A Reliability Assessment Method and System for Reservoir Unmanned Aerial Vehicle (UAV) Inspection System

Abstract

This invention relates to the field of unmanned aerial vehicle (UAV) system reliability assessment technology, and provides a method and system for mission reliability assessment and optimization of a reservoir UAV inspection system. By constructing a dual-mode failure probability calculation based on a cumulative damage model (standby and online), a recursive mission reliability assessment based on a probability quality function, and an improved genetic algorithm optimization integrating two-layer integer encoding and an adaptive elite strategy, this invention solves the problems of difficulty in accurately assessing the reliability of heterogeneous UAV swarms in serial inspection missions and the difficulty in finding optimal resource allocation schemes under constraints of payload coverage, operating costs, and total number of swarms. It has the advantages of accurately quantifying the multi-mode failure probability of heterogeneous UAV swarms and supporting optimized configuration of UAV resource allocation and activation order under multiple constraints, thereby improving the mission reliability and resource utilization efficiency of the reservoir inspection system.

Description

Technical Field

[0001] This application relates to the field of unmanned aerial vehicle (UAV) system reliability assessment technology, and more specifically, to a method and system for assessing the mission reliability of a UAV inspection system for reservoirs. Background Technology

[0002] Reservoir safety inspection is a crucial link in ensuring the normal operation of water conservancy infrastructure. Traditional manual inspection methods are inefficient and struggle to cover high-risk areas such as dam structures and stilling basins. The introduction of drone technology has effectively improved inspection efficiency and coverage. However, reservoir inspection tasks typically consist of multiple sequential sub-tasks, each with varying requirements for drone type, payload configuration, and operational performance. In actual operation, drones face multiple failure risks, including equipment aging, payload wear, and exposure to complex environments. If the primary drone fails in a sub-task and there is a lack of effective redundancy switching mechanisms, the entire sequential inspection task will be interrupted. Existing technologies often employ single-drone execution or simple redundancy configurations based on experience. These technologies fail to fully consider the differences in damage accumulation between drones in standby mode and online operation mode, and lack methods for quantitatively optimizing drone model allocation and activation sequence under constraints such as total cost, total fleet size, and payload coverage. This makes it difficult to achieve a synergistic improvement in task reliability and resource allocation efficiency.

[0003] To address the aforementioned issues, existing technologies urgently need improvement. Summary of the Invention

[0004] The purpose of this application is to provide a method and system for assessing the reliability of a reservoir UAV inspection system. This method and system have the advantages of accurately quantifying the multi-mode failure probability of heterogeneous UAV groups and supporting the optimized configuration of UAV resource allocation and activation sequence under multiple constraints, thereby improving the reliability and resource utilization efficiency of the reservoir inspection system.

[0005] This application provides a method for assessing the reliability of a reservoir unmanned aerial vehicle (UAV) inspection system. The reservoir inspection task includes multiple sequential subtasks, each executed by a heterogeneous UAV swarm. The UAV swarm includes a master UAV and at least one standby UAV, comprising: The execution time of each subtask is obtained, and the execution time is discretized into multiple time intervals; For each drone in the drone swarm, the failure probability of the drone in each time interval is determined based on the sum of its standby time and online working time, wherein the standby time is converted into equivalent online working time according to the damage equivalence relationship between standby mode and online working mode. Based on the failure probability, the time interval distribution of successive failures of each drone in the drone group is recursively calculated using a probability mass function. Based on the time interval distribution, the success probability of each sub-task being successfully completed by different drones is determined, and the task reliability of each sub-task is calculated based on the success probability. The overall reliability of the reservoir inspection system is calculated based on the reliability of each sub-task.

[0006] Furthermore, determining the failure probability of the drone in each time interval includes: Determine the pre-takeover failure probability of the drone during standby period; Determine the failure probability at the end of each time interval after the drone takes over and operates online until the end of each time interval; Determine the probability of incomplete task failure when the corresponding sub-task is not completed by the end of each time interval after the drone takes over and works online.

[0007] Furthermore, the recursive calculation of the time interval distribution of successive failures of each drone in the drone swarm using a probability mass function includes: Initialize the probability mass function of the main UAV failing in each time interval; For each subsequent drone in the drone swarm, after its preceding drone fails in a certain time interval, the subsequent drone takes over and performs the remaining work in that time interval. Based on the failure time probability mass function of the preceding drone, the failure probability of the subsequent drone before taking over, and the failure probability at the end of the interval, the probability mass function of the first time interval in which all drones in the drone swarm fail successively is iteratively updated.

[0008] Furthermore, determining the success probability of each sub-task being successfully completed by different drones based on the time interval distribution includes: For each drone in the drone swarm, calculate the conditional success probability of taking over and working online until the end of the subtask, provided that the preceding drone fails in each time interval. The conditional success probability of taking over and working online until the end of the subtask includes the remaining time interval in which the drone works online at least for the subtask. The success probability of each drone under the given conditions is summed to obtain the task reliability of the subtask.

[0009] Furthermore, the method also includes: Obtain the payload capacity, operating costs, and payload requirements for each sub-task of various types of drones; With the goal of maximizing the overall mission reliability, and under the conditions of satisfying the constraints of payload coverage, total operating cost, and the upper limit of the number of drones allocated to each sub-mission, the drone model allocation scheme and activation order for each sub-mission are determined.

[0010] Furthermore, the damage equivalence relationship between the standby mode and the online working mode is characterized by a standby coefficient, which is a preset constant greater than or equal to 0 and less than or equal to 1, used to convert unit standby time into equivalent online working time.

[0011] Furthermore, the iterative update of the probability mass function for the first time interval in which all drones in the drone swarm successively fail includes: Multiply the value of the preceding drone's probability mass function in the current time interval by the failure probability of the subsequent drone before takeover, and add it to the probability mass function of the subsequent drone in the same time interval. Furthermore, the value of the probability mass function of the preceding drone in any failure time interval is multiplied by the failure probability at the end of the interval of the subsequent drone, and then accumulated into the probability mass function of the subsequent drone in the delayed time interval. The number of delayed time intervals is equal to the number of intervals in which the subsequent drone is online.

