Multi-stage unmanned aerial vehicle inspection method

Abstract

The multi-stage unmanned aerial vehicle inspection method comprises the following steps: for an inspection task containing M unmanned aerial vehicles and H stages, a M*H stage conditional reliability matrix R and a conditional unreliability matrix Q are constructed; the reliability matrix R and the conditional unreliability matrix Q are taken as inputs, and a compressed state forward recursion algorithm is used to perform task reliability evaluation on the unmanned aerial vehicle inspection system; and according to an unmanned aerial vehicle distribution scheme corresponding to the task reliability, the unmanned aerial vehicle is dispatched. The multi-machine distribution of the present application can make the task reliability increase by 1.8% at most; in a large-scale problem with more stages and unmanned aerial vehicles, the reliability can be increased by 9.7% at most. The present application provides an effective solution for multi-stage unmanned aerial vehicle inspection task design and reliability improvement.

Description

Technical Field

[0001] This invention relates to the field of drone inspection, and in particular to a multi-stage drone inspection method. Background Technology

[0002] In multi-stage inspection missions, drone swarms are affected by stage-specific environmental stresses (wind speed, ambient temperature, etc.) and inspection workloads (cruise duration, maneuver intensity, scanning coverage, etc.). Drones can dynamically degrade in complex operating environments, increasing the risk of operational failure during inspections. Therefore, optimizing drone allocation to improve the reliability of inspection missions has become a crucial requirement. Summary of the Invention

[0003] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a highly reliable multi-stage unmanned aerial vehicle (UAV) inspection method.

[0004] To achieve the above objectives, the technical solution of the present invention is: a multi-stage unmanned aerial vehicle (UAV) inspection method, comprising the following steps: S1: For an inspection task involving M drones and H stages, construct an M×H stage conditional reliability matrix R and a conditional unreliability matrix Q; set up For the lifetime of UAV i, its cumulative failure distribution is as follows: ; in, For the drone's serial number, , Let i be the Weibull distribution parameters of UAV i; The reliability function for UAV i is: ; To identify whether drone i is assigned to participate in phase k, where k is the phase of the inspection task, Define a binary assignment indicator variable. , : Drone i is assigned to execution phase k; Drone i is not assigned execution phase k; The cumulative equivalent working time of drone i at the end of stage k is defined as: ; In the formula, For the stage acceleration factor, For the stage The actual execution time; The recursive form of the cumulative equivalent working time is: ; Will Substitution The cumulative failure probability of drone i at the end of stage k can be written as: ; For UAV i, the conditional reliability of stage k is defined as: ; Using conditional probability relations, we get: ; The conditional unreliability of drone i in stage k is: ;when At that time, the cumulative equivalent working time is updated to The conditional reliability is satisfied: ; when At that time, the cumulative equivalent working time remains unchanged. The conditional reliability is satisfied: ; For an inspection task involving M drones and H stages, an M×H stage conditional reliability matrix R and a conditional unreliability matrix Q can be constructed: ; S2: Using the reliability matrix R and the conditional unreliability matrix Q as inputs, the compressed state forward recursive algorithm is used to evaluate the mission reliability of the UAV inspection system. S2.1: Define the compression state and feasible pruning; Three types of drone sets are defined for each mission phase: The collection has been activated. , including the deadline phase All drones that have been assigned to perform at least one phase; Future demand set , including stages All drones will then be assigned to perform the subsequent phases; Related sets, It only includes drones that are already activated and needed in the future; Based on relevant sets ,stage Compression state vector Defined as a full-state vector In the relevant set Limitations on: ; set up For the stage The set of all possible compressible states at the end; for Each compression state Define the future feasibility function ; From the current compression state Setting off will complete the mission; Starting from this compressed state, the task will inevitably fail; based on Feasibility pruning is used to remove invalid states that cannot guarantee the success of subsequent tasks, thereby reducing the number of states involved in recursion. Single drone allocation scheme: if there is a phase satisfy , And the drone i is in a compressed state If it fails, then ; Multi-drone allocation scheme: if there is a phase satisfy ,and All drones in the compressed state If both fail, then ; The status is passed to the next stage; S2.2: Forward recursive evaluation based on compression state; Two types of explicit operators are defined: expansion operators and projection operators, to realize the mutual mapping between the compressed state and its expanded state, which contains all relevant UAVs in the current stage; Extension operator: ; Compressed state Mapped to extended state , included All drones in China; phase Newly activated drone Set the state to 1; Projection operator: ; Extended state Mapped to compressed state Only keep The drone in the middle, namely ; No drones were activated before the start of the first phase; the initial set of activated drones was already in place. Initial compression state Set as dimension A vector of all 1s, i.e. This indicates that all drones assigned to the first phase at the initial moment of the mission are functioning perfectly. Definition phase The system is in a compressed state at the end. and stage 1 to The probability of all joint operations being successfully completed is:

