Method and system for optimizing electronic spare parts configuration of a ship based on time-varying failure rate

Abstract

This invention discloses a method and system for optimizing the configuration of ship electronic spare parts based on time-varying failure rate. The method includes: determining the ship's mission cycle, the configuration quantity of various electronic spare parts, and their unit cost; inputting the ship's mission cycle and the configuration quantity of various electronic spare parts into a spare parts demand model based on time-varying failure rate, and outputting the success probability of each type of electronic spare part; the spare parts demand model based on time-varying failure rate is constructed by combining the Weibull distribution function, the NHPP function, and the Poisson distribution function; constructing a bi-objective optimization configuration problem based on the success probability, configuration quantity, and unit cost; transforming the bi-objective optimization configuration problem into a single-objective optimization configuration problem using the IPM method; and solving the single-objective optimization configuration problem using the ALNS algorithm to obtain the globally optimal ship electronic spare parts configuration scheme. This invention achieves a better trade-off between reliability and cost, resulting in the optimal configuration scheme for ship electronic spare parts.

Description

Technical Field

[0001] This invention relates to the field of electronic spare parts optimization configuration technology, and in particular to a method and system for optimizing the configuration of marine electronic spare parts based on time-varying failure rate. Background Technology

[0002] Marine electronic systems are characterized by complex mission environments, high timeliness requirements for support, and limited maintenance conditions. If critical components fail during missions and spare parts are insufficient, it often leads to equipment downtime, functional degradation, or even mission interruption. In recent years, the optimal allocation of marine spare parts has received increasing attention. Related reviews indicate that the spare parts issue has gradually evolved from traditional inventory control into a comprehensive decision-making problem integrating reliability, maintenance, and operational optimization.

[0003] Existing research has yielded a relatively rich model system for optimizing spare parts allocation. One type of research focuses on the joint optimization of maintenance and spare parts inventory, incorporating equipment degradation, preventive maintenance, condition-based maintenance, and spare parts replenishment into a unified decision-making framework to improve system reliability and reduce life cycle costs. For example, some studies have established joint optimization models for condition-based maintenance and inventory control for systems composed of components with multiple degradation states; other studies have investigated the coupled optimization problems of preventive maintenance, opportunistic maintenance, inventory strategies, and system structural constraints for scenarios such as standby systems, series-parallel systems, and multi-unit complex systems.

[0004] As reliability, cost, inventory, and system structure constraints increase in spare parts optimization problems, the optimization models typically exhibit complex nonlinear characteristics, significantly increasing the difficulty of solving them. Therefore, researchers have conducted extensive studies at the algorithmic level. For large-scale, strongly coupled, and nonlinear spare parts optimization problems, an increasing number of studies are employing genetic algorithms, heuristic search, and improved intelligent optimization algorithms.

[0005] Although existing research has made significant progress in model building and algorithm solution methods, most studies often employ a constant failure rate assumption in failure description. While this approach simplifies modeling and solving, for marine electronic spare parts, the failure rate often changes dynamically over mission time. The constant failure rate assumption struggles to accurately describe the time-varying failure characteristics within the mission cycle, easily leading to biased estimation of cumulative failure intensity, and consequently affecting the rationality of spare parts demand forecasting and configuration schemes.

[0006] Therefore, how to achieve the optimal configuration of ship electronic spare parts has become an urgent problem to be solved.

[0007] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0008] The main objective of this invention is to provide a method and system for optimizing the configuration of ship electronic spare parts based on time-varying failure rate, aiming to solve the technical problem of how to achieve the optimal configuration of ship electronic spare parts.

[0009] To achieve the above objectives, the present invention provides a method for optimizing the configuration of ship electronic spare parts based on time-varying failure rate, the method comprising: Determine the ship's mission cycle, the quantity of various electronic spare parts, and their unit cost; The ship's mission cycle and the configuration quantity of various electronic spare parts are input into the spare parts demand model based on time-varying failure rate, and the success probability of ensuring various electronic spare parts is output. The spare parts demand model based on time-varying failure rate is constructed by combining the Weibull distribution function, the NHPP function and the Poisson distribution function. Based on the success probability, configuration quantity, and unit cost of various electronic spare parts, a dual-objective optimization configuration problem is constructed, and the dual-objective optimization configuration problem is transformed into a single-objective optimization configuration problem using the IPM method. The single-objective optimization configuration problem is solved by the ALNS algorithm to obtain the globally optimal configuration scheme for ship electronic spare parts.

