Equipment system synthesis optimization method and system based on linear constant discrete system

Abstract

The application provides a kind of equipment system synthesis optimization method and system based on linear constant discrete system, comprising: step S1: the equipment system structure and equipment performance integrated model represented by linear constant discrete system state space equation are established;Step S2: the strain capacity, the damage resistance, the response capacity, the task completion capacity of equipment system are analyzed and evaluated;Step S3: the equipment system synthesis optimization model including optimization variable, optimization target, constraint condition is established;Step S4: based on equipment system optimization model, optimization algorithm is used to solve the optimization variable that meets constraint condition and realizes optimization target, realizes the comprehensive optimization of equipment system.The application realizes the unified modeling description from equipment system, equipment system two dimensions, simplifies the complexity of model, is favorable for carrying out system analysis and optimization work.

Description

Technical Field

[0001] This invention relates to, specifically, a method and system for comprehensive optimization of equipment systems based on linear time-invariant discrete systems; more specifically, it relates to a method for comprehensive optimization of equipment configuration, cooperation relationships, cooperation processes, and equipment performance of equipment systems based on linear time-invariant discrete systems. Background Technology

[0002] With the development of information technology and equipment technology, the relationships between equipment in an equipment system have become closer and more complex. This necessitates higher-level coordination and optimization of the equipment system to enhance its capabilities and fully realize its effectiveness. This has significant guiding significance for equipment system construction and equipment development demonstration. The literature (Cheng Ben, et al. Research progress on weapon and equipment system optimization methods [J]. Systems Engineering and Electronics, 2012) summarizes equipment system optimization methods. These methods primarily address the optimization of equipment system architecture and equipment configuration. Some methods require extensive simulation experiments, resulting in a large workload and significant time consumption. The capabilities of an equipment system are determined by factors at both the equipment system and equipment system levels. The equipment system level mainly involves the organization of multiple pieces of equipment, including equipment configuration, collaborative relationships, and collaborative processes (reflecting the equipment system architecture). The equipment system level mainly involves the performance of each piece of equipment. Existing methods focus on single-dimensional optimization of equipment systems and equipment systems. While some ideas have been proposed for the joint optimization of equipment systems and equipment systems, few specific methods have been developed.

[0003] Patent document CN114841502A (application number: CN202210261830.4) discloses a method for evaluating the effectiveness of a joint operations equipment system, including the following steps: Step 1, classifying the relationship between the effectiveness of the equipment system and the effectiveness of various types of equipment into four types of equipment system effectiveness aggregation equivalence relationships: complementary relationship, synergistic relationship, joint relationship, or optimal synergistic relationship; Step 2, constructing the basic structure of the joint operations equipment system from three aspects: combat equipment, information support equipment, and integrated support equipment; Step 3, based on the aforementioned four types of equipment system effectiveness aggregation equivalence relationships, establishing effectiveness evaluation models for combat equipment, information support equipment, and integrated support equipment respectively, and establishing a joint operations equipment system effectiveness evaluation model based on these models. However, this invention does not establish an integrated model of equipment configuration, cooperative relationships, cooperative processes, and equipment performance based on a linear time-invariant discrete system. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a comprehensive optimization method and system for equipment systems based on linear time-invariant discrete systems.

[0005] According to the present invention, a method for comprehensive optimization of equipment systems based on linear time-invariant discrete systems includes:

[0006] Step S1: Establish an integrated model of equipment architecture and equipment performance, represented by the state-space equations of a linear time-invariant discrete system.

[0007] Step S2: Analyze and evaluate the equipment system's adaptability, survivability, response capability, and mission completion capability;

[0008] Step S3: Establish a comprehensive optimization model for the equipment system, including optimization variables, optimization objectives, and constraints;

[0009] Step S4: Based on the equipment system optimization model, use optimization algorithms to solve for the optimization variables that satisfy the constraints and achieve the optimization objectives, thereby realizing the comprehensive optimization of the equipment system.

[0010] Preferably, in step S1:

[0011] An integrated model of equipment system architecture and performance is established, represented by the state-space equation G of a linear time-invariant discrete system. The equipment system architecture considers the equipment configuration, cooperative relationships, and cooperative processes. Here, the state vector of G is x, with the last state representing the final state of system operation. The remaining states correspond one-to-one with all the equipment constituting the system. The initial value of x is set according to the analysis requirements. The system matrix A of G represents the equipment configuration, cooperative relationships, cooperative processes, and equipment performance of the equipment system. Each element in A is assigned a corresponding value according to the specific analysis and optimization requirements. The input variable u of G represents the external signal driving the operation of the equipment system, and u is set according to the analysis requirements. The output variable y of G takes the final state of system operation from the state vector x.

[0012] The state-space equation G of a linear time-invariant discrete system is as follows:

[0013] x(k+1)=Ax(k)+Bu(k)

[0014] y(k)=Cx(k) (1)

[0015] k = 0, 1, 2, ...

[0016] In the formula, k is a discrete time variable, x is an n-dimensional state vector, u is an input variable, y is an output variable, A is an n×n-dimensional system matrix, B is an n×1-dimensional input matrix, C is a 1×n-dimensional output matrix, the first n-1 states of x correspond to all the equipment to be constituted in the system, and the nth state is the final state; when the element a in the i-th row and j-th column of A... ij When the value is non-zero, it indicates that the j-th equipment participates in the system operation and has a cooperative relationship with the i-th equipment. The cooperative process is from the j-th equipment to the i-th equipment; otherwise, a ij=0, non-zero a ij The value of 1 reflects only the system architecture of the equipment system, or it can be a value related to the performance of the j-th equipment, reflecting the impact of the equipment performance on the system operation. Array B is set so that u acts on the state of the corresponding system operation start-end equipment to drive the system operation. The states of the system operation end-end equipment all point to the termination state. Array C is set so that y takes the termination state of the system operation.

[0017] Preferably, in step S2:

[0018] Adaptability refers to the ability of an equipment system to complete a task through multiple means; damage resistance refers to the ability of an equipment system to withstand equipment loss or failure while still being able to complete a task; response capability refers to the efficiency of an equipment system in completing a task; and task completion capability refers to the probability of an equipment system successfully completing a task. By setting initial values ​​for x and u, and assigning corresponding values ​​to the system matrix A of the state-space equation G based on the equipment configuration, cooperation relationship, cooperation process, and equipment performance of the equipment system, an evaluation index model for calculating the above capabilities is established. Based on the state motion equation of the state-space equation G, the evaluation index values ​​of each capability are calculated.

[0019] The state motion expressions x(k) and the corresponding output y(k) of the state-space equation G are respectively

[0020]

[0021] To establish a model for evaluating resilience, survivability, response capability, and mission completion capability, 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.

[0022]

[0023] Substituting equation (3) into equation (2), we get

[0024] y(k)=CA k-1 B (4)

[0025] Step S2.1: Establish a strain capacity evaluation index model:

[0026] Let A be an n×n matrix, and let a be the element in the i-th row and j-th column. ij It is 1 or 0, when i≠n, j≠n and a ij 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 ij 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 ijWhen it is equal to 1, 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, and the strain capacity evaluation index is denoted as I. v , 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 has to complete the operation process and reach the termination state, and the stronger the variability ability.

[0027] Step S2.2: Establish a response ability evaluation index model:

[0028] Let the n×n-dimensional matrix A t be:

[0029] A t = A*T (5)

[0030] 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 and σ>0, t ij is the time-consuming of the j-th equipment in the operation process, that is, after t ij time, the operation process transfers from the j-th equipment to the i-th equipment or the termination state, where j < n, and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension. According to Equation (4), there is:

[0031]

[0032] Among them, y t (k) is the output of the system state space equation with A t as the system matrix, B as the input matrix, and C as the output matrix. k is the discrete time variable, is the (k - 1)th power of the matrix A t in Equation (5);

[0033] Calculate the integer k that makes y t (k)>0, and then sum all y t (k) greater than zero, and organize it into the following form:

[0034]

[0035] In the formula, t c represents the time-consuming of the c-th way for the equipment system to complete the operation process, c = 1, 2,..., I v , let the response ability evaluation index I t be:

[0036]

[0037] The responsiveness is evaluated by the mean value of the exponential function of the time taken for the equipment system to complete the operation process and reach the termination state, I t The smaller it is, the stronger the reaction ability;

[0038] Step S2.3: Establish a task completion ability evaluation index model:

[0039] Let the n×n dimensional matrix A p be

[0040] A p = A * P (9)

[0041] In the formula, P is an n×n dimensional matrix, and its element in the i-th row and j-th column is p ij , p ij is the success rate of the j-th equipment completing its task in the operation process, that is, the operation process transfers to the i-th equipment or the termination state with a probability of p ij from the j-th equipment, where j < n, and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension. According to formula (4), there is:<00..​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0050] Based on the strain capability evaluation index model, a damage resistance evaluation index model is established. The first n-1 columns of matrix A are set to zero, representing that a certain piece of equipment in the system or the communication link related to that equipment is damaged or fails due to an attack. 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, indicating the 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 minimum case, set the remaining n-2 columns of the first n-1 columns of A 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 = Set A to zero column number - 1; I r The higher the value, the fewer pieces of equipment are required in the equipment system to ensure the completion of the mission, the greater the amount of equipment loss that can be tolerated, and the stronger the resistance to destruction.

[0051] Preferably, in step S3:

[0052] The system matrix A with G as the optimization variable represents the equipment configuration, cooperation relationship, cooperation process and equipment performance of the equipment system; the optimization objectives are selected from the evaluation indicators of adaptability, survivability, response capability and mission completion capability; the constraints include equipment cost constraints, cooperation relationship between equipment and cooperation process constraints.