[0005] Initial compression state The probability mass is set as: At the start of the task, there is only one possible state, namely... ; For the set of compressed states Each compression state in ( Perform forward recursion as follows: S2.2.1 State expansion and activation set update; For compression state Apply the extension operator to obtain the extended state. ; included in the allocation set All drones in the group will have their activation sets updated to... ; S2.2.2 Generate extended successor states; definition For the stage At the beginning, in The allocation set that works normally All drones inside: ; Based on the independence of UAV failures, enumerate all possible failure subsets. For each subset of failures, the extended state will be... The corresponding state variable of the UAV flips from 1 to 0, forming a phase. Extended successor state at the end ; S2.2.3 Calculate the transition probability of the stage; For each extended successor state Calculation of extended state based on component-level conditional reliability parameters arrive Conditional transition probability:

[0006] In the formula: The joint failure probability of the UAVs within the failure subset; The combined survival probability of the remaining normal drones; S2.2.4 Cumulative extended state probability quality; Through accumulated compression state The product of the probability quality of the phase transition and the phase success factor achieves the cumulative extended state probability quality. ; Introduction of success factors Ensure that only the corresponding stage is retained. Successfully executed extended successor state; S2.2.5 State compression and probabilistic quality merging; Calculation phase Future demand set With related sets For each extended successor state Applying the projection operator, it is mapped to a compressed state. Projecting to the same compression state Multiple extended successor states Sum their probabilities and masses to obtain the compressed state. Probability mass:

[0007] S2.2.6 Feasibility pruning and forming the next stage of the compressed state set; For all compression states Only retain those that meet the requirements. and The state, constituting the stage The set of compressed states at the end Used for the next stage of recursion: ; After completing the forward recursion for all H stages using the steps described above, compress the state set for the final stage. The final mission reliability is obtained by summing the probabilistic masses of all compressed states:

[0008] S4 Based on task reliability The corresponding drone allocation scheme dispatches drones to carry out inspections of multi-stage inspection tasks.

[0009] Preferably, the following steps are also included: S3: Optimize task reliability using a genetic algorithm; S3.1 uses integer set encoding to encode the UAV allocation scheme into a string; the encoded string is defined as follows: The string length is the total number of task stages. , For the stage The drone allocation set; S3.2 The fitness function is the task reliability of the coded string U corresponding to the UAV allocation scheme. ; S3.3 Genetic Operations: Selection: The roulette wheel selection method is used, and the selection probability is set according to the fitness value to ensure that superior genes are inherited. Crossover: Single-point crossover is used, with crossover probability... Retain the best allocation schemes from the parent generation and introduce new combinations; Mutation: Random mutation is used, with mutation probability... To prevent the population from converging to a local optimum prematurely; S3.4 The genetic algorithm terminates when it meets the dual conditions of convergence in both the number of iterations and the fitness level. Apply to step S4; Number of iterations: The number of iterations the algorithm has completed to reach the preset maximum number of iterations. ; Fitness convergence: The change in the optimal fitness value of the population is less than a threshold for 20 consecutive generations. .

[0010] By adopting the above technical solution, the beneficial effects of this invention are as follows: This invention addresses the reliability assessment and optimization problem of multi-stage inspection systems subjected to stage-dependent environmental stresses, where UAVs are unrepairable and failure times are arbitrarily distributed. It proposes an efficient assessment algorithm that can quantify stage reliability and overall mission reliability under single-unit and multi-unit allocation schemes. Three technologies significantly reduce the complexity of actual calculations: 1. Activation-based compression: reducing the state space dimension to a small-scale cardinality of related sets. The correlation is based on the total number of drones, not the total number M. 2. Feasibility pruning: Remove compressed states that will inevitably lead to task failure, and eliminate a large number of meaningless state paths in recursion; 3. State merging: Eliminate duplicate and compress states, reducing the size of the active state set.

