, taking σ = 1.2;

[0110]

[0111]

[0112] According to the reaction capability evaluation index I t Calculation formula:

[0113]

[0114]

[0115] tc The time taken for the cth path representing the completion of the equipment system's operational process.

[0116] Based on the above calculations, the time t1 for the equipment system to complete the first operational process (S1→Z1→G1→F1→T) is 15s, and the time t2 for the equipment system to complete the second operational process (S2→Z2→G2→F2→T) is 16s. The reaction capability evaluation index I... t =16.948;

[0117] (3) Evaluation index model and analysis of task completion ability

[0118] Based on the mission success rate performance of the equipment in the operational process, the values ​​of matrix P are as follows (Note: If two pieces of equipment do not have a flow relationship in the operational process, the corresponding elements in matrix P are zero, which does not affect the capability analysis), matrix A p The calculation is as follows:

[0119]

[0120]

[0121] According to task capability evaluation index I p Calculation formula:

[0122]

[0123]

[0124] p c The success rate of the cth path representing the equipment system completing its operational process and reaching the termination state.

[0125] Based on the above calculations, the mission success rate p1 for the first path (S1→Z1→G1→F1→T) of the equipment system's operational process is 0.2205, and the mission success rate p2 for the second path (S2→Z2→G2→F2→T) is 0.3584. The mission completion capability evaluation index I... p =0.28945;

[0126] (4) Evaluation index model and analysis of damage resistance

[0127] Let matrix A v Columns 1 through 8 are set to zero, I v All values ​​are 1; matrix A v Set the first column to zero, then set matrix A v Columns 2 through 8 are set to zero, I vA minimum value of 0 indicates the possibility of an attack on two pieces of equipment or the communication links associated with those equipment, potentially preventing the system from completing its operational process. This is the resilience evaluation index I. r =1.

[0128] Table 1. Calculation process of damage resistance index

[0129]

[0130]

[0131] In contrast, suppose an equipment system (denoted as Equipment System 2) has the same equipment composition as Equipment System 1, and its communication connections and operation procedures are as follows: Figure 3 As shown, the modeling and analysis methods are the same as above, the difference being that the system matrix A of the state-space equation G of the linear time-invariant discrete system is as follows:

[0132]

[0133] Calculations yielded the following:

[0134] Multivariable Ability Evaluation Index I v =20;

[0135] Reaction capability evaluation index I t =20.1422;

[0136] Task completion capability evaluation index I p =0.29088;

[0137] Damage resistance evaluation index I r =1.

[0138] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0139] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method of analyzing an equipment system based on a linear time-invariant discrete system, characterized by, include: Step 1: Establish an integrated model of the equipment system, including its composition, communication relationships, operational flow, and performance, expressed in the state-space equation G of a linear time-invariant discrete system; where the state vector of G is... x The system matrix of G A The input variables of G represent the equipment composition, communication relationships, operational procedures, and equipment performance of the equipment system. u The output variable of G represents the external signal that drives the operation of the equipment system. y Values ​​are determined based on the analysis requirements; Step 2: Conduct a comprehensive analysis of the equipment system's operational capabilities: This includes the equipment system's versatility, responsiveness, mission completion capabilities, and survivability, and then adjust the settings accordingly. x initial value and u And assign the system matrix to the state-space equation G. A For different values, establish an evaluation index model to calculate the above capabilities, and calculate the evaluation index values ​​of each capability based on the state motion expression of the state space equation G. The state-space equation G of a linear time-invariant discrete system is in the following form: …………(1) In the formula, x for n 3D column vector, containing n -1 equipment state and 1 termination state, with the default termination state being the last state; A for n × n 3D matrix; B for n 3D column vector; u For input variables; C for n 3D row vector; y For output variables; k It is an integer not less than zero; matrix A The first in i Line 1 j Column elements are a ij ,when i ≠ n , j ≠ n and a ij ≠0 represents the first i The and the first j Each piece of equipment is incorporated into the equipment system, and they communicate with each other. The operational process is as follows: j The equipment to the first i One piece of equipment, a ij The specific values ​​are related to equipment performance and are set according to the analysis and evaluation requirements in step 2. i = n , j ≠ n and a ij ≠0 represents the first j The system operation process terminates after each piece of equipment has finished operating, i.e., the first... j Each piece of equipment is the terminal equipment in the operation process; matrix B Make input variables u It acts on the state of the equipment at the beginning of the operational process; matrix C Make the output variable y Pick x The termination state in the process.

