Task termination policy for polymorphic voting system equipped with protection device

Abstract

The invention discloses a task termination strategy for a polymorphic voting system provided with protection devices, the polymorphic voting system is composed of a plurality of subsystems provided with the protection devices, the influence of impact, the protection mechanism of the protection devices and the like are fully considered, and the degradation rates of the subsystems and the protection devices thereof are obtained; based on the comprehensive state information of the subsystems and the protection devices, making a multi-criterion task termination strategy for each subsystem, determining a state transition rate matrix of the subsystem according to a state transition rule of the subsystem provided with the protection devices, and obtaining a task success probability index, a survival probability index and the like of each subsystem; obtaining task success probability and survival probability indexes of the whole polymorphic voting system by using a general generation function method; establishing a task termination strategy optimization model, and solving and obtaining an optimal system task termination strategy; according to the method, the optimal task termination strategy for the polymorphic voting system provided with the protection device can be accurately calculated and formulated.

Description

Technical Field

[0001] This invention relates to the field of system reliability calculation technology, and in particular to a task termination strategy for a multi-state voting system equipped with a protection device. Background Technology

[0002] Engineering systems equipped with protective devices perform critical tasks but also face significant risks of failure. Under certain conditions, mission termination and rescue procedures must be initiated to balance system survivability and mission success probability. In practice, engineering systems are easily affected by internal degradation and external random shocks, leading to system performance degradation or even random system failure. To ensure smooth system operation and enhance system durability, various protective devices are installed. Protective devices used in actual engineering include engine system cooling devices and collision avoidance devices for automated guided vehicles. Some protective devices provide multiple protective functions; for example, a cooling system used as a protective device can mitigate the impact of heat on sensitive equipment by regulating the coolant flow rate.

[0003] In industrial applications, some systems equipped with protective devices need to perform specific functions or tasks, such as drones with cooling systems and automated guided vehicles with collision avoidance mechanisms. These systems can degrade or even fail during mission execution due to external influences. Not only can the mission fail, but the costs of system failure are also very high.

[0004] However, existing technologies regarding optimal task termination strategies for polymorphic voting systems equipped with protection devices have three shortcomings. First, they do not study task termination strategies for polymorphic systems with protection devices, neglecting the role of protection devices in these strategies. Protection devices can improve the reliability of polymorphic systems, therefore, it is necessary to study optimal task termination strategies for polymorphic systems with protection devices. Second, the definition of successful task completion is mainly based on the system's task execution time, lacking consideration for criteria for successful task completion in systems with complex structures. Therefore, it is necessary to redefine the criteria for successful task completion in complex systems. Third, the protection mechanisms of protection devices emphasize reducing internal degradation rates, reducing the probability of effective impacts, and isolating faulty components. Therefore, it is necessary to study new polymorphic protection mechanisms for protection devices, i.e., protection devices in different states provide different protection effects to subsystems, such as reducing the impact intensity on subsystems. To address the above problems, an optimal task termination strategy for a polymorphic voting system equipped with protection devices is researched and designed. Summary of the Invention

[0005] Therefore, it is necessary to propose a task termination strategy for a polymorphic voting system equipped with a protection device to address the above problems.

[0006] A task termination strategy for a polymorphic voting system equipped with protection devices, wherein the polymorphic voting system comprises multiple subsystems equipped with protection devices, the strategy including:

[0007] S1. The failure conditions of the entire polymorphic voting system, the arrival rate of different impact intensities, and the protection mechanism of the protection device were determined, and the degradation rate of each subsystem and the protection device was obtained; a task termination strategy was designed, and competitive task termination criteria, degradation rules of subsystems and their protection devices, and task success criteria and survival criteria of the entire polymorphic voting system were proposed.

[0008] S2. Based on the degradation rates of each subsystem and protection device, the competition task termination criteria, and the degradation rules of the subsystem and its protection device obtained in step S1, establish:

[0009] Without considering the task termination strategy, a first embedded Markov process is used to obtain a first transition rule, and a first transition rate matrix is ​​obtained based on the first transition rule. The lifetime cumulative distribution function, lifetime probability density function, and reliability function of the subsystem are obtained based on the first transition rate matrix.

[0010] The second embedded Markov process is considered in relation to the task termination strategy; the second transition rule is obtained based on the second embedded Markov process, and the second transition rate matrix is ​​obtained based on the second transition rule; the cumulative distribution function and probability density function of the task execution time considering the task termination strategy are obtained based on the second transition rate matrix, where the task execution time refers to the random time interval from the start of the task to the end of the task.

[0011] S3. Obtain the task success probability and survival probability of the subsystem according to the first embedded Markov process and the second embedded Markov process in step S2;

[0012] S4. Based on the reliability function of each subsystem obtained in step S2, obtain the general generating function expression of the working state of each subsystem, and then obtain the general generating function expression of the entire polymorphic voting system with respect to the number of failed subsystems and the reliability function of the polymorphic voting system.

[0013] S5. Based on the task success probability of the subsystem obtained in step S3, construct a general generating function for the task completion result of the subsystem, and further obtain the task success probability of the entire polymorphic voting system according to the task success criterion of the entire polymorphic voting system; according to the survival criterion of the entire polymorphic voting system, multiply the survival probabilities of each subsystem to obtain the survival probability of the entire polymorphic voting system.

[0014] S6. Based on the success probability of the entire polymorphic voting system and the survival probability of the entire polymorphic voting system obtained in step S5, two optimization models for the task termination strategy are established with the objective functions of maximizing the success probability of the task and minimizing the total cost, respectively. The optimal task termination strategy is obtained by solving the optimization models.

[0015] This invention fully considers multi-state voting systems equipped with protection devices. Based on the comprehensive state information of subsystems and protection devices, it formulates multi-standard task termination strategies for each subsystem. This addresses the problem in existing reliability calculation methods that the optimal task termination strategy and protection mechanism of the system are not fully considered, and cannot solve the optimal task termination strategy for multiple multi-state systems equipped with protection devices. This invention can more accurately calculate and formulate the optimal task termination strategy for multi-state voting systems equipped with protection devices. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] in:

[0018] Figure 1 A flowchart of a task termination strategy for a polymorphic voting system equipped with a protection device in one embodiment;

[0019] Figure 2 This is a diagram showing the operation process and task termination strategy of the i-th subsystem in one embodiment.

[0020] Figure 3 This is a schematic diagram illustrating the reliability of three automated guided vehicles (AGVs) and the entire AGV system over time in one embodiment.

[0021] Figure 4 This is a sensitivity analysis chart of the critical ratio on the overall task success probability in one embodiment;

[0022] Figure 5 This is a graph showing the changing trends of the survival probability and mission success probability of the entire automated guided vehicle system when different task allocation ratios are taken in one embodiment.

[0023] Figure 6 This is a graph showing the impact of different protection effects of the protection devices on the mission success probability and survival probability of the second automated guided vehicle and the entire automated guided vehicle system in one embodiment.

[0024] Figure 7This is a structural block diagram of a computer device in one embodiment. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] To address the technical problems in the background art, this application provides a task termination strategy for a multi-state voting system equipped with protection devices. The multi-state voting system comprises multiple subsystems equipped with protection devices, such as... Figure 1 As shown, it includes the following steps:

[0027] S1. Determine the failure conditions of the entire polymorphic voting system, the arrival rate of different impact intensities, and the protection mechanism of the protection device, and obtain the degradation rate of each subsystem and the protection device; design a task termination strategy, and propose competitive task termination criteria, degradation rules of subsystems and their protection devices, as well as task success criteria and survival criteria of the entire polymorphic voting system.

[0028] S2. Based on the degradation rates of each subsystem and protection device, the competition task termination criteria, and the degradation rules of the subsystem and its protection device obtained in step S1, the following was established:

[0029] Without considering the task termination strategy, a first embedded Markov process is used to obtain a first transition rule, and a first transition rate matrix is ​​obtained based on the first transition rule. The lifetime cumulative distribution function, lifetime probability density function, and reliability function of the subsystem are obtained based on the first transition rate matrix.

[0030] The second embedded Markov process is considered in relation to the task termination strategy; the second transition rule is obtained based on the second embedded Markov process, and the second transition rate matrix is ​​obtained based on the second transition rule; the cumulative distribution function and probability density function of the task execution time considering the task termination strategy are obtained based on the second transition rate matrix, where the task execution time refers to the random time interval from the start of the task to the end of the task.

[0031] S3. Obtain the task success probability and survival probability of the subsystem according to the first embedded Markov process and the second embedded Markov process in step S2;

[0032] S4. Based on the reliability function of each subsystem obtained in step S2, obtain the general generating function expression of the working state of each subsystem, and then obtain the general generating function expression of the entire polymorphic voting system with respect to the number of failed subsystems and the reliability function of the polymorphic voting system.

[0033] S5. Based on the task success probability of the subsystem obtained in step S3, construct a general generating function for the task completion result of the subsystem, and further obtain the task success probability of the entire polymorphic voting system according to the task success criterion of the entire polymorphic voting system; according to the survival criterion of the entire polymorphic voting system, multiply the survival probabilities of each subsystem to obtain the survival probability of the entire polymorphic voting system.

[0034] S6. Based on the success probability of the entire polymorphic voting system and the survival probability of the entire polymorphic voting system obtained in step S5, two optimization models for the task termination strategy are established with the objective functions of maximizing the success probability of the task and minimizing the total cost, respectively. The optimal task termination strategy is obtained by solving the optimization models.

