A reserve component replacement optimization method for a balancing system

Abstract

The application provides a reserve component replacement optimization method of a balanced system, which comprises the following steps: determining the degradation rate and random degradation degree of different types of components in the balanced system, obtaining the distribution function of the random degradation degree of the different types of components, formulating a reserve component switching and rebalancing strategy of the balanced system according to the situation of the balanced system, and obtaining the state transition rate matrix of the balanced system during operation; obtaining the reliability function of the balanced system and the life distribution function of the balanced system according to the state transition rate matrix; obtaining the corresponding running expected total cost of the balanced system under different reserve component purchase quantities through the reserve component purchase cost, the unit time expected downtime cost and the life distribution function of the balanced system, and outputting the reserve component purchase quantity corresponding to the minimum running expected total cost of the balanced system as the optimal reserve component purchase quantity. The application can obtain the highest system running reliability with the minimum running expected total cost.

Description

Technical Field

[0001] The invention belongs to the field of balancing system operation strategy optimization, and specifically discloses a method for optimizing the replacement of reserve components of a balancing system.

[0002] Background

[0003] In recent years, the reliability of balanced systems has become a research hotspot in the field of reliability. Compared to traditional engineering systems, balanced systems must maintain relative stability in the position and state of their components during operation. Imbalance in a balanced system can severely impact its reliability. Therefore, the structure and operating principles of balanced systems are unique and complex. Balanced systems have crucial applications in numerous engineering fields, including aerospace, new energy storage, mechanical manufacturing, and weaponry, for example, solar-powered drone propulsion systems, new energy vehicle battery packs, and assembly line systems. Current research can categorize balanced systems into three types based on the definition of balance: Balanced systems based on component position, where balance is defined as the simultaneous operation and inactivity of spatially symmetrically positioned components; Balanced systems based on component number, where these systems typically contain multiple operating zones, each containing multiple components, and where the number of operating components in each zone must be equal or within a certain range; and Balanced systems based on component state, where components typically have multiple operating states, where system balance is defined as the state difference between specific components within the system not exceeding a certain threshold.

[0004] The operating strategy of a balanced system generally refers to the measures and methods for effectively controlling the operating status of the system in order to achieve a certain goal. When the system is unbalanced, the operating strategies are generally divided into three categories. The first operating strategy is to shut down components when a working component fails or restart a shut-down component to maintain balance. If a component fails, the system will forcibly shut down or restore another component to maintain balance. The second operating strategy is to dynamically adjust the working components to rebalance the system. This is done by identifying components with high status and adjusting them to a lower status to rebalance the system. The third operating strategy is the reserve component switching mechanism, which rebalances the system by putting some working components into reserve mode or allowing reserve components to resume working.

[0005] Existing technology models the degradation process of balancing systems, particularly those requiring the replacement of reserve components. This strategy proposes a rebalancing strategy for balancing systems with a reserve component pool. This method defines the system's balance as the maximum state difference between all working components. If the system becomes unbalanced or a fault occurs, a qualified reserve component from the reserve pool is selected to replace the working component. In modern industrial systems, the existence of a reserve component pool is crucial for ensuring the system's continued stable operation. By increasing the number of components in the reserve component pool, the system can more quickly find replacement parts in the event of a sudden failure or maintenance need, thereby reducing downtime and improving overall operational reliability. This strategy helps maintain system continuity and avoids financial losses caused by equipment downtime. However, the procurement and management of reserve components also incur costs. Excessive reserve components can lead to excessive capital expenditures, increase inventory management complexity, and even cause components to expire or become obsolete. Therefore, simply increasing the number of reserve components is not a panacea. A balance must be struck between improving system reliability and controlling costs. Therefore, it is necessary to optimize the number of reserve components in the reserve component pool from the perspective of optimal cost to achieve the highest system operation reliability at the lowest expected total cost. In response to the above problems, it is necessary to research and design a new reserve component replacement optimization method for the balancing system to overcome the problems existing in the existing balancing system optimization methods. Summary of the Invention

[0006] The present invention proposes a method for optimizing the replacement of reserve components of a balancing system to solve the problem in existing balancing system optimization methods that it is difficult to find a balance between the number of reserve components and improving system reliability and controlling costs.

[0007] The present invention provides a method for optimizing replacement of reserve components of a balancing system, comprising the following steps:

[0008] S1. Determine the operational degradation rates of components of different types in the balancing system based on historical information of the balancing system. Determine the random degradation degrees of components of different types in the balancing system based on the operational degradation rates of components of different types in the balancing system. Determine the distribution functions of the random degradation degrees of components of different types based on the random degradation degrees of components of different types in the balancing system. Develop a reserve component switching and rebalancing strategy for the balancing system based on the conditions of the balancing system.