[0010] Optionally, the step of inputting the ship's mission cycle and the configuration quantity of various electronic spare parts into a spare parts demand model based on time-varying failure rate, and outputting the success probability of ensuring the availability of various electronic spare parts, includes: The ship's mission cycle and the configuration quantity of various electronic spare parts are input into the spare parts demand model based on time-varying failure rate; The time-varying failure rate of various electronic spare parts is approximated by the Weibull distribution function; Based on the ship's mission cycle, the cumulative failure intensity of various electronic spare parts is obtained through the NHPP function according to the approximate time-varying failure rate. Based on the configuration quantity and cumulative failure intensity of various electronic spare parts, the success probability of ensuring various electronic spare parts is obtained through the Poisson distribution function; The time-varying failure rate-based spare parts demand model outputs the success probability of ensuring the availability of various electronic spare parts.

[0011] Optionally, the Weibull distribution function is:

[0012] In the formula, For the first Electronic spare parts at all times Time-varying efficiency The trend of failure rate. It is a lifespan timescale.

[0013] Optionally, the NHPP function is:

[0014] In the formula, For the first Electronic spare parts during the ship's mission cycle The cumulative failure strength within, For the first Electronic spare parts at all times The time-varying efficiency.

[0015] Optionally, the Poisson distribution function is:

[0016] In the formula, The number of times the failure occurred. For the first The number of electronic spare parts configured. For the first The success rate of ensuring the maintenance of electronic spare parts. For the first Electronic spare parts during the ship's mission cycle The cumulative failure strength within.

[0017] Optionally, the dual-objective optimization configuration problem based on the success probability, configuration quantity, and unit cost of various electronic spare parts includes: Based on the success probability of various electronic spare parts, the system reliability is calculated using the system reliability function. Calculate the total spare parts cost based on the configuration quantity and unit cost of various electronic spare parts; A dual-objective optimization configuration problem is constructed based on the system reliability and the total spare parts cost.

[0018] Optionally, the step of constructing a dual-objective optimization configuration problem based on the system reliability and the total spare parts cost includes: Based on the configuration quantity of various electronic spare parts, construct constraints on the quantity of various electronic spare parts and the total number of spare parts, and construct reliability constraints based on the system reliability. Based on the constraints on the quantity of various electronic spare parts, the total number of spare parts, the reliability constraint, and the integer constraint of spare parts, a bi-objective optimization configuration problem is constructed according to the system reliability and the total spare parts cost.

[0019] Optionally, the step of transforming the bi-objective optimization configuration problem into a single-objective optimization configuration problem using the IPM method includes: The system reliability and total spare parts cost are determined based on the aforementioned dual-objective optimization configuration problem; The system reliability and the total spare parts cost are normalized respectively, and the reliability weighting coefficient and the cost weighting coefficient are determined. Based on the IPM method, a single-objective weighted function is constructed according to the reliability weight coefficient, the cost weight coefficient, the normalized system reliability, and the total spare parts cost. Based on various constraints on the quantity of electronic spare parts, the total number of spare parts, reliability, and the integer number of spare parts, a single-objective optimization configuration problem is constructed according to the single-objective weighting function.

[0020] Optionally, the step of solving the single-objective optimization configuration problem using the ALNS algorithm to obtain the globally optimal ship electronic spare parts configuration scheme includes: Construct a feasible initial solution based on the single-objective optimization configuration problem; The current solution is obtained from the feasible initial solution by using the destruction operator and the repair operator; Determine whether to update the current solution based on the simulated annealing acceptance criterion; If an update is needed, determine whether the current iteration count has reached a preset threshold. When the current iteration count reaches the preset threshold, the globally optimal configuration scheme for ship electronic spare parts is determined based on the current solution.

[0021] Furthermore, to achieve the above objectives, the present invention also proposes a ship electronic spare parts optimization configuration system based on time-varying failure rate, the ship electronic spare parts optimization configuration system based on time-varying failure rate includes: The determination module is used to determine the ship's mission cycle, the configuration quantity of various electronic spare parts, and the unit cost; The calculation module is used to input the ship's mission cycle and the configuration quantity of various electronic spare parts into the spare parts demand model based on time-varying failure rate, and output the success probability of support for various electronic spare parts. The spare parts demand model based on time-varying failure rate is constructed by combining the Weibull distribution function, the NHPP function and the Poisson distribution function. The transformation module is used to construct a dual-objective optimization configuration problem based on the success probability, configuration quantity and unit cost of various electronic spare parts, and to transform the dual-objective optimization configuration problem into a single-objective optimization configuration problem using the IPM method. The configuration module is used to solve the single-objective optimization configuration problem using the ALNS algorithm to obtain the globally optimal configuration scheme for ship electronic spare parts.

[0022] Furthermore, to achieve the above objectives, the present invention also proposes a ship electronic spare parts optimization configuration device based on time-varying failure rate. The device includes: a memory, a processor, and a ship electronic spare parts optimization configuration program based on time-varying failure rate stored in the memory and executable on the processor. The ship electronic spare parts optimization configuration program based on time-varying failure rate is configured to implement the steps of the ship electronic spare parts optimization configuration method based on time-varying failure rate as described above.