[0035] In one embodiment, the condition for the polymorphic voting system to fail is when the number of failed subsystems in the polymorphic voting system reaches a certain threshold. At that point, the entire multi-state voting system will fail.

[0036] The subsystem is affected by three types of shocks. When the subsystem is subjected to an extreme shock, if the current state is good, its state will degrade to a certain extent. If the current state of the subsystem is bad, the degree of state degradation will be greater. An effective shock will cause the current state of the subsystem to change to an adjacent worse state, while an ineffective shock will not affect the state of the subsystem.

[0037] The protection device is affected by effective and ineffective impacts during operation. Effective impacts cause the protection device's state to deteriorate to an adjacent worse state. When an impact of a specific intensity arrives, the subsystem's protection device will activate to reduce the impact intensity acting on the subsystem. The protection effect of the protection device varies depending on its state. The competition task termination criteria include two points: Criterion I is that the subsystem state does not exceed a first preset threshold. Criterion II is that the state of the subsystem belongs to And the status of the protection device is less than or equal to the second preset threshold. Once any one of the criteria is met, the subsystem's task should be terminated if the subsystem has completed more tasks than the task volume threshold. When this happens, choose not to execute the task termination strategy.

[0038] The survival probability of a subsystem is the sum of its mission success probability and its successful rescue probability after mission termination. Each subsystem is equipped with a polymorphic protection device. The polymorphic voting system executes m tasks and distributes them to n subsystems. The proportion of tasks handled by the i-th subsystem, where the number of tasks assigned to the i-th subsystem is... And satisfy Each subsystem and its protection device starts working simultaneously. This represents the efficiency (work completed per unit time) of the i-th subsystem. When the number of faulty subsystems in the polymorphic voting system reaches [a certain threshold], [the efficiency is determined]. When this happens, the entire polymorphic voting system fails; the state space of the i-th subsystem is... , where 0 and These represent failure and optimal states, respectively. For the i-th subsystem, from state arrive The degradation rate; the subsystem is subject to shocks during operation, and the arrival process of the shocks follows the parameters. The homogeneous Poisson process, for the i-th subsystem, when the impact intensity Exceed When this is defined as an extreme shock, its probability is... When the subsystem is subjected to an extreme shock, if its current state is greater than When, its state decreases When the state of the subsystem is less than or equal to At that time, the state of the subsystem decreases. A valid shock will cause the subsystem to change to a worse adjacent state, with a probability of . Invalid shocks do not affect the state of the subsystem, and their probability is... .

[0039] The state space of the protection device of the i-th subsystem is: , where 0 and These represent the fault and the optimal state, respectively. Furthermore, the probability that a valid impact causes the protection device's condition to deteriorate to an adjacent, worse state is... The probability of an invalid shock is The i-th protection device is in state arrive The degradation rate Furthermore, the original strength is When the impact reaches the i-th subsystem, it is in operation. The protection device for the state is weakened to Under the protection device of the i-th subsystem, the probability of extreme impact decreases from... Reduce to Effective impact from Become Correspondingly, the probability of the subsystem experiencing an invalid shock increases to And satisfy When the i-th protection device is running, the degradation rate of the i-th subsystem decreases to The degree to which protective devices reduce impact intensity varies depending on their condition. Sometimes, .

[0040] In one embodiment, to balance the survival probability of a subsystem and the success probability of a task, a task termination strategy is designed. If the i-th subsystem runs continuously... Time and completed If the task is completed, then the task is successful. The calculation formula is , Assign the number of tasks to the i-th subsystem. The efficiency of the i-th subsystem is considered. For the i-th subsystem, the designed task termination strategy includes a first competitive task termination criterion and a second competitive task termination criterion. The task of the i-th subsystem is terminated once either criterion is met.

[0041] First competition task termination criterion: The state of the i-th subsystem is less than or equal to the first preset threshold. ;

[0042] Second competition task termination criterion: The state of the i-th subsystem belongs to And the status of the protection device Less than or equal to the third preset threshold .

[0043] The time interval from the start to the end of the task for the i-th subsystem is shown below:

[0044]

[0045] in, Let be the time interval from the start to the end of the task for the i-th subsystem; Let i be the state of the i-th subsystem at time t; The first preset threshold; The second preset threshold; This represents the state of the i-th protection device at time t. This is the third preset threshold.

[0046] The lifetime of the i-th subsystem is shown below:

[0047]

[0048] in, For the lifetime of the i-th subsystem, Let be the state of the i-th subsystem at time t.

[0049] The lifetime of the entire multi-state voting system is as follows:

[0050]

[0051] in, For the lifetime of the entire polymorphic voting system; This represents the number of subsystems that fail in the polymorphic voting system at time t; This is a threshold for the number of faulty subsystems in a polymorphic voting system. When it exceeds... At that point, the entire multi-state voting system fails.

[0052] When the i-th subsystem initiates a rescue operation after meeting its mission termination conditions, the required rescue time is: The remaining time for the i-th subsystem to complete its task is When the rescue time is not less than the remaining time to complete the mission, that is... If no rescue operation is required, the i-th subsystem should continue to perform the remaining tasks; assuming the task load threshold is... The number of tasks completed by the i-th subsystem exceeds the task volume threshold. If the task execution time exceeds the time threshold, the task termination policy will not be executed. If the task continues to execute, the task termination policy will not be implemented. If the i-th subsystem operates continuously throughout the entire task without any interruption or failure, and the task is successfully completed, then the success probability of the i-th subsystem can be expressed as follows:

[0053]

[0054] in, Let be the probability of task success for the i-th subsystem. Let the lifetime of the i-th subsystem be denoted as . Let i be the continuous running time of the i-th subsystem; Let be the time interval from the start to the end of the task for the i-th subsystem; This is a predetermined threshold for the amount of tasks already completed by the i-th subsystem; This represents the work efficiency of the i-th subsystem (the amount of work completed per unit time).

[0055] The survival probability of the i-th subsystem is defined as the total probability of completing the task and the probability of successful rescue. If the i-th subsystem can be rescued without failure after its task is terminated, then its survivability is achieved. Therefore, the survival probability of the i-th subsystem is as follows:

[0056]

[0057] in, Let be the survival probability of the i-th subsystem; Let be the success probability of the task in the i-th subsystem; Let the lifetime of the i-th subsystem be denoted as . Let be the time interval from the start to the end of the task for the i-th subsystem. When the task execution time is The required rescue time; This is a predetermined threshold for the amount of tasks already completed by the i-th subsystem; This represents the work efficiency of the i-th subsystem (the amount of work completed per unit time).

[0058] exist Figure 2 The paper proposes three scenarios to demonstrate the operation process of the subsystem and the task termination strategy adopted. It considers the i-th subsystem in a polymorphic voting system and its related parameters as follows: , , , , , , , In case 1 At time 1, the i-th subsystem experiences an extreme shock, causing its state to change to state 2, triggering the task termination condition of criterion I, thus terminating the task; in case 2, similarly at time 1... At time t, the i-th protection device remains in state after experiencing an invalid impact, but subsequently undergoes a valid impact, changing its state to state 1. According to criterion II, the i-th subsystem... The task will terminate immediately; in case 3, the time threshold will be exceeded. At this point, the task termination strategy is no longer considered. After experiencing multiple shocks, the i-th subsystem decreases from state 2 to state 0 and satisfies the subsystem failure criterion, causing the task to terminate. It expires at any time.

[0059] In one embodiment, a first embedded Markov process is established, using To describe the degradation process of the subsystem without considering the task termination strategy, in middle This represents the state of the i-th subsystem at time t. This represents the state of its protection device at time t. The state space is shown below:

[0060]

[0061] in, This represents the state space of the i-th subsystem without considering the task termination strategy. This indicates an absorption state, meaning that the i-th subsystem has failed. This represents the state of the i-th subsystem at time t. This represents the state of its protection device at time t; This represents the optimal state of the i-th subsystem. This represents the optimal state of the protection device for the i-th subsystem.

[0062]

[0063] in, This represents the reduction in the state of the i-th subsystem after it suffers an extreme shock. This represents the optimal state of the i-th subsystem. For the defined state value, when the current state of the i-th subsystem is greater than... At that time, the state of the subsystem decreases after being subjected to extreme shocks. When the current state of the i-th subsystem is less than or equal to At that time, the state of the subsystem decreases after being subjected to extreme shocks. ; Defined as an indicator function, the value is 1 if event x is true, and 0 if event x is false.

[0064] The first transition rule between the Markov process states of the i-th subsystem is in the following five forms:

[0065] Form 1: If and The state transition is as follows: The state transition rate is: ;

[0066] Form 2: If and The state transition is as follows: The state transition rate is: ;

[0067] Form 3: If and The state transition is as follows: The state transition rate is: ;

[0068] Form 4: If and , The state transition is as follows: The state transition rate is: ;

[0069] Form 5: If and The state transition is as follows: The state transition rate is: .