[0011] Furthermore, genetic algorithms can be used as optimization tools to search for drone allocation schemes that maximize task reliability. An example based on actual reservoir inspection parameters shows that multi-drone allocation can improve task reliability by up to 1.8%; in large-scale problems with more stages and more drones, the optimized allocation obtained by the genetic algorithm can improve reliability by up to 9.7%. This invention provides an effective solution for the design and reliability improvement of multi-stage drone inspection tasks. Detailed Implementation

[0012] The following specific embodiments further illustrate the present invention.

[0013] The multi-stage drone inspection method includes the following steps: S1: For an inspection task involving M drones and H stages, construct an M×H stage conditional reliability matrix R and a conditional unreliability matrix Q.

[0014] S2: Using the reliability matrix R and the conditional unreliability matrix Q as input, the compressed state forward recursive algorithm is used to evaluate the mission reliability of the UAV inspection system.

[0015] S3: Optimize task reliability using a genetic algorithm.

[0016] S4 Based on task reliability The corresponding drone allocation scheme dispatches drones to carry out inspections of multi-stage inspection tasks.

[0017] The UAV inspection system researched in this invention is configured with M UAVs. Each UAV serves as the execution unit for daily inspection tasks and possesses dual-state operation, independent failure characteristics, and unrepairable attributes.

[0018] The inspection task consists of H consecutive and non-overlapping phases, each assigned an independent and predefined inspection task. These consecutive phases differ significantly in environmental conditions and inspection workload, and this difference is quantified by a phase-specific acceleration factor, which directly adjusts the time-varying failure probability of a single UAV.

[0019] definition Assign a set to the drones in stage k. .like Then stage k is executed by a single drone; if Then stage k is executed by multiple redundant drones.

[0020] definition Let i be a binary variable at the end of stage k: Drone i continues to function normally when phase k is completed. The drone i became invalid before the end of phase k. Since all drones are unrepairable, their state variables exhibit non-increasing properties as the mission progresses: For any ,like Then there must be Only when hour, It can be 1 (stage k2 remains normal) or 0 (failure before stage k2 ends).

[0021] definition For the stage The system state vector at the end:

[0022] The system state vector inherits the non-increasing property of the UAV state variables. yes The non-increasing subset indicates that the state of the drone swarm can only deteriorate and cannot be recovered during the mission.

[0023] definition For the stage acceleration factor, For the stage The actual execution time.

[0024] The workload and accuracy requirements of the inspection in stage k are determined by the amount of work and the accuracy requirements. The quantification of the accelerating effects of environmental stress (wind speed, ambient temperature, etc.) and inspection workload (cruise duration, maneuver intensity, scan coverage, etc.) on UAV aging and failure. The incremental equivalent working time of the drone assigned to stage k.

[0025] Acceptability function in the definition phase , with system state vector The input is a binary result (1 indicates success, 0 indicates failure).

[0026] Single-UAV allocation scheme: In phase k, only a single UAV i is allocated, i.e. A phase k is successful if and only if the assigned drone functions correctly at the end of phase k. The phase acceptability function is:

[0027] In the formula As an indicator function, when event A is true. ,otherwise .

[0028] Multi-UAV allocation scheme: Stage k allocates a redundant set of UAVs, i.e. A phase k is successful if and only if at least one drone in the allocation set functions correctly at the end of the phase. The phase acceptability function is:

[0029] Unlike independent static tasks, inspection is a serial, multi-stage, time-series task with a system state sequence. It follows an irreversible and irreparable degradation process. The system state at stage k. Strictly subject to the previous state Constraints exist, with all stage state vectors being temporally coupled and statistically dependent. Overall task success requires that stage acceptability constraints be continuously met throughout the entire state evolution sequence.