[0023] Furthermore, to achieve the above objectives, the present invention also proposes a storage medium storing a time-varying failure rate-based optimized configuration program for ship electronic spare parts. When the time-varying failure rate-based optimized configuration program is executed by a processor, it implements the steps of the time-varying failure rate-based optimized configuration method for ship electronic spare parts as described above.

[0024] This invention first determines the ship's mission cycle, the configuration quantity of various electronic spare parts, and their unit cost. Then, it inputs the ship's mission cycle and the configuration quantity of various electronic spare parts into a spare parts demand model based on time-varying failure rates. The model outputs the success probability of ensuring the availability of various electronic spare parts. This time-varying failure rate-based spare parts demand model is constructed by combining the Weibull distribution function, the NHPP function, and the Poisson distribution function. Next, a bi-objective optimization configuration problem is constructed based on the success probability of ensuring the availability of various electronic spare parts, their configuration quantity, and their unit cost. This bi-objective optimization configuration problem is then transformed into a single-objective optimization configuration problem using the IPM method. Finally, the single-objective optimization configuration problem is solved using the ALNS algorithm to obtain the globally optimal ship electronic spare parts configuration scheme. This invention, through Weibull, NHPP, and Poisson methods, transforms a continuous-time failure process into a discrete spare parts demand. Then, it uses IPM to transform the bi-objective problem into a single-objective problem and uses ALNS for solution, achieving a better trade-off between reliability and cost, thereby obtaining the optimal configuration scheme for ship electronic spare parts. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the structure of a ship electronic spare parts optimization configuration device based on time-varying failure rate in the hardware operating environment involved in the embodiments of the present invention; Figure 2 This is a flowchart illustrating the first embodiment of the method for optimizing the configuration of ship electronic spare parts based on time-varying failure rate according to the present invention. Figure 3 This is a flowchart of the ALNS algorithm in the first embodiment of the ship electronic spare parts optimization configuration method based on time-varying failure rate of the present invention; Figure 4 This is a structural block diagram of the first embodiment of the ship electronic spare parts optimization configuration system based on time-varying failure rate of the present invention.

[0026] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0027] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0028] Reference Figure 1 , Figure 1 This is a schematic diagram of the end-to-end robust time synchronization device structure of the Advanced Driver Assistance Systems (ADAS) hardware operating environment involved in the embodiments of the present invention.

[0029] like Figure 1 As shown, the time-varying failure rate-based marine electronic spare parts optimization configuration device may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to enable communication between these components. The user interface 1003 may include a display screen or an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wireless-Fidelity (Wi-Fi) interface). The memory 1005 may be high-speed random access memory (RAM) or stable non-volatile memory (NVM), such as a disk storage device. Optionally, the memory 1005 may also be a storage system independent of the aforementioned processor 1001.

[0030] Those skilled in the art will understand that Figure 1 The structure shown does not constitute a limitation on the optimized configuration of ship electronic spare parts based on time-varying failure efficiency, and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0031] like Figure 1 As shown, the memory 1005, which serves as a storage medium, may include an operating system, a network communication module, a user interface module, and a ship electronic spare parts optimization configuration program based on time-varying failure rate.

[0032] exist Figure 1In the time-varying failure rate-based marine electronic spare parts optimization configuration device shown, the network interface 1004 is mainly used for data communication with the network server; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and memory 1005 in the time-varying failure rate-based marine electronic spare parts optimization configuration device of the present invention can be set in the time-varying failure rate-based marine electronic spare parts optimization configuration device. The time-varying failure rate-based marine electronic spare parts optimization configuration device calls the time-varying failure rate-based marine electronic spare parts optimization configuration program stored in the memory 1005 through the processor 1001, and executes the time-varying failure rate-based marine electronic spare parts optimization configuration method provided in the embodiment of the present invention.

[0033] This invention provides a method for optimizing the configuration of ship electronic spare parts based on time-varying failure rate, referring to... Figure 2 , Figure 2 This is a flowchart illustrating the first embodiment of the method for optimizing the configuration of ship electronic spare parts based on time-varying failure rate according to the present invention.

[0034] In this embodiment, the method for optimizing the configuration of ship electronic spare parts based on time-varying failure rate includes the following steps: S1 determines the ship's mission cycle, the quantity of various electronic spare parts, and their unit cost.

[0035] It is easy to understand that the executing entity of this embodiment can be a ship electronic spare parts optimization configuration system based on time-varying failure rate with functions such as data processing, network communication and program operation, or other computer equipment with similar functions. This embodiment does not limit it.