[0053] The equipment system optimization model can be represented as:

[0054]

[0055] In the formula, g a (A) The cost of integrating equipment into the system and establishing collaborative relationships with other equipment, b a As the upper limit of equipment cost, a ij Let be the element in the i-th row and j-th column of matrix A; matrix A is the optimization variable, representing equipment configuration, cooperation relationship, and cooperation process. t1 I p1 In this context, T and P represent the equipment's performance in terms of mission completion time and mission success rate, respectively; I v1 I t1 I p1 I r1 These are the strain capability evaluation indicators I v Response capability evaluation index I t Task completion ability evaluation index Ip , the normalized value of the anti - destruction ability evaluation index I r ;

[0056]

[0057] Among them, I vu is the upper limit of the value of I v , I tu is the upper limit of the value of I t , I ru is the upper limit of the value of I r ; w v , w r , w t , w p are the weights of the indicators, set by the designers; the constraints and are the constraints on the equipment cooperation relationship and cooperation process, ensuring that the optimized equipment cooperation relationship and cooperation process conform to the functional characteristics of each equipment. Among them, I n is an n - dimensional unit column vector, M is an n×n - dimensional cooperation relationship and process constraint matrix, and its element in the i - th row and j - th column is denoted as m ij . When i≠n, j≠n and m ij = 1, it means that the j - th equipment can cooperate with the i - th equipment and the cooperation process is from the j - th equipment to the i - th equipment. When i≠n, j≠n and m ij = 0, it means that the j - th equipment cannot cooperate with the i - th equipment. When i = n, j≠n and m ij = 1, it means that the system operation process can terminate after the j - th equipment runs, that is, the j - th equipment is the terminal equipment of the operation process; the constraint g a (A)-b a ≤0 is the equipment cost constraint. The function g a (A) represents the cost of incorporating the equipment into the system operation and establishing a cooperation relationship with other equipment. g a (A)-b a ≤0 can be calculated according to the following formula:

[0058]

[0059] In the formula, C a is an n×n - dimensional equipment cost matrix, and its element in the i - th row and j - th column c aij represents the cost of incorporating the j - th equipment into the system operation, where j < n, and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension.

[0060] Preferably, in the step S4:

[0061] Comprehensive optimization of equipment system structure and performance: Based on the established equipment system optimization model, optimization algorithms are used to solve for the optimization variable A that satisfies the constraints and achieves the optimization objective. o This enables comprehensive optimization of equipment configuration, collaborative relationships, collaborative processes, and equipment performance within the equipment system.

[0062] The optimal solution A of the equipment system optimization model (14) is obtained by using an algorithm. o The algorithms include branch and bound algorithm and genetic algorithm, based on matrix A. o After determining the optimized equipment to be included in the system, as well as the collaborative relationships and processes between the equipment, referring to equations (6) and (10), we have:

[0063]

[0064] Among them, A to A is the optimized equipment operation time performance index matrix. po The optimized equipment mission success rate performance index matrix;

[0065] According to matrix A to and A po The elements of non-zero are used to determine the performance indicators of equipment operation time and mission success rate to be included in the system. If A to The element a in row i and column j toij If the value is non-zero, then the performance index of the running time of the j-th equipment is:

[0066] t oij =log σ a toij (17)

[0067] Among them, a toij Let matrix A to The element in the i-th row and j-th column;

[0068] For example, A po The element a in row i and column j poij If the value is non-zero, then the mission success rate performance index of the j-th equipment is:

[0069] p oij =a poij (18)

[0070] To achieve the optimal matching of equipment configuration, cooperation relationships, cooperation processes, and equipment performance.

[0071] According to the present invention, an equipment system comprehensive optimization system based on a linear time-invariant discrete system includes:

[0072] Module M1: Establish an integrated model of equipment architecture and equipment performance, represented by the state-space equations of a linear time-invariant discrete system.

[0073] Module M2: Analyzes and evaluates the equipment system's adaptability, survivability, response capability, and mission completion capability;

[0074] Module M3: Establish a comprehensive optimization model for the equipment system, including optimization variables, optimization objectives, and constraints;

[0075] Module M4: Based on the equipment system optimization model, it uses optimization algorithms to solve for the optimization variables that satisfy the constraints and achieve the optimization objectives, thereby realizing the comprehensive optimization of the equipment system.

[0076] Preferably, in module M1:

[0077] An integrated model of equipment system architecture and performance is established, represented by the state-space equation G of a linear time-invariant discrete system. The equipment system architecture considers the equipment configuration, cooperative relationships, and cooperative processes. Here, the state vector of G is x, with the last state representing the final state of system operation. The remaining states correspond one-to-one with all the equipment constituting the system. The initial value of x is set according to the analysis requirements. The system matrix A of G represents the equipment configuration, cooperative relationships, cooperative processes, and equipment performance of the equipment system. Each element in A is assigned a corresponding value according to the specific analysis and optimization requirements. The input variable u of G represents the external signal driving the operation of the equipment system, and u is set according to the analysis requirements. The output variable y of G takes the final state of system operation from the state vector x.

[0078] The state-space equation G of a linear time-invariant discrete system is as follows:

[0079] x(k+1)=Ax(k)+Bu(k)

[0080] y(k)=Cx(k) (1)

[0081] k = 0, 1, 2, ...

[0082] In the formula, k is a discrete time variable, x is an n-dimensional state vector, u is an input variable, y is an output variable, A is an n×n-dimensional system matrix, B is an n×1-dimensional input matrix, C is a 1×n-dimensional output matrix, the first n-1 states of x correspond to all the equipment to be constituted in the system, and the nth state is the final state; when the element a in the i-th row and j-th column of A... ij When the value is non-zero, it indicates that the j-th equipment participates in the system operation and has a cooperative relationship with the i-th equipment. The cooperative process is from the j-th equipment to the i-th equipment; otherwise, a ij =0, non-zero a ijThe value of 1 reflects only the system architecture of the equipment system, or it can be a value related to the performance of the j-th equipment, reflecting the impact of the equipment performance on the system operation. Array B is set so that u acts on the state of the corresponding system operation start-end equipment to drive the system operation. The states of the system operation end-end equipment all point to the termination state. Array C is set so that y takes the termination state of the system operation.

[0083] Preferably, in module M2:

[0084] Adaptability refers to the ability of an equipment system to complete a task through multiple means; damage resistance refers to the ability of an equipment system to withstand equipment loss or failure while still being able to complete a task; response capability refers to the efficiency of an equipment system in completing a task; and task completion capability refers to the probability of an equipment system successfully completing a task. By setting initial values ​​for x and u, and assigning corresponding values ​​to the system matrix A of the state-space equation G based on the equipment configuration, cooperation relationship, cooperation process, and equipment performance of the equipment system, an evaluation index model for calculating the above capabilities is established. Based on the state motion equation of the state-space equation G, the evaluation index values ​​of each capability are calculated.

[0085] The state motion expressions x(k) and the corresponding output y(k) of the state-space equation G are respectively

[0086]

[0087] To establish a model for evaluating resilience, survivability, response capability, and mission completion capability, 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.

[0088]

[0089] Substituting equation (3) into equation (2), we get

[0090] y(k)=CA k-1 B (4)

[0091] Module M2.1: Establishing a strain capacity evaluation index model:

[0092] Let A be an n×n matrix, and let a be the element in the i-th row and j-th column. ij It is 1 or 0, when i≠n, j≠n and a ij 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 ij 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 ijWhen it is equal to 1, 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, and the strain capacity evaluation index is denoted as I v , according to formula (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 has to complete the operation process and reach the termination state, and the stronger the variability ability;

[0093] Module M2.2: Establish a response ability evaluation index model:

[0094] Let the n×n-dimensional matrix A t be:

[0095] A t =A*T (5)

[0096] 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 and σ>0, t ij is the time-consuming of the j-th equipment in the operation process, that is, after t ij time, the operation process transfers from the j-th equipment to the i-th equipment or the termination state, where j<n, and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension. According to formula (4), there is:

[0097]

[0098] Among them, y t (k) is the output of the system state space equation with A t as the system matrix, B as the input matrix, and C as the output matrix. k is the discrete time variable, is the (k-1)th power of matrix A t in formula (5);

[0099] Calculate the integer k that makes y t (k)>0, and then sum all y t (k) greater than zero, and organize it into the following form:

[0100] <X

[0101] In the formula, t c represents the time-consuming of the c-th way for the equipment system to complete the operation process, c = 1, 2,..., I v , let the response ability evaluation index I t be:

[0102] <000X0744>

[0103] The responsiveness is evaluated by the mean value of the exponential function of the time taken for the equipment system to complete the operation process and reach the termination state, I t The smaller it is, the stronger the reaction ability;

[0104] Module M2.3: Establish an evaluation index model for task completion ability:

[0105] Let the n×n dimensional matrix A p be

[0106] A p = A*P (9)

[0107] In the formula, P is an n×n dimensional matrix, and its element in the i-th row and j-th column is p ij , p ij is the success rate of the j-th equipment completing its task in the operation process, that is, the operation process transfers from the j-th equipment to the i-th equipment or the termination state with probability p ij , where j < n, and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension. According to formula (4), we have:

[0108]

[0109] Among them, y p (k) is the output of the system state space equation with A p as the system matrix, B as the input matrix, and C as the output matrix. k is the discrete time variable, is the (k - 1)th power of the matrix A in formula (9) p ;

[0110] Calculate the integer k that makes y p (k) > 0, and then sum all y p (k) greater than zero, and organize it into the following form

[0111]

[0112] In the formula, p c represents the success rate of the c-th way for the equipment system to complete the operation process and reach the termination state, c = 1, 2,..., I v , let the evaluation index I of the task completion ability p be defined as:

[0113]

[0114] The task completion ability is evaluated by the mean value of the success rates of all possible ways for the equipment system to complete the operation process, I p The larger it is, the stronger the task completion ability;

[0115] Module M2.4: Establish an evaluation index model for anti-destruction ability:

[0116] Based on the strain capability evaluation index model, a damage resistance evaluation index model is established. The first n-1 columns of matrix A are set to zero, representing that a certain piece of equipment in the system or the communication link related to that equipment is damaged or fails due to an attack. 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, indicating the 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 minimum case, set the remaining n-2 columns of the first n-1 columns of A 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 = Set A to zero column number - 1; I r The higher the value, the fewer pieces of equipment are required in the equipment system to ensure the completion of the mission, the greater the amount of equipment loss that can be tolerated, and the stronger the resistance to destruction.

[0117] Preferably, in module M3:

[0118] The system matrix A with G as the optimization variable represents the equipment configuration, cooperation relationship, cooperation process and equipment performance of the equipment system; the optimization objectives are selected from the evaluation indicators of adaptability, survivability, response capability and mission completion capability; the constraints include equipment cost constraints, cooperation relationship between equipment and cooperation process constraints.