[0009] S2. Obtain a state transition rate matrix of the balanced system at runtime based on the distribution function and the reserve component switching rebalancing strategy obtained in step S1;

[0010] S3. According to the state transition rate matrix obtained in step S2, the reliability function of the balanced system and the life distribution function of the balanced system are obtained;

[0011] S4. Obtain the expected total operating cost of the balancing system corresponding to different purchase quantities of reserve components through the purchase cost of the reserve components of the balancing system, the expected downtime cost per unit time of the balancing system, and the life distribution function of the balancing system obtained in step S2, and output the reserve component purchase quantity corresponding to the minimum expected total operating cost of the balancing system as the optimal reserve component purchase quantity.

[0012] According to a method for optimizing replacement of reserve components of a balancing system in some embodiments of the present application, in step S1, the balancing system includes multiple components, and the state space of the components is S = {0, 1, 2, ..., k}, wherein k represents that the component is in a brand new state, 0 represents that the component is in a failed state, and numbers between 0-k represent that the component is in an intermediate state from a brand new state to a failed state. The components include working components and reserve components, and the working components are from state l to l-1, wherein (l = 1, 2, ..., k), and the degradation rate of the working components is Where r represents the working component, and the degradation rate of the reserve component is Wherein, s represents a reserve component, and the balancing system further includes a reserve component pool, in which the reserve component will not degenerate, and the balance degree of the balancing system is As shown in formula (1):

[0013]

[0014] in, Indicates the optimal state of the working component, represents the worst state of the working component, n represents the number of working components, Indicates the status of the component, and α indicates the type of component, whether it is a normal component or a reserve component.

[0015] According to a method for optimizing replacement of reserve components of a balancing system in some embodiments of the present application, in step S1, the reserve component switching rebalancing strategy of the balancing system includes: when the balancing system is running, if it is detected that the performance of the v-th working component has declined, then judging whether the v-th working component has failed; if the v-th working component has failed, then selecting from the reserve component pool whether there is a reserve component that can replace the v-th working component; if there is a reserve component that can replace the v-th working component and the state of the reserve component is better than the state of the v-th working component, then selecting the reserve component with the best state from all the reserve components that can replace the v-th working component to replace the v-th working component; if there is no reserve component that can replace ..., then selecting the reserve component with the best state from all the reserve components that can replace the v-th working component; if there is no reserve component that can replace the v-th working component, then selecting the reserve component with the best state from all the reserve components that can replace the v-th working component. If it is a reserve component of the vth working component and the status of the best reserve component in the reserve component pool is better than the status of the vth working component, then determine whether the best reserve component in the reserve component pool can replace the uth working component with degraded performance. If it can replace the uth working component, then use the reserve component pool with the best status in the reserve component pool to replace the uth working component. If the status of the best reserve component in the reserve component pool is worse than the status of the uth working component, then the balancing system stops working. If the status of the best reserve component in the reserve component pool is worse than the status of the vth working component, then the balancing system stops working. Each working component replaced becomes the reserve component pool in the reserve component pool.

[0016] According to a method for optimizing replacement of reserve components of a balancing system in some embodiments of the present application, in step S1, the system state space of the balancing system is as shown in formula (2):

[0017]

[0018] in, represents the state of the equilibrium system, n s Indicates the number of reserve components, E f represents the absorbing state of the equilibrium system.

[0019] According to a method for optimizing replacement of reserve components of a balancing system according to some embodiments of the present application, in step S2, the state transition rate of the balancing system during operation includes:

[0020] For a working component to degrade once, the component does not fail and the balance degree does not exceed the threshold d, the state transition rate of the balanced system is

[0021] For a working component to degrade once, the component fails, and the state transition rate of the equilibrium system is

[0022] For the working component degradation once, the component does not fail and the balance difference does not exceed the threshold d, the vth working component cannot be replaced, the u th working component is replaced, and the balanced system continues to run, the state transition rate of the balanced system is

[0023] For the working component degradation once, the component does not fail and the balance difference does not exceed the threshold d, the vth working component cannot be replaced, the u th working component is replaced, and the balanced system continues to run, the state transition rate of the balanced system is

[0024] For the working component degradation once, the component does not fail and the balance difference does not exceed the threshold d, the vth working component cannot be replaced, the u th working component is replaced, and the balanced system continues to run, the state transition rate of the balanced system is

[0025] The state transition rate matrix of the balanced system in operation is obtained as shown in formula (3):

[0026]

[0027] Wherein, Q represents the one-step transition rate matrix of the balanced system, the value of the a th row and the b th column in the one-step transition rate matrix represents that the component is in the state of X a The state is transferred to the state of X b The state transition rate, X a Indicates the state of the component at a time, X b Indicates the state of the component at b time, |Ω| represents the base number of the system state space, A represents the transition rate matrix between the transition states of the balanced system, the size of the transition rate matrix between the transition states of the balanced system is |Ω-1|×|Ω-1|, B represents the transition rate matrix of the balanced system from each transition state to the absorbing state, the size of the transition rate matrix of the balanced system from each transition state to the absorbing state is |Ω-1|×1.