[0036] Suppose a ship is performing a mission in the open sea, and the mission period is... The system involves Electronic spare parts, No. The configuration quantity of the spare parts is denoted as Unit cost is denoted as .

[0037] To facilitate the subsequent calculation of the spare parts demand model based on the time-varying failure rate, the following assumptions are made: (1) All devices in the electronic system are described using a two-state model, considering only the two states of normal operation and failure.

[0038] (2) Various electronic spare parts are independent of each other and do not affect each other.

[0039] (3) The failure rate of electronic spare parts is approximated by the Weibull distribution, mainly considering The increasing failure rate.

[0040] (4) The failure arrival process of various spare parts during the task cycle follows a non-homogeneous Poisson process (NHPP), and the number of failures during the task cycle follows a Poisson distribution.

[0041] (5) When the equipment fails and there are enough spare parts, the time interval between the failure state and the working state after the spare parts are replaced is negligible.

[0042] S2, input the ship's mission cycle and the configuration quantity of various electronic spare parts into the spare parts demand model based on time-varying failure rate, and output the success probability of ensuring various electronic spare parts. The spare parts demand model based on time-varying failure rate is constructed by combining the Weibull distribution function, the NHPP function and the Poisson distribution function.

[0043] In the specific implementation, based on the above basic assumptions, the Weibull distribution, NHPP and Poisson distribution are introduced to construct a spare parts demand modeling framework. Based on the spare parts demand modeling framework, a spare parts demand model based on time-varying failure rate is obtained, realizing the transformation from continuous-time failure process to discrete spare parts demand distribution.

[0044] Furthermore, the ship's mission cycle and the configuration quantity of various electronic spare parts are input into the spare parts demand model based on time-varying failure rate. The time-varying failure rate of various electronic spare parts is approximated by the Weibull distribution function. Based on the ship's mission cycle, the cumulative failure intensity of various electronic spare parts is obtained through the NHPP function according to the approximate time-varying failure rate. Based on the configuration quantity and cumulative failure intensity of various electronic spare parts, the success probability of maintenance for various electronic spare parts is obtained through the Poisson distribution function. The success probability of maintenance for various electronic spare parts is output through the spare parts demand model based on time-varying failure rate.

[0045] In this embodiment, the Weibull distribution is used for the first... The time-varying failure rate of the spare parts is approximated. Let the first... The lifespan of such spare parts follows the parameter of shape parameters. and scale parameters The Weibull distribution, the Weibull distribution function is: (1) In the formula, For the first Electronic spare parts at all times Time-varying efficiency The trend of failure rate. For lifespan timescales. When When the failure rate is constant, the Weibull distribution degenerates into an exponential distribution; when When, the failure rate decreases over time; when The failure rate increases over time. Considering that the failure rate characteristic is more consistent with that of shipboard electronic spare parts, this paper mainly studies... This is to describe the variation pattern of the failure rate of electronic spare parts in the E type.

[0046] During the task cycle Inside, Intensity is defined as the integral of the intensity function over that interval, and the NHPP function is: (2) Substituting the Weibull failure rate function into the above equation, we get: (3) The integral yields: (4) in, Indicates the first Spare parts during the task cycle Cumulative failure strength within, Indicates the first The current failure rate of this type of spare part. As can be seen from this formula, the cumulative failure intensity is not only related to the mission time... It is related to, and also affected by, shape parameters and scale parameters The combined effects of these factors.

[0047] Under the NHPP assumption, the first Spare parts during the task cycle The number of failures within is recorded as Based on the fundamental properties of NHPP, Obtain the parameter as The Poisson distribution, i.e.:

[0048] Therefore, the first Spare parts happen to occur within the task cycle. The probability of this failure is: (5) If the first The configuration quantity of this type of spare part is If the actual number of failures during the mission period does not exceed the configured number of spare parts, then it can be considered that this type of spare parts can meet the guarantee requirements. Therefore, the first... The success rate of ensuring the availability of such spare parts during the mission cycle The reliability of this type of spare parts subsystem can be expressed as: (6) Based on the cumulative distribution function of the Poisson distribution, i.e., the Poisson distribution function: (7) Substituting equation (4) into the equation, we get: (8) This formula shows that the first There are three reliable decision variables for spare parts: first, task time. Secondly, the failure parameters of this type of spare parts. , Thirdly, the number of configurations. .when When added, the reliability of the subsystem Monotonically increasing; as task duration increases or failure intensity increases, cumulative failure intensity... The increase in the number of spare parts leads to a decrease in the probability of success given a fixed number of spare parts.

[0049] S3. Based on the success probability, configuration quantity and unit cost of various electronic spare parts, a dual-objective optimization configuration problem is constructed, and the dual-objective optimization configuration problem is transformed into a single-objective optimization configuration problem through the IPM method.