[0070] in, express The range is , express ; Let be the impact intensity suffered by the i-th subsystem; and The set impact strength threshold is used when the impact strength exceeds... At that time, it is defined as an extreme impact; In the state of Under the protection of the protective device, the impact intensity suffered by the i-th subsystem can be reduced by a certain amount; express The range is , express ; ; This represents the arrival rate of the shock suffered by the i-th subsystem; This indicates that the i-th subsystem is in a failed state; This means that, under the protection of the i-th subsystem, the probability of extreme impact is reduced to... ; This means that under the action of the protection device of the i-th subsystem, the probability of effective impact becomes... ; This indicates that the probability of an ineffective impact on the subsystem increases under the action of the protection device of the i-th subsystem. And satisfy ; Let be the probability that the i-th subsystem suffers an invalid shock; The probability of an effective impact occurring; Let be the probability of an extreme shock suffered by the i-th subsystem; For the i-th subsystem in state i Degradation rate at that time; Let the state of the i-th subsystem at time t be Its protection device is in the following state: Degradation rate at that time; In a state The degradation rate of the protection device; It is in the absorption state;

[0071] in, Representing a Markov process The total number of transition states; according to the above state transition rules, when the subsystem fails and enters the absorption state, the first transition rate matrix can be obtained as shown below. , , where the dimension is of This represents the transition rate matrix between transition states, with dimension 1. of This represents the transition rate matrix from the transition state to the absorption state. and It is a zero matrix, containing the transition rates from the absorption state to the transition state and from the absorption state to the absorption state; after obtaining the first transition rate matrix... Subsequently, the reliability function, cumulative lifetime distribution function, and lifetime probability density function of the i-th subsystem at time t are respectively as follows:

[0072] The reliability function of the i-th subsystem at time t is as follows:

[0073] (8)

[0074] The cumulative lifetime distribution function of the i-th subsystem is as follows:

[0075] (9)

[0076] The lifetime probability density function of the i-th subsystem is as follows:

[0077] (10)

[0078] in, Let be the initial state probability vector of the i-th subsystem without considering the task termination strategy. ; It is a column vector where the last element is 0 and all other elements are 1. ; ; Let be the reliability function of the i-th subsystem at time t; Let the lifetime of the i-th subsystem be denoted as . This is the first transition rate matrix; Let be the cumulative distribution function of the lifetime of the i-th subsystem; Let be the probability density function of the lifetime of the i-th subsystem.

[0079] When implementing a task termination strategy with multiple competition criteria for the i-th subsystem, a second embedded Markov process can be established in the corresponding state space. The following describes the running process of the i-th subsystem before the task is terminated:

[0080] (11)

[0081] in, Consider the state space of the i-th subsystem under the task termination strategy; Let i be the state of the i-th subsystem at time t; The state of the protection device of the i-th subsystem; This represents the optimal state of the i-th subsystem. , The preset threshold for the subsystem state. The preset threshold for the state of the protection device is defined when the state of the i-th subsystem belongs to... And the status of the protection device Less than or equal to the preset threshold When the task termination criteria are met; This represents the optimal state of the protection device for the i-th subsystem. This is a new absorption state, which merges all states that satisfy the task termination condition with the fault absorption state. .

[0082] In one embodiment, the second transition rule of the Markov process considering the task termination strategy takes the following eleven forms:

[0083] Form 1: If ,and , The state transition is as follows: The state transition rate is: ;

[0084] Form 2: If ,and , The state transition is as follows: The state transition rate is: ;

[0085] Form 3: If ,and The state transition is as follows: The state transition rate is: ;

[0086] Form 4: If ,and The state transition is as follows: The state transition rate is: ;

[0087] Form 5: If ,and The state transition is as follows: The state transition rate is: ;

[0088] Form Six: If ,and The state transition is as follows: The state transition rate is: ;

[0089] Form Seven: If ,and , , The state transition is as follows: The state transition rate is: ;

[0090] Form 8: If ,and , The state transition is as follows: The state transition rate is: ;

[0091] Form Nine: If ,and , , The state transition is as follows: The state transition rate is: ;

[0092] Form 10: If ,and , The state transition is as follows: The state transition rate is: ;

[0093] Form 11: If ,and The state transition is as follows: The state transition rate is: .

[0094] in, , and Similar to the concepts described above, the second transition matrix of the Markov process is: , express The total number of transition states, with dimension . of It is the transition rate matrix between transient states, with dimension 1. of It is the transition rate matrix from the transient state to the absorption state. and It is a zero matrix.

[0095] The task termination time of the subsystem (random variable) The cumulative distribution function of () is as follows:

[0096] (12)

[0097] The task termination time of the subsystem (random variable) The probability density function of () is shown below:

[0098] (13)

[0099] in, Let be the initial state probability vector of the i-th subsystem considering the task termination strategy. ; Given a column vector whose elements are all 1s, ; The cumulative distribution function of task execution time; Let be the time interval from the start to the end of the task for the i-th subsystem; It considers the transition rate matrix between transition states under the task termination criterion; Let be the probability density function of the task execution duration; Let be the time interval from the start to the end of the task for the i-th subsystem.

[0100] In one embodiment, the state space of the i-th subsystem without considering the task termination strategy... Considering the state space of the i-th subsystem under the task termination strategy All states are numbered and sorted to... For example, in the state space There is A state, a degradation process The absorption state in is the first There are states; the u-th state is The vth state is ,when and When the u-th state is better than the v-th state, that is... ,but ;when and When, it indicates ,but .

[0101] State set Including all In this state, one only needs one step to enter the absorption state. This refers to a state that meets the task termination criteria; state With state space In Corresponding state set Includes all The state.

[0102] Considering the possibility of task termination, it can be based on the initial state. The probability vectors of each state in the Markov process state space at time t are obtained from the probability vectors of the initial state and the initial state, as shown below:

[0103] (14)

[0104] Among them, among them, Let be the state probability vector of the i-th subsystem at time t in the second embedded Markov process; Let be the initial state probability vector of the i-th subsystem considering the task termination strategy. ; It considers the transition rate matrix between transition states under the task termination criterion; Let t be the probability that the i-th subsystem is in the first state in the state space of the second embedded Markov process after time t. Let t be the probability that the i-th subsystem is in the second state in the state space of the second embedded Markov process after time t; This indicates that after time t, the i-th subsystem is in the state space of the second embedded Markov process. The probability of each state.

[0105] Normalized vector As shown below:

[0106] (15)

[0107] Among them, when hour ;when hour, ; Let be the normalized state probability vector of the i-th subsystem at time t in the second embedded Markov process; The normalized probability that the i-th subsystem is in the first state in the state space of the second embedded Markov process after time t; The normalized probability that the i-th subsystem is in the second state in the state space of the second embedded Markov process after time t; For the normalized subsystem after time t, the i-th subsystem is in the state space of the second embedded Markov process. The probability of each state.

[0108] The probability that the i-th subsystem meets the task termination criterion at time t, but does not terminate the task and eventually completes the task is as follows:

[0109] (16)

[0110] in, The lifetime index is defined from the time the i-th subsystem task terminates. Let i be the continuous running time of the i-th subsystem; Let be the time interval from the start to the end of the task for the i-th subsystem; Let be the initial state probability vector of the first embedded Markov process of the i-th subsystem when the task termination criterion is met at time t. ;when hour, ;when hour ; Let be the probability that the i-th subsystem is in the first state in the state space of the first embedded Markov process when the task termination criterion is met at time t. Let be the probability that the i-th subsystem is in the second state in the state space of the first embedded Markov process when the task termination criterion is met at time t. For the i-th subsystem to be in the state space of the first embedded Markov process when the task termination criterion is met at time t, The probability of each state; This represents the transition rate matrix between transition states without considering the task termination strategy; Let be a row vector whose elements are all 1s. , for The transpose of is a column vector with all elements equal to 1.

[0111] The i-th subsystem in the time interval The probabilities of satisfying the task termination criteria are as follows:

[0112] (17)

[0113] in, The probability of the task termination criterion; Let be the state probability vector of the i-th subsystem at time t in the second embedded Markov process; It is the transition rate matrix from the transition state to the absorption state under the consideration of the task termination strategy;

[0114] The success probability of the i-th subsystem can be evaluated using the following method:

[0115] (18)

[0116] in, Let be the success probability of the task in the i-th subsystem; Let the lifetime of the i-th subsystem be denoted as . Let i be the continuous running time of the i-th subsystem; Let be the time interval from the start to the end of the task for the i-th subsystem; This is a predetermined threshold for the amount of tasks already completed by the i-th subsystem; This represents the work efficiency of the i-th subsystem (the amount of work completed per unit time). It considers the transition rate matrix between transition states under the task termination strategy; , ; Let be the initial state probability vector of the first embedded Markov process of the i-th subsystem when the task termination criterion is met at time t; This represents the transition rate matrix between transition states without considering the task termination strategy; Let be a row vector whose elements are all 1s. , for The transpose of is a column vector with all elements equal to 1; Let be the state probability vector of the i-th subsystem at time t in the second embedded Markov process; It is the transition rate matrix from the transition state to the absorption state under the consideration of the task termination strategy.