2. The equipment system analysis method based on linear time-invariant discrete systems according to claim 1, characterized in that, State motion expressions of the state space equation G x ( k ) and the corresponding output y ( k ) are respectively: …………(2) To establish a model for evaluating variability, responsiveness, task completion ability, and resilience, an initial state vector is taken. x (0) is the zero vector, taking the input variable. u ( k ) represents a unit pulse signal, i.e.: …………(3) Substituting equation (3) into equation (2), we get: …………(4) Construct a variable capability evaluation index model, denoted as... n × n 3D matrix A v , No. i Line 1 j Column elements a vij It is 1 or 0, when i ≠ n , j ≠ n and a vij When =1, it means selecting the first... j The equipment and the first i Each piece of equipment is incorporated into the equipment system and their communication relationships are established. The operational process is initiated by the first... j The equipment to the first i One piece of equipment, when i ≠ n , j ≠ n and a vij When =0, it represents the first... j The equipment and the first i The equipment has no communication relationship and no operational flow relationship; when i = n , j ≠ n and a vij =1 represents the first j The system operation process terminates after each piece of equipment has finished operating, i.e., the first... j Each piece of equipment is the terminal equipment in the operational process; the matrix of the state-space equation G is taken. A = A v According to equation (4): …………(5) Then the multi-variable capability evaluation index I v is: …………(6) According to equation (4), calculate the result that makes y ( k Integers greater than 0 k Then all those greater than zero y ( k Sum of the results I v , I v The larger the value, the more ways the equipment system can complete its operation and reach the final state, and the stronger its versatility. Construct a survivability evaluation index model. Based on the variable capability evaluation index model, establish a survivability evaluation index model, and use a matrix... A v The former n The -1 column is set to zero, representing that a piece of equipment in the system or its related communication link has been attacked, damaged, or failed. The corresponding variable capability evaluation index is then calculated. I v ,like I v The minimum value is 0, then the damage resistance evaluation index I r =0, meaning there is a possibility that an attack on a piece of equipment or the communication link associated with that equipment could prevent the system from completing its operation. like I v If the minimum value is greater than 0, then take... I v In the smallest case, then A v forward n The remaining columns in column -1 n Set columns -2 to zero and calculate the corresponding variable capability evaluation indicators. I v until I v The minimum value is 0, then the damage resistance evaluation index I r = A v Set the number of columns to zero by 1; I r The larger the value, the fewer pieces of equipment are required in the equipment system to ensure the completion of the mission, meaning that the greater the amount of equipment loss that can be tolerated, and the stronger the resilience.

3. The equipment system analysis method based on linear time-invariant discrete systems according to claim 2, characterized in that, The reaction capability evaluation index model is constructed, which is set as n × n dimension matrix A t : …………(7) In the formula, T for n × n A dimensional matrix, whose dimensional matrix is ​​the first dimensional matrix. i Line number j Column elements are σ tij , σ It is a constant greater than zero. t ij For the first j The time consumed by each piece of equipment during its operation process j < n The operator * represents the element-wise multiplication of two matrices of the same dimension; take the matrix of the state-space equation G. A = A t According to equation (4): …………(8) With reference to equation (6), the integers y t ( k )>0 are calculated k and all the integers y t ( k ) greater than zero are summed up, and arranged in the form of: …………(9) In the formula, t c The time consumption of the first c approach representing the equipment system to complete the operation process, c = 1, 2, …, I v The reaction capacity evaluation index I t is: …………(10) The reactivity is evaluated by the mean value of the exponential function of the time taken by the equipment system to complete the operating flow to reach the end state, I t The smaller, the stronger the reactivity.