[0050] Furthermore, the approach to addressing the dual-objective optimization configuration problem based on the success probability, configuration quantity, and unit cost of various electronic spare parts is as follows: Calculate the system reliability using a system reliability function based on the success probability of various electronic spare parts; calculate the total spare parts cost based on the configuration quantity and unit cost of various electronic spare parts; and construct a dual-objective optimization configuration problem based on the system reliability and the total spare parts cost.

[0051] In the specific implementation, assume the system contains a total of Class of spare parts, No. The number of spare parts configured is Its subsystem reliability (i.e., the probability of successful maintenance of various electronic spare parts) is: Then the reliability function of the entire ship's electronic spare parts support system (i.e., the support system reliability function) can be written as: (9) in, Let be the spare parts quantity vector, representing the system spare parts configuration scheme. Substituting this into the reliability expressions of each subsystem, we obtain the system reliability as: (10) Substituting the cumulative failure strength expression into the equation, we get: (11) The overall system reliability is given by formula (10), and the total system cost is the sum of the costs of purchasing various spare parts. , can be represented as: (12) Therefore, the problem of optimizing the configuration of ship electronic spare parts can be formulated as a bi-objective optimization problem:

[0052] The first objective is to maximize system reliability during the task cycle, while the second objective is to minimize spare parts costs while maintaining reliability.

[0053] Furthermore, the approach to constructing the dual-objective optimization configuration problem based on system reliability and the total spare parts cost is as follows: construct quantity constraints for various types of electronic spare parts and total spare parts constraints based on the configuration quantity of various types of electronic spare parts, and construct reliability constraints based on system reliability; based on the quantity constraints for various types of electronic spare parts, total spare parts constraints, reliability constraints, and spare parts integer constraints, construct the dual-objective optimization configuration problem based on system reliability and total spare parts cost.

[0054] (1) Quantity constraints of each spare part Considering that each spare part is limited by both storage space and carrying capacity during the mission, the first The quantity of spare parts should meet its upper and lower bound requirements, that is:

[0055] in, Indicates the first Minimum quantity of this type of spare part Indicates the maximum quantity.

[0056] (2) Total number of spare parts constraint To ensure basic support capabilities during the mission, while avoiding an excessively low overall configuration quantity, a minimum constraint is set for the total number of spare parts:

[0057] in, This indicates the minimum total number of spare parts required for a vessel to perform its mission.

[0058] (3) System reliability constraints: To ensure the system can continue operating during the mission, the overall system reliability should not fall below a preset threshold, namely:

[0059] in, This represents the lower limit of system reliability, reflecting the minimum requirements of the task for assurance capabilities.

[0060] (4) Integer constraints Since the number of spare parts can only be an integer, Since it is a positive integer, we have:

[0061] In summary, the bi-objective optimization configuration problem can be written as: (13) Furthermore, the method of transforming the bi-objective optimization configuration problem into a single-objective optimization configuration problem using the IPM method is as follows: Determine the system reliability and total spare parts cost based on the bi-objective optimization configuration problem; normalize the system reliability and total spare parts cost respectively, and determine the reliability weight coefficient and cost weight coefficient; construct a single-objective weighting function based on the IPM method, using the reliability weight coefficient, cost weight coefficient, normalized system reliability, and total spare parts cost; and construct a single-objective optimization configuration problem based on the single-objective weighting function, considering constraints on the quantity of various electronic spare parts, the total number of spare parts, reliability constraints, and spare parts integer constraints.

[0062] In this embodiment, to reduce the difficulty of the solution and facilitate the simultaneous comparison of reliability and cost, IPM is introduced to transform the dual objectives into a single objective. First, the ideal and anti-ideal values ​​of each objective are determined. Then, normalization is used to eliminate dimensional differences. Finally, a unified evaluation function is constructed based on the deviation distance between each objective and the ideal point, transforming the solution process into "finding the configuration scheme closest to the ideal point." This method can better balance the two objectives of reliability and cost, avoiding the bias problem caused by single-objective optimization.

[0063] (1) Target normalization Due to system reliability Total system cost The dimensions are inconsistent in both order of magnitude and dimension, so dimensionless processing is required first.

[0064] Let the lower and upper bounds of the system reliability be respectively. and The lower and upper bounds of the system cost are respectively and The normalized deviation of the reliability target can then be expressed as: (14) Similarly, the normalized deviation of the cost target can be expressed as: (15) in, (16) (17) (2) Construction of weighted single objective function Considering that different tasks place varying degrees of emphasis on system reliability and cost, a weighting coefficient is further introduced. and , representing the importance of the reliability objective and the cost objective respectively, satisfying:

[0065] Therefore, the single-objective function constructed based on the ideal point method is: (18) Substituting the normalization expression, we get: (19) The smaller the objective function, the closer the configuration scheme is to the ideal state in terms of both "high reliability" and "low cost". Therefore, the dual-objective optimization configuration problem can be transformed into the following single-objective optimization configuration problem: (20) S4. Solve the single-objective optimization configuration problem using the ALNS algorithm to obtain the globally optimal configuration scheme for ship electronic spare parts.