[0028] According to the spare part replacement optimization method of the balanced system according to some embodiments of the present application, the reliability function of the balanced system in step S3 is shown in formula (4):

[0029] R(t)=αexp(Qt)e′ (4)

[0030] Wherein, t represents the time t, R(t) represents the reliability of the balanced system in [0,t], the reliability is the probability that the balanced system completes the specified function, α represents the initial probability of the balanced system, α contains a row vector with |Ω| elements, the first element is 1 and the remaining elements are 0, e=(1,1,...,1,0) 1×|Ω| , e represents the probability that the balanced system is in the working state, and'represents transposition,

[0031] The life distribution function of the balanced system is shown in formula (5):

[0032] F T (t)=P{T≤t}=1-ηexp(At)e′ t (5)

[0033] Among them, F T (t) represents the lifetime distribution function of the equilibrium system, T represents the lifetime of the equilibrium system, P{T≤t} represents the probability that the system lifetime is less than or equal to t, and the lifetime T of the equilibrium system follows a continuous phase distribution, which is expressed as T~PH(η,A), t represents the time t, and η=(1,0,0,...,0) 1×(|Ω|-1) , η represents the initial probability that the equilibrium system is in the working state, e t =(1,1,...,1) 1＝(|Ω|-1) represents the probability that the equilibrium system is in the working state, and ′ represents the transpose.

[0034] According to a method for optimizing replacement of reserve components of a balancing system in some embodiments of the present application, in step S4, the expected total cost of operation of the balancing system is as shown in formula (6):

[0035]

[0036] Where C represents the total cost of the balancing system, n s Indicates the number of reserve components, c s represents the cost of purchasing each reserve component, c f represents the downtime cost per unit time, T d Indicates the time required for the system to complete the task.

[0037] According to a method for optimizing replacement of reserve components of a balancing system in some embodiments of the present application, in step S4, the expected total operating cost of the balancing system corresponding to the purchase quantity of all reserve components is obtained by enumeration.

[0038] The present invention also provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program; the processor is configured to execute the computer program in the memory to implement the above method.

[0039] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program implements the above method when executed by a processor.

[0040] The present invention proposes a method for optimizing the replacement of reserve components of a balancing system. Considering a balancing system with reserve components in a degraded state, a reserve component replacement mechanism with a reserve component pool is proposed. The reliability function and the life distribution function of the balancing system are determined by the Markov embedding method. Then, the purchase cost of the reserve components and the expected downtime cost per unit time of the balancing system are comprehensively considered. From the perspective of the optimal expected total operating cost, the number of reserve components in the reserve component pool is optimized, achieving the goal of ensuring the highest system operation reliability with the minimum expected total operating cost. In addition, the balancing system optimized by this method has a lower total operating cost and higher reliability than any single system. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A schematic flow chart of a method for optimizing replacement of reserve components of a balancing system according to the present invention;

[0042] Figure 2 This is a schematic diagram of the transfer process of the drone swarm system in Example 3;

[0043] Figure 3 is a reliability curve diagram of the balancing system in Example 3 when the balancing system operates with different numbers of reserve components;

[0044] Figure 4 This is a graph of the expected total cost of the balancing system in Example 3 when operating with different numbers of reserve components. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0046] It should be noted that the terms "including," "having," and any variations thereof in the embodiments and drawings of this application are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to the process, method, product, or apparatus.

[0047] Example 1: This example provides a method for optimizing the replacement of reserve components of a balancing system. Figure 1 As shown, the following steps are included:

[0048] S1. Determine the operational degradation rates of components of different types in the balancing system based on historical information of the balancing system. Determine the random degradation degrees of components of different types in the balancing system based on the operational degradation rates of components of different types in the balancing system. Determine the distribution functions of the random degradation degrees of components of different types based on the random degradation degrees of components of different types in the balancing system. Develop a reserve component switching and rebalancing strategy for the balancing system based on the conditions of the balancing system.