[0012] Furthermore, the probability of success of the condition is calculated in the following way: Obtain the probability that all preceding drones fail in each time interval, where each time interval is less than the total number of time intervals of the subtask; To obtain the probability of unfinished task failure required for a subsequent drone to take over and work online for at least the number of remaining intervals after experiencing the corresponding number of standby intervals; Multiply the failure probability of the preceding drone by one and subtract the failure probability of the unfinished task to obtain the conditional probability of the subsequent drone successfully completing the sub-task, and sum over each time interval.

[0013] Furthermore, the constraints also include: the total number of drones allocated to all sub-tasks is equal to the preset total number of available drones; and the determination of the drone model allocation scheme and activation order for each sub-task is solved using an improved genetic algorithm, wherein the improved genetic algorithm uses a two-layer integer encoding, the first layer encoding representing the number of drones allocated to each sub-task, and the second layer encoding representing the drone activation order for each sub-task.

[0014] Secondly, this embodiment also proposes a reliability assessment system for a reservoir drone inspection system. The reservoir inspection task includes multiple serial sub-tasks, each of which is executed by a heterogeneous drone swarm. The drone swarm includes a master drone and at least one standby drone, comprising: The acquisition module is used to acquire the execution time of each subtask and discretize the execution time into multiple time intervals; The determination module is used to determine the failure probability of each drone in the drone group in each time interval based on the sum of its standby time and online working time, wherein the standby time is converted into equivalent online working time according to the damage equivalence relationship between standby mode and online working mode. The first calculation module is used to recursively calculate the time interval distribution of successive failures of each drone in the drone group based on the failure probability and through a probability mass function. The second calculation module is used to determine the success probability of each sub-task being successfully completed by different drones based on the time interval distribution, and to calculate the task reliability of each sub-task based on the success probability. The third calculation module is used to calculate the overall task reliability of the reservoir inspection system based on the task reliability of each sub-task.

[0015] As can be seen from the above, the reliability assessment method and system for a reservoir UAV inspection system provided in this application solves the problems of difficulty in accurately assessing the reliability of heterogeneous UAV groups in serial inspection tasks and difficulty in finding the optimal resource allocation scheme under the constraints of payload coverage, operating cost and total number of UAVs in the constraints of cumulative damage model standby and online dual-mode failure probability calculation, recursive task reliability assessment based on probability quality function, and improved genetic algorithm optimization that integrates two-layer integer coding and adaptive elite strategy. It has the advantages of being able to accurately quantify the multi-mode failure probability of heterogeneous UAV groups and support the optimized configuration of UAV resource allocation and activation order under multiple constraints, thereby improving the reliability and resource utilization efficiency of the reservoir inspection system. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is an example diagram of a reservoir drone inspection disclosed in an embodiment of the present invention; Figure 2 This is a schematic diagram of the reliability assessment method for a reservoir unmanned aerial vehicle (UAV) inspection system disclosed in an embodiment of the present invention. Figure 3 This is a schematic diagram of the structure of the reservoir drone inspection system for mission reliability assessment disclosed in an embodiment of the present invention. Detailed Implementation

[0018] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which these embodiments belong; the terminology used herein and in the specification of the application is for the purpose of describing particular embodiments only and is not intended to limit these embodiments; the terms "comprising" and "having," and any variations thereof, in the specification of these embodiments and the foregoing drawings, are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification of these embodiments and the foregoing drawings are used to distinguish different objects, not to describe a particular order.

[0019] The implementation details of the technical solution in this embodiment are described in detail below: Firstly, this embodiment proposes a method for evaluating the reliability of a reservoir drone inspection system. The reservoir inspection task includes multiple serial sub-tasks, each of which is executed by a heterogeneous drone group. The drone group includes a master drone and at least one standby drone.

[0020] This embodiment takes the inspection of a medium-sized reservoir in eastern China as an example. Figure 1 The diagram shown is an example of a reservoir drone inspection in this embodiment. The reservoir inspection task consists of five sequential tasks, executed according to a standardized operating procedure: the first is the reservoir perimeter inspection, the second is the dam structure inspection, the third is water level and hydrological monitoring, the fourth is the bank slope stability inspection, and the fifth is the stilling basin and spillway inspection. The scope, workload, and payload requirements of each sub-task vary, and there is a strict sequential execution order between them; the next sub-task can only proceed after the previous one is successfully completed, thus forming a complete sequential inspection process. If all drones assigned to a certain sub-task malfunction and cannot complete it, the entire reservoir inspection task fails.

[0021] Each subtask is executed by a dedicated drone swarm. The drone swarm includes a master drone and at least one standby drone. One drone in the swarm acts as the primary execution unit, while the others remain in standby mode. Drones within each swarm can be heterogeneous, possessing different models, payloads, and operational capabilities. Drones exist only in two states: normal operation and malfunction. When the master drone fails due to internal or external factors, standby drones take over in a preset activation order to complete the current subtask. Once a drone is assigned to a specific subtask, it is permanently bound to that subtask and cannot be reassigned to other subtasks during operation; the activation order is only valid within its assigned subtask. The drone fault detection and standby switching time is much shorter than the subtask duration, and this time is ignored in this embodiment. Standby drones are powered on, and their failure rate is significantly lower than that of online drones.

[0022] Assuming the operations and maintenance department has sufficient heterogeneous drones, it can independently configure drone execution groups for all tasks based on task content and reliability requirements. In this embodiment, the payload capacity, operating cost, and payload requirements of each sub-task of various drone types can be obtained. With the goal of maximizing the overall task reliability, and under the conditions of satisfying payload coverage constraints, total operating cost constraints, and the upper limit constraints on the number of drones allocated to each sub-task, the drone model allocation scheme and activation order for each sub-task are determined.

[0023] The constraints also include: the total number of drones allocated to all sub-tasks is equal to the preset total number of available drones; and the determination of the drone model allocation scheme and activation order for each sub-task is solved using an improved genetic algorithm. The improved genetic algorithm uses a two-layer integer encoding, where the first layer of encoding represents the number of drones allocated to each sub-task and the second layer of encoding represents the activation order of drones for each sub-task.