[0066] Furthermore, a feasible initial solution is constructed based on the single-objective optimization configuration problem; the current solution is obtained from the feasible initial solution through the destruction operator and the repair operator; the current solution is updated according to the simulated annealing acceptance criterion; if updated, it is determined whether the current iteration number has reached the preset threshold; when the current iteration number reaches the preset threshold, the globally optimal ship electronic spare parts configuration scheme is determined based on the current solution.

[0067] In the specific implementation, the decision variable is a vector of the configuration quantity of various spare parts: (twenty one) This problem includes system reliability constraints, total number of spare parts constraints, and cost objectives. It is a typical nonlinear integer programming problem. Since the strong constraints, nonlinearity, and integer characteristics are consistent with the features of the ALNS algorithm, the improved ALNS algorithm is selected as the solution method. Based on the standard framework, the simulated annealing acceptance criterion and periodic local neighborhood search are introduced to improve the convergence stability and solution quality of the algorithm.

[0068] It's important to note that the core of the ALNS algorithm is to perform a large-scale perturbation of the current solution through a destruction-repair mechanism to achieve efficient exploration of the solution space. First, a feasible initial solution satisfying all constraints is constructed as the starting point for both the current solution and the global optimum. Then, an iterative search phase begins. In each iteration, a destruction operator is selected using a roulette wheel approach based on adaptive weights. This operator performs partial destruction on the current solution to obtain an intermediate solution, and then a repair operation generates a new feasible solution that satisfies the constraints. A simulated annealing criterion is then introduced to determine whether to accept the new solution as the next generation current solution. Simultaneously, a local neighborhood search based on single-step exchange is performed every certain number of iterations to further improve the quality of the solution. Throughout the process, the algorithm continuously updates the global optimum and outputs the optimal spare parts configuration scheme after reaching the maximum number of iterations. This process, through the alternation of destruction and repair, adaptive weight adjustment, and the combination of simulated annealing, effectively balances global exploration and local development. (Reference) Figure 3 , Figure 3 This is a flowchart of the ALNS algorithm in the first embodiment of the ship electronic spare parts optimization configuration method based on time-varying failure rate of the present invention.

[0069] The specific steps of the ALNS algorithm are as follows: (1) Initial solution construction Initial solution It is generated by adding random perturbation to the minimum configuration quantity vector of various spare parts, and its feasibility is guaranteed by a repair function: (twenty two) in, This represents the initial feasible solution constructed by the algorithm. Indicates the amplitude of random disturbance. Indicate the guarantee constraint: (twenty three) (2) Destruction-Repair Operator and Iterative Update ALNS performs an iterative search using destruction and repair operators. Let the... The current solution in the next iteration is The destruction operator removes some spare parts configurations: (twenty four) The repair operator performs random greedy repair on the corrupted solution based on task importance and reliability contribution, and combines the introduced simulated annealing acceptance criterion to determine whether to update the current solution: (25) when And a random number uniformly distributed in the interval [0,1] satisfies If a new solution is found, update the current solution; otherwise, reject the new solution. Indicates the current solution After applying the destruction and repair operators, the newly generated candidate solutions are... This indicates the number of spare parts removed from the current solution by the destruction operator. This represents the increment of the objective function. This indicates the simulated annealing temperature.

[0070] (3) System evaluation During the iteration process, operator weights Adaptive adjustment based on historical performance: (26) The pause-and-restart mechanism ensures that the search process does not get stuck in local optima. .in, Operator The cumulative contribution score of producing high-quality solutions in historical iterations. Operator Number of times used in historical iterations, This represents the globally optimal solution found by the algorithm so far.

[0071] (4) Iteration End and Output When the number of iterations reaches its maximum value At that time, output the globally optimal spare parts configuration scheme: (27) in, This represents the globally optimal solution. Through the above process, the ALNS algorithm can effectively search in the high-dimensional integer solution space, balancing system reliability and cost optimization, and ensuring the stability and convergence of the solution.