[0117] The survival probability calculation for the i-th subsystem includes the following two cases: First, the subsystem successfully completes its assigned task without experiencing any failures during operation; second, the task is prematurely terminated after the subsystem meets the task termination threshold, but the rescue operation is successfully completed. Therefore, the formula for calculating the survival probability of the i-th subsystem is:

[0118] (19)

[0119] in, To consider the survival probability of the i-th subsystem under the task termination strategy; To consider the task success probability of the i-th subsystem under the task termination strategy; Let the lifetime of the i-th subsystem be denoted as . Let be the time interval from the start to the end of the task for the i-th subsystem; This is a predetermined threshold for the amount of tasks already completed by the i-th subsystem; This represents the work efficiency of the i-th subsystem (the amount of work completed per unit time). Let t be the rescue time required by the i-th subsystem when the execution time is t; Let be the initial state probability vector of the first embedded Markov process of the i-th subsystem when the task termination criterion is met at time t; This represents the transition rate matrix between transition states without considering the task termination strategy; When the task execution time is The required rescue time; Let be the state probability vector of the Markov process of the i-th subsystem at time t; It is the transition rate matrix from the transition state to the absorption state under the consideration of the task termination strategy; Let be a row vector whose elements are all 1s. , for The transpose of is a column vector with all elements equal to 1.

[0120] In one embodiment, the general generating function expression for the working state of the i-th subsystem is represented as follows:

[0121] (20)

[0122] in, Let be the general generating function expression for the working state of the i-th subsystem; Let be the reliability of the i-th subsystem; This indicates that the i-th subsystem did not experience a failure; This indicates that the i-th subsystem has failed.

[0123] The general generating function expression for the number of subsystem failures in the first i subsystems of the polymorphic voting system is as follows:

[0124] Step (1): Let ;

[0125] Step (2): For Repeated derivation ;

[0126] (twenty one)

[0127] in, The general generating function expression represents the number of subsystem failures in the first i subsystems of this polymorphic voting system, where The number of subsystem failures in the first i subsystems is denoted as . , This indicates the probability of its occurrence; The general generating function expression represents the number of subsystem failures in the first i-1 subsystems, where The number of subsystem failures in the first i-1 subsystems is denoted as . , This indicates the probability of its occurrence; A general generating function expression representing the working state of the i-th subsystem. Let be the reliability of the i-th subsystem; This indicates that the i-th subsystem did not experience a failure; This indicates that the i-th subsystem has failed; The number of subsystem failures in the first i subsystems is denoted as . ; The number of subsystem failures in the first i subsystems is denoted as . .

[0128] In one embodiment, the general generating function expression for the number of failed subsystems in the entire polymorphic voting system is... As shown below:

[0129] (twenty two)

[0130] in, A general generating function expression for the number of failed subsystems in the entire polymorphic voting system; The number of failed subsystems in the entire polymorphic voting system is denoted as . , That is the corresponding probability.

[0131] Define a random variable ,if ,So This indicates that the number of faulty subsystems is below a certain threshold. The entire multi-state voting system can operate normally; if ,So This indicates that when the number of faulty subsystems reaches or exceeds a certain threshold. At that time, the multi-state voting system malfunctioned; Indicates different situations The probability of occurrence is as follows:

[0132] (twenty three)

[0133] (twenty four)

[0134] in, The number of faulty subsystems is below a threshold The probability of it occurring; The number of faulty subsystems reaches or exceeds the number threshold. The probability of it occurring; It represents the total number of subsystems in a failed state within a polymorphic voting system. It represents the corresponding probability; This is the failure threshold for the entire polymorphic voting system. When the total number of failed subsystems exceeds this threshold... At that time, the entire multi-state voting system fails; Let be the characteristic function, when the total number of failed subsystems in the polymorphic voting system is... Greater than or equal to the threshold At that time, The value is 1, when it is not true, that is hour, The value is 0.

[0135] The reliability function of the entire multi-state voting system is shown below:

[0136] (25)

[0137] in, This is the reliability function of the entire polymorphic voting system; The number of faulty subsystems is below a threshold The probability of it occurring.

[0138] In one embodiment, considering the task termination strategy, the i-th subsystem is in one of two scenarios;

[0139] In scenario one, the subsystem failed to complete the corresponding task;

[0140] In scenario two, the subsystem successfully completed the corresponding task;

[0141] Use symbols This represents the result of the i-th subsystem completing the task, where a value of 0 corresponds to scenario one and a value of 1 corresponds to scenario two. This indicates that the feasible outcome for the i-th subsystem in completing the task is... The probability of that time.

[0142] The general generating function expression for the task completion result of the i-th subsystem is as follows:

[0143] (26)

[0144] in, Let be the general generating function expression for the task completion result of the i-th subsystem; where when When it is 0, This represents the probability of the i-th subsystem task failing, when... When it is 1, This represents the probability of success for the i-th subsystem task. Let be the success probability of the task in the i-th subsystem; This indicates that the i-th subsystem failed to complete the task. This indicates that the i-th subsystem has successfully completed the task; Defined as an integer, it can be obtained using the following formula:

[0145] (27)

[0146] Where r represents a percentage between 0 and 1. If the proportion of subsystems that successfully complete the corresponding task in the polymorphic voting system exceeds r, then the entire polymorphic voting system is considered to have completed the task. This represents an upper bound function that produces functions greater than or equal to... The smallest integer; therefore, Returns strictly greater than The smallest integer; The general generating function expression representing the completion results of the first i subsystem tasks in the polymorphic voting system can be obtained through the following recursive process:

[0147] Step 1: Let ;

[0148] Step 2: For Repeated derivation ;

[0149] (28)

[0150] in, Describes the general generating function expression for the completion results of the first i subsystem tasks in a polymorphic voting system, where Let the number of subsystems that successfully complete the task in the first i subsystems be denoted as . , This indicates the probability of its occurrence; Let represent the general generating function expression for the completion results of the first i-1 subsystem tasks in a polymorphic voting system, where Let the number of subsystems that successfully complete the task in the first i-1 subsystems be denoted as . , This indicates the probability of its occurrence; The general generating function expression represents the task completion result of the i-th subsystem, where when When it is 0, This represents the probability of the i-th subsystem task failing. This indicates that the i-th subsystem has not completed its task. When it is 1, This represents the probability of success for the i-th subsystem task. This indicates that the i-th subsystem has completed its task. Let be the success probability of the task in the i-th subsystem; when When it is 0, The number of subsystems that complete the assigned tasks in the first i subsystems is denoted as . ;when When it is 1, The number of subsystems that complete the assigned tasks in the first i subsystems is denoted as . .

[0151] therefore, And the success probability of the task in the entire polymorphic voting system It is obtained through the following expression:

[0152] (29)

[0153] (30)

[0154] in A general generating function expression representing the task completion result of a subsystem in a polymorphic voting system. This represents the number of subsystems in the entire polymorphic voting system that successfully complete their assigned tasks. The number of subsystems that successfully completed the task among all subsystems is denoted as . , This indicates the probability of its occurrence; The probability of task success for the entire polymorphic voting system. Let be the characteristic function, representing the number of subsystems in a polymorphic voting system that successfully complete their assigned tasks. Greater than or equal to hour, The value is 1, when it is not true, that is hour, The value is 0; Including the task termination policy parameters of the i-th subsystem, i.e. .

[0155] The survival probability of the entire polymorphic voting system, which is the probability that the entire polymorphic voting system will survive if all subsystems survive, can be obtained by the following formula:

[0156] (31)

[0157] in, The survival probability of the entire polymorphic voting system; To consider the survival probability of the i-th subsystem under the task termination strategy; Including the task termination policy parameters of the i-th subsystem, i.e. .

[0158] In one embodiment, to balance the probability of task success and system survival probability ,in Two optimization models were established, one for maximizing the success probability of the task and the other for minimizing the total cost. In both models, the decision variables are a series of quantitative thresholds in the designed task termination strategy. , , ,in The following are examples:

[0159] (32)

[0160] (33)

[0161]

[0162] in, To maximize the success probability of the task in the entire polymorphic voting system, To minimize total cost; The survival probability of the entire polymorphic voting system. Including the task termination policy parameters of the i-th subsystem, i.e. , A preset threshold representing the system's survival probability. This represents the optimal state of the i-th subsystem. , The preset threshold for the subsystem state. The preset threshold for the state of the protection device is defined when the state of the i-th subsystem belongs to... And the status of the protection device Less than or equal to the preset threshold When the task termination criteria are met, This represents the optimal state of the protection device for the i-th subsystem.

[0163] and These represent the costs of task failure and system malfunction, respectively. The primary goal is to reduce the total cost of task failures and system malfunctions. Ultimately, the optimal threshold and optimal task termination strategy are obtained through solution. This invention fully considers polymorphic voting systems equipped with protection devices. Based on the comprehensive state information of subsystems and protection devices, a multi-criteria task termination strategy is formulated for each subsystem. This addresses the problems in existing reliability calculation methods, such as incomplete consideration of protection mechanisms, inability to solve for optimal task termination strategies for multiple polymorphic systems equipped with protection devices, and the problem that the definition of successful task completion is mainly based on the execution time of simple systems, lacking consideration for task success criteria in complex structures. This invention can more accurately calculate and formulate the optimal task termination strategy for polymorphic voting systems equipped with protection devices.

[0164] In one embodiment, considering random shocks, the optimal task termination strategy for a multi-state voting system equipped with protection devices is studied, and a new protection mechanism is proposed: when the state of the protection device degrades, the shock intensity acting on the subsystem increases; different subsystems are assigned different numbers of tasks, and their working efficiency is also different. A new task termination criterion is designed based on the comprehensive state of the subsystems and their corresponding protection devices; after a subsystem takes task termination measures, a rescue process will be activated. The success of the entire system's task is defined as the number of subsystems that have completed their assigned tasks exceeding a certain ratio. In summary, an optimal task termination strategy for a multi-state voting system equipped with protection devices is designed.