[0024] The optimization objective is to determine the optimal UAV configuration for each task. This problem is called the UAV Resource Allocation and Activation Order Optimization Problem 1 (RAASOP1). The definitions of relevant symbols in RAASOP1 are shown in Table 1.

[0025] Table 1 Definitions of RAASOP1 Related Symbols

[0026] Specifically, the overall reliability of the inspection system is the product of the reliability of each individual task. Therefore, the objective function of RAASOP1 is:

[0027] RAASOP1 contains three types of constraints: 1. Mounting Override Constraints: ,in ,

[0028] 2. Total cost constraint:

[0029] 3. Allocation quantity constraints:

[0030] In this embodiment, the constraint parameters are calibrated according to actual engineering conditions: maximum number of UAVs allocated per mission. The total operating cost ceiling is 4, and C is the maximum total operating cost. totalThe value is 150. An improved genetic algorithm is used to solve RAASOP1, yielding an optimal task reliability of 0.9942, a total operation cost of 148, and a total of 12 allocated drones. The optimal scheme is [2,2,2,3,3; 2,2,2,2,2,2,1,1,1,3,3,3]. In this scheme, the quantity layer [2,2,2,3,3] indicates that the five sub-tasks are allocated 2, 2, 2, 3, and 3 drones respectively; the sequence layer arranges the drone activation order of each sub-task in the order of the tasks, with the first two digits [2,2] indicating that the main drone and the first standby drone for task 1 are both type 2, and subsequent gene positions follow the same pattern.

[0031] Furthermore, to analyze the impact of the total activity cost constraint on task reliability, with other parameters kept constant, the upper limit of the total activity cost C is set... total Adjust from 100 to 250 in increments of 50. When C total When C = 100, the optimal task reliability is 0.8475, and the total number of drones allocated is 8; when C total When C = 150, the optimal task reliability increases to 0.9934, with a total of 12 drones allocated, representing a 17.21% improvement in reliability compared to the cost constraint of 100; when C total When C = 200, the optimal task reliability is 0.9997, with a total of 16 drones allocated, representing only a 0.75% improvement in reliability compared to the cost constraint of 150; when C total When the cost is 250, the optimal task reliability is 0.9999, and the total number of drones allocated is 18. The results show that task reliability monotonically increases with the increase of the total operating cost ceiling, but the rate of increase gradually slows down, exhibiting a clear law of diminishing marginal returns. Specifically, when the total cost increases from 100 to 150, adding standby drones significantly improves reliability; however, when it increases from 150 to 200, the reliability gain is limited. This diminishing return law indicates that in engineering practice, a balance must be struck between reliability improvement and resource investment to avoid cost waste caused by over-allocation.

[0032] In real-world scenarios, the total number of drones in an operations and maintenance department may be limited by factors such as fleet construction budget, site storage conditions, and the number of professional operators. Assume the department has a total of [number missing] heterogeneous drones. Based on the above constraints, add The problem involving constraints is called RAASOP2. In summary, RAASOP2 modeling is as follows:

[0033] Constraints:

[0034]

[0035]

[0036]

[0037] Furthermore, the determination of the drone model allocation scheme and activation order for each sub-task is solved using an improved genetic algorithm. This improved genetic algorithm employs a two-layer integer encoding: the first layer represents the number of drones allocated to each sub-task, and the second layer represents the activation order of the drones in each sub-task. All feasible solutions are encoded using a two-layer integer encoding, consisting of a quantity layer and a sequence layer. Quantity layer: of length J, where the j-th gene bit represents the number of drones assigned to task j. ,satisfy (RAASOP1 / RAASOP2), and satisfy RAASOP2 .

[0038] Sequence layer: length is The activation order of drones for each task is arranged according to the task sequence. The gene value is the drone model index, and the mounting coverage constraint must be met.

[0039] Taking 5 tasks, with 2 drones assigned to each task as an example, the encoding string would look like this: Among them, the quantity layer This indicates that each task is assigned 2 drones; the first 2 bits of the sequence layer represent the activation order of task 1 [2,1], and the subsequent bits represent the activation order of other tasks.

[0040] like Figure 2 As shown in this embodiment, the reliability assessment method for the reservoir drone inspection system specifically includes: S201, obtain the execution time of each subtask, and discretize the execution time into multiple time intervals.

[0041] Before conducting a task reliability assessment, step S101 is first performed: the execution time of each sub-task is obtained, and the execution time is discretized into multiple time intervals. Specifically, based on the actual operational requirements of a medium-sized reservoir inspection system in eastern China, the execution time of each sub-task is pre-set, and the number of time intervals for each sub-task is reasonably set based on the principle of balancing computational accuracy and efficiency. Duration Divided into equal parts A time interval, a task The duration of a single interval is:

[0042] In this embodiment, the execution time of the reservoir perimeter inspection task is 30 minutes, which is divided into 10 equal time intervals, resulting in a single interval duration of 3 minutes; the execution time of the dam structure inspection task is 40 minutes, which is divided into 10 equal time intervals, resulting in a single interval duration of 4 minutes; the execution time of the water level and hydrological monitoring task is 20 minutes, which is divided into 5 equal time intervals, resulting in a single interval duration of 4 minutes; the execution time of the bank slope stability inspection task is 35 minutes, which is divided into 10 equal time intervals, resulting in a single interval duration of 3.5 minutes; and the execution time of the stilling basin and spillway inspection task is 25 minutes, which is divided into 8 equal time intervals, resulting in a single interval duration of 3.125 minutes. Through the above discretization process, the continuous task execution times are transformed into a discrete time interval sequence, thereby establishing a unified time benchmark for subsequent recursive reliability assessment based on the cumulative damage model and probabilistic quality function.

[0043] S202, For each drone in the drone group, the failure probability of the drone in each time interval is determined according to the sum of its standby time and online working time, wherein the standby time is converted into equivalent online working time according to the damage equivalence relationship between standby mode and online working mode. Furthermore, determining the failure probability of the drone in each time interval includes: determining the failure probability before takeover when the drone fails during the standby period; determining the failure probability at the end of each time interval when the drone fails while working online after takeover; and determining the failure probability of incomplete task when the drone has not completed the corresponding sub-task while working online after takeover.