[0072] Taking a certain ship performing a mission as an example, assuming the mission cycle at sea is 90 days, the system has a total of 10 types of electronic spare parts, and the unit cost vector is... =[0.05, 0.02, 0.17, 0.03, 0.08, 0.12, 0.04, 0.09, 0.06, 0.14], corresponding to the Weibull shape parameters and scale parameters respectively. =[1.6, 1.9, 1.7, 2.0, 1.8, 2.0, 1.7, 2.2, 1.5, 1.9], =[110, 90, 100, 80, 105, 85, 95, 75, 115, 88], minimum spare parts configuration quantity is =[1, 2, 3, 3, 3, 3, 2, 1, 1, 1], with the maximum configuration quantity uniformly set to 12. The parameters of each spare part of the ship are shown in Table 1.

[0073] Table 1

[0074] Simultaneously, a minimum total number of spare parts is set at 18, and a minimum system reliability is set at 0.93. In the ideal point method, the reliability weight is taken as... Cost weighting and adopt , Reliability normalization is performed, and the upper and lower bounds of cost are determined by the total cost corresponding to the minimum and maximum configuration schemes. The maximum number of iterations for the three algorithms is uniformly set to 180. The main parameters of ALNS are set as follows: stagnation threshold 35, initial temperature 0.025, cooling coefficient 0.988, and local 1-swap scan frequency is executed once every 2 iterations.

[0075] Based on the Weibull–NHPP–Poisson modeling framework, the first step is to calculate the time required for various spare parts during the task cycle. Cumulative failure strength within days The values ​​are 0.7254, 1.0000, 0.8360, 1.2656, 0.7577, 1.1211, 0.9122, 1.4935, 0.6923, and 1.0436, respectively. Secondly, under the parameter settings and constraints, the objective function value of ALNS rapidly decreases from 0.9189 to approximately 0.18 within the first 20 iterations. Subsequently, it undergoes minor adjustments around several high-quality solutions in the later stages and eventually converges stably. The optimal configuration is [5, 6, 5, 7, 5, 6, 6, 7, 5, 5].

[0076] In this embodiment, the increasing failure rate of electronic spare parts is characterized by introducing the Weibull distribution, the cumulative failure intensity within the task cycle is obtained by integrating the failure rate function using NHPP, and the failure frequency distribution is described by combining the Poisson distribution, thus completing the transformation from a continuous-time failure process to discrete spare parts requirements. In terms of optimization modeling, the dual-objective problem of maximizing system reliability and minimizing cost is transformed into a single-objective problem through IPM. In terms of solution method, the ALNS algorithm adopted effectively improves the global search capability and convergence stability by combining the destruction-repair mechanism, adaptive weight update and simulated annealing acceptance criterion.

[0077] Reference Figure 4 , Figure 4 This is a structural block diagram of the first embodiment of the ship electronic spare parts optimization configuration system based on time-varying failure rate of the present invention.

[0078] like Figure 4 As shown, the ship electronic spare parts optimization configuration system based on time-varying failure rate proposed in this embodiment of the invention includes: Module 4001 is used to determine the ship's mission cycle, the configuration quantity of various electronic spare parts, and the unit cost; The calculation module 4002 is used to input the ship's mission cycle and the configuration quantity of various electronic spare parts into the spare parts demand model based on time-varying failure rate, and output the success probability of various electronic spare parts. The spare parts demand model based on time-varying failure rate is constructed by combining the Weibull distribution function, the NHPP function and the Poisson distribution function. The transformation module 4003 is used to construct a dual-objective optimization configuration problem based on the success probability, configuration quantity and unit cost of various electronic spare parts, and to transform the dual-objective optimization configuration problem into a single-objective optimization configuration problem using the IPM method. Configuration module 4004 is used to solve the single-objective optimization configuration problem using the ALNS algorithm to obtain the globally optimal configuration scheme for ship electronic spare parts.

[0079] Other embodiments or specific implementations of the ship electronic spare parts optimization configuration system based on time-varying failure rate of the present invention can be referred to the above-described method embodiments, and will not be repeated here.

[0080] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0081] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0082] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory / random access memory, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0083] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for optimizing the configuration of ship electronic spare parts based on time-varying failure rate, characterized in that, The method includes the following steps: Determine the ship's mission cycle, the quantity of various electronic spare parts, and their unit cost; The ship's mission cycle and the configuration quantity of various electronic spare parts are input into the spare parts demand model based on time-varying failure rate, and the success probability of ensuring various electronic spare parts is output. The spare parts demand model based on time-varying failure rate is constructed by combining the Weibull distribution function, the NHPP function and the Poisson distribution function. Based on the success probability, configuration quantity, and unit cost of various electronic spare parts, a dual-objective optimization configuration problem is constructed, and the dual-objective optimization configuration problem is transformed into a single-objective optimization configuration problem using the IPM method. The single-objective optimization configuration problem is solved by the ALNS algorithm to obtain the globally optimal configuration scheme for ship electronic spare parts.