[0165] This embodiment mainly utilizes the Markov process embedding method to describe the operation process of each subsystem and calculate the relevant probability indicators of the subsystem. It uses the general generating function method to obtain the system's task success rate and survival rate, and finally establishes two optimization models with the objectives of maximizing the task success probability and minimizing the expected total cost, respectively. This yields an optimal task termination strategy for a polymorphic voting system equipped with protection devices. Taking an automated guided vehicle (AGV) system as an example, the method specifically includes the following steps:

[0166] Step 1, taking a warehouse fleet of three AGVs as an example, where, The first automated guided vehicle and its protective devices both have four states ( , The second and third automated guided vehicles have five states (); Its protection device also has five states ( ), During operation, each automated guided vehicle (AGV) is subjected to external impacts, with an impact arrival rate of [missing information]. ( Furthermore, the impact intensity during the operation of the automated guided vehicle follows a normal distribution, expressed as... To reduce external impacts, each automated guided vehicle (AGV) is equipped with a safety buffer device as a protective measure. This device reduces the impact intensity suffered by the AGV to varying degrees under different conditions. When the number of AGV malfunctions reaches 2 (a threshold), [further measures are taken]. When the automatic guided vehicle system malfunctions, the entire system fails.

[0167] Table 1. Relevant System Parameters

[0168]

[0169] Table 1 summarizes relevant parameters of the automated guided vehicle (AGV), including its degradation rate, the probability of its protective devices being effectively impacted, the protection mechanism of the protective devices, the operating speed of the AGV, the task ratio of the AGV, and the impact intensity threshold. For the safety buffer device in state The probability of receiving an effective impact. For the safety buffer device in state The amount of reduction in impact strength at that time. Let the working efficiency of the i-th automated guided vehicle be . The task allocation ratio for the i-th automated guided vehicle. The first strength threshold for effective impact, This represents the maximum strength threshold for effective impact strength.

[0170] The total number of tasks that the entire automated guided vehicle system needs to complete is Before the mission began, these tasks were arranged proportionally. They are assigned to each automated guided vehicle.

[0171] The number of tasks that the i-th automated guided vehicle needs to complete is The working speed of the i-th automated guided vehicle in completing the task is Because these automated guided vehicles (AGVs) are expensive, system survival is more important than task completion during mission execution. For the i-th AGV, successfully completing the assigned task requires time. ,Right now .

[0172] To ensure the survivability of the entire automated guided vehicle (AGV) system, the i-th AGV should terminate its mission when either of the following two criteria is met: First, the i-th AGV's state is below... Second, the state of the i-th automated guided vehicle is... At that time, and the state of its safety buffer device is not greater than If the amount of work completed by the i-th automated guided vehicle exceeds the task threshold When choosing not to execute the task termination policy, among which... , If the i-th automated guided vehicle terminates its mission at time t, then the time required for its rescue is... When the number of automated guided vehicles (AGVs) that have completed their tasks in the entire automated guided vehicle (AGV) system exceeds 60% of the total number of AGVs (… ),Right now Only when all automated guided vehicles survive can the entire automated guided vehicle system be considered to have successfully completed its mission. The survivability of the entire automated guided vehicle system can only be realized when all automated guided vehicles survive.

[0173] Step 2: By constructing the first embedded Markov process, the reliability functions of each automated guided vehicle (AGV) and the entire AGV system can be obtained. The reliability curves of the entire AGV system and each AGV change over time as follows: Figure 3 As shown, the reliability function of the first automated guided vehicle (AGV) is plotted in diagram (a), the second AGV in diagram (b), the third AGV in diagram (c), and the reliability function of the entire AGV system in diagram (d). Because the subsystems of the second and third AGVs have higher self-state and safety buffer device states, their degradation rates are slower than those of the first AGV. Although the other parameters of the second and third AGVs are the same, their degradation rate is still lower than that of the third AGV due to the higher effective impact threshold of the second AGV.

[0174] Step 3: First, three task termination thresholds were set for the automated guided vehicles (AGVs). The threshold for the first AGV was... The threshold for the second automated guided vehicle is The threshold for the third automated guided vehicle is Based on the constructed first and second embedded Markov processes, the trend of the mission success probability (MSP) of the entire automated guided vehicle system as r changes from 1% to 100% is as follows: Figure 4 As shown. From Figure 4 As can be seen, since the entire automated guided vehicle system comprises three subsystems, the overall trend of the system's mission success probability only shows a certain trend. and Significant changes only occur when r decreases. It's worth noting that as r decreases, the overall success rate of the automated guided vehicle (AGV) system increases. This is because when r is low, fewer subsystems are needed to successfully complete the specified task while ensuring the overall success of the AGV system. Therefore, stricter task completion conditions reduce the probability of task completion.

[0175] Figure 5 The diagram illustrates how the success probability (MSP) and survival probability (SSP) of the entire automated guided vehicle (AGV) system change when the proportion of tasks assigned to each AGV varies. Figure (a) corresponds to the first AGV, Figure (b) to the second AGV, and Figure (3) to the third AGV. Figure 5 In (a), the task ratio of the first automated guided vehicle (AGV) increases continuously, its degradation rate is relatively fast, its work efficiency is relatively slow, and the survival probability of the entire AGV system continues to increase until its task ratio reaches a limit. As time goes on, the probability of survival gradually decreases. However, in Figure 5In (c), the third automated guided vehicle has too many tasks (exceeding the limit). If the third automated guided vehicle (AGV) has a relatively slower degradation rate and higher working efficiency, then the survival probability of the entire AGV system will gradually decrease after reaching its peak. Therefore, compared to relying on a single high-performance subsystem to handle all tasks, reasonable task allocation can enable the entire AGV system to achieve efficient collaborative operation. The success probability of the entire AGV system depends not only on the success probability of individual subsystems but also on the number of subsystems that successfully complete the tasks. Therefore, as the task allocation ratio of the AGVs changes, the task completion rate also exhibits various trends. Figure 6 In the diagram, (a) represents the mission completion probability of the entire automated guided vehicle (AGV) system, (b) represents the survival probability of the entire AGV system, (c) represents the mission completion probability of the third AGV, and (d) represents the survival probability of the third AGV. Figure 6 As shown, when the protection capability of the safety buffer device to which the third automated guided vehicle belongs increases... As the probability increases, the survival probability, mission completion probability, and other related probability indicators of the automated guided vehicle increase monotonically and show a convergence trend. It is worth noting that when... When the protection level is increased to 7, although the protection effect continues to improve, its impact on the survival probability and mission success probability of the third automated guided vehicle (AGV) and the entire AGV system is no longer significant. This clearly demonstrates that the marginal impact of the safety buffer device's protection effect on the system's key indicators gradually weakens. This observation can provide a basis for guiding the reliability management of AGVs and saving on the cost of protection devices in engineering practice, as excessively increasing the protection effect of the protection device may not bring corresponding benefits.

[0176] Step 4: Two optimization models were established, with the objective functions of maximizing the mission success probability and minimizing the total cost, respectively. After solving the two optimization models, the optimal setting of the mission termination strategy was proposed. Optimization Model I aims to maximize the mission success probability within the constraint of the overall survivability of the automated guided vehicle system, while Optimization Model II aims to minimize the expected total cost, which is determined by system failures. and task failure The total cost is determined by this.

[0177] Table 2. Optimal Solution Obtained Through Model I

[0178]

[0179] In optimization model I, given , and The optimal solutions for different values ​​are shown in Table 2. This represents the degradation rate of the i-th subsystem. These represent the task proportions corresponding to the first, second, and third automated guided vehicles (AGVs), and the task termination thresholds corresponding to the first, second, and third AGVs are respectively... , and , It represents the probability that the entire automated guided vehicle system will complete its mission under the optimal mission termination strategy determined by the solution. It is the survival probability of the entire automated guided vehicle system under the optimal task termination strategy obtained by solving the problem. To determine the survival probability of the entire automated guided vehicle system without considering the task termination strategy, we need to find the optimal task termination strategy. This indicates the impact of adopting the proposed mission termination strategy on the overall survivability of the automated guided vehicle system. .when To improve the overall survivability of the automated guided vehicle system when increased within a certain range, the mission termination threshold is lowered when more frequent impacts occur.

[0180] Table 3. Optimal Solution Obtained Through Optimization Model II

[0181]

[0182] For optimization model II, when and At that time, the optimal expected cost increases with... and Increases with the increase. When As the threshold increases, the task termination threshold becomes smaller, indicating that stricter task termination policy guidelines can reduce the likelihood of higher task failure costs. Furthermore, The increase of has a minor impact on the optimal solution of the task termination strategy, only when When the threshold for mission termination of the first automated guided vehicle is increased from 5500 to 6000. It will only grow larger if the task termination threshold is reached. If the size increases, the system is more likely to decide to terminate the task, thereby increasing its chances of survival.

[0183] also, This indicates the impact of adopting the proposed task termination strategy on the expected total cost of optimization models I and II, where... , This represents the expected total cost without considering the mission termination strategy. Tables 2 and 3 conclude that the optimal mission termination strategy under optimization model I significantly improves the survivability of the entire automated guided vehicle (AGV) system, while the optimal mission termination strategy under optimization model II reduces the expected total cost. Furthermore, for optimization model I, the optimal mission termination strategy is more effective in worse environments (larger... The impact on improving the overall survivability of the automated guided vehicle (AGV) system is more significant under the following conditions. For Optimization Model II, when the system failure cost is higher, the positive impact of adopting the optimal task termination strategy on saving total costs is more obvious.