[0044] The damage equivalence relationship between the standby mode and the online working mode is characterized by the standby coefficient, which is a preset constant greater than or equal to 0 and less than or equal to 1, used to convert the unit standby time into the equivalent online working time.

[0045] Specifically, in this embodiment, step S202 is executed as follows: For each drone in the drone group, the failure probability of the drone in each time interval is determined based on the sum of its standby time and online working time. Specifically, each drone in the execution group exists in two modes: standby and online working. The operational stress experienced by the drone differs significantly between the two modes. To uniformly quantify the damage accumulation under different modes, the standby time of the k-th drone in the execution group for task j is converted into an equivalent online working time using a standby coefficient. The standby coefficient for the k-th drone in the execution group for task j is... A preset constant greater than or equal to 0 and less than or equal to 1 is used to convert the unit standby time into the equivalent online working time, thereby achieving unified quantification of damage accumulation in standby mode and online working mode.

[0046] The cumulative distribution function of the drone's failure time is G(t), where t is the sum of the actual online working time and the equivalent working time in standby mode. Based on the cumulative damage model, the total working time of the drone is:

[0047] The number of standby intervals for this drone, i.e., the number of intervals from the mission. The number of time intervals elapsed from the start of the standby drone taking over the mission; The actual number of online working intervals after the drone took over.

[0048] remember The drone experienced The probability of failure within a standby period before takeover is calculated as follows:

[0049] remember The drone experienced The standby area has been successfully taken over and is operating online. The probability of failure exactly after a certain number of intervals is calculated as follows:

[0050]

[0051]

[0052] remember The drone experienced The standby area was successfully taken over, but online work... Failed or incomplete tasks within a given range The probability is calculated as follows:

[0053] This probability measures the risk that a drone, despite successfully taking over, may fail during its online operation due to accumulated damage before reaching the time required to complete the entire sub-task. When subsequently calculating the conditional success probability of each drone successfully completing its sub-task, the conditional probability contribution of the corresponding drone successfully completing the sub-task is obtained by multiplying the probability mass function value of the preceding drone's failure within a certain time interval by one and subtracting the aforementioned failure probability of not completing the task. This provides the foundational data for the recursive evaluation of task reliability.

[0054] S203, Based on the failure probability, the time interval distribution of successive failures of each drone in the drone group is recursively calculated using a probability mass function; Furthermore, the recursive calculation of the time interval distribution of successive failures of each drone in the drone swarm through the probability mass function includes: initializing the probability mass function of the master drone's failure in each time interval; for each subsequent drone in the drone swarm, after its predecessor drone fails in a certain time interval, the subsequent drone takes over and performs the remaining work in that time interval, and iteratively updates the probability mass function of the first time interval in which all drones in the drone swarm fail successively based on the failure time probability mass function of the predecessor drone, the failure probability of the subsequent drone before taking over, and the failure probability at the end of the interval.

[0055] The iterative update of the probability quality function for the first time interval in which all drones in the drone group successively fail includes: multiplying the value of the probability quality function of the preceding drone in the current time interval by the failure probability of the subsequent drone before takeover, and accumulating it into the probability quality function of the subsequent drone in the same time interval; and multiplying the value of the probability quality function of the preceding drone in any failure time interval by the failure probability at the end of the interval of the subsequent drone, and accumulating it into the probability quality function of the subsequent drone in the delayed time interval, wherein the number of delayed time intervals is equal to the number of intervals in which the subsequent drone is online.

[0056] Specifically, definition Let be a discrete random variable, representing the task. Execute the group before The probability mass function (PMF) for the first time interval after all drones fail is:

[0057] Initial conditions:

[0058] This indicates that no drones were assigned or failed at the start of the mission.

[0059]

[0060] Indicates the main drone in the The interval just happened to be invalid.

[0061] If the first The drone in Each interval failed ( ), No. The drone took over and executed the first The remaining work for each interval.

[0062] 1. If the first A drone in The standby interval expires before takeover ( ), then the former The first section where the entire structure failed is still The probability of this event is:

[0063] 2. If the first A drone in Successfully took over after a standby period and is now working online. If the interval becomes invalid after a certain number of intervals, then the previous interval... The first section where the entire frame fails is The probability of this event is:

[0064] Based on the above mutually exclusive events, the task Execute the group before The drone in The probability that all time intervals will fail is:

[0065] In the formula, the first term: the... The probability of drone standby mode failure; Second item: The probability of failure in the online working mode of a drone.

[0066] Tasks can be computed sequentially The probability that all assigned drones within a drone group will fail sequentially: .

[0067] Furthermore, the array length for each probability mass function is... (average) Therefore, the storage space complexity of the proposed algorithm is O(n). The computational complexity of the proposed task reliability assessment algorithm is determined by the traversal of the UAV execution group sequence and the time interval, and is as follows:

[0068] in, Total number of drones The algorithm stores the probability mass function through an iterative update method, requiring only the probability mass functions of two adjacent drones to be saved. This is the average number of drones in each task time interval. and There is no need to store the probability mass functions for all drones. Furthermore, the array length for each probability mass function is... (average) Therefore, the storage space complexity of the proposed algorithm is O(n). .

[0069] S204. Based on the time interval distribution, determine the success probability of each sub-task being successfully completed by different UAVs, and calculate the task reliability of each sub-task based on the success probability.

[0070] Furthermore, in S204, determining the success probability of each subtask being successfully completed by different drones based on the time interval distribution includes: for each drone in the drone group, calculating the conditional success probability of it taking over and working online until the end of the subtask under the condition that the preceding drone fails in each time interval, wherein working online until the end of the subtask after taking over includes the remaining time interval of working online at least the subtask; summing the conditional success probabilities of each drone to obtain the task reliability of the subtask.