[0030] Let G be the task success event. Considering the temporal dependence and degradation propagation of adjacent system states, the task success condition covering all coupled stage states is:

[0031] In the formula: The drone swarm exhibits an irreversible degradation relationship; the current system state can only deteriorate from the previous stage. : Initial state where all drones are in perfect working order before the mission begins definition For the reliability of the drone inspection system, i.e., given the drone allocation scheme The probability of a task being successfully completed (G):

[0032] This invention aims to find the optimal drone allocation scheme for multi-stage drone inspection tasks. This improves mission reliability. maximize:

[0033] The decision variable is the set of drone allocations for each stage. .

[0034] Symbol explanation.

[0035]

[0036] Phase reliability assessment: As an integrated system of electronic components, mechanical structures, and software systems, the failure characteristics of unmanned aerial vehicles (UAVs) conform to the Weibull distribution in application scenarios. Specifically, the failure behavior of each UAV i is determined by shape parameters. With scale parameters The Weibull distribution characterization allows for flexible modeling of early failure, constant failure, and aging failure modes of UAVs under varying inspection workloads and environmental stresses. Although the algorithm in this invention uses the Weibull failure time distribution, it is applicable to any failure time distribution of UAVs.

[0037] set up For the lifespan of drone i Its cumulative failure distribution is as follows:

[0038] The reliability function for UAV i is:

[0039] To identify whether drone i is assigned to participate in phase k ( Define a binary assignment indicator variable. : : Drone i is assigned to execution phase k Drone i is not assigned execution phase k. Under the execution-driven aging assumption, drone i contributes equivalent working time only within the assigned phase. Therefore, the cumulative equivalent working time of drone i at the end of phase k is defined as:

[0040] In the formula For the stage acceleration factor, For the stage The actual execution time.

[0041] The recursive form of the cumulative equivalent working time is:

[0042] Will Substituting into equation (6), the cumulative failure probability of UAV i at the end of stage k can be written as:

[0043] For UAV i, the conditional reliability of stage k (known to be that it survives all assigned preceding stages) is defined as:

[0044] Using conditional probability relations, we get:

[0045] The conditional unreliability of drone i in stage k is:

[0046] when At that time, the cumulative equivalent working time is updated to The conditional reliability is satisfied:

[0047] when At that time, the cumulative equivalent working time remains unchanged. The conditional reliability is satisfied:

[0048] For an inspection task involving M drones and H stages, an M×H stage conditional reliability matrix R and a conditional unreliability matrix Q can be constructed:

[0049] The two matrices mentioned above will serve as inputs to the task reliability assessment algorithm in the next section.

[0050] Mission reliability assessment Task reliability assessment based on full state vectors suffers from severe state space explosion as the number of UAVs and the mission stages increase, leading to unacceptable computational costs. This section proposes a task reliability assessment algorithm based on compressed states, providing a definition of compressed states and feasible pruning to achieve efficient state space compression, and constructing a forward recursive process for accurate and efficient assessment of task reliability.

[0051] Compression State and Feasible Pruning To facilitate state space compression, three types of drone sets are defined for each stage: 1. Activated set , including the deadline phase All drones have been assigned to perform at least one phase.

[0052] 2. Future Demand Set , including stages All drones will then be assigned to perform the subsequent phases.

[0053] 3. Related sets It only includes drones that are already activated and needed in the future.

[0054] During the multi-stage task process, the activated set Non-decreasing expansion as the task progresses; future demand set As the mission progresses and subsequent phases unfold, non-decreasing contraction is reduced. Their intersection. number of elements This is much smaller than the total number of drones M, providing support for state space compression. Based on relevant sets... ,stage Compression state vector Defined as a full-state vector In the relevant set Limitations on:

[0055] because state space Compared to the full state space, the dimension of This significantly reduces computational costs.

[0056] set up For the stage The set of all possible compressible states at the end. Each compression state Define the future feasibility function : From the current compression state Departure will complete the mission. The task will inevitably fail if it starts from this compressed state. based on Feasibility pruning eliminates invalid states that cannot guarantee the success of subsequent tasks, effectively reducing the number of states involved in recursion and further optimizing computational efficiency.

[0057] Single drone allocation scheme: if there is a phase satisfy , And the drone i is in a compressed state If it fails, then .

[0058] Multi-drone allocation scheme: if there is a phase satisfy ,and All drones in the compressed state If both fail, then .

[0059] only The status is passed on to the next stage.