[0119] The equipment system optimization model can be represented as:

[0120]

[0121] In the formula, g a (A) The cost of integrating equipment into the system and establishing collaborative relationships with other equipment, b a As the upper limit of equipment cost, a ij Let be the element in the i-th row and j-th column of matrix A; matrix A is the optimization variable, representing equipment configuration, cooperation relationship, and cooperation process. t1 I p1 In this context, T and P represent the equipment's performance in terms of mission completion time and mission success rate, respectively; I v1 I t1 I p1 I r1 These are the strain capability evaluation indicators I v Response capability evaluation index I t Task completion ability evaluation index Ip 、 Normalized value of the anti - destruction ability evaluation index I r ;

[0122]

[0123] Among them, I vu is the upper limit of the value of I v , I tu is the upper limit of the value of I t , I ru is the upper limit of the value of I r ; w v , w r , w t , w p are the weights of the indicators, set by the designers; Constraint and are the constraints on the equipment cooperation relationship and cooperation process, ensuring that the optimized equipment cooperation relationship and cooperation process conform to the functional characteristics of each equipment. Among them, I n is an n - dimensional unit column vector, M is an n×n - dimensional cooperation relationship and process constraint matrix, and its element in the i - th row and j - th column is denoted as m ij . When i≠n, j≠n and m ij = 1, it means that the j - th equipment can cooperate with the i - th equipment and the cooperation process is from the j - th equipment to the i - th equipment. When i≠n, j≠n and m ij = 0, it means that the j - th equipment cannot cooperate with the i - th equipment. When i = n, j≠n and m ij = 1, it means that the system operation process can terminate after the j - th equipment runs, that is, the j - th equipment is the terminal equipment of the operation process; Constraint g a (A)-b a ≤0 is the equipment cost constraint. The function g a (A) represents the cost of incorporating the equipment into the system operation and establishing a cooperation relationship with other equipment. g a (A)-b a ≤0 can be calculated according to the following formula:

[0124]

[0125] In the formula, C a is an n×n - dimensional equipment cost matrix, and its element in the i - th row and j - th column c aij represents the cost of incorporating the j - th equipment into the system operation, where j < n, and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension.

[0126] Preferably, in the module M4:

[0127] Comprehensive optimization of equipment system structure and performance: Based on the established equipment system optimization model, optimization algorithms are used to solve for the optimization variable A that satisfies the constraints and achieves the optimization objective. o This enables comprehensive optimization of equipment configuration, collaborative relationships, collaborative processes, and equipment performance within the equipment system.

[0128] The optimal solution A of the equipment system optimization model (14) is obtained by using an algorithm. o The algorithms include branch and bound algorithm and genetic algorithm, based on matrix A. o After determining the optimized equipment to be included in the system, as well as the collaborative relationships and processes between the equipment, referring to equations (6) and (10), we have:

[0129]

[0130] Among them, A to A is the optimized equipment operation time performance index matrix. po The optimized equipment mission success rate performance index matrix;

[0131] According to matrix A to and A po The elements of non-zero are used to determine the performance indicators of equipment operation time and mission success rate to be included in the system. If A to The element a in row i and column j toij If the value is non-zero, then the performance index of the running time of the j-th equipment is:

[0132] t oij =log σ a toij (17)

[0133] Among them, a toij Let matrix A to The element in the i-th row and j-th column;

[0134] For example, A po The element a in row i and column j poij If the value is non-zero, then the mission success rate performance index of the j-th equipment is:

[0135] p oij =a poij (18)

[0136] To achieve the optimal matching of equipment configuration, cooperation relationships, cooperation processes, and equipment performance.

[0137] Compared with the prior art, the present invention has the following beneficial effects:

[0138] 1. Based on linear time-invariant discrete systems, this invention establishes an integrated model of equipment configuration, cooperation relationships, cooperation processes, and equipment performance of the equipment system, realizing unified modeling and description from two dimensions: equipment system and equipment system. This simplifies the complexity of the model and is conducive to carrying out system analysis and optimization work.

[0139] 2. Compared with the analysis method based on complex networks, this invention further considers the functional characteristics of the equipment itself (constraints exist in the cooperation relationship and cooperation process with other equipment) and the dynamic characteristics of the system operation. It uses the state motion expression of linear time-invariant discrete system to establish a variety of evaluation index models for evaluating the system capability of equipment, and supports the analysis of the impact of system structure and equipment performance on system capability.

[0140] 3. This invention considers the constraints of equipment cooperation relationships and cooperation processes, as well as equipment cost constraints, and also considers the optional values ​​of equipment performance, so as to realize the joint optimization of equipment configuration, cooperation relationships, cooperation processes, and equipment performance of the equipment system and improve the efficiency of equipment system demonstration and design.

[0141] 4. Compared with system optimization methods based on system simulation, the present invention has lower requirements for simulation modeling, does not require large-scale simulation experiments, and improves the efficiency of equipment system optimization design. Attached Figure Description

[0142] 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:

[0143] Figure 1 These are the implementation steps of the equipment system comprehensive optimization method based on linear time-invariant discrete systems proposed in this invention.

[0144] Figure 2 This is an example of the equipment configuration, cooperation relationship, and cooperation process of the equipment system before optimization in the embodiment of the equipment system comprehensive optimization method based on linear time-invariant discrete system proposed in this invention.

[0145] Figure 3 This is an example of the optimized equipment system configuration, cooperation relationship, and cooperation process in an embodiment of the equipment system comprehensive optimization method based on linear time-invariant discrete systems proposed in this invention. Detailed Implementation

[0146] 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.

[0147] Example 1:

[0148] This invention discloses a comprehensive optimization method for equipment systems based on linear time-invariant discrete systems. This method primarily addresses the comprehensive optimization of equipment configuration, collaborative relationships, collaborative processes, and equipment performance within an equipment system. The proposed method is implemented through the following steps: 1. Integrated modeling of equipment system structure and performance; 2. Equipment system capability analysis and evaluation; 3. Modeling of a comprehensive optimization model for the equipment system; 4. Comprehensive optimization of equipment system structure and performance. Based on a linear time-invariant discrete system model, the proposed method establishes an integrated model of equipment configuration, collaborative relationships, collaborative processes, and equipment performance. According to the state-motion characteristics of the linear time-invariant discrete system, it evaluates the equipment system's resilience, survivability, response capability, and mission completion capability. Using equipment cost, collaborative relationships, and processes as constraints, it achieves optimal matching of equipment configuration, collaborative relationships, collaborative processes, and equipment performance, realizing joint optimization of equipment system structure and performance, and improving the efficiency of equipment system demonstration and design.

[0149] According to the present invention, a comprehensive optimization method for equipment systems based on linear time-invariant discrete systems is provided, such as... Figures 1-3 As shown, it includes:

[0150] Step S1: Establish an integrated model of equipment architecture and equipment performance, represented by the state-space equations of a linear time-invariant discrete system.

[0151] Specifically, in step S1:

[0152] An integrated model of equipment system architecture and performance is established, represented by the state-space equation G of a linear time-invariant discrete system. The equipment system architecture considers the equipment configuration, cooperative relationships, and cooperative processes. Here, the state vector of G is x, with the last state representing the final state of system operation. The remaining states correspond one-to-one with all the equipment constituting the system. The initial value of x is set according to the analysis requirements. The system matrix A of G represents the equipment configuration, cooperative relationships, cooperative processes, and equipment performance of the equipment system. Each element in A is assigned a corresponding value according to the specific analysis and optimization requirements. The input variable u of G represents the external signal driving the operation of the equipment system, and u is set according to the analysis requirements. The output variable y of G takes the final state of system operation from the state vector x.

[0153] The state-space equation G of a linear time-invariant discrete system is as follows:

[0154] x(k+1)=Ax(k)+Bu(k)

[0155] y(k)=Cx(k) (1)

[0156] k = 0, 1, 2, ...

[0157] In the formula, k is a discrete time variable, x is an n-dimensional state vector, u is an input variable, y is an output variable, A is an n×n-dimensional system matrix, B is an n×1-dimensional input matrix, C is a 1×n-dimensional output matrix, the first n-1 states of x correspond to all the equipment to be constituted in the system, and the nth state is the final state; when the element a in the i-th row and j-th column of A... ij When the value is non-zero, it indicates that the j-th equipment participates in the system operation and has a cooperative relationship with the i-th equipment. The cooperative process is from the j-th equipment to the i-th equipment; otherwise, a ij =0, non-zero a ij The value of 1 reflects only the system architecture of the equipment system, or it can be a value related to the performance of the j-th equipment, reflecting the impact of the equipment performance on the system operation. Array B is set so that u acts on the state of the corresponding system operation start-end equipment to drive the system operation. The states of the system operation end-end equipment all point to the termination state. Array C is set so that y takes the termination state of the system operation.

[0158] Step S2: Analyze and evaluate the equipment system's adaptability, survivability, response capability, and mission completion capability;

[0159] Specifically, in step S2:

[0160] Adaptability refers to the ability of an equipment system to complete a task through multiple means; damage resistance refers to the ability of an equipment system to withstand equipment loss or failure while still being able to complete a task; response capability refers to the efficiency of an equipment system in completing a task; and task completion capability refers to the probability of an equipment system successfully completing a task. By setting initial values ​​for x and u, and assigning corresponding values ​​to the system matrix A of the state-space equation G based on the equipment configuration, cooperation relationship, cooperation process, and equipment performance of the equipment system, an evaluation index model for calculating the above capabilities is established. Based on the state motion equation of the state-space equation G, the evaluation index values ​​of each capability are calculated.

[0161] The state motion expressions x(k) and the corresponding output y(k) of the state-space equation G are respectively

[0162]

[0163] To establish a model for evaluating resilience, survivability, response capability, and mission completion capability, 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.