[0049] S2. Obtain a state transition rate matrix of the balanced system at runtime based on the distribution function and the reserve component switching rebalancing strategy obtained in step S1;

[0050] S3. According to the state transition rate matrix obtained in step S2, the reliability function of the balanced system and the life distribution function of the balanced system are obtained;

[0051] S4. Obtain the expected total operating cost of the balancing system corresponding to different purchase quantities of reserve components through the purchase cost of the balancing system's reserve components, the expected downtime cost per unit time of the balancing system, and the life distribution function of the balancing system obtained in step S2, and output the reserve component purchase quantity corresponding to the minimum expected total operating cost of the balancing system as the optimal reserve component purchase quantity.

[0052] Example 2: This example provides a method for optimizing replacement of reserve components of a balancing system, comprising the following steps:

[0053] S1. Determine the operational degradation rates of components of different types in the balancing system based on historical information of the balancing system. Determine the random degradation degrees of components of different types in the balancing system based on the operational degradation rates of components of different types in the balancing system. Determine the distribution functions of the random degradation degrees of components of different types based on the random degradation degrees of components of different types in the balancing system. Develop a reserve component switching and rebalancing strategy for the balancing system based on the conditions of the balancing system.

[0054] Specifically, the equilibrium system includes multiple components, and the state space of the components is S = {0, 1, 2, ..., k}, where k represents the component in a brand new state, 0 represents the component in a failed state, and the numbers between 0-k represent the component in an intermediate state from a brand new state to a failed state. The components include working components and reserve components. The working component goes from state l to l-1, where (l = 1, 2, ..., k), and the degradation rate of the working component is Among them, r represents the working part, and the degradation rate of the reserve part is Where s represents the reserve component. The balanced system also includes a reserve component pool. The reserve component will not degrade in the reserve component pool. However, when the reserve component and the working component work in the same state at the same time, the degradation rate of the reserve component is higher than the degradation rate of the working component, that is, Balance system Balance of the system As shown in formula (1):

[0055]

[0056] in, Indicates the optimal state of the working component, represents the worst state of the working component, n represents the number of working components, Indicates the status of the component, α indicates the type of component is a normal component or a reserve component,

[0057] Balance system Balance of the system Determined by the state difference between the best and worst states of the component during operation;

[0058] The reserve component switching rebalancing strategy of the balancing system includes: when the balancing system is running, if it is detected that the performance of the vth working component has deteriorated, then it is judged whether the vth working component has failed; if the vth working component has failed, then it is selected from the reserve component pool whether there is a reserve component that can replace the vth working component; if there is a reserve component that can replace the vth working component and the state of the reserve component is better than the state of the vth working component, then the reserve component with the best state is selected from all the reserve components that can replace the vth working component to replace the vth working component; if there is no reserve component that can replace the vth working component and the state of the reserve component in the reserve component pool .... If the state of a good reserve component is better than that of the vth working component, then determine whether the best reserve component in the reserve component pool can replace the uth working component with degraded performance. If it can replace the uth working component, then use the best reserve component in the reserve component pool to replace the uth working component. If the state of the best reserve component in the reserve component pool is worse than that of the uth working component, then the balancing system stops working. If the state of the best reserve component in the reserve component pool is worse than that of the vth working component, then the balancing system stops working. Each time a working component is replaced, it becomes the reserve component pool in the reserve component pool.

[0059] The system state space of the equilibrium system is shown in formula (2):

[0060]

[0061] in, represents the state of the equilibrium system, n s Indicates the number of reserve components, E f represents the absorbing state of the equilibrium system.

[0062] S2. Obtain a state transition rate matrix of the balanced system at runtime based on the distribution function and the reserve component switching rebalancing strategy obtained in step S1;

[0063] Specifically, the state transition rate of the balanced system during operation includes:

[0064] For a working component to degrade once, the component does not fail and the balance degree does not exceed the threshold d, the state transition rate of the balanced system is

[0065] For a working component to degrade once, the component fails, and the state transition rate of the equilibrium system is

[0066] If a working component degrades once, the component does not fail and the balance degree does not exceed the threshold d, the balance system continues to operate after the vth working component is replaced. The state transition rate of the balance system is

[0067] For a working component that degrades once, the component does not fail and the balance difference does not exceed the threshold d, the vth working component cannot be replaced, and the balanced system continues to operate after the uth working component is replaced. The state transition rate of the balanced system is

[0068] For a working component degradation, component failure or balance difference does not exceed the threshold d and there is no reserve component for replacement, the balance system fails, and the state transition rate of the balance system is

[0069] The state transition rate matrix of the equilibrium system during operation is shown in formula (3):

[0070]

[0071] Among them, Q represents the one-step transfer rate matrix of the equilibrium system, and the value of the a-th row and b-th column in the one-step transfer rate matrix represents the component composed of X a State transfer to X b State transition rate, X a Indicates the state of the component at time a, X b Represents the state of the component at time b, |Ω| represents the cardinality of the system state space, A represents the transfer rate matrix between the transition states of the equilibrium system, and the size of the transfer rate matrix between the transition states of the equilibrium system is |Ω-1|×|Ω-1|, B represents the transfer rate matrix from each transition state to the absorbing state of the equilibrium system, and the size of the transfer rate matrix from each transition state to the absorbing state of the equilibrium system is |Ω-1|×1.