[0060] Forward recursive evaluation algorithm based on compressed state First, two types of explicit operators are defined: expansion operators and projection operators, to realize the mutual mapping between the compressed state and its expanded state, which contains all relevant UAVs in the current stage.

[0061] 1. Extended Operator

[0062] Compressed state Mapped to extended state , included All drones in China; phase Newly activated drone The state is set to 1.

[0063] 2. Projection Operator

[0064] Extended state Mapped to compressed state Only keep The drone in the middle, namely No drones were activated before the start of the first phase; the initial set of activated drones was already set. Initial compression state Set as dimension A vector of all 1s, i.e. This indicates that all drones assigned to the first phase at the initial moment of the mission are functioning perfectly.

[0065] Definition phase The system is in a compressed state at the end. and stage 1 to The probability of all joint operations being successfully completed is:

[0066] Initial compression state The probability mass is set as:

[0067] At the start of the task, there is only one possible state, therefore the initial set of compressed states is... For only the initial state A single-element set, i.e. .

[0068] For the set of compressed states Each compression state in ( Perform forward recursion in the following six steps: 1. State expansion and activation set update For compression state Apply the extension operator to obtain the extended state. ; Include in the allocation set All drones in the group will have their activation sets updated to... .

[0069] 2. Generate extended successor state definition For the stage At the beginning, in The allocation set that works normally All drones inside:

[0070] Based on the independence of UAV failures, enumerate all possible failure subsets. For each subset of failures, the extended state will be... The corresponding state variable of the UAV flips from 1 to 0, forming a phase. Extended successor state at the end .

[0071] 3. Calculate the transition probability of each stage. For each extended successor state Calculation of extended state based on component-level conditional reliability parameters arrive Conditional transition probability:

[0072] In the formula: the first term is the joint failure probability of the drones in the failed subset; the second term is the joint survival probability of the remaining normal drones.

[0073] Cumulative extended state probability quality Different compression states It may generate the same extended successor state. It is necessary to accumulate the probabilities of all generated paths to obtain The probabilistic quality. In practice, this can be achieved through the accumulation of compressed states. The product of probability quality, stage transition probability, and stage success factor is implemented as follows:

[0074] Introduction of success factors Ensure that only the corresponding stage is retained. Successfully executed extended successor state.

[0075] State compression and probabilistic mass merging Calculation phase Future demand set With related sets For each extended successor state Applying the projection operator, it is mapped to a compressed state. Projecting to the same compression state. Multiple extended successor states Sum their probabilities and masses to obtain the compressed state. Probability mass:

[0076] This state merging operation effectively reduces the number of recursive states.

[0077] Feasible pruning and formation of the next stage of compressed state set For all compression states Only retain those that meet the requirements. (Non-zero probability) and The (future feasible) state constitutes a stage. The set of compressed states at the end Used for the next stage of recursion:

[0078] After completing the forward recursion for all H stages using the steps described above, compress the state set for the final stage. The final mission reliability is obtained by summing the probabilistic masses of all compressed states:

[0079] The traditional full-state enumeration method for multi-stage task reliability assessment has a computational complexity of: The complexity is exponentially related to the total number of drones M, and this exponential complexity is the fundamental reason why the full-state method cannot be applied to large-scale drone swarms.

[0080] set up In compressed state The branching factor represents the branching factor of the branching factor. The number of extended successor states generated. A rough upper bound on the total computational complexity of the algorithm of this invention is:

[0081] branching factor much smaller ,because The algorithm's complexity upper bound is much lower than that of the full-state enumeration method because it depends only on the number of drones in execution phase k, rather than the total number of drones in the cluster.

[0082] Example Analysis Taking a UAV inspection system for a medium-sized reservoir in southern China as an example, the effectiveness of the compressed state forward recursive algorithm proposed in Section 4 is verified.

[0083] System Description This reservoir example includes six inspection areas: 1—dam crest section, 2—upstream face of the dam body, 3—spillway, 4—water conveyance culvert, 5—nearshore area of ​​the reservoir, and 6—farshore area of ​​the reservoir. Four consecutive, non-overlapping inspection phases are planned. Three drones with different performance levels are configured, and the failure time of each drone follows a Weibull distribution.