[0164]

[0165] Substituting equation (3) into equation (2), we get

[0166] y(k)=CA k-1 B (4)

[0167] Step S2.1: Establish a resilience evaluation index model:

[0168] Let the n×n-dimensional matrix A, and the element a at the i-th row and j-th column ij be 1 or 0. When i≠n, j≠n and a ij = 1, it represents that the j-th equipment and the i-th equipment are included in the equipment system and their communication relationship is established, and the operation process is from the j-th equipment to the i-th equipment. When i≠n, j≠n and a ij = 0, it represents that there is no communication relationship between the j-th equipment and the i-th equipment and there is no transfer relationship in the operation process; when i = n, j≠n and a ij = 1, it represents that the operation process of the system terminates after the operation of the j-th equipment, that is, the j-th equipment is the terminal equipment of the operation process. Denote the resilience evaluation index as I v , calculate the integer k that makes y(k)>0 according to Equation (4), and then sum all y(k) greater than zero to get I v , I v The larger the value, the more ways there are for the equipment system to complete the operation process and reach the termination state, and the stronger the variability ability;

[0169] Step S2.2: Establish a response ability evaluation index model:

[0170] Let the n×n-dimensional matrix A t be:

[0171] A t = A*T (5)

[0172] In the formula, T is an n×n-dimensional matrix, and its element at the i-th row and j-th column is σ tij , σ is a constant and σ>0, t ij is the time-consuming of the j-th equipment in the operation process, that is, after t ij time, the operation process transfers from the j-th equipment to the i-th equipment or the termination state, where j < n, and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension. According to Equation (4), there is:

[0173]

[0174] Among them, y t (k) is the output of the system state space equation with A t as the system matrix, B as the input matrix, and C as the output matrix. k is the discrete time variable, is the (k - 1)th power of the matrix A t in Equation (5);

[0175] Calculate the integer k that makes y t (k)>0, and then sum all yt (k) Summation and rearrangement result in the following form:

[0176]

[0177] In the formula, t c represents the time consumption for the c-th way of the equipment system to complete the operation process, where c = 1, 2,..., I v , let the response ability evaluation index I t be:

[0178]

[0179] The response ability is evaluated by the mean value of the exponential function of the time consumed for the equipment system to complete the operation process and reach the termination state. The smaller I t , the stronger the reaction ability;

[0180] Step S2.3: Establish a task completion ability evaluation index model:

[0181] Let the n×n dimensional matrix A [[ID=2〕8] p be

[0182] ]>`A p = A * P (9)

[0183] In the formula, 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, that is, the operation process transfers from the j-th equipment to the i-th equipment or the termination state with probability p ij , where j < n, and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension. According to formula (4), we have:

[0184]

[0185] Among them, y p (k) is the output of the system state space equation with A p as the system matrix, B as the input matrix, and C as the output matrix. k is the discrete time variable, is the (k - 1)-th power of the matrix A p in formula (9);

[0186] Calculate the integer k that makes y p (k)>0, and then sum all y p (k) and rearrange to form the following form

[0187]

[0188] In the formula, p cThe 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 Let I be the evaluation index for the ability to complete the task. p Defined as:

[0189]

[0190] Mission completion capability is evaluated by the average success rate of the equipment system in completing the operational process through all possible means. p The larger the value, the stronger the ability to complete the task;

[0191] Step S2.4: Establish a survivability evaluation index model:

[0192] Based on the strain capability evaluation index model, a damage resistance evaluation index model is established. The first n-1 columns of matrix A are set to zero, representing that a certain piece of equipment in the system or the communication link related to that equipment is damaged or fails due to an attack. 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, indicating the 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 minimum case, set the remaining n-2 columns of the first n-1 columns of A 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 = Set A to zero column number - 1; I r The higher the value, the fewer pieces of equipment are required in the equipment system to ensure the completion of the mission, the greater the amount of equipment loss that can be tolerated, and the stronger the resistance to destruction.

[0193] Step S3: Establish a comprehensive optimization model for the equipment system, including optimization variables, optimization objectives, and constraints;

[0194] Specifically, in step S3:

[0195] The system matrix A with G as the optimization variable represents the equipment configuration, cooperation relationship, cooperation process and equipment performance of the equipment system; the optimization objectives are selected from the evaluation indicators of adaptability, survivability, response capability and mission completion capability; the constraints include equipment cost constraints, cooperation relationship between equipment and cooperation process constraints.

[0196] The equipment system optimization model can be represented as:

[0197]

[0198] In the formula, g a (A) The cost of integrating equipment into the system and establishing collaborative relationships with other equipment, b a As the upper limit of equipment cost, a ij Let be the element in the i-th row and j-th column of matrix A; matrix A is the optimization variable, representing equipment configuration, cooperation relationship, and cooperation process. t1 I p1 In this context, T and P represent the equipment's performance in terms of mission completion time and mission success rate, respectively; I v1 I t1 I p1 I r1 These are the strain capability evaluation indicators I v Response capability evaluation index I t Task completion ability evaluation index I p Damage resistance evaluation index I r The normalized value;

[0199]

[0200] Among them, I vu For I v Upper limit of value, I tu For I t Upper limit of value, I ru For I r Value limit; w v w r w t w p The weights of the indicators are set by the designers; constraints and To constrain equipment collaboration relationships and processes, ensuring that the optimized collaboration relationships and processes conform to the functional characteristics of each piece of equipment, among which, I n Let M be an n-dimensional unit column vector, and M be an n×n-dimensional matrix of collaboration relationships and process constraints, with the element in the i-th row and j-th column denoted as m. ij When i≠n, j≠n and m ij When = 1, it means that the j-th equipment can cooperate with the i-th equipment and the cooperation process is from the j-th equipment to the i-th equipment. When i ≠ n, j ≠ n and m ij When = 0, it means that the j-th equipment cannot cooperate with the i-th equipment. When i = n, j ≠ n and m ij When = 1, it means that the system operation process can terminate after the j-th equipment finishes running, that is, the j-th equipment is the terminal equipment of the operation process; constraint g a (A)-b a ≤0 represents the equipment cost constraint, and the function g a(A) represents the cost of incorporating equipment into the system operation and establishing collaborative relationships with other equipment, g a (A)-b a ≤0 can be calculated according to the following formula:

[0201]

[0202] In the formula, C a is an n×n dimensional equipment cost matrix, and the element c aij in its i-th row and j-th column represents the cost of incorporating the j-th equipment into the system operation, where j < n, and the operator * represents the multiplication of corresponding elements of two matrices of the same dimension.

[0203] Step S4: Based on the equipment system optimization model, use an optimization algorithm to solve the optimization variables that meet the constraint conditions and achieve the optimization goal, so as to realize the comprehensive optimization of the equipment system.

[0204] Specifically, in the said step S4:

[0205] Comprehensive optimization of equipment system structure and equipment performance: Based on the established equipment system optimization model, use an optimization algorithm to solve the optimization variable A o that meets the constraint conditions and achieves the optimization goal, so as to realize the comprehensive optimization of the equipment configuration, collaborative relationship, collaborative process, and equipment performance of the equipment system;

[0206] Use an algorithm to search for the optimal solution A o of the equipment system optimization model formula (14). The algorithm includes the branch and bound algorithm and the genetic algorithm. According to the matrix A o determine the equipment incorporated into the system after optimization and the collaborative relationship and collaborative process between the equipment. Referring to formulas (6) and (10), there are:

[0207]

[0208] Among them, A to is the matrix of equipment operation time-consuming performance indicators after optimization, and A po is the matrix of equipment mission success rate performance indicators after optimization;

[0209] According to the non-zero elements in the matrices A to and A po , determine the operation time-consuming and mission success rate performance indicators of the equipment incorporated into the system. If the element a to in the i-th row and j-th column of A toij is non-zero, then the operation time-consuming performance indicator of the j-th equipment is:

[0210] t oij ​​​​​​

[0211] Among them, a toij Let matrix A to The element in the i-th row and j-th column;

[0212] For example, A po The element a in row i and column j poij If the value is non-zero, then the mission success rate performance index of the j-th equipment is:

[0213] p oij =a poij (18)

[0214] To achieve the optimal matching of equipment configuration, cooperation relationships, cooperation processes, and equipment performance.

[0215] According to the present invention, an equipment system comprehensive optimization system based on a linear time-invariant discrete system includes:

[0216] Module M1: Establish an integrated model of equipment architecture and equipment performance, represented by the state-space equations of a linear time-invariant discrete system.

[0217] Specifically, in module M1:

[0218] An integrated model of equipment system architecture and performance is established, represented by the state-space equation G of a linear time-invariant discrete system. The equipment system architecture considers the equipment configuration, cooperative relationships, and cooperative processes. Here, the state vector of G is x, with the last state representing the final state of system operation. The remaining states correspond one-to-one with all the equipment constituting the system. The initial value of x is set according to the analysis requirements. The system matrix A of G represents the equipment configuration, cooperative relationships, cooperative processes, and equipment performance of the equipment system. Each element in A is assigned a corresponding value according to the specific analysis and optimization requirements. The input variable u of G represents the external signal driving the operation of the equipment system, and u is set according to the analysis requirements. The output variable y of G takes the final state of system operation from the state vector x.

[0219] The state-space equation G of a linear time-invariant discrete system is as follows:

[0220] x(k+1)=Ax(k)+Bu(k)

[0221] y(k)=Cx(k) (1)

[0222] k = 0, 1, 2, ...

[0223] In the formula, k is a discrete time variable, x is an n-dimensional state vector, u is an input variable, y is an output variable, A is an n×n-dimensional system matrix, B is an n×1-dimensional input matrix, C is a 1×n-dimensional output matrix, the first n-1 states of x correspond to all the equipment to be constituted in the system, and the nth state is the final state; when the element a in the i-th row and j-th column of A...ij When the value is non-zero, it indicates that the j-th equipment participates in the system operation and has a cooperative relationship with the i-th equipment. The cooperative process is from the j-th equipment to the i-th equipment; otherwise, a ij =0, non-zero a ij The value of 1 reflects only the system architecture of the equipment system, or it can be a value related to the performance of the j-th equipment, reflecting the impact of the equipment performance on the system operation. Array B is set so that u acts on the state of the corresponding system operation start-end equipment to drive the system operation. The states of the system operation end-end equipment all point to the termination state. Array C is set so that y takes the termination state of the system operation.

[0224] Module M2: Analyzes and evaluates the equipment system's adaptability, survivability, response capability, and mission completion capability;

[0225] Specifically, in module M2:

[0226] Adaptability refers to the ability of an equipment system to complete a task through multiple means; damage resistance refers to the ability of an equipment system to withstand equipment loss or failure while still being able to complete a task; response capability refers to the efficiency of an equipment system in completing a task; and task completion capability refers to the probability of an equipment system successfully completing a task. By setting initial values ​​for x and u, and assigning corresponding values ​​to the system matrix A of the state-space equation G based on the equipment configuration, cooperation relationship, cooperation process, and equipment performance of the equipment system, an evaluation index model for calculating the above capabilities is established. Based on the state motion equation of the state-space equation G, the evaluation index values ​​of each capability are calculated.