[0071] The conditional success probability is calculated as follows: obtain the probability that all preceding drones fail in each time interval, where each time interval is less than the total number of time intervals for the subtask; obtain the probability of unfinished task failure required for the subsequent drone to take over and work online for at least the remaining intervals after experiencing the corresponding number of standby intervals; multiply the failure probability of the preceding drone by one and subtract the probability of unfinished task failure to obtain the conditional probability of the subsequent drone successfully completing the subtask, and sum the results over each time interval.

[0072] Specifically, in this embodiment, the definition is as follows: For the task The first in the drone execution group An event in which a drone successfully completed its mission. The drone was only in front The task will only be taken over after all components have failed. Therefore, the task... Reliability For all mutually exclusive events The sum of probabilities:

[0073] No. To successfully complete the mission, the drone It must meet the following conditions: The drone in Each interval failed ( ), and the first After the drone takes over, it can work online at least There are several time intervals. Therefore, The calculation is as follows:

[0074] Finally, according to equation (1), the overall reliability of the inspection system is... The product of the reliability of all tasks:

[0075] The probability of conditional success is calculated as follows: The probability of all preceding drones failing in each time interval is obtained, where each time interval is less than the total number of time intervals for the subtask. This probability is derived from the probability mass function of the first time interval in which the entire preceding drone group fails. Given, where y = 0, 1, ..., m j 1; Obtain the probability of unfinished task failure required for a subsequent drone to take over and operate online for at least the remaining number of intervals after experiencing the corresponding number of standby intervals. This probability is determined by... The given value indicates that the k-th drone successfully took over after y standby intervals, but remains online. The probability of failure or incomplete task j within each interval; multiply the failure probability of the preceding UAV by one and subtract the failure probability of the incomplete task to obtain the conditional probability of the subsequent UAV successfully completing the sub-task, and sum over each time interval, i.e., through equation (13).

[0076] The numerical implementation of the task reliability assessment algorithm mentioned above can be summarized by the following pseudocode.

[0077]

[0078] S105, Calculate the overall task reliability of the reservoir inspection system based on the task reliability of each sub-task.

[0079] Specifically, since the subtasks of the reservoir inspection system are executed sequentially, the failure of any one subtask will lead to the failure of the entire inspection task. Therefore, the overall reliability of the inspection system is the product of the reliability of each subtask. Specifically, the overall reliability of the reservoir inspection system can be obtained by multiplying the reliability of each subtask according to the sequential task logic, as shown in formula (1).

[0080] Furthermore, based on the reliability assessment results of each sub-task determined in the aforementioned steps, taking a medium-sized reservoir inspection system in eastern China as an example, the reservoir inspection task includes five sequential sub-tasks. Based on the parameters in Tables 2 and 3 and the UAV resource allocation and activation sequence scheme shown in Table 4, the proposed evaluation algorithm is used to recursively calculate the following: the reliability of the first task, reservoir perimeter inspection, is 0.9980; the reliability of the second task, dam structure detection, is 0.9965; the reliability of the third task, water level and hydrological monitoring, is 0.9999; the reliability of the fourth task, bank slope stability inspection, is 0.9960; and the reliability of the fifth task, stilling basin and spillway detection, is 0.9843. Based on formula (14), the reliability of the above five sub-tasks is multiplied together to obtain the total task reliability of the reservoir inspection system. Substituting the reliability values ​​of each sub-task into the calculation, the total task reliability of the system is 0.9749.

[0081] To verify the computational accuracy of the proposed evaluation algorithm, a Monte Carlo simulation with a sample size of 10⁶ was used to analyze the same system. The Monte Carlo simulation simulates the UAV failure process through a large number of random simulations, and the reliability is obtained by statistically analyzing the percentage of successful mission completion. Under the same hardware environment, the overall mission reliability obtained from the Monte Carlo simulation is 0.9756, with a relative error of only 0.718% compared to the proposed algorithm's result of 0.9749, indicating that the proposed method for calculating overall mission reliability has high numerical accuracy.

[0082] Furthermore, to quantify the effectiveness of the standby mechanism in improving system reliability, the above configuration scheme was compared with a system without standby drones. In the standby drone configuration, only one main drone was configured for each sub-task, resulting in a total system reliability of 0.6031. After introducing standby drones, the total system reliability increased to 0.9749, a 37.17% improvement compared to the system without standby, fully validating the significant effectiveness of the standby mechanism in improving the reliability of the reservoir drone inspection system. Looking at the contribution distribution of each sub-task to the total reliability, the fifth task, stilling basin and spillway monitoring, had the lowest reliability at 0.9843. This is mainly because only type 3 drones can perform this sub-task, which has a low Weibull scale parameter and a high standby coefficient, leading to a relatively high failure probability and becoming a weak link restricting the overall system reliability. The third task, water level and hydrological monitoring, had the highest reliability at 0.9999, due to its short duration and execution by type 2 drones with a lower failure risk.

[0083] Furthermore, in this embodiment, the proposed evaluation algorithm is used to evaluate... Figure 1 The reservoir inspection system underwent mission reliability analysis, and the algorithm accuracy was verified by comparison with Monte Carlo simulation (MCS). Sensitivity analysis was also conducted to provide quantitative basis for UAV resource allocation / sequencing and parameter calibration in practical engineering. Figure 1As shown, the reservoir inspection task includes Each task has a pre-set duration based on the scope and workload. To balance calculation accuracy and efficiency, the number of time intervals is appropriately set. Table 2 summarizes the parameter values ​​for each task.

[0084] Table 2 Reservoir Inspection Task Parameter Settings

[0085] Based on the requirements of the inspection mission, three types of inspection agencies were selected to form a heterogeneous cluster. The failure time of this type of UAV follows a Weibull distribution, and the cumulative distribution function is:

[0086] This conforms to the failure patterns of equipment aging and wear. Standby coefficient. Weibull scale parameters With shape parameters The reliability of the drones was calibrated through a real-world reservoir test. Detailed parameters of the heterogeneous drone swarm are shown in Table 3.