[0084] Inspection tasks, inspection routes, and durations for each stage With acceleration factor As shown in Table 1, the acceleration factor is set according to the actual operating conditions of the reservoir. For example, the acceleration factor is higher on the upstream face of the dam (region 2) and the spillway (region 3) due to strong winds, high humidity, and complex airflow; the acceleration factor is even higher during the emergency inspection phase (phase 4) due to the high intensity of the operation.

[0085] Table 1 Stage Parameter Settings

[0086] Weibull distribution parameters (shape parameters) of 3 UAVs Scale parameters As shown in Table 2, the parameters are determined based on the UAV model, manufacturer's technical manual, and engineering measurement data.

[0087] Table 2. UAV Weibull Distribution Parameter Settings

[0088] Single-drone allocation scheme: Each phase of the task is undertaken independently by a single drone. .

[0089] Multi-drone allocation scheme: Dual-drone redundancy is adopted in critical phases. That is, phases 2 and 4 use dual-machine redundancy, while the remaining phases still use a single machine.

[0090] Stage condition reliability calculation Based on the phased reliability assessment method in Section 3, the reliability of each UAV i in each phase is first calculated. Cumulative equivalent working time Then, the stage condition reliability matrices under the two allocation schemes are obtained. With stage condition unreliability matrix

[0091] Table 3 Conditional Reliability / Unreliability (Single Machine Allocation Scheme)

[0092] Table 4 Conditional Reliability / Unreliability (Multi-machine Allocation Scheme)

[0093] For drones not assigned to phase k (e.g., drone 1 in phase 1), the phase condition reliability is 1.0 and the unreliability is 0.0; for drones assigned to phase k (e.g., drone 3 in phase 1), the phase condition unreliability reflects the phase-specific failure risk (e.g., ...). In the multi-drone allocation scheme, UAV 1 is assigned to phase 2, thus resulting in non-zero unreliability (e.g., ).

[0094] Mission reliability assessment The compressed state forward recursive algorithm from Section 4 is used to evaluate the task of the example UAV inspection system.

[0095] Single-machine allocation scheme: Task reliability .

[0096] Multi-machine allocation scheme: task reliability .

[0097] The recursive statistics for each stage are shown in Tables 5 and 6.

[0098] End of Phase Number of activated drones Stage The number of drones needed in the future Number of drones tracked in compressed state Stage Number of compressed states retained at the end Stage Number of extended successor states generated Number of unique compressed states after projection Merge ratio: The ratio of the number of expanded states to the number of unique compressed states. The number of unique states that can be pruned and removed: Phase failure cumulative probability quality ass: Cumulative probability quality of successful execution of a phase Table 5. Recursive statistics for each stage (single-machine allocation scheme)

[0099] As shown in Table 5, dimensional compression begins from stage 3. This indicates that after phase 2, there are no stateless and future-related drones, and the recursive states are extremely compact. All phases This indicates that under this single-machine allocation, the feasibility and relevance structure causes the recursion to degenerate into a single compressed state at each stage. Much smaller than the size of the full state space This verifies the effectiveness of activation-based state compression. This indicates that all unique states are feasible in the future, satisfying the single-machine allocation constraint.

[0100] Table 6 Recursive statistics for each stage (multi-machine allocation scheme)

[0101] In a multi-machine allocation scenario, Phase 2 This indicates that all three drones are already activated and will be needed in the future; therefore, the recursion needs to track more components. Increase to 3; to stage 4, The process recursively compresses the data back into a single active state. The merging ratio in Phase 4 reaches a high of 8.0, indicating that a large number of extended successor branches are projected and merged into the same compressed state, validating the effectiveness of the projection + merging mechanism. Compared to the single-machine solution, the failure probability quality of Phases 2 and 4 is significantly reduced, verifying that multi-machine allocation can significantly reduce the probability of phase failures and improve the task success rate.

[0102] Multi-machine solutions offer improved reliability compared to single-machine solutions. This represents a relative improvement of approximately 1.8%. This improvement stems from the redundancy mechanism's ability to tolerate single-machine failures during critical phases.

[0103] From the perspective of computational complexity advantage, the traditional full-state method requires processing the most computational complexity per stage. There are 8 states when M=3, which quickly becomes infeasible as the scale increases; while the algorithm of this invention only tracks the activation-future related set and only propagates compressed states, which is much smaller than the number of states. In this example, the standalone solution is implemented throughout the entire process. Multi-machine solution peak The compression effect is significant.