[0227] The state motion expressions x(k) and the corresponding output y(k) of the state-space equation G are respectively

[0228]

[0229] To establish a model for evaluating resilience, survivability, response capability, and mission completion capability, 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.

[0230]

[0231] Substituting equation (3) into equation (2), we get

[0232] y(k)=CA k-1 B (4)

[0233] Module M2.1: Establishing a strain capacity evaluation index model:

[0234] Let A be an n×n matrix, and let a be the element in the i-th row and j-th column. ij It is 1 or 0, when i≠n, j≠n and a ijWhen \(a = 1\), it means that the \(j\)-th equipment and the \(i\)-th equipment are selected into the equipment system and their communication relationship is established. The operation process is from the \(j\)-th equipment to the \(i\)-th equipment. When \(i\neq n\), \(j\neq n\) and \(a\) ij When \(a = 0\), it means that there is no communication relationship between the \(j\)-th equipment and the \(i\)-th equipment, and there is no transfer relationship in the operation process; when \(i = n\), \(j\neq n\) and \(a\) ij When \(a = 1\), it means that the operation process of the system terminates after the operation of the \(j\)-th equipment. That is, the \(j\)-th equipment is the terminal equipment of the operation process. Denote the evaluation index of adaptability as \(I\) v According to Equation (4), calculate the integer \(k\) that makes \(y(k)>0\), and then sum all \(y(k)\) greater than zero to get \(I\) v \(I\) v The larger the value of \(I\), the more ways there are for the equipment system to complete the operation process and reach the termination state, and the stronger the variability ability;

[0235] Module M2.2: Establish a response ability evaluation index model:

[0236] Let the \(n\times n\) matrix \(A\) t be:

[0237] \(A\) t \(=A*T\ (5)\) <##

[0238] In the formula, \(T\) is an \(n\times n\) matrix, and the element in its \(i\)-th row and \(j\)-th column is \(\sigma\) tij , \(\sigma\) is a constant and \(\sigma>0\), \(t\) ij is the time-consuming of the \(j\)-th equipment in the operation process, that is, after \(t\) ij time, the operation process transfers from the \(j\)-th equipment to the \(i\)-th equipment or the termination state, where \(j < n\). The operator \(*\) represents the multiplication of the corresponding elements of two matrices of the same dimension. According to Equation (4), we have:

[0239]

[0240] Among them, \(y\) t (k) is the output of the system state space equation with \(A\) t as the system matrix, \(B\) as the input matrix, and \(C\) as the output matrix. \(k\) is the discrete time variable, is the \((k - 1)\)-th power of the matrix \(A\) t in Equation (5);

[0241] Calculate the integer \(k\) that makes \(y\) t (k)>0, and then sum all \(y\) t (k) greater than zero, and organize it into the following form:

[0242]

[0243] In the formula, \(t\) cDenote the time taken for the $c$-th path of the equipment system to complete the operation process, where $c = 1, 2, \cdots, I$. v , let the response ability evaluation index $I$ t be:

[0244]

[0245] The response ability is evaluated by the mean value of the exponential function of the time taken for the equipment system to complete the operation process and reach the termination state, $I$ t The smaller it is, the stronger the reaction ability;

[0246] Module M2.3: Establish a task completion ability evaluation index model:

[0247] Let the $n\times n$ matrix $A$ p be

[0248] $A$ p $= A*P\ (9)$

[0249] where $P$ is an $n\times n$ 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, that is, the operation process transfers from the $j$-th equipment to the $i$-th equipment or the termination state with probability $p$ ij , where $j < n$, and the operator $*$ represents the multiplication of the corresponding elements of two matrices of the same dimension. According to Equation (4), we have:

[0250]

[0251] where $y$ p $(k)$ is the output of the system state space equation with $A$ p as the system matrix, $B$ as the input matrix, and $C$ as the output matrix. $k$ is the discrete time variable, is the $(k - 1)$-th power of the matrix $A$ in Equation (9) p ;

[0252] Calculate the integer $k$ that makes $y$ p $(k)>0$, and then sum all $y$ p $(k)$ greater than zero and organize it into the following form

[0253] <00010s8>

[0254] where $p$ c represents the success rate of the $c$-th path for the equipment system to complete the operation process and reach the termination state, $c = 1, 2, \cdots, I$ v , let the task completion ability evaluation index $I$ p be defined as:

[0255]

[0256] Mission completion capability is evaluated by the average success rate of the equipment system in completing the operational process through all possible means. p The larger the value, the stronger the ability to complete the task;

[0257] Module M2.4: Establishing a model for evaluating survivability:

[0258] Based on the strain capability evaluation index model, a damage resistance evaluation index model is established. The first n-1 columns of matrix A are set to zero, representing that a certain piece of equipment in the system or the communication link related to that equipment is damaged or fails due to an attack. 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, indicating the 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 minimum case, set the remaining n-2 columns of the first n-1 columns of A 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 = Set A to zero column number - 1; I r The higher the value, the fewer pieces of equipment are required in the equipment system to ensure the completion of the mission, the greater the amount of equipment loss that can be tolerated, and the stronger the resistance to destruction.

[0259] Module M3: Establish a comprehensive optimization model for the equipment system, including optimization variables, optimization objectives, and constraints;

[0260] Specifically, in module M3:

[0261] The system matrix A with G as the optimization variable represents the equipment configuration, cooperation relationship, cooperation process and equipment performance of the equipment system; the optimization objectives are selected from the evaluation indicators of adaptability, survivability, response capability and mission completion capability; the constraints include equipment cost constraints, cooperation relationship between equipment and cooperation process constraints.

[0262] The equipment system optimization model can be represented as:

[0263]

[0264] In the formula, g a (A) The cost of integrating equipment into the system and establishing collaborative relationships with other equipment, b a As the upper limit of equipment cost, a ijLet be the element in the i-th row and j-th column of matrix A; matrix A is the optimization variable, representing equipment configuration, cooperation relationship, and cooperation process. t1 I p1 In this context, T and P represent the equipment's performance in terms of mission completion time and mission success rate, respectively; I v1 I t1 I p1 I r1 These are the strain capability evaluation indicators I v Response capability evaluation index I t Task completion ability evaluation index I p Damage resistance evaluation index I r The normalized value;

[0265]

[0266] Among them, I vu For I v Upper limit of value, I tu For I t Upper limit of value, I ru For I r Value limit; w v w r w t w p The weights of the indicators are set by the designers; constraints and To constrain equipment collaboration relationships and processes, ensuring that the optimized collaboration relationships and processes conform to the functional characteristics of each piece of equipment, among which, I n Let M be an n-dimensional unit column vector, and M be an n×n-dimensional matrix of collaboration relationships and process constraints, with the element in the i-th row and j-th column denoted as m. ij When i≠n, j≠n and m ij When = 1, it means that the j-th equipment can cooperate with the i-th equipment and the cooperation process is from the j-th equipment to the i-th equipment. When i ≠ n, j ≠ n and m ij When = 0, it means that the j-th equipment cannot cooperate with the i-th equipment. When i = n, j ≠ n and m ij When = 1, it means that the system operation process can terminate after the j-th equipment finishes running, that is, the j-th equipment is the terminal equipment of the operation process; constraint g a (A)-b a ≤0 represents the equipment cost constraint, and the function g a (A) represents the cost of integrating equipment into the system and establishing collaborative relationships with other equipment, g a (A)-b a ≤0 can be calculated using the following formula:

[0267]

[0268] Where C a is an n×n dimensional equipment cost matrix, and the element c aij in its i-th row and j-th column represents the cost of incorporating the j-th equipment into the system operation, where j < n, and the operator * represents the multiplication of corresponding elements of two matrices of the same dimension.

[0269] Module M4: Based on the equipment system optimization model, an optimization algorithm is used to solve the optimization variables that satisfy the constraint conditions and achieve the optimization objectives, so as to realize the comprehensive optimization of the equipment system. <00​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​If the value is non-zero, then the mission success rate performance index of the j-th equipment is:

[0279] p oij =a poij (18)

[0280] To achieve the optimal matching of equipment configuration, cooperation relationships, cooperation processes, and equipment performance.

[0281] Example 2:

[0282] Example 2 is a preferred example of Example 1, and is used to illustrate the present invention in more detail.

[0283] To address the problem of comprehensive optimization of equipment systems, particularly the multi-dimensional comprehensive analysis and optimization of equipment systems and equipment configurations, collaboration relationships, collaboration processes, and equipment performance, this paper provides a comprehensive optimization method for equipment systems based on linear time-invariant discrete systems.

[0284] The equipment system comprehensive optimization method based on linear time-invariant discrete systems includes the following steps:

[0285] Step 1: Integrated Modeling of Equipment System Structure and Performance: Establish an integrated model of equipment system structure and performance, represented by the state-space equation G of a linear time-invariant discrete system. The equipment system structure mainly considers the equipment configuration, cooperative relationships, and cooperative processes. Here, the state vector x of G represents the final state of the system operation, with the remaining states corresponding one-to-one with all the equipment constituting the system. The initial value of x can be set according to the analysis requirements. The system matrix A of G represents the equipment configuration, cooperative relationships, cooperative processes, and equipment performance of the equipment system. Each element in A can be assigned a corresponding value according to the specific analysis and optimization requirements. The input variable u of G represents the external signal driving the operation of the equipment system, and u can be set according to the analysis requirements. The output variable y of G is taken from the final state of the system operation in the state vector x.

[0286] Step 2, Equipment System Capability Analysis and Evaluation: This includes the equipment system's adaptability, damage resistance, response capability, and mission completion capability. Adaptability refers to the equipment system's ability to complete tasks through multiple methods; damage resistance refers to the equipment system's ability to withstand equipment loss (or failure) while still being capable of completing the task; response capability refers to the equipment system's ability to quickly complete the task; and mission completion capability refers to the probability of the equipment system successfully completing the task. By setting appropriate initial values ​​for x and u, and assigning corresponding values ​​to the system matrix A of the state-space equation G based on the equipment configuration, collaborative relationships, collaborative processes, and equipment performance, an evaluation index model for calculating the above capabilities is established. Based on the state motion equations of the state-space equation G, the evaluation index values ​​for each capability are calculated.