2. The method as described in claim 1, characterized in that, The process involves inputting the ship's mission cycle and the configuration quantity of various electronic spare parts into a spare parts demand model based on time-varying failure rate, and outputting the success probability of ensuring the availability of various electronic spare parts, including: The ship's mission cycle and the configuration quantity of various electronic spare parts are input into the spare parts demand model based on time-varying failure rate; The time-varying failure rate of various electronic spare parts is approximated by the Weibull distribution function; Based on the ship's mission cycle, the cumulative failure intensity of various electronic spare parts is obtained through the NHPP function according to the approximate time-varying failure rate. Based on the configuration quantity and cumulative failure intensity of various electronic spare parts, the success probability of ensuring various electronic spare parts is obtained through the Poisson distribution function; The time-varying failure rate-based spare parts demand model outputs the success probability of ensuring the availability of various electronic spare parts.

3. The method as described in claim 2, characterized in that, The Weibull distribution function is: In the formula, For the first Electronic spare parts at all times Time-varying efficiency The trend of failure rate. It is a lifespan timescale.

4. The method as described in claim 2, characterized in that, The NHPP function is: In the formula, For the first Electronic spare parts during the ship's mission cycle The cumulative failure strength within, For the first Electronic spare parts at all times The time-varying efficiency.

5. The method as described in claim 2, characterized in that, The Poisson distribution function is: In the formula, The number of times the failure occurred. For the first The number of electronic spare parts configured. For the first The success rate of ensuring the maintenance of electronic spare parts. For the first Electronic spare parts during the ship's mission cycle The cumulative failure strength within.

6. The method as described in claim 1, characterized in that, The aforementioned dual-objective optimization configuration problem, based on the success probability, configuration quantity, and unit cost of various electronic spare parts, includes: Based on the success probability of various electronic spare parts, the system reliability is calculated using the system reliability function. Calculate the total spare parts cost based on the configuration quantity and unit cost of various electronic spare parts; A dual-objective optimization configuration problem is constructed based on the system reliability and the total spare parts cost.

7. The method as described in claim 6, characterized in that, The dual-objective optimization configuration problem based on the system reliability and the total spare parts cost includes: Based on the configuration quantity of various electronic spare parts, construct constraints on the quantity of various electronic spare parts and the total number of spare parts, and construct reliability constraints based on the system reliability. Based on the constraints of the quantity of various electronic spare parts, the total number of spare parts, the reliability constraint, and the spare parts integer constraint, a bi-objective optimization configuration problem is constructed according to the system reliability and the total spare parts cost.

8. The method as described in claim 1, characterized in that, The process of transforming the bi-objective optimization configuration problem into a single-objective optimization configuration problem using the IPM method includes: The system reliability and total spare parts cost are determined based on the aforementioned dual-objective optimization configuration problem; The system reliability and the total spare parts cost are normalized respectively, and the reliability weighting coefficient and the cost weighting coefficient are determined. Based on the IPM method, a single-objective weighted function is constructed according to the reliability weight coefficient, the cost weight coefficient, the normalized system reliability, and the total spare parts cost. Based on various constraints on the quantity of electronic spare parts, the total number of spare parts, reliability, and the integer number of spare parts, a single-objective optimization configuration problem is constructed according to the single-objective weighting function.

9. The method as described in claim 1, characterized in that, The process of solving the single-objective optimization configuration problem using the ALNS algorithm to obtain the globally optimal ship electronic spare parts configuration scheme includes: Construct a feasible initial solution based on the single-objective optimization configuration problem; The current solution is obtained from the feasible initial solution by using the destruction operator and the repair operator; Determine whether to update the current solution based on the simulated annealing acceptance criterion; If an update is needed, determine whether the current iteration count has reached a preset threshold. When the current iteration count reaches the preset threshold, the globally optimal configuration scheme for ship electronic spare parts is determined based on the current solution.

10. A ship electronic spare parts optimization configuration system based on time-varying failure rate, characterized in that, The system includes: The determination module is used to determine the ship's mission cycle, the configuration quantity of various electronic spare parts, and the unit cost; The calculation module is used to input the ship's mission cycle and the configuration quantity of various electronic spare parts into the spare parts demand model based on time-varying failure rate, and output the success probability of support for various electronic spare parts. The spare parts demand model based on time-varying failure rate is constructed by combining the Weibull distribution function, the NHPP function and the Poisson distribution function. The transformation module is used to construct a dual-objective optimization configuration problem based on the success probability, configuration quantity and unit cost of various electronic spare parts, and to transform the dual-objective optimization configuration problem into a single-objective optimization configuration problem using the IPM method. The configuration module is used to solve the single-objective optimization configuration problem using the ALNS algorithm to obtain the globally optimal configuration scheme for ship electronic spare parts.

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