4. The equipment system analysis method based on linear time-invariant discrete systems according to claim 3, characterized in that, The completed task ability evaluation index model is set as n × n dimension matrix A p : …………(11) In the formula, P for n × n A dimensional matrix, whose dimensional matrix is ​​the first dimensional matrix. i Line 1 j Column elements are p ij , p ij For the first j The success rate of a piece of equipment in completing its mission during the operation process, the operator * represents the element-wise multiplication of two matrices of the same dimension, taking the matrix of the state space equation G. A = A p According to equation (4): …………(12) Referring to equation (6), calculate to make y p ( k Integers greater than 0 k Then all those greater than zero y p ( k Add them together and rearrange them to form the following form: …………(13) In the formula, p c The equipment system has completed its operational process and reached the termination state. c The success rate of this approach c =1,2,..., I v Evaluation indicators of task completion ability I p Defined as: …………(14) The mission completion capability is evaluated by the average success rate of the equipment system to complete the operational flow through all possible routes, I p The larger, the stronger the mission completion capability.

5. An equipment system analysis system based on a linear time-invariant discrete system, characterized by comprising: include: Module M1 establishes an integrated model of equipment composition, communication relationships, operation flow, and equipment performance, represented by the state-space equation G of a linear time-invariant discrete system; where the state vector of G is... x The system matrix of G A The input variables of G represent the equipment composition, communication relationships, operational procedures, and equipment performance of the equipment system. u The output variable of G represents the external signal that drives the operation of the equipment system. y Values ​​are determined based on the analysis requirements; Module M2 conducts a comprehensive analysis of the equipment system's operational capabilities, including its versatility, responsiveness, mission completion capabilities, and survivability, through the setting of appropriate parameters. x initial value and u And assign the system matrix to the state-space equation G. A For different values, establish an evaluation index model to calculate the above capabilities, and calculate the evaluation index values ​​of each capability based on the state motion expression of the state space equation G. The state-space equation G of a linear time-invariant discrete system is in the following form: …………(1) In the formula, x for n A dimensional column vector containing n -1 equipment state and 1 termination state, with the default termination state being the last state; A for n × n 3D matrix; B for n 3D column vector; u For input variables; C for n 3D row vector; y For output variables; k It is an integer not less than zero; matrix A The first in i Line number j Column elements are a ij ,when i ≠ n , j ≠ n and a ij ≠0 represents the first i The and the first j Each piece of equipment is incorporated into the equipment system, and they communicate with each other. The operational process is as follows: j The equipment to the first i One piece of equipment, a ij The specific values ​​are related to equipment performance and are set according to the analysis and evaluation requirements in module M2. i = n , j ≠ n and a ij ≠0 represents the first j The system operation process terminates after each piece of equipment has finished operating, i.e., the first... j Each piece of equipment is the terminal equipment in the operation process; matrix B Make input variables u It acts on the state of the equipment at the beginning of the operational process; matrix C Make the output variable y Pick x The termination state in the process.