[0072] S3. According to the state transition rate matrix obtained in step S2, the reliability function of the balanced system and the life distribution function of the balanced system are obtained; preferably, the reliability function of the balanced system and the life distribution function of the balanced system can be obtained by the Markov embedding method;

[0073] Specifically, the reliability function of the equilibrium system is shown in formula (4):

[0074] R(t)=αexp(Qt)e′(4)

[0075] Where R(t) represents the reliability of the equilibrium system in [0, t]. Reliability is the probability that the equilibrium system completes its specified function. t represents time t. α represents the initial probability of the equilibrium system. α is a row vector containing |Ω| elements, where the first element is 1 and the rest are 0. e = (1, 1, ..., 1, 0) 1×|Ω| , e represents the probability that the equilibrium system is in the working state, ′ represents the transposition,

[0076] The life distribution function of the equilibrium system is shown in formula (5):

[0077] F T (t)=P{T≤t}=1-ηexp(At)e′ t (5)

[0078] Among them, F T (t) represents the lifetime distribution function of the equilibrium system, T represents the lifetime of the equilibrium system, P{T≤t} represents the probability that the system lifetime is less than or equal to t, and the lifetime T of the equilibrium system follows a continuous phase distribution, which is expressed as T~PH(η,A), t represents the time t, and η=(1,0,0,...,0) 1×(|Ω|-1) , η represents the initial probability that the equilibrium system is in the working state, e t =(1,1,...,1) 1×(|Ω|-1) represents the probability that the equilibrium system is in the working state, and ′ represents the transpose.

[0079] S4. Using the purchase cost of the balancing system's reserve components, the expected downtime cost per unit time of the balancing system, and the life distribution function of the balancing system obtained in step S2, the expected total operating cost of the balancing system corresponding to different reserve component purchase quantities is calculated. The reserve component purchase quantity that minimizes the expected total operating cost of the balancing system is output as the optimal reserve component purchase quantity.

[0080] Specifically, the expected total cost of operating the balanced system is shown in formula (6):

[0081]

[0082] Where C represents the total cost of the balancing system, n s Indicates the number of reserve components, c s represents the cost of purchasing each reserve component, c f represents the downtime cost per unit time, T d Indicates the time required for the system to complete the task.

[0083] Furthermore, the possible purchase quantities of all reserve components can be enumerated to obtain the expected total operating cost of the balancing system for all purchase quantities. The joint optimization process proposed in this method simultaneously considers the reliability and total system cost of the balancing system to determine the optimal number of reserve components. A smaller number of reserve components reduces system reliability, increases downtime costs, and thus increases total system cost. Conversely, a larger number of reserve components improves system reliability and reduces downtime costs, but also increases procurement costs, which also increases total system cost. Therefore, the optimal number of reserve components is obtained using this method.

[0084] This embodiment further provides an electronic device, including a memory and a processor, wherein the memory stores a computer program; the processor is configured to execute the computer program in the memory to implement the above method.

[0085] This embodiment further provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above method is implemented.

[0086] Example 3. This example provides a method for optimizing the replacement of reserve components of a balancing system. The balancing system of this example is a balancing system with a reserve component pool. This method simultaneously considers the characteristics of different types of reserve components and the impact of downtime costs and procurement costs. From a cost perspective, the number of reserve components in the reserve component pool is optimized to achieve the lowest total cost of operation of the balancing system and the highest reliability of the balancing system.

[0087] This embodiment mainly uses the Markov embedding method to calculate the reliability of the balance system, the life distribution function of the balance system, and the expected value of the balance system life, and then calculates the total cost of the system, and jointly optimizes to obtain the optimal number of reserve components. The method specifically includes the following steps:

[0088] Step 1: Define component states and partition the component state space into S = {0, 1, 2, ..., k}, where 0 indicates a failed component in the system and k indicates a brand new component. By integrating the actual operating process of the balancing system, the operating state of the balancing system is partitioned to determine the component state space. For example, using a drone swarm for multi-point maintenance of a high-voltage power grid, based on relevant production process parameters such as drone weight and raw materials used, the state space of the drone swarm system is defined as S = {0, 1, 2}, where "1-2" indicates the drone is still operational and "0" indicates it is completely inoperable.