[0287] Step 3: Modeling the comprehensive optimization model of the equipment system: Establish a comprehensive optimization model of the equipment system that includes optimization variables, optimization objectives, and constraints; wherein, the optimization variable is the system matrix A of G, which represents the equipment configuration, cooperation relationship, cooperation process, and equipment performance of the equipment system; the optimization objective is selected from the evaluation index of the capability described in Step 2; the constraints include equipment cost constraints, cooperation relationship between equipment, and cooperation process constraints.

[0288] Step 4: Comprehensive Optimization of Equipment System Structure and Performance: Based on the equipment system optimization model established in Step 3, an optimization algorithm is used to solve for the optimization variable A that satisfies the constraints and achieves the optimization objective. o This enables comprehensive optimization of equipment configuration, collaborative relationships, collaborative processes, and equipment performance within the equipment system.

[0289] Preferably, in step 1, the state-space equation G of the linear time-invariant discrete system is in the following form:

[0290] x(k+1)=Ax(k)+Bu(k)

[0291] y(k)=Cx(k) (1)

[0292] k = 0, 1, 2, ...

[0293] In the formula, k is a discrete time variable, x is an n-dimensional state vector, u is an input variable, y is an output variable, A is an n×n-dimensional system matrix, B is an n×1-dimensional input matrix, and C is a 1×n-dimensional output matrix. The first n-1 states of x correspond to all the equipment to be constructed into the system, and the nth state is the final state; when the element a in the i-th row and j-th column of A... ij When the value is non-zero, it indicates that the j-th equipment participates in the system operation and has a cooperative relationship with the i-th equipment. The cooperative process is from the j-th equipment to the i-th equipment; otherwise, a ij =0, non-zero a ij The value of can be 1, which only reflects the system architecture of the equipment system, or it can be a value related to the performance of the j-th equipment, reflecting the impact of the equipment performance on the system operation; set up array B so that u acts on the state of the corresponding system operation start-end equipment to drive the system operation, and the state of the system operation end equipment all point to the termination state; set up array C so that y takes the termination state of the system operation.

[0294] Preferably, in step 2, the state motion expression x(k) and the corresponding output y(k) of the state space equation G are respectively

[0295]

[0296] To establish a model for evaluating the indicators of resilience, survivability, responsiveness, and mission completion ability, the initial state vector x(0) is taken as a zero vector, and the input variable u(k) is taken as a unit impulse signal, that is

[0297]

[0298] Substituting Equation (3) into Equation (2), we have

[0299] y(k) = CA k-1 B (4)

[0300] 1) Resilience evaluation index model

[0301] Let the n×n matrix A, and the element a at the i-th row and j-th column ij be 1 or 0. When i≠n, j≠n and a ij = 1, it means that the j-th equipment and the i-th equipment are selected into the equipment system and their communication relationship is established, and the operation process is from the j-th equipment to the i-th equipment. When i≠n, j≠n and a ij = 0, it means that there is no communication relationship between the j-th equipment and the i-th equipment and there is no transfer relationship in the operation process; when i = n, j≠n and a ij = 1, it means that the operation process of the system terminates after the operation of the j-th equipment, that is, the j-th equipment is the terminal equipment of the operation process. Denote the resilience evaluation index as I v , the integer k that makes y(k)>0 can be calculated according to Equation (4), and then the sum of all y(k) greater than zero can be obtained to get I v , I v The larger the value, the more ways the equipment system has to complete the operation process and reach the termination state, and the stronger the variability ability;

[0302] 2) Responsiveness evaluation index model

[0303] Let the n×n matrix A t [[ID=�9]]be

[0304] A t = A*T (5)

[0305] In the formula, T is an n×n matrix, and its element at the i-th row and j-th column is σ tij , σ is a constant (σ>0), t ij is the time consumed by the j-th (j < n) equipment in the operation process (that is, after t ij time, the operation process transfers from the j-th equipment to the i-th equipment or the termination state), and the operator * represents the multiplication of the corresponding elements of two matrices of the same dimension. According to Equation (4), we have

[0306]

[0307] Calculate the integer \(k\) for which \(y t (k)>0\), and then sum all \(y t (k)\) that are greater than zero and organize them into the following form

[0308]

[0309] In the formula, \(t c represents the time taken for the \(c\)-th path of the equipment system to complete the operation process, where \(c = 1, 2, \cdots, I v , and let the response ability evaluation index \(I t be

[0310]

[0311] That is, the response ability is the mean evaluation of the time exponential function from the equipment system completing the operation process to the termination state. The smaller \(I t , the stronger the reaction ability;

[0312] 3) Task completion ability evaluation index model

[0313] Let the \(n\times n\) matrix \(A p be

[0314] A p = A * P (9)

[0315] In the formula, \(P\) is an \(n\times n\) matrix, and the element in its \(i\)-th row and \(j\)-th column is \(p ij , and \(p ij is the success rate of the \(j\)-th (\(j < n\)) equipment completing its task in the operation process (that is, the operation process transfers from the \(j\)-th equipment to the \(i\)-th equipment or the termination state with probability \(p ij ). The operator * represents the multiplication of the corresponding elements of two matrices of the same dimension. According to formula (4), we have

[0316]

[0317] Calculate the integer \(k\) for which \(y p (k)>0\), and then sum all \(y A p (k)\) that are greater than zero and organize them into the following form

[0318]

[0319] In the formula, \(p c represents the success rate of the \(c\)-th path for the equipment system to complete the operation process and reach the termination state, where \(c = 1, 2, \cdots, I v , and let the task completion ability evaluation index \(I p A be defined as

[0320]

[0321] In other words, mission completion capability is evaluated by the average success rate of the equipment system in completing the operational process through all possible means. p The larger the value, the stronger the ability to complete the task;

[0322] 4) Damage resistance evaluation index model

[0323] Based on the strain capability evaluation index model, a damage resistance evaluation index model is established. The first n-1 columns of matrix A are set to zero, representing that a certain piece of equipment in the system or the communication link related to that equipment is damaged or fails due to an attack. 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 minimum case, set the remaining n-2 columns of the first n-1 columns of A 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 = Set A to zero column number - 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.

[0324] Preferably, in step 3, the equipment system optimization model can be expressed as:

[0325]

[0326] In the formula, matrix A is the optimization variable, representing equipment configuration, cooperation relationship, and cooperation process, which is implicit in I. t1 I p1 In this context, T and P represent the equipment's performance in terms of mission completion time and mission success rate, respectively; I v1 I t1 I p1 I r1 These are the strain capability evaluation indicators I v Response capability evaluation index I t Task completion ability evaluation index I p Damage resistance evaluation index I r The normalized value,

[0327]

[0328] Among them, I vuFor I v Value upper limit, I tu For I t Value upper limit, I ru For I r Value upper limit; w v , w r , w t , w p Are the weights of the indicators, set by the designers; Constraints And Are the equipment cooperation relationships and cooperation process constraints, ensuring that the optimized equipment cooperation relationships and cooperation processes conform to the functional characteristics of each equipment, where n Is an n-dimensional unit column vector, M is an n×n-dimensional cooperation relationship and process constraint matrix, and its element in the i-th row and j-th column is denoted as m ij , when i≠n, j≠n and m ij =1, it means that the j-th equipment can cooperate with the i-th equipment and the cooperation process is from the j-th equipment to the i-th equipment. When i≠n, j≠n and m ij =0, it means that the j-th equipment cannot cooperate with the i-th equipment. When i=n, j≠n and m ij =1, it means that the system operation process can be terminated after the j-th equipment runs, that is, the j-th equipment is the terminal equipment of the operation process; Constraint g a (A)-b a ≤0 is the equipment cost constraint, and the function g a (A v ) represents the cost of incorporating the equipment into the system operation and establishing cooperation relationships with other equipment. g a (A)-b a ≤0 can be calculated according to the following formula:

[0329]

[0330] In the formula, C a Is an n×n-dimensional equipment cost matrix, and its element in the i-th row and j-th column c aij Represents the cost of incorporating the j-th (j<n) equipment into the system operation. The operator * represents the multiplication of the corresponding elements of two matrices of the same dimension.

[0331] Preferably, in step 4, algorithms such as the branch and bound algorithm, genetic algorithm, etc. can be used to search for the optimal solution A of the equipment system optimization model formula (14) o , and according to the matrix A o Determine the equipment incorporated into the system after optimization (i.e., equipment configuration) and the cooperation relationships and cooperation processes between equipment. Referring to formulas (6) and (10), there are

[0332]

[0333] According to matrix A to and A po The elements of non-zero are used to determine the performance indicators of equipment operation time and mission success rate to be included in the system, such as A. to The element a in row i and column j toij If the value is non-zero, then the performance index of the running time of the j-th equipment is:

[0334] t oij =log σ a toij (17)

[0335] For example, A po The element a in row i and column j poij If the value is non-zero, then the mission success rate performance index of the j-th equipment is:

[0336] p oij =a poij (18)

[0337] Ultimately, the goal is to achieve the optimal match between equipment configuration, collaborative relationships, collaborative processes, and equipment performance.

[0338] Example 3:

[0339] Example 3 is a preferred example of Example 1, and is used to illustrate the present invention in more detail.

[0340] Combination Figure 1 The specific implementation details of the present invention are as follows, and the scope of protection of this patent is not limited to the specific implementation of this embodiment:

[0341] Assume an equipment system with possible equipment configurations including eight types: S1, S2, Z1, Z2, G1, G2, F1, and F2. S1 and S2 are the initial equipment in the operational process, as are F1 and F2. Before optimization, the communication connections and operational processes 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 state (T). The solid line with arrows represents the communication relationship between equipment and the arrow indicates the operation process. The dashed line with arrows represents the process from the end of the operation of the starting equipment to the termination state.

[0342] Step 1: Integrated modeling of equipment system architecture and equipment performance. Figure 2 For the equipment system shown, an integrated model of equipment configuration, cooperation relationships, cooperation processes, 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.

[0343]

[0344] 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.

[0345]

[0346] C = [0 0 0 0 0 0 0 0 1]

[0347] Step 2: Equipment system capability analysis and evaluation. Let the initial value of vector x(0) be the zero vector, and the input variable u(k) be a unit impulse signal.

[0348]

[0349] Establish evaluation index models for adaptability, survivability, response capability, and mission completion capability respectively:

[0350] (1) Evaluation index model and analysis of adaptability

[0351] Let matrix A in G be

[0352]

[0353] According to the strain capacity evaluation index I v Calculation formula:

[0354]

[0355] Strain capability 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;

[0356] (2) Evaluation index model and analysis of response capability

[0357] 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 and optimization), matrix A t The calculation is as follows, taking σ = 1.2.