[0087]

[0088] Table 3 Parameter Settings for Heterogeneous UAV Swarm For ease of explanation, a sample scheme for UAV resource allocation and activation order is constructed based on engineering experience, as shown in Table 4. Each task is configured with 1 master UAV + 1 standby UAV, and the activation order is set according to the UAV performance priority principle. Taking task 1 as an example, it can be executed by either type 1 or type 2 UAV; as shown by the Weibull failure time parameters in Table 3, within the task duration, type 2 UAV ( , Reliability is higher than that of Type 1. , Therefore, the activation order is adopted. That is, Type 2 will be prioritized as the primary UAV, while Type 1 will be on standby. The same applies to Mission 4. For missions 2 and 3, only the Type 2 UAV meets the payload requirements; therefore, both the primary and backup UAVs are Type 2. The activation order is as follows: Mission 5 can only be performed by three types of drones, activation order. .

[0089] Table 4 Example Scheme

[0090] Based on the parameters in Tables 2 and 3 and the scheme in Table 4, the evaluation algorithm proposed in Section 3 is used to calculate the reliability of each task and the overall task reliability. To verify the proposed algorithm, a sample size of [missing information] is used. The MCS was used to analyze the same system. MCS obtained reliability by statistically analyzing the success rate of tasks through numerous random simulations of drone failures. To ensure fairness in the comparison, all calculations were performed on the same hardware environment (Intel Core i7-12700H processor, 16GB DDR4 memory, 512GB SSD; Windows 11). Table 5 shows the task and system reliability results and relative errors:

[0091] Table 5 Reliability Results and Relative Error

[0092] As shown in Table 5, the reliability results calculated by the proposed evaluation algorithm are highly consistent with those of the MCS, with all relative errors less than 1% (0.1%). Looking at the reliability distribution of each task, Task 5 has the lowest reliability, mainly because only Type 3 UAVs can perform it, and their Weibull scale parameters... (Below Type 1 and 2), Standby Coefficient (Higher than Types 1 and 2), with a relatively higher probability of failure. Mission 3 has the highest reliability because it is the shortest (20 minutes) and is performed by a Type 2 UAV with a lower failure risk. Under this scheme, the overall mission reliability of the system is 0.9749, which is 37.17% higher than the non-standby UAV inspection system (reliability 0.6031), verifying the effectiveness of the standby mechanism in improving mission reliability.

[0093] Table 6 compares the computation time and maximum memory consumption of the two methods, highlighting the significant advantages of the proposed algorithm in terms of computational and space efficiency. Specifically, compared with the MCS method, the computational efficiency is improved by approximately 5000 times, enabling real-time and rapid reliability assessment of the reservoir UAV inspection system. The proposed algorithm only stores the probability mass functions of two adjacent UAVs simultaneously, eliminating the need to store massive amounts of simulation data. Memory consumption is reduced by 94.5% compared to MCS, allowing it to run on low-configuration devices such as ordinary industrial tablets and handheld terminals.

[0094] Table 6 Comparison of computational efficiency and memory consumption

[0095] Furthermore, standby coefficient These are key parameters for modeling the aging behavior of UAVs in standby mode. Table 7 shows the standby coefficients for Type 1 UAVs. When the reliability of Task 1 changes from 0 to 1 in steps of 0.1, The changes are evident. The smaller the value, the higher the system reliability, the slower the aging effect, and the lower the probability of standby failure. When When in standby mode, there is no risk of aging or failure, and the task reliability is the highest; when At that time, the degradation rate of the standby mode is the same as that of the online working mode, and the task reliability drops to a minimum of 0.9932.

[0096] Table 7 Reliability of Task 1 Treatment of life coefficient Sensitivity

[0097] The number of drones assigned to each task was gradually increased from 1 (no standby) to 4 (1 primary and 3 backups), and the overall task reliability was calculated under different allocation numbers. The results are shown in Table 8. It can be seen that task reliability increases monotonically with the number of allocated drones, but the rate of increase gradually slows down, exhibiting a clear diminishing marginal return. Specifically, when the number increases from 1 to 2, the system reliability improves by 0.3717, showing the most significant increase and representing the most cost-effective configuration optimization; increasing from 2 to 3 only improves by 0.0239; and increasing from 3 to 4 only improves by 0.0012. This diminishing trend indicates that adding more standby drones beyond 2 provides limited reliability gains but brings additional resource and cost burdens. Therefore, over-configuration reduces overall resource and cost efficiency and cannot effectively improve task reliability.

[0098] Table 8. Sensitivity of mission reliability to the number of UAVs allocated.

[0099] Weibull shape parameters Characterize the trend of drone failure rate. This indicates that the failure rate increases over time. The larger the value, the faster the failure rate increases. Taking Mission 2 as an example, the Weibull shape parameters of the Type 2 UAV... The value changed from 1.5 to 3.0 in steps of 0.3. The trend shown in Table 9 is derived from the characteristics of the Weibull distribution and the task duration. A joint decision. Regarding the task duration. hour, The larger the value, the lower the cumulative failure probability and the higher the mission reliability. The higher. Specifically, From 1.5 to 3.0, the reliability of Task 2 increased significantly from 0.9659 to 0.9990, and the growth rate gradually slowed down, indicating that with the increase in reliability, the reliability of Task 2 improved significantly. As the value increases, the reliability-enhancing effect diminishes. It is worth noting that... and The positive correlation only occurs when the task duration is less than the critical point. This holds true when the operating time exceeds the critical point, according to the properties of the Weibull cumulative distribution function. hour, The larger the value, the faster the failure rate increases over time, leading to decreased mission reliability. reduce.

[0100] Table 9 Reliability of Task 2 For Weibull shape parameters Sensitivity

[0101] Traditional genetic algorithms can theoretically solve the optimization problem of reservoir UAV inspection systems, but they generally suffer from slow convergence and premature convergence, easily getting trapped in local optima. Therefore, this paper improves upon the traditional GA by designing an Integral Genetic Algorithm (IGA), with the following improvements: 1. Encoding Method. A two-layer integer encoding is used for all feasible solutions, consisting of a quantity layer and a sequence layer: Quantity layer: of length J, where the j-th gene bit represents the number of drones assigned to task j. ,satisfy (RAASOP1 / RAASOP2), and satisfy RAASOP2 .

[0102] Sequence layer: length is The activation order of drones for each task is arranged according to the task sequence. The gene value is the drone model index, and the mounting coverage constraint must be met.