[0089] Analyze the external operating environment of the UAV swarm system and characterize the state transition rules of the components. The degradation rate of a normal component from state l to state l-1 is Among them, (l=1,2,...,k), the degradation rate of the reserve component is The reserve components will not degrade in the reserve component pool. When the reserve components and normal components are working in the same state at the same time, the degradation rate of the reserve components is higher than that of the normal components, that is, Normal components and reserve components have the same function when working, but different degradation rates. Under the same working conditions, the degradation rate of normal components is lower than that of reserve components. Based on the relevant parameters in the actual operation process, such as endurance time, control distance, etc., the degradation rate of normal components is defined as The degradation rate of the reserve component is defined as and

[0090] Step 2: Determine the transfer rate matrix of the drone swarm system. After the components in the drone swarm system have degraded, according to the rebalancing mechanism of component replacement and combined with the operation process of the system, the state space of the drone swarm system is:

[0091]

[0092] Among them, E f It represents the absorption state of the equilibrium system, which means the system fails. According to the system transfer process, the state transfer rate matrix Q of the drone swarm system can be obtained. The transfer process of the drone swarm system is as follows: Figure 2 As shown, the initial state of the drone swarm system is X1, with X 14 For example, if the first normal component degrades from 1 to 0, the normal component fails, causing the system to fail. After being replaced with the reserve component, the state of the drone swarm system becomes X 17 , the transfer rate of the UAV swarm system is The matrix Q is represented as, q 14,17 = 0.2. If the second working reserve component is from 1 s Degenerates to 0 s , then the reserve component fails, causing the drone swarm system to fail. After replacing it with the reserve component, the drone swarm system status changes to X 20 , the transfer rate of the drone swarm system is In the matrix Q, it is represented as q 14,20 =0.2.

[0093] Step 3: Reliability evaluation of the UAV swarm system. The reliability function of the UAV swarm system is shown in formula (7):

[0094] R(t)=αexp(Qt)e′(7)

[0095] Where R(t) represents the reliability of the equilibrium system in [0, t]. Reliability is the probability that the equilibrium system completes its specified function. t represents time t. α represents the initial probability of the equilibrium system. α is a row vector containing |Ω| elements, where the first element is 1 and the rest are 0. α = (1, 0, 0, ..., 0) 1×25 , e=(1,1,...,1,0) 1×25 , e represents the probability that the equilibrium system is in the working state, ′ represents the transposition, and the reliability of the UAV swarm system under different numbers of reserve components is as follows: Figure 3 shown.

[0096] The life distribution function of the UAV swarm system is shown in formula (8):

[0097] F T (t)=P{T≤t}=1-ηexp(At)e′ t , (8)

[0098] Among them, F T (t) represents the lifetime distribution function of the equilibrium system, P{T≤t} represents the probability that the system lifetime is less than or equal to t, T represents the equilibrium system lifetime, and the equilibrium system lifetime T follows a continuous phase distribution, which is expressed as T~PH(η,A), t represents the time t, and η=(1,0,0,...,0) 1×24 , η represents the initial probability that the equilibrium system is in the working state, e t =(1,1,...,1) 1×24 It represents the probability that the equilibrium system is in the working state.

[0099] Step 4: Modeling the total cost function. During the operation of the drone swarm system, the following two types of costs will be incurred: the cost of purchasing each reserve component c s , downtime cost per unit time c f According to the relevant parameters in the actual maintenance process, including the number of points to be repaired and the amount of maintenance tasks, the time T required for the drone swarm system to complete the task is calculated. d Set to 40, the cost of purchasing each reserve component is c s Set to 30, the downtime cost per unit time c f Set to 15. The total cost of the drone swarm system is shown in formula (9):

[0100]

[0101] Where C represents the total cost of the balancing system, n s Indicates the number of reserve parts.

[0102] By enumerating the possible purchase quantities of all reserve components and obtaining the expected total cost of the balanced system under all the reserve component purchase quantities, we can find that under the above settings, the optimal number of reserve components in the reserve component pool of the drone swarm system is 7. The expected total cost of the drone swarm system under different reserve component quantities is as follows: Figure 4 As shown, the optimal number of reserve components can be obtained eventually.

[0103] This method considers the impact of the balancing system's external operating environment and the inherent characteristics of its components on the failure process, providing decision makers with a more accurate solution. This method, based on component status detection and component replacement, considers the characteristics of different reserve components and the impact of downtime and procurement costs. This method provides a more practical reserve component strategy, including reserve component procurement and reserve component switching strategies during system operation.