[0184] These results enable decision-makers to weigh the pros and cons of system survivability against the probability of task success, thereby reducing risk. Before a task begins, managers can use optimization models to set task termination thresholds for specific tasks and systems. Task termination strategies will be implemented during task execution based on real-time monitoring of the system's operational status.

[0185] Figure 7 An internal structural diagram of a computer device in one embodiment is shown. This computer device can specifically be a terminal or a server. Figure 7 As shown, the computer device includes a processor, memory, and a network interface connected via a system bus. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and may also store a computer program. When executed by the processor, this computer program enables the processor to implement a task termination strategy for a polymorphic voting system with protection mechanisms. The internal memory may also store a computer program, which, when executed by the processor, enables the processor to implement a task termination strategy for a polymorphic voting system with protection mechanisms. Those skilled in the art will understand that… Figure 7 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0186] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0187] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0188] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A task termination strategy for a polymorphic voting system equipped with a protection device, wherein the polymorphic voting system comprises multiple subsystems equipped with protection devices, characterized in that, The strategy includes: S1. The failure conditions of the entire polymorphic voting system, the arrival rate of different impact intensities, and the protection mechanism of the protection device were determined, and the degradation rate of each subsystem and the protection device was obtained; a task termination strategy was designed, and competitive task termination criteria, degradation rules of subsystems and their protection devices, and task success criteria and survival criteria of the entire polymorphic voting system were proposed. S2. Based on the degradation rates of each subsystem and protection device, the competition task termination criteria, and the degradation rules of the subsystem and its protection device obtained in step S1, establish: Without considering the task termination strategy, a first embedded Markov process is used to obtain a first transition rule, and a first transition rate matrix is ​​obtained based on the first transition rule. The lifetime cumulative distribution function, lifetime probability density function, and reliability function of the subsystem are obtained based on the first transition rate matrix. The second embedded Markov process is considered in relation to the task termination strategy; the second transition rule is obtained based on the second embedded Markov process, and the second transition rate matrix is ​​obtained based on the second transition rule; the cumulative distribution function and probability density function of the task execution time considering the task termination strategy are obtained based on the second transition rate matrix, where the task execution time refers to the random time interval from the start of the task to the end of the task. S3. Obtain the task success probability and survival probability of the subsystem according to the first embedded Markov process and the second embedded Markov process in step S2; S4. Based on the reliability function of each subsystem obtained in step S2, obtain the general generating function expression of the working state of each subsystem, and then obtain the general generating function expression of the entire polymorphic voting system with respect to the number of failed subsystems and the reliability function of the polymorphic voting system. S5. Based on the task success probability of the subsystem obtained in step S3, construct a general generating function for the task completion result of the subsystem, and further obtain the task success probability of the entire polymorphic voting system according to the task success criterion of the entire polymorphic voting system; according to the survival criterion of the entire polymorphic voting system, multiply the survival probabilities of each subsystem to obtain the survival probability of the entire polymorphic voting system. S6. Based on the success probability of the entire polymorphic voting system and the survival probability of the entire polymorphic voting system obtained in step S5, two optimization models for the task termination strategy are established with the objective functions of maximizing the success probability of the task and minimizing the total cost, respectively. The optimal task termination strategy is obtained by solving the optimization models.

2. The task termination strategy of the multi-state voting system equipped with a protection device according to claim 1, characterized in that, The condition for the multi-state voting system to fail is that when the number of failed subsystems in the multi-state voting system reaches a certain threshold, the entire multi-state voting system will fail. The subsystem is subjected to three types of shocks. When the subsystem is subjected to an extreme shock, if the current state is good, its state will degrade to a certain extent. If the current state of the subsystem is bad, the state will degrade by a greater amount. An effective shock will cause the current state of the subsystem to change to an adjacent worse state, while an ineffective shock will not affect the state of the subsystem. The protection device is affected by effective and ineffective impacts during operation. Effective impacts cause the protection device to deteriorate to an adjacent worse state. When an impact of a specific intensity arrives, the protection device of the subsystem will activate to reduce the impact intensity acting on the subsystem. The protection effect of the protection device varies depending on the state. The competition task termination criteria include two items: Criterion I is that the subsystem state does not exceed a first preset threshold. Criterion II is that the state of the subsystem belongs to And the status of the protection device is less than or equal to the second preset threshold. Once any one of the criteria is met, the subsystem's task should be terminated if the subsystem has completed more tasks than the task volume threshold. When this happens, choose not to execute the task termination strategy; The survival probability of the subsystem is the sum of the subsystem's mission success probability and the subsystem's successful rescue probability after the mission ends.

3. The task termination strategy of the multi-state voting system equipped with a protection device according to claim 1, characterized in that, Each subsystem is equipped with a polymorphic protection device. The polymorphic voting system executes m tasks and distributes them among n subsystems. The proportion of tasks handled by the i-th subsystem, where the number of tasks assigned to the i-th subsystem is... And satisfy Each subsystem and its protection device starts working simultaneously. This represents the work efficiency (work completed per unit time) of the i-th subsystem. When the number of faulty subsystems in the polymorphic voting system reaches [a certain threshold], [the efficiency is determined]. When this happens, the entire polymorphic voting system fails; the state space of the i-th subsystem is... , where 0 and These represent failure and optimal states, respectively. For the i-th subsystem, from state arrive The degradation rate; the subsystem is subject to shocks during operation, and the arrival process of the shocks follows the parameters. The homogeneous Poisson process, for the i-th subsystem, when the impact intensity Exceed When this is defined as an extreme shock, its probability is... When the subsystem is subjected to an extreme shock, if its current state is greater than When, its state decreases When the state of the subsystem is less than or equal to At that time, the state of the subsystem decreases. A valid shock will cause the subsystem to change to a worse adjacent state, with a probability of . Invalid shocks do not affect the state of the subsystem, and their probability is... ; The state space of the protection device of the i-th subsystem is: , where 0 and These represent the fault and the optimal state, respectively. Furthermore, the probability that a valid impact causes the protection device's condition to deteriorate to an adjacent, worse state is... The probability of an invalid shock is The i-th protection device is in state arrive The degradation rate ; Furthermore, the original strength is When the impact reaches the i-th subsystem, it is in operation. The protection device for the status was weakened to Under the protection device of the i-th subsystem, the probability of extreme impact decreases from... Reduce to Effective impact from Become Correspondingly, the probability of the subsystem experiencing an invalid shock increases to And satisfy When the i-th protection device is running, the degradation rate of the i-th subsystem decreases to The degree to which protective devices reduce impact intensity varies depending on their condition. Sometimes, ; If the i-th subsystem runs continuously Time and completed If the task is completed, then the task is successful. The calculation formula is , Assign the number of tasks to the i-th subsystem. The efficiency of the i-th subsystem is considered. For the i-th subsystem, the designed task termination strategy includes a first competitive task termination criterion and a second competitive task termination criterion. The task of the i-th subsystem is terminated once either criterion is met. First competition task termination criterion: The state of the i-th subsystem is less than or equal to the first preset threshold. ; Second competition task termination criterion: The state of the i-th subsystem belongs to And the status of the protection device Less than or equal to the third preset threshold ; The time interval from the start to the end of the task for the i-th subsystem is shown below: in, Let be the time interval from the start to the end of the task for the i-th subsystem; Let i be the state of the i-th subsystem at time t; The first preset threshold; The second preset threshold; This represents the state of the i-th protection device at time t. The third preset threshold; The lifetime of the i-th subsystem is shown below: in, Let the lifetime of the i-th subsystem be denoted as . The lifetime of the entire multi-state voting system is as follows: in, For the lifetime of the entire polymorphic voting system; This represents the number of subsystems that fail in the polymorphic voting system at time t; This is a threshold for the number of faulty subsystems in a polymorphic voting system. When it exceeds... At that time, the entire multi-state voting system fails; When the i-th subsystem initiates a rescue operation after meeting its mission termination conditions, the required rescue time is: The remaining time for the i-th subsystem to complete its task is When the rescue time is not less than the remaining time to complete the mission, that is... If no rescue operation is required, the i-th subsystem should continue to perform the remaining tasks; assuming the task load threshold is... The number of tasks completed by the i-th subsystem exceeds the task volume threshold. If the task execution time exceeds the time threshold, the task termination policy will not be executed. If the task continues to execute, the task termination policy will not be implemented. If the i-th subsystem operates continuously throughout the entire task without any interruption or failure, and the task is successfully completed, then the success probability of the i-th subsystem can be expressed as follows: in, Let be the success probability of the task in the i-th subsystem, when the state of the i-th subsystem belongs to . And the status of the protection device Less than or equal to the preset threshold When the task termination criteria are met; Let the lifetime of the i-th subsystem be denoted as . Let i be the continuous running time of the i-th subsystem; Let be the time interval from the start to the end of the task for the i-th subsystem; This is a predetermined threshold for the amount of tasks already completed by the i-th subsystem; This represents the working efficiency of the i-th subsystem; The survival probability of the i-th subsystem is defined as the total probability of completing the mission and a successful rescue. If the i-th subsystem can be rescued without failure after its mission terminates, its survivability is achieved. Therefore, the survival probability of the i-th subsystem is as follows: in, Let be the survival probability of the i-th subsystem; Let be the success probability of the task in the i-th subsystem; Let the lifetime of the i-th subsystem be denoted as . Let be the time interval from the start to the end of the task for the i-th subsystem. When the task execution time is The required rescue time; This is a predetermined threshold for the amount of tasks already completed by the i-th subsystem; This represents the working efficiency of the i-th subsystem.