6. The equipment system analysis system based on linear time-invariant discrete systems according to claim 5, characterized in that, State motion expressions of the state space equation G x ( k ) and the corresponding output y ( k ) are respectively: …………(2) To establish the model of evaluation index of multi-variable ability, reaction ability, task completion ability and anti-destroying ability, take the initial state vector x (0) as a zero vector, take the input variable u ( k ) as a unit pulse signal, that is: …………(3) Substituting equation (3) into equation (2), we get: …………(4) Construct a variable capability evaluation index model, denoted as... n × n 3D matrix A v , No. i Line number j Column elements a vij It is 1 or 0, when i ≠ n , j ≠ n and a vij When =1, it means selecting the first... j The equipment and the first i Each piece of equipment is incorporated into the equipment system and their communication relationships are established. The operational process is initiated by the first... j The equipment to the first i One piece of equipment, when i ≠ n , j ≠ n and a vij When =0, it represents the first... j The equipment and the first i The equipment has no communication relationship and no operational flow relationship; when i = n , j ≠ n and a vij =1 represents the first j The system operation process terminates after each piece of equipment has finished operating, i.e., the first... j Each piece of equipment is the terminal equipment in the operational process; the matrix of the state-space equation G is taken. A = A v According to equation (4): …………(5) Then the multi-variable capability evaluation index I v is: …………(6) According to equation (4), calculate the result that makes y ( k Integers greater than 0 k Then all those greater than zero y ( k Sum of the results I v , I v The larger the value, the more ways the equipment system can complete its operation and reach the final state, and the stronger its versatility. Construct a survivability evaluation index model. Based on the variable capability evaluation index model, establish a survivability evaluation index model, and use a matrix... A v The former n The -1 column is set to zero, representing that a piece of equipment in the system or its related communication link has been attacked, damaged, or failed. The corresponding variable capability evaluation index is then calculated. I v ,like I v The minimum value is 0, then the damage resistance evaluation index I r =0, meaning there is a possibility that an attack on a piece of equipment or the communication link associated with that equipment could prevent the system from completing its operation. like I v If the minimum value is greater than 0, then take... I v In the smallest case, then A v forward n The remaining columns in column -1 n Set columns -2 to zero and calculate the corresponding variable capability evaluation indicators. I v until I v The minimum value is 0, then the damage resistance evaluation index I r = A v Set the number of columns to zero by 1; I r The larger the value, the fewer pieces of equipment are required in the equipment system to ensure the completion of the mission, meaning that the greater the amount of equipment loss that can be tolerated, and the stronger the resilience.

7. The equipment system analysis system based on linear time-invariant discrete systems according to claim 6, characterized in that, Construct a response capability evaluation index model, denoted as n × n 3D matrix A t : …………(7) In the formula, T for n × n A dimensional matrix, whose dimensional matrix is ​​the first dimensional matrix. i Line 1 j Column elements are σ tij , σ It is a constant greater than zero. t ij For the first j The time consumed by each piece of equipment during its operation process j < n The operator * represents the element-wise multiplication of two matrices of the same dimension; take the matrix of the state-space equation G. A = A t According to equation (4): …………(8) Referring to equation (6), calculate to make y t ( k Integers greater than 0 k Then all those greater than zero y t ( k Add them together and rearrange them to form the following form: …………(9) In the formula, t c The first step in completing the operational process of the equipment system c The time consumed by each approach c =1,2,..., I v Response capability evaluation indicators I t for: …………(10) Responsiveness is evaluated by the mean of an exponential function of the time taken for the equipment system to complete its operational process and reach the final state. I t The smaller the size, the stronger the reaction ability.

8. The equipment system analysis system based on linear time-invariant discrete systems according to claim 7, characterized in that, Construct a performance evaluation index model for task completion, denoted as . n × n 3D matrix A p : …………(11) In the formula, P for n × n A dimensional matrix, whose dimensional matrix is ​​the first dimensional matrix. i Line number j Column elements are p ij , p ij For the first j The success rate of a piece of equipment in completing its mission during the operation process, the operator * represents the element-wise multiplication of two matrices of the same dimension, taking the matrix of the state space equation G. A = A p According to equation (4): …………(12) With reference to equation (6), the integers y p ( k )>0 are calculated k and all the integers y p ( k ) greater than zero are summed up, and arranged in the form: …………(13) In the formula, p c The equipment system has completed its operational process and reached the termination state. c The success rate of this approach c =1,2,..., I v Evaluation indicators of task completion ability I p Defined as: …………(14) The ability to complete a mission is evaluated by the average success rate of the equipment system in completing the operational process through all possible means. I p The larger the size, the stronger the ability to complete tasks.

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