[0358]

[0359]

[0360] According to response capability evaluation index I t Calculation formula:

[0361]

[0362]

[0363] Based on the above calculations, the time t1 for the equipment system to complete the first operational process (S1→Z1→G1→F1→T) is 11s, and the time t2 for the equipment system to complete the second operational process (S2→Z2→G2→F2→T) is 12s. The response capability evaluation index I... t =8.17;

[0364] (3) Evaluation index model and analysis of task completion ability

[0365] 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 and optimization), matrix A p The calculation is as follows:

[0366]

[0367]

[0368] According to task completion ability evaluation index I p Calculation formula:

[0369] p1 = 0.1152, p2 = 0.2058

[0370]

[0371] 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 0.1152, and the mission success rate p2 for the second path (S2→Z2→G2→F2→T) is 0.2058. The mission completion capability evaluation index I... p =0.1605;

[0372] (4) Evaluation index model and analysis of damage resistance

[0373] Set columns 1 through 8 of matrix A to zero, I v All values ​​are 1; set the first column of matrix A to zero, then set the second to eighth columns of matrix A to zero respectively, 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.

[0374] Table 1. Calculation process of damage resistance index

[0375]

[0376] Step 3: Equipment System Comprehensive Optimization Model Building. Establish an equipment system optimization model. The equipment performance-cost function adopts a linear function, as follows:

[0377]

[0378]

[0379] Regarding the normalization of competency evaluation indicators, take I vu =16、I tu =σ 21 =46.005, I ru =8; Regarding the indicator weights, take w v =0.25, w r =0.25, w t =0.25, w p =0.25;

[0380] Optimize the initial value of variable A.

[0381]

[0382] Regarding constraints, the collaboration relationship and process constraint matrix M is as follows:

[0383]

[0384] Let b be the upper limit of the equipment configuration optimization cost. a =7, let the equipment cost matrix C a for

[0385]

[0386] Step 4: Comprehensive optimization of equipment system structure and performance. A genetic algorithm is used to search for the optimal solution A of the equipment system optimization model (14). o ,have

[0387]

[0388] The optimized equipment system includes equipment configuration, collaborative relationships, and collaborative processes, such as... Figure 3As shown, the optimized equipment system excludes equipment F2, with an equipment cost of 6.8 and an optimization index value of 0.212. The matrix describing the equipment's operating time performance and mission success rate performance is as follows:

[0389]

[0390]

[0391] 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.

[0392] 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 comprehensive optimization method for equipment systems based on linear time-invariant discrete systems, characterized in that, include: Step S1: Establish an integrated model of equipment architecture and equipment performance, represented by the state-space equations of a linear time-invariant discrete system. Step S2: Analyze and evaluate the equipment system's adaptability, survivability, response capability, and mission completion capability; Step S3: Establish a comprehensive optimization model for the equipment system, including optimization variables, optimization objectives, and constraints; Step S4: Based on the equipment system optimization model, use optimization algorithms to solve for the optimization variables that satisfy the constraints and achieve the optimization objectives, thereby realizing the comprehensive optimization of the equipment system; In step S1: An integrated model of equipment architecture and performance is established, represented by the state-space equation G of a linear time-invariant discrete system. The equipment architecture considers equipment configuration, cooperative relationships, and cooperative processes within the system. The state vector of G is... x The last state represents the termination of system operation; the remaining states correspond one-to-one with all the equipment that constitutes the proposed system. x The initial values ​​are set according to the analysis requirements; the system matrix of G. A This refers to the equipment configuration, collaborative relationships, collaborative processes, and equipment performance of the equipment system, and assigns specific requirements based on the analysis and optimization needs. A The corresponding values ​​of each element in G; the input variables of G. u External signals representing the operation of the driving equipment system. u Set the output variables of G according to the analysis requirements. y Take the state vector x The system is in a terminated state. The state-space equation G of a linear time-invariant discrete system is as follows: (1) In the formula, k For discrete time variables, x for n dimensional state vector, u For input variables, y For output variables, A for n × n 3D system matrix, B for n ×1 dimensional input matrix, C 1× n 3D output matrix, x The former n -1 states correspond to all the equipment that constitute the proposed system, the first state n The state is the termination state; when A The i Line number j Column elements a ij When it is not 0, it represents the first... j Each piece of equipment participates in the system operation and is related to the first i There is a collaborative relationship between the equipment, and the collaboration process is initiated by the first... j The equipment to the first i One piece of equipment, otherwise a ij =0, non-zero a ij A value of 1 reflects only the system architecture of the equipment system, or a value equal to the first... j Each equipment performance-related value reflects the impact of equipment performance on system operation; [Settings] B Array Master u This affects the state of the corresponding system's starting equipment, driving system operation. The states of the system's terminal equipment all point to the termination state. C Array Master y Take the terminated state of the system operation; In step S2: Adaptability refers to the ability of an equipment system to complete a task through multiple means; resilience refers to the ability of an equipment system to withstand equipment loss or failure while still being capable of completing the task; responsiveness refers to the efficiency with which an equipment system completes a task; and task completion capability refers to the probability of an equipment system successfully completing a task. This is achieved by setting... x initial value and u Based on the equipment configuration, cooperation relationships, cooperation processes, and equipment performance of the equipment system, a state-space equation G system matrix is ​​assigned. A Based on the corresponding values, establish an evaluation index model for calculating the above capabilities, and calculate the evaluation index values ​​for each capability based on the state motion equation of the state space equation G. State-space equation G: state-motion expression x ( k ) and corresponding output y ( k ) are respectively (2) To establish a model for evaluating resilience, survivability, responsiveness, and mission completion capability, an initial state vector is taken. x (0) is the zero vector, taking the input variable. u ( k () is a unit pulse signal, that is (3) Substituting equation (3) into equation (2), we get (4) Step S2.1: Establish a strain capacity evaluation index model: set up n × n 3D matrix A , No. i Line number j Column elements a ij It is 1 or 0, when i ≠ n , j ≠ n and a ij 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 ij 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 ij =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, and the response capability evaluation index is denoted as follows. I v According to equation (4), calculate the result that makes y ( k Integers greater than 0 k Then all those greater than zero y ( k ) plus 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. Step S2.2: Establish a response capability evaluation index model: set up n × n 3D matrix A t for: (5) 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 and σ >0, t ij For the first j The time consumed by a piece of equipment during its operation, that is, the time it takes to complete the process. t ij The process will run after the time limit by the first j The equipment was transferred to the first... i Each piece of equipment or terminated state, among which j < n The operator * represents the element-wise multiplication of two matrices of the same dimension, according to equation (4): (6) in, For A t For the system matrix, with B For the input matrix, with C The output of the system state-space equation is the output matrix. k For discrete time variables, For the matrix of equation (5) A t of k -1 power; Calculation makes 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: (7) 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 Set response capability evaluation indicators I t for: (8) Response capability 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; Step S2.3: Establish a task completion capability evaluation index model: set up n × n 3D matrix A p for (9) 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, that is, the probability of the operation process. p ij By the j The equipment was transferred to the first... i Each piece of equipment or terminated state, among which j < n， The operator * represents the element-wise multiplication of two matrices of the same dimension, according to equation (4): (10) in, For A p For the system matrix, with B For the input matrix, with C The output of the system state-space equation is the output matrix. k For discrete time variables, For the matrix of equation (9) A p of k -1 power; Calculation makes 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. (11) 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 Set evaluation indicators for task completion capabilities I p Defined as: (12) Mission completion capability 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 value, the stronger the ability to complete the task; Step S2.4: Establish a survivability evaluation index model: Based on the strain capability evaluation index model, a rupture resistance evaluation index model is established, which uses a matrix... A 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, indicating the 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, then A 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 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, the greater the amount of equipment loss that can be tolerated, and the stronger the resistance to destruction. In step S4: Comprehensive optimization of equipment system structure and performance: Based on the established equipment system optimization model, optimization algorithms are used to solve for the optimization variables that satisfy the constraints and achieve the optimization objectives. A o This enables comprehensive optimization of equipment configuration, collaborative relationships, collaborative processes, and equipment performance within the equipment system. The optimal solution of the equipment system optimization model (13) is obtained by using an algorithm. A o According to the matrix A o After determining the optimized equipment to be included in the system, as well as the collaborative relationships and processes between the equipment, referring to equations (6) and (10), we have: (16) in, The optimized equipment operation time performance index matrix, The optimized equipment mission success rate performance index matrix; According to the matrix A to and A po The elements of China and Africa are used to determine the performance indicators of equipment operation time and mission success rate to be included in the system. A to No. i Line number j Column elements a toij If it is non-zero, then the first... j The operating time performance indicators of each piece of equipment are as follows: (17) in, For matrix A to The i Line number j Column elements; like A po No. i Line number j Column elements a poij If it is non-zero, then the first... j The mission success rate performance index of each piece of equipment is: (18) To achieve the optimal matching of equipment configuration, cooperation relationships, cooperation processes, and equipment performance.