4. The task termination strategy of the multi-state voting system equipped with a protection device according to claim 1, characterized in that, Establish the first embedded Markov process, using To describe the degradation process of the subsystem without considering the task termination strategy, in middle This represents the state of the i-th subsystem at time t. This represents the state of its protection device at time t. The state space is shown below: in, This represents the state space of the i-th subsystem without considering the task termination strategy. This indicates an absorption state, meaning that the i-th subsystem has failed. This represents the state of the i-th subsystem at time t. This represents the state of its protection device at time t; This represents the optimal state of the i-th subsystem. This represents the optimal state of the protection device for the i-th subsystem. in, This represents the reduction in the state of the i-th subsystem after it suffers an extreme shock. This represents the optimal state of the i-th subsystem. For the defined state value, when the current state of the i-th subsystem is greater than... At that time, the state of the subsystem decreases after being subjected to extreme shocks. When the current state of the i-th subsystem is less than or equal to At that time, the state of the subsystem decreases after being subjected to extreme shocks. ; Defined as an indicator function, its value is 1 if event x is true, and 0 if event x is false; The first transition rule between the Markov process states of the i-th subsystem is in the following five forms: Form 1: If and The state transition is as follows: The state transition rate is: ; Form 2: If and The state transition is as follows: The state transition rate is: ; Form 3: If and The state transition is as follows: The state transition rate is: ; Form 4: If and , The state transition is as follows: The state transition rate is: ; Form 5: If and The state transition is as follows: The state transition rate is: ; in, express The range is , express ; Let be the impact intensity suffered by the i-th subsystem; and The set impact strength threshold is used when the impact strength exceeds... At that time, it is defined as an extreme impact; In the state of Under the protection of the protective device, the impact intensity suffered by the i-th subsystem can be reduced by a certain amount; express The range is , express ; ; This represents the arrival rate of the shock suffered by the i-th subsystem; This indicates that the i-th subsystem is in a failed state; This means that, under the protection of the i-th subsystem, the probability of extreme impact is reduced to... ; This means that under the action of the protection device of the i-th subsystem, the probability of effective impact becomes... ; This indicates that the probability of an ineffective impact on the subsystem increases under the action of the protection device of the i-th subsystem. And satisfy ; Let be the probability that the i-th subsystem suffers an invalid shock; The probability of an effective impact occurring; Let be the probability of an extreme shock suffered by the i-th subsystem; For the i-th subsystem in state i Degradation rate at that time; Let the state of the i-th subsystem at time t be Its protection device is in the following state: Degradation rate at that time; In a state The degradation rate of the protection device; It is in the absorption state; in, Representing a Markov process The total number of transition states; according to the above state transition rules, when the subsystem fails and enters the absorption state, the first transition rate matrix can be obtained as shown below. , , where the dimension is of This represents the transition rate matrix between transition states, with dimension 1. of This represents the transition rate matrix from the transition state to the absorption state. and It is a zero matrix, containing the transition rates from the absorption state to the transition state and from the absorption state to the absorption state; after obtaining the first transition rate matrix... Subsequently, the reliability function, cumulative lifetime distribution function, and lifetime probability density function of the i-th subsystem at time t are respectively as follows: The reliability function of the i-th subsystem at time t is as follows: The cumulative lifetime distribution function of the i-th subsystem is as follows: The lifetime probability density function of the i-th subsystem is as follows: in, , , ; Let be the reliability function of the i-th subsystem at time t; Let the lifetime of the i-th subsystem be denoted as . This is the first transition rate matrix; Let be the cumulative distribution function of the lifetime of the i-th subsystem; Let be the probability density function of the lifetime of the i-th subsystem; Let be the initial state probability vector of the i-th subsystem without considering the task termination strategy; It is a column vector where the last element is 0 and all other elements are 1; When implementing a task termination strategy with multiple competition criteria for the i-th subsystem, a second embedded Markov process can be established in the corresponding state space. The following describes the running process of the i-th subsystem before the task is terminated: in, Consider the state space of the i-th subsystem under the task termination strategy; Let i be the state of the i-th subsystem at time t; The state of the protection device of the i-th subsystem; This represents the optimal state of the i-th subsystem. , The preset threshold for the subsystem state. Preset threshold for the status of the protection device; This represents the optimal state of the protection device for the i-th subsystem. This is a new absorption state that combines all states that satisfy the task termination condition with the fault absorption state. merge.

5. The task termination strategy of the multi-state voting system equipped with a protection device according to claim 4, characterized in that, The second transition rule of the Markov process considering the task termination strategy is in the following eleven forms: Form 1: If ,and , The state transition is as follows: The state transition rate is: ; Form 2: If ,and , The state transition is as follows: The state transition rate is: ; Form 3: If ,and The state transition is as follows: The state transition rate is: ; Form 4: If ,and The state transition is as follows: The state transition rate is: ; Form 5: If ,and The state transition is as follows: The state transition rate is: ; Form Six: If ,and The state transition is as follows: The state transition rate is: ; Form Seven: If ,and , , The state transition is as follows: The state transition rate is: ; Form 8: If ,and , The state transition is as follows: The state transition rate is: ; Form Nine: If ,and , , The state transition is as follows: The state transition rate is: ; Form 10: If ,and , The state transition is as follows: The state transition rate is: ; Form 11: If ,and The state transition is as follows: The state transition rate is: ; in, , and Similar to the concepts described above, the second transition matrix of the Markov process is: , express The total number of transition states, with dimension . of It is the transition rate matrix between transient states, with dimension 1. of It is the transition rate matrix from the transient state to the absorption state. and It is a zero matrix; The cumulative distribution function of the subsystem at the task termination time is as follows: The probability density function of the subsystem at the task termination time is shown below: in, Let be the initial state probability vector of the i-th subsystem considering the task termination strategy. ; Given a column vector whose elements are all 1s, ; Let be the cumulative distribution function of task execution time; Let be the time interval from the start to the end of the task for the i-th subsystem; It considers the transition rate matrix between transition states under the task termination criterion; Let be the probability density function of the task execution duration; Let be the time interval from the start to the end of the task for the i-th subsystem.

6. The task termination strategy of the multi-state voting system equipped with a protection device according to claim 1, characterized in that, The state space of the i-th subsystem without considering the task termination strategy Considering the state space of the i-th subsystem under the task termination strategy All states are numbered and sorted to... For example, in the state space There is A state, a degradation process The absorption state in is the first There are states; the u-th state is The vth state is ,when and When the u-th state is better than the v-th state, that is... ,but ;when and When, it indicates ,but ; State set Including all In this state, one only needs one step to enter the absorption state. This refers to a state that meets the task termination criteria; state With state space In Corresponding state set Includes all The state; Considering the possibility of task termination, it can be based on the initial state. The probability vectors of each state in the Markov process state space at time t are obtained from the probability vectors of the initial state and the initial state, as shown below: in, Let be the state probability vector of the i-th subsystem at time t in the second embedded Markov process; Let be the initial state probability vector of the i-th subsystem considering the task termination strategy. ; It considers the transition rate matrix between transition states under the task termination criterion; Let t be the probability that the i-th subsystem is in the first state in the state space of the second embedded Markov process after time t. Let t be the probability that the i-th subsystem is in the second state in the state space of the second embedded Markov process after time t; This indicates that after time t, the i-th subsystem is in the state space of the second embedded Markov process. The probability of each state; Normalized vector As shown below: Among them, when hour ;when hour, ; Let be the normalized state probability vector of the i-th subsystem at time t in the second embedded Markov process; The normalized probability that the i-th subsystem is in the first state in the state space of the second embedded Markov process after time t; The normalized probability that the i-th subsystem is in the second state in the state space of the second embedded Markov process after time t; For the normalized subsystem after time t, the i-th subsystem is in the state space of the second embedded Markov process. The probability of each state; The probability that the i-th subsystem meets the task termination criterion at time t, but does not terminate the task and eventually completes the task is as follows: in, Let be a row vector whose elements are all 1s. , for The transpose of is a column vector with all elements equal to 1; Let be the initial state probability vector of the first embedded Markov process of the i-th subsystem when the task termination criterion is met at time t. ;when hour, ;when hour, ; The lifetime index is defined from the time the i-th subsystem task terminates. This represents the transition rate matrix between transition states without considering the task termination strategy; Let i be the continuous running time of the i-th subsystem; Let be the time interval from the start to the end of the task for the i-th subsystem; Let be the probability that the i-th subsystem is in the first state in the state space of the first embedded Markov process when the task termination criterion is met at time t. Let be the probability that the i-th subsystem is in the second state in the state space of the first embedded Markov process when the task termination criterion is met at time t. For the i-th subsystem to be in the state space of the first embedded Markov process when the task termination criterion is met at time t, The probability of each state; The i-th subsystem in the time interval The probabilities of satisfying the task termination criteria are as follows: in, The probability of the task termination criterion; Let be the state probability vector of the i-th subsystem at time t in the second embedded Markov process; It is the transition rate matrix from the transition state to the absorption state under the consideration of the task termination strategy; The success probability of the i-th subsystem can be evaluated using the following method: in, Let be the success probability of the task in the i-th subsystem; Let the lifetime of the i-th subsystem be denoted as . Let i be the continuous running time of the i-th subsystem; Let be the time interval from the start to the end of the task for the i-th subsystem; This is a predetermined threshold for the amount of tasks already completed by the i-th subsystem; This represents the work efficiency of the i-th subsystem (the amount of work completed per unit time). It considers the transition rate matrix between transition states under the task termination strategy; , ; Let be the initial state probability vector of the first embedded Markov process of the i-th subsystem when the task termination criterion is met at time t; This represents the transition rate matrix between transition states without considering the task termination strategy; Let be a row vector whose elements are all 1s. , for The transpose of is a column vector with all elements equal to 1; Let be the state probability vector of the Markov process of the i-th subsystem at time t; It is the transition rate matrix from the transition state to the absorption state under the consideration of the task termination strategy; The survival probability calculation of the i-th subsystem includes the following two cases: First, the subsystem successfully completes its assigned task and does not experience any failures during operation; second, the task is terminated early after the subsystem meets the task termination threshold, but the rescue operation is successfully completed. Therefore, the formula for calculating the survival probability of the i-th subsystem is: in, To consider the survival probability of the i-th subsystem under the task termination strategy; To consider the task success probability of the i-th subsystem under the task termination strategy; Let the lifetime of the i-th subsystem be denoted as . Let be the time interval from the start to the end of the task for the i-th subsystem; This is a predetermined threshold for the amount of tasks already completed by the i-th subsystem; This represents the work efficiency of the i-th subsystem (the amount of work completed per unit time). Let t be the rescue time required by the i-th subsystem when the execution time is t; Let be the initial state probability vector of the first embedded Markov process of the i-th subsystem when the task termination criterion is met at time t; This represents the transition rate matrix between transition states without considering the task termination strategy; When the task execution time is The required rescue time; Let be the state probability vector of the i-th subsystem at time t in the second embedded Markov process; It is the transition rate matrix from the transition state to the absorption state under the consideration of the task termination strategy; .