[0103] Taking 5 tasks, with 2 drones assigned to each task as an example, the encoding string would look like this: Among them, the quantity layer This indicates that each task is assigned 2 drones; the first 2 bits of the sequence layer represent the activation order of task 1 [2,1], and the subsequent bits represent the activation order of other tasks.

[0104] Construct a fitness function that integrates task reliability and constraint penalty terms:

[0105] In the formula: The overall reliability of the task corresponding to deserializing X; Task j violates mounting override constraint; : Maximum allocation threshold constraint violation for task j; Total cost constraint violation; : RAASOP2 total quantity constraint violation. The value is 1 if the above violation occurs, otherwise 0. The penalty factor is set according to the importance of the constraint.

[0106] Adaptive crossover and mutation probabilities are used and dynamically adjusted according to the population fitness: superior individuals with fitness higher than the population average are given smaller crossover and mutation probabilities to retain excellent genes; individuals with fitness lower than the population average are given larger crossover and mutation probabilities to enhance local search capabilities.

[0107] The top 10% of individuals with the highest fitness in the population are selected as elite individuals and directly preserved to the next generation to avoid the loss of superior genes; at the same time, low-probability mutations are performed on the elite individuals to improve global search capabilities.

[0108] The specific parameter settings for IGA are shown in Table 10.

[0109] Table 10 IGA Parameter Settings

[0110] The IGA algorithm was used to solve the mission reliability optimization problem of the aforementioned reservoir UAV inspection system. The mission parameters and heterogeneous UAV parameters are as shown in Tables 2 and 3; the constraint parameters were calibrated according to the actual engineering conditions, as shown in Table 11.

[0111] Table 11 Constraint Parameter Settings

[0112] RAASOP1 was solved using IGA, GA, and RSA respectively. Performance was compared in terms of optimal task reliability, number of convergence iterations, and optimal allocation scheme. The results are shown in Table 12. IGA achieved an optimal task reliability of 0.9942, higher than GA and RSA. IGA only required 29 iterations to converge, while GA required 80. This is because IGA's adaptive crossover and mutation strategy and elite retention strategy improved global search capability. The total cost of the optimal IGA solution was 148, effectively utilizing the limited budget to improve task reliability.

[0113] Table 12 Optimization results of different algorithms for the RAASOP1 problem

[0114] With other parameters fixed, use IGA to solve the total cost constraint. The optimal task reliability when varying from 100 to 250 (step size 50) is shown in Table 13. The number of drones increased from 100 to 150, improving mission reliability by 17.21%. The total number of drones allocated increased from 8 to 12, and the addition of standby drones significantly improved reliability. Increasing the reliability from 150 to 200 only improved it by 0.75%, showing a clear diminishing marginal return.

[0115] Table 13 Task Reliability vs. Total Cost Sensitivity

[0116] Study separately (Sufficient resources) and (Resource constraints) In two scenarios, the optimal IGA solution is compared with the empirical solution with 10 drones in Table 4, and the results are shown in Table 14. The total amount of available resources has a significant impact on reliability: when the number of drones is reduced from 10 to 8, the reliability of the optimal mission decreases by 8.28%; with the same configuration of 10 drones, the reliability of the empirical solution is 0.33% lower than that of the optimal IGA solution.

[0117] Table 14 Optimization results for different numbers of drones in the RAASOP2 problem

[0118] This embodiment focuses on the reliability modeling and optimization of a reservoir UAV inspection system. Two types of UAV resource allocation and activation order optimization problems (RAASOP1 and RAASOP2) are constructed to maximize mission reliability while satisfying constraints on payload coverage, operational cost, and UAV cluster resources. Based on a cumulative damage model, an efficient mission reliability assessment algorithm is proposed. The example uses a Weibull distribution, demonstrating that the proposed method is applicable to any UAV failure time distribution. An improved genetic algorithm is designed to solve the optimization problem. The accuracy and efficiency of the proposed assessment and optimization algorithm are verified using a medium-sized reservoir inspection as an example. 1. The proposed reliability assessment algorithm was tested using Monte Carlo simulation ( (Sample) verification, the computation time is reduced by about 5000 times, memory consumption is reduced by 94.5%, and efficient real-time reliability analysis is supported; 2. The proposed IGA outperforms traditional GA and RSA, achieving higher optimal task reliability, faster convergence speed, and a better resource-cost tradeoff under constraints; 3. For RAASOP2 with a fixed total number of drones, IGA achieves higher reliability than the empirical approach; when the number of drones is reduced from 10 to 8, the optimal mission reliability decreases by 8.28%.

[0119] Sensitivity analysis shows that mission reliability increases monotonically with the number of drones assigned to a single mission, but the marginal benefit decreases. Adding one standby drone can bring a significant improvement in reliability, and further increases have limited gains. A lower standby coefficient can slow down drone standby aging and improve mission reliability. When the mission duration is less than the Weibull scale parameter, the larger the shape parameter, the lower the cumulative failure probability and the higher the mission reliability.

[0120] Secondly, this embodiment proposes a reliability assessment system for a reservoir drone inspection system. The reservoir inspection task includes multiple serial subtasks, each of which is executed by a heterogeneous drone swarm. The drone swarm includes a master drone and at least one standby drone, comprising: The acquisition module 301 is used to acquire the execution time of each subtask and discretize the execution time into multiple time intervals; The determination module 302 is used to determine the failure probability of each drone in the drone group in each time interval based on the sum of its standby time and online working time, wherein the standby time is converted into equivalent online working time according to the damage equivalence relationship between standby mode and online working mode. The first calculation module 303 is used to recursively calculate the time interval distribution of successive failures of each UAV in the UAV group based on the failure probability and through a probability mass function. The second calculation module 304 is used to determine the success probability of each sub-task being successfully completed by different drones based on the time interval distribution, and to calculate the task reliability of each sub-task based on the success probability. The third calculation module 305 is used to calculate the total task reliability of the reservoir inspection system based on the task reliability of each sub-task.

[0121] This system can be used to perform the reliability assessment method for the reservoir drone inspection system described in the first aspect, which will not be elaborated here.