[0104] This proposed method for rebalancing a balanced system is a component status-based strategy optimization approach. This method targets balanced systems, where the health gap between active components should not exceed a threshold. This method considers the impact of the system's external operating environment and the inherent characteristics of components on their failures, integrating component status monitoring with rebalancing and replacement activities to determine the optimal number of reserve components based on cost trade-offs.

[0105] Experimental comparative analysis: The reserve component replacement rebalancing method proposed in this embodiment is compared with the single operation method.

[0106] The expected life of the equilibrium system is shown in formula (10):

[0107] E(T)=-ηA -1 e′ t (10)

[0108] Where E(T) represents the expected value of the equilibrium system life.

[0109] The following table compares system lifespans with different numbers of reserve components. The last column shows the percentage increase in expected system lifespan compared to no reserve components. The table shows that the rebalancing method of this embodiment can extend the lifespan of the balancing system compared to the single-operation method. From the single-operation method to the one with a reserve component, the expected system lifespan increases by approximately 60%. As the number of reserve components increases, the expected system lifespan also increases significantly, validating the superiority of the reserve component replacement optimization method for the balancing system proposed in this embodiment.

[0110]

[0111] Based on the above embodiments, an embodiment of the present application also provides an electronic device, which includes: one or more processors, a memory, and one or more programs; wherein the one or more programs are stored in the memory, and the one or more programs include instructions, which, when executed by the electronic device, enable the electronic device to execute the method provided in the above embodiments.

[0112] Based on the above embodiments, an embodiment of the present application further provides a computer storage medium, in which a computer program is stored. When the computer program is executed by a computer, the computer executes the method provided in the above embodiments.

[0113] The storage medium may be any available medium that can be accessed by a computer. By way of example and not limitation, computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage media or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer.

[0114] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0115] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0116] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0117] The embodiments of the present application are presented by way of example and description, and are not intended to be exhaustive or to limit the application to the form disclosed. Many modifications and variations will be apparent to those skilled in the art. Embodiments are chosen and described in order to best explain the principles of the application and its practical application, and to thereby enable others skilled in the art to best utilize the application in various embodiments and with various modifications as are suited to the particular use contemplated.

Claims

1. A method for optimizing the replacement of reserve components of a balancing system, characterized in that: The steps include: S1. Determine the operational degradation rates of components of different types in the balancing system based on historical information of the balancing system. Determine the random degradation degrees of components of different types in the balancing system based on the operational degradation rates of components of different types in the balancing system. Determine the distribution functions of the random degradation degrees of components of different types based on the random degradation degrees of components of different types in the balancing system. Develop a reserve component switching and rebalancing strategy for the balancing system based on the conditions of the balancing system. S2. Obtain a state transition rate matrix of the balanced system at runtime based on the distribution function and the reserve component switching rebalancing strategy obtained in step S1; S3. According to the state transition rate matrix obtained in step S2, the reliability function of the balanced system and the life distribution function of the balanced system are obtained; S4. Calculate the expected total operating cost of the balancing system for different reserve component purchase quantities using the reserve component purchase cost of the balancing system, the expected downtime cost per unit time of the balancing system, and the life distribution function of the balancing system obtained in step S2. The reserve component purchase quantity that minimizes the expected total operating cost of the balancing system is output as the optimal reserve component purchase quantity. In step S3, the life distribution function of the equilibrium system is shown in formula (1): F T (t)=P{T≤t}=1-ηexp(At)e′ t (1) Among them, F T (t) represents the lifetime distribution function of the equilibrium system, T represents the lifetime of the equilibrium system, P{T≤t} represents the probability that the system lifetime is less than or equal to t, and the lifetime T of the equilibrium system follows a continuous phase distribution, which is expressed as T~PH(η,A), t represents the time t, and η=(1,0,0,...,0) 1×(|Ω|-1) , η represents the initial probability that the equilibrium system is in the working state, e t =(1,1,...,1) 1×(|Ω|-1) represents the probability that the equilibrium system is in the working state, ′ represents the transpose; In step S4, the expected total cost of operating the balancing system is as shown in formula (2): Where C represents the total cost of the balancing system, n s Indicates the number of reserve components, c s represents the cost of purchasing each reserve component, c f represents the downtime cost per unit time, T d Indicates the time required for the system to complete the task.