2. The equipment system comprehensive optimization method based on linear time-invariant discrete systems according to claim 1, characterized in that, In step S3: The system matrix with optimization variable G A This represents the equipment configuration, collaborative relationships, collaborative processes, and equipment performance of the equipment system; the optimization targets include evaluation indicators for adaptability, resilience, responsiveness, and mission completion capability; and the constraints include equipment cost constraints, collaborative relationships between equipment, and collaborative process constraints. The equipment system optimization model can be represented as: (13) In the formula, The cost of integrating equipment into the system and establishing collaborative relationships with other equipment, This is the upper limit for equipment costs. For matrix A The i Line number j Column elements; matrix A To optimize variables, representing equipment configuration, collaborative relationships, and collaborative processes, in I t1 , I p1 In T and P These represent the equipment's performance in terms of mission completion time and mission success rate, respectively. I v1 , I t1 , I p1 , I r1 These are the evaluation indicators of strain capacity. I v Response capability evaluation indicators I t Task completion ability evaluation indicators I p Damage resistance evaluation indicators I r The normalized value; (14) in, I vu For I v Value limit, I tu For I t Value limit, I ru For I r Value limit; w v , w r , w t , w p The weights of the indicators are set by the designers; constraints and To constrain equipment collaboration relationships and processes, ensuring that the optimized collaboration relationships and processes conform to the functional characteristics of each piece of equipment, among which, I n for n 1D unit column vector M for n × n The dimensional collaboration relationship and process constraint matrix, its first... i Line number j Column elements are denoted as m ij ,when i ≠ n , j ≠ n and m ij When =1, it represents the first... j The equipment can be used with the first i The equipment collaborates, and the collaboration process is initiated by the first... j The equipment to the first i One piece of equipment, when i ≠ n , j ≠ n and m ij When =0, it represents the first... j The equipment cannot be used with the first i Each piece of equipment works together, when i = n , j ≠ n and m ij When =1, it represents the first... j The system operation process can be terminated after the operation of each piece of equipment is completed, that is, the first... j Each piece of equipment is the terminal equipment in the operational process; constraints Due to equipment cost constraints, the function g a ( A This represents the cost of integrating equipment into the system and establishing collaborative relationships with other equipment. It can be calculated using the following formula: (15) In the formula, C a for n × n The cost matrix of dimensional equipment, its first i Line number j Column elements c aij The representative will be the first j The cost of incorporating individual equipment into the system operation, among which j < n， The operator * represents the element-wise multiplication of two matrices of the same dimension.

3. A comprehensive optimization system for equipment systems based on linear time-invariant discrete systems, characterized in that, include: Module M1: Establish an integrated model of equipment architecture and equipment performance, represented by the state-space equations of a linear time-invariant discrete system. Module M2: Analyzes and evaluates the equipment system's adaptability, survivability, response capability, and mission completion capability; Module M3: Establish a comprehensive optimization model for the equipment system, including optimization variables, optimization objectives, and constraints; Module M4: Based on the equipment system optimization model, it uses optimization algorithms to solve for the optimization variables that satisfy the constraints and achieve the optimization objectives, thereby realizing the comprehensive optimization of the equipment system; In module M1: An integrated model of equipment architecture and performance is established, represented by the state-space equation G of a linear time-invariant discrete system. The equipment architecture considers equipment configuration, cooperative relationships, and cooperative processes within the system. The state vector of G is... x The last state represents the termination of system operation; the remaining states correspond one-to-one with all the equipment that constitutes the proposed system. x The initial values ​​are set according to the analysis requirements; the system matrix of G. A This refers to the equipment configuration, collaborative relationships, collaborative processes, and equipment performance of the equipment system, and assigns specific requirements based on the analysis and optimization needs. A The corresponding values ​​of each element in G; the input variables of G. u External signals representing the operation of the driving equipment system. u Set the output variables of G according to the analysis requirements. y Take the state vector x The system is in a terminated state. The state-space equation G of a linear time-invariant discrete system is as follows: (1) In the formula, k For discrete time variables, x for n dimensional state vector, u For input variables, y For output variables, A for n × n 3D system matrix, B for n ×1 dimensional input matrix, C 1× n 3D output matrix, x The former n -1 states correspond to all the equipment that constitute the proposed system, the first state n The state is the termination state; when A The i Line number j Column elements a ij When it is not 0, it represents the first... j Each piece of equipment participates in the system operation and is related to the first i There is a collaborative relationship between the equipment, and the collaboration process is initiated by the first... j The equipment to the first i One piece of equipment, otherwise a ij =0, non-zero a ij A value of 1 reflects only the system architecture of the equipment system, or a value equal to the first... j Each equipment performance-related value reflects the impact of equipment performance on system operation; [Settings] B Array Master u This affects the state of the corresponding system's starting equipment, driving system operation. The states of the system's terminal equipment all point to the termination state. C Array Master y Take the terminated state of the system operation; In module M2: Adaptability refers to the ability of an equipment system to complete a task through multiple means; resilience refers to the ability of an equipment system to withstand equipment loss or failure while still being capable of completing the task; responsiveness refers to the efficiency with which an equipment system completes a task; and task completion capability refers to the probability of an equipment system successfully completing a task. This is achieved by setting... x initial value and u Based on the equipment configuration, cooperation relationships, cooperation processes, and equipment performance of the equipment system, a state-space equation G system matrix is ​​assigned. A Based on the corresponding values, establish an evaluation index model for calculating the above capabilities, and calculate the evaluation index values ​​for each capability based on the state motion equation of the state space equation G. State-space equation G: state-motion expression x ( k ) and corresponding output y ( k ) are respectively (2) To establish a model for evaluating resilience, survivability, responsiveness, and mission completion capability, an initial state vector is taken. x (0) is the zero vector, taking the input variable. u ( k () is a unit pulse signal, that is (3) Substituting equation (3) into equation (2), we get (4) Module M2.1: Establishing a strain capacity evaluation index model: set up n × n 3D matrix A , No. i Line number j Column elements a ij It is 1 or 0, when i ≠ n , j ≠ n and a ij 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 ij 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 ij =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, and the response capability evaluation index is denoted as follows. I v According to equation (4), calculate the result that makes y ( k Integers greater than 0 k Then all those greater than zero y ( k ) plus 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. Module M2.2: Establishing a response capability evaluation index model: set up n × n 3D matrix A t for: (5) 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 and σ >0, t ij For the first j The time consumed by a piece of equipment during its operation, that is, the time it takes to complete the process. t ij The process will run after the time limit by the first j The equipment was transferred to the first... i Each piece of equipment or terminated state, among which j < n The operator * represents the element-wise multiplication of two matrices of the same dimension, according to equation (4): (6) in, For A t For the system matrix, with B For the input matrix, with C The output of the system state-space equation is the output matrix. k For discrete time variables, For the matrix of equation (5) A t of k -1 power; Calculation makes 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: (7) 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 Set response capability evaluation indicators I t for: (8) Response capability 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; Module M2.3: Establish a task completion capability evaluation index model: set up n × n 3D matrix A p for (9) 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, that is, the probability of the operation process. p ij By the j The equipment was transferred to the first... i Each piece of equipment or terminated state, among which j < n， The operator * represents the element-wise multiplication of two matrices of the same dimension, according to equation (4): (10) in, For A p For the system matrix, with B For the input matrix, with C The output of the system state-space equation is the output matrix. k For discrete time variables, For the matrix of equation (9) A p of k -1 power; Calculation makes 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. (11) 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 Set evaluation indicators for task completion capabilities I p Defined as: (12) Mission completion capability 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 value, the stronger the ability to complete the task; Module M2.4: Establishing a model for evaluating survivability: Based on the strain capability evaluation index model, a rupture resistance evaluation index model is established, which uses a matrix... A 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, indicating the 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, then A 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 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, the greater the amount of equipment loss that can be tolerated, and the stronger the resistance to destruction. In module M4: Comprehensive optimization of equipment system structure and performance: Based on the established equipment system optimization model, optimization algorithms are used to solve for the optimization variables that satisfy the constraints and achieve the optimization objectives. A o This enables comprehensive optimization of equipment configuration, collaborative relationships, collaborative processes, and equipment performance within the equipment system. The optimal solution of the equipment system optimization model (13) is obtained by using an algorithm. A o The algorithms include branch and bound algorithms and genetic algorithms, etc., based on the matrix. A o After determining the optimized equipment to be included in the system, as well as the collaborative relationships and processes between the equipment, referring to equations (6) and (10), we have: (16) in, The optimized equipment operation time performance index matrix, The optimized equipment mission success rate performance index matrix; According to the matrix A to and A po The elements of China and Africa are used to determine the performance indicators of equipment operation time and mission success rate to be included in the system. A to No. i Line number j Column elements a toij If it is non-zero, then the first... j The operating time performance indicators of each piece of equipment are as follows: (17) in, For matrix A to The i Line number j Column elements; like A po No. i Line number j Column elements a poij If it is non-zero, then the first... j The mission success rate performance index of each piece of equipment is: (18) To achieve the optimal matching of equipment configuration, cooperation relationships, cooperation processes, and equipment performance.

4. The equipment system comprehensive optimization system based on a linear time-invariant discrete system according to claim 3, characterized in that, In module M3: The system matrix with optimization variable G A This represents the equipment configuration, collaborative relationships, collaborative processes, and equipment performance of the equipment system; the optimization targets include evaluation indicators for adaptability, resilience, responsiveness, and mission completion capability; and the constraints include equipment cost constraints, collaborative relationships between equipment, and collaborative process constraints. The equipment system optimization model can be represented as: (13) In the formula, The cost of integrating equipment into the system and establishing collaborative relationships with other equipment, This is the upper limit for equipment costs. For matrix A The i Line number j Column elements; matrix A To optimize variables, representing equipment configuration, collaborative relationships, and collaborative processes, in I t1 , I p1 In T and P These represent the equipment's performance in terms of mission completion time and mission success rate, respectively. I v1 , I t1 , I p1 , I r1 These are the evaluation indicators of strain capacity. I v Response capability evaluation indicators I t Task completion ability evaluation indicators I p Damage resistance evaluation indicators I r The normalized value; (14) in, I vu For I v Value limit, I tu For I t Value limit, I ru For I r Value limit; w v , w r , w t , w p The weights of the indicators are set by the designers; constraints and To constrain equipment collaboration relationships and processes, ensuring that the optimized collaboration relationships and processes conform to the functional characteristics of each piece of equipment, among which, I n for n 1D unit column vector M for n × n The dimensional collaboration relationship and process constraint matrix, its first... i Line number j Column elements are denoted as m ij ,when i ≠ n , j ≠ n and m ij When =1, it represents the first... j The equipment can be used with the first i The equipment collaborates, and the collaboration process is initiated by the first... j The equipment to the first i One piece of equipment, when i ≠ n , j ≠ n and m ij When =0, it represents the first... j The equipment cannot be used with the first i Each piece of equipment works together, when i = n , j ≠ n and m ij When =1, it represents the first... j The system operation process can be terminated after the operation of each piece of equipment is completed, that is, the first... j Each piece of equipment is the terminal equipment in the operational process; constraints Due to equipment cost constraints, the function g a ( A This represents the cost of integrating equipment into the system and establishing collaborative relationships with other equipment. It can be calculated using the following formula: (15) In the formula, C a for n × n The cost matrix of dimensional equipment, its first i Line number j Column elements c aij The representative will be the first j The cost of incorporating individual equipment into the system operation, among which j < n， The operator * represents the element-wise multiplication of two matrices of the same dimension.

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