7. The task termination strategy of the multi-state voting system equipped with a protection device according to claim 1, characterized in that, The general generating function expression for the working state of the i-th subsystem is shown below: in, Let be the general generating function expression for the working state of the i-th subsystem; Let be the reliability of the i-th subsystem; This indicates that the i-th subsystem did not experience a failure; This indicates that the i-th subsystem has failed; The general generating function expression for the number of subsystem failures in the first i subsystems of the polymorphic voting system is as follows: Step 1: Let ; Step 2: For Repeated derivation ; in, The general generating function expression represents the number of subsystem failures in the first i subsystems of this polymorphic voting system, where The number of subsystem failures in the first i subsystems is denoted as . , This indicates the probability of its occurrence; The general generating function expression represents the number of subsystem failures in the first i-1 subsystems, where The number of subsystem failures in the first i-1 subsystems is denoted as . , This indicates the probability of its occurrence; A general generating function expression representing the working state of the i-th subsystem. Let be the reliability of the i-th subsystem; This indicates that the i-th subsystem did not experience a failure; This indicates that the i-th subsystem has failed; The number of subsystem failures in the first i subsystems is denoted as . ; The number of subsystem failures in the first i subsystems is denoted as . .

8. The task termination strategy of the multi-state voting system equipped with a protection device according to claim 7, characterized in that, The general generating function expression for the number of failed subsystems in the entire polymorphic voting system As shown below: in, A general generating function expression for the number of failed subsystems in the entire polymorphic voting system; The number of failed subsystems in the entire polymorphic voting system is denoted as . , It represents the corresponding probability; Define a random variable ,if ,So This indicates that the number of faulty subsystems is below a certain threshold. The entire multi-state voting system can operate normally; if ,So This indicates that when the number of faulty subsystems reaches or exceeds a certain threshold. At that time, the multi-state voting system malfunctioned; Indicates different situations The probability of occurrence is as follows: in, The number of faulty subsystems is below a threshold The probability of it occurring; The number of faulty subsystems reaches or exceeds the number threshold. The probability of it occurring; It represents the total number of subsystems in a failed state within a polymorphic voting system. It represents the corresponding probability; This is the failure threshold for the entire polymorphic voting system. When the total number of failed subsystems exceeds this threshold... At that time, the entire multi-state voting system fails; Let be the characteristic function, when the total number of failed subsystems in the polymorphic voting system is... Greater than or equal to the threshold At that time, The value is 1, when it is not true, that is hour, The value is 0; The reliability function of the entire multi-state voting system is shown below: in, This is the reliability function of the entire polymorphic voting system; The number of faulty subsystems is below a threshold The probability of it occurring.

9. The task termination strategy of the multi-state voting system equipped with a protection device according to claim 6, characterized in that, Considering the task termination strategy, the i-th subsystem is in one of two scenarios; In scenario one, the subsystem failed to complete the corresponding task; In scenario two, the subsystem successfully completed the corresponding task; Use symbols This represents the result of the i-th subsystem completing the task, where a value of 0 corresponds to scenario one and a value of 1 corresponds to scenario two. This indicates that the feasible outcome for the i-th subsystem in completing the task is... The probability of that time; The general generating function expression for the task completion result of the i-th subsystem is as follows: in, Let be the general generating function expression for the task completion result of the i-th subsystem; where when When it is 0, Represents the probability of the i-th subsystem task failing, when When it is 1, This represents the probability of success for the i-th subsystem task. Let be the success probability of the task in the i-th subsystem; This indicates that the i-th subsystem failed to complete the task. This indicates that the i-th subsystem has successfully completed the task; Defined as an integer, it can be obtained using the following formula: Where r represents a percentage between 0 and 1. If the proportion of subsystems that successfully complete the corresponding task in the polymorphic voting system exceeds r, then the entire polymorphic voting system is considered to have completed the task. This represents an upper bound function that produces functions greater than or equal to... The smallest integer; therefore, Return strictly greater than The smallest integer; The general generating function expression representing the completion results of the first i subsystem tasks in the polymorphic voting system can be obtained through the following recursive process: Step 1: Let ; Step 2: For Repeated derivation ; in, Describes the general generating function expression for the completion results of the first i subsystem tasks in a polymorphic voting system, where Let the number of subsystems that successfully complete the task in the first i subsystems be denoted as . , This indicates the probability of its occurrence; Let represent the general generating function expression for the completion results of the first i-1 subsystem tasks in a polymorphic voting system, where Let the number of subsystems that successfully complete the task in the first i-1 subsystems be denoted as . , This indicates the probability of its occurrence; The general generating function expression represents the task completion result of the i-th subsystem, where when When it is 0, This represents the probability of the i-th subsystem task failing. This indicates that the i-th subsystem has not completed its task. When it is 1, This represents the probability of success for the i-th subsystem task. This indicates that the i-th subsystem has completed its task. Let be the success probability of the task in the i-th subsystem; when When it is 0, The number of subsystems that complete the assigned tasks in the first i subsystems is denoted as . ;when When it is 1, The number of subsystems that complete the assigned tasks in the first i subsystems is denoted as . ; therefore, And the success probability of the task in the entire polymorphic voting system It is obtained through the following expression: in A general generating function expression representing the task completion result of a subsystem in a polymorphic voting system. This represents the number of subsystems in the entire polymorphic voting system that successfully complete their assigned tasks. The number of subsystems that successfully completed the task among all subsystems is denoted as . , This indicates the probability of its occurrence; The probability of task success for the entire polymorphic voting system. Let be the characteristic function, representing the number of subsystems in a polymorphic voting system that successfully complete their assigned tasks. Greater than or equal to hour, The value is 1, when it is not true, that is hour, The value is 0; Including the task termination policy parameters of the i-th subsystem, i.e. ; The survival probability of the entire polymorphic voting system, which is the probability that the entire polymorphic voting system will survive if all subsystems survive, can be obtained by the following formula: in, The survival probability of the entire polymorphic voting system; To consider the survival probability of the i-th subsystem under the task termination strategy; Including the task termination policy parameters of the i-th subsystem, i.e. .

10. The task termination strategy of the multi-state voting system equipped with a protection device according to claim 1, characterized in that, To balance the probability of task success and system survival probability ,in Two optimization models were established, one for maximizing the success probability of the task and the other for minimizing the total cost. In both models, the decision variables are a series of quantitative thresholds in the designed task termination strategy. , , ,in The following are examples: in, To maximize the success probability of the task in the entire polymorphic voting system, To minimize total cost; The survival probability of the entire polymorphic voting system. Including the task termination policy parameters of the i-th subsystem, i.e. , A preset threshold representing the system's survival probability. This represents the optimal state of the i-th subsystem. , The preset threshold for the subsystem state. The preset threshold for the state of the protection device is defined when the state of the i-th subsystem belongs to... And the status of the protection device Less than or equal to the preset threshold When the task termination criteria are met, This represents the optimal state of the protection device for the i-th subsystem. and These represent the costs of task failure and system malfunction, respectively. The primary goal is to reduce the total cost of task failures and system malfunctions. Ultimately, the optimal threshold is obtained through solving, and the optimal task termination strategy is derived.

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