2. The method for optimizing replacement of reserve components of a balancing system according to claim 1, characterized in that: In step S1, the balancing system includes multiple components, and the state space of the components is S = {0, 1, 2, ..., k}, where k represents a component in a brand new state, 0 represents a component in a failed state, and numbers between 0 and k represent components in an intermediate state from a brand new state to a failed state. The components include working components and reserve components. The working component goes from state l to l-1, where (l = 1, 2, ..., k), and the degradation rate of the working component is Where r represents the working component, and the degradation rate of the reserve component is Wherein, s represents a reserve component, and the balancing system further includes a reserve component pool, in which the reserve component will not degenerate, and the balance degree of the balancing system is As shown in formula (3): in, Indicates the optimal state of the working component, represents the worst state of the working component, n represents the number of working components, Indicates the status of the component, and α indicates the type of component, whether it is a normal component or a reserve component.

3. The method for optimizing replacement of reserve components of a balancing system according to claim 2, characterized in that: In step S1, the reserve component switching rebalancing strategy of the balancing system includes: when the balancing system is running, if it is detected that the performance of the vth working component has deteriorated, then it is determined whether the vth working component has failed; if the vth working component has failed, then it is selected from the reserve component pool whether there is a reserve component that can replace the vth working component; if there is a reserve component that can replace the vth working component and the state of the reserve component is better than the state of the vth working component, then the reserve component with the best state is selected from all the reserve components that can replace the vth working component to replace the vth working component; if there is no reserve component that can replace the vth working component and the reserve component is in a better state than the state of the vth working component, then it ... If the status of the best reserve component in the spare parts pool is better than the status of the vth working component, then determine whether the best reserve component in the spare parts pool can replace the uth working component with degraded performance. If it can replace the uth working component, then use the best reserve component pool in the spare parts pool to replace the uth working component. If the status of the best reserve component in the spare parts pool is worse than the status of the uth working component, then the balancing system stops working. If the status of the best reserve component in the spare parts pool is worse than the status of the vth working component, then the balancing system stops working. Each time the working component is replaced, it becomes the reserve component pool in the spare parts pool.

4. The method for optimizing replacement of reserve components of a balancing system according to claim 3, characterized in that: In step S1, the system state space of the balancing system is shown in formula (4): in, represents the state of the equilibrium system, n s Indicates the number of reserve components, E f represents the absorbing state of the equilibrium system.

5. The method for optimizing replacement of reserve components of a balancing system according to claim 1, characterized in that: In step S2, the state transition rate of the balancing system during operation includes: For a working component to degrade once, the component does not fail and the balance degree does not exceed the threshold d, the state transition rate of the balanced system is For a working component to degrade once, the component fails, and the state transition rate of the equilibrium system is If a working component degrades once, the component does not fail and the balance degree does not exceed the threshold d, the balance system continues to operate after the vth working component is replaced. The state transition rate of the balance system is For a working component that degrades once, the component does not fail and the balance difference does not exceed the threshold d, the vth working component cannot be replaced, and the balanced system continues to operate after the uth working component is replaced. The state transition rate of the balanced system is For a working component degradation, component failure or balance difference does not exceed the threshold d and there is no reserve component for replacement, the balance system fails, and the state transition rate of the balance system is The state transition rate matrix of the equilibrium system during operation is shown in formula (5): Among them, Q represents the one-step transfer rate matrix of the equilibrium system, and the value of the a-th row and b-th column in the one-step transfer rate matrix represents the component composed of X a State transfer to X b State transition rate, X a Indicates the state of the component at time a, X b Represents the state of the component at time b, |Ω| represents the cardinality of the system state space, A represents the transfer rate matrix between the transition states of the equilibrium system, and the size of the transfer rate matrix between the transition states of the equilibrium system is |Ω-1|×|Ω-1|, B represents the transfer rate matrix from each transition state to the absorbing state of the equilibrium system, and the size of the transfer rate matrix from each transition state to the absorbing state of the equilibrium system is |Ω-1|×1.

6. The method for optimizing replacement of reserve components of a balancing system according to claim 5, characterized in that: In step S3, the reliability function of the balancing system is shown in formula (6): R(t)=αexp(Qt)e′ (6) Where t represents time t, R(t) represents the reliability of the equilibrium system in [0, t], α represents the initial probability of the equilibrium system, and α is a row vector containing |Ω| elements, where the first element is 1 and the rest are 0, e = (1, 1, ..., 1, 0) 1×|Ω| , e represents the probability that the equilibrium system is in the working state, and ′ represents the transpose.

7. The method for optimizing replacement of reserve components of a balancing system according to claim 1, characterized in that: In step S4, the expected total cost of operating the balancing system corresponding to the purchase quantity of all reserve components is obtained by enumeration.

8. An electronic device, characterized in that: The method comprises a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the processor implements the method according to any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores instructions, which, when executed on a computer, enable the computer to execute the method according to any one of claims 1 to 7.

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