[0122] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for assessing the reliability of a reservoir unmanned aerial vehicle (UAV) inspection system, characterized in that, The reservoir inspection task includes multiple sequential sub-tasks, each executed by a heterogeneous drone swarm. The drone swarm includes a master drone and at least one standby drone. The task is characterized by including: The execution time of each subtask is obtained, and the execution time is discretized into multiple time intervals; For each drone in the drone swarm, the failure probability of the drone in each time interval is determined based on the sum of its standby time and online working time, wherein the standby time is converted into equivalent online working time according to the damage equivalence relationship between standby mode and online working mode. Based on the failure probability, the time interval distribution of successive failures of each drone in the drone group is recursively calculated using a probability mass function. Based on the time interval distribution, the success probability of each sub-task being successfully completed by different drones is determined, and the task reliability of each sub-task is calculated based on the success probability. The overall reliability of the reservoir inspection system is calculated based on the reliability of each sub-task.

2. The method for assessing the reliability of a reservoir UAV inspection system according to claim 1, characterized in that, Determining the failure probability of the UAV in each time interval includes: Determine the pre-takeover failure probability of the drone during standby period; Determine the failure probability at the end of each time interval after the drone takes over and operates online until the end of each time interval; Determine the probability of incomplete task failure when the corresponding sub-task is not completed by the end of each time interval after the drone takes over and works online.

3. The method for assessing the reliability of a reservoir unmanned aerial vehicle (UAV) inspection system according to claim 1, characterized in that, The recursive calculation of the time interval distribution of successive failures of each drone in the drone swarm using a probability mass function includes: Initialize the probability mass function of the main UAV failing in each time interval; For each subsequent drone in the drone swarm, after its preceding drone fails in a certain time interval, the subsequent drone takes over and performs the remaining work in that time interval. Based on the failure time probability mass function of the preceding drone, the failure probability of the subsequent drone before taking over, and the failure probability at the end of the interval, the probability mass function of the first time interval in which all drones in the drone swarm fail successively is iteratively updated.

4. The method for assessing the reliability of a reservoir drone inspection system according to claim 1, characterized in that, The step of determining the success probability of each sub-task being successfully completed by different drones based on the time interval distribution includes: For each drone in the drone swarm, calculate the conditional success probability of taking over and working online until the end of the subtask, provided that the preceding drone fails in each time interval. The conditional success probability of taking over and working online until the end of the subtask includes the remaining time interval in which the drone works online at least for the subtask. The success probability of each drone under the given conditions is summed to obtain the task reliability of the subtask.

5. The method for assessing the reliability of a reservoir UAV inspection system according to claim 1, characterized in that, The method further includes: Obtain the payload capacity, operating costs, and payload requirements for each sub-task of various types of drones; With the goal of maximizing the overall mission reliability, and under the conditions of satisfying the constraints of payload coverage, total operating cost, and the upper limit of the number of drones allocated to each sub-mission, the drone model allocation scheme and activation order for each sub-mission are determined.

6. The method for assessing the reliability of a reservoir UAV inspection system according to claim 1, characterized in that, The damage equivalence relationship between the standby mode and the online working mode is characterized by the standby coefficient, which is a preset constant greater than or equal to 0 and less than or equal to 1, used to convert the unit standby time into the equivalent online working time.

7. The method for assessing the reliability of a reservoir UAV inspection system according to claim 3, characterized in that, The iterative update of the probability mass function for the first time interval in which all drones in the drone swarm successively fail includes: Multiply the value of the preceding drone's probability mass function in the current time interval by the failure probability of the subsequent drone before takeover, and add it to the probability mass function of the subsequent drone in the same time interval. Furthermore, the value of the probability mass function of the preceding drone in any failure time interval is multiplied by the failure probability at the end of the interval of the subsequent drone, and then accumulated into the probability mass function of the subsequent drone in the delayed time interval. The number of delayed time intervals is equal to the number of intervals in which the subsequent drone is online.

8. The method for assessing the mission reliability of a reservoir unmanned aerial vehicle (UAV) inspection system according to claim 1, characterized in that, The probability of success under the condition is calculated in the following way: Obtain the probability that all preceding drones fail in each time interval, where each time interval is less than the total number of time intervals of the subtask; To obtain the probability of unfinished task failure required for a subsequent drone to take over and work online for at least the number of remaining intervals after experiencing the corresponding number of standby intervals; Multiply the failure probability of the preceding drone by one and subtract the failure probability of the unfinished task to obtain the conditional probability of the subsequent drone successfully completing the sub-task, and sum over each time interval.

9. The method for assessing the mission reliability of a reservoir unmanned aerial vehicle (UAV) inspection system according to claim 5, characterized in that, The constraints also include: the total number of drones allocated to all sub-tasks is equal to the preset total number of available drones; and the determination of the drone model allocation scheme and activation order for each sub-task is solved using an improved genetic algorithm. The improved genetic algorithm uses a two-layer integer encoding, where the first layer of encoding represents the number of drones allocated to each sub-task and the second layer of encoding represents the activation order of drones for each sub-task.

10. A reliability assessment system for a reservoir unmanned aerial vehicle (UAV) inspection system, wherein the reservoir inspection task includes multiple sequential sub-tasks, each sub-task being executed by a heterogeneous UAV swarm, the UAV swarm including a master UAV and at least one standby UAV, characterized in that... include: The acquisition module is used to acquire the execution time of each subtask and discretize the execution time into multiple time intervals; The determination module is used to determine the failure probability of each drone in the drone group in each time interval based on the sum of its standby time and online working time, wherein the standby time is converted into equivalent online working time according to the damage equivalence relationship between standby mode and online working mode. The first calculation module is used to recursively calculate the time interval distribution of successive failures of each drone in the drone group based on the failure probability and through a probability mass function. The second calculation module is used to determine the success probability of each sub-task being successfully completed by different drones based on the time interval distribution, and to calculate the task reliability of each sub-task based on the success probability. The third calculation module is used to calculate the overall task reliability of the reservoir inspection system based on the task reliability of each sub-task.

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