[0104] Task reliability optimization This section aims to maximize overall mission reliability by rationally planning the drone allocation scheme at each stage. For this combinatorial optimization problem involving discrete decision variables and a nonlinear objective function, a genetic algorithm for drone allocation optimization is designed, and a larger-scale drone inspection example is constructed to test the optimization performance.

[0105] Genetic Algorithm Design Genetic algorithms (GA) iteratively search for the optimal solution in the solution space by simulating the selection-crossover-mutation process of biological evolution

[30] . For the optimization problem of this invention, the designed genetic algorithm includes encoding method, initial population generation, fitness function and genetic operations (selection, crossover, mutation).

[0106] Encoding method (decoding representation) The drone allocation scheme is encoded into a string using integer set encoding. The encoded string is defined as follows: The string length is the total number of task stages. , For the stage The drone allocation set.

[0107] fitness function The fitness function is the task reliability of the coded string U corresponding to the UAV allocation scheme. A higher fitness value indicates a better allocation scheme.

[0108] Genetic operations Selection: The roulette wheel selection method is adopted, and the selection probability is set according to the fitness value to ensure that superior genes are inherited.

[0109] Crossover: Single-point crossover is used, with crossover probability... Retain the best allocation schemes from the parent generation and introduce new combinations.

[0110] Mutation: Random mutation is used, with mutation probability... To avoid the population converging to a local optimum too early.

[0111] Algorithm Termination Condition Set dual termination conditions to ensure algorithm convergence and avoid redundant computation: Number of iterations: The number of iterations the algorithm has completed to reach the preset maximum number of iterations. ; Fitness convergence: The change in the optimal fitness value of the population is less than a threshold for 20 consecutive generations. .

[0112] Example Analysis Using a larger inspection example than in Section 5, the number of inspection stages... Number of drones The relevant parameters for each stage are shown in Table 7, and the parameters for the Weibull distribution are shown in Table 8.

[0113] Single-drone solution: Only one drone is allocated for each phase.

[0114] Multi-machine solution: Single machine execution for some stages, dual-machine redundancy for critical or flexible stages.

[0115] Specific requirements: Single-machine stage: 1, 4, 7, 12; Dual-machine stage: 3, 6, 9, 11; Flexible stage (can be single-machine or dual-machine): 2, 5, 8, 10.

[0116] Table 7 Stage Parameter Settings

[0117] Table 8. UAV Weibull Distribution Parameter Settings

[0118] Genetic algorithm parameter settings: population size Crossover probability Probability of mutation Maximum number of iterations Convergence threshold .

[0119] Table 9 Optimal Allocation Scheme (Single Machine)

[0120] Task reliability after single-machine allocation scheme optimization: .

[0121] This approach does not concentrate all tasks on the seemingly most powerful drones, but rather distributes them evenly across the cluster to balance cumulative exposure. The most reliable drones, 3 and 5, are used more frequently, but their cumulative aging remains within acceptable limits; drone 1 is deployed only once, indicating that, given the phase sequence and Weibull parameters, the least reliable drone is reserved for a single, independent early phase, maximizing its marginal contribution.

[0122] Table 10 Optimal Allocation Scheme (Multi-machine)

[0123] Task reliability after multi-machine allocation scheme optimization: .

[0124] The solution is highly balanced: drones 1, 2, 3, and 4 each participate in 4 phases, while drone 5 participates in 3 phases. Although the optimization objective is task reliability, the genetic algorithm automatically discovers that distributing tasks among multiple drones reduces excessive aging of a single drone while preserving redundancy in critical phases. Compared to the optimized single-drone solution, this represents an absolute improvement. This represents a relative improvement of approximately 9.79%, which is of great significance for mission-critical applications.

[0125] Table 11 Recursive statistics for each stage (single machine)

[0126] Table 12 Recursive Statistics for Each Stage (Multi-Machine)

[0127] Genetic algorithm optimization essentially relies on the iterative calls of the task reliability assessment module. The computational efficiency of the compressed state forward recursion technique in this invention ensures that GA can be used for large-scale problems. Key recursion statistics for the two optimization schemes are shown in Tables 11 and 12: 1. Optimized single-machine allocation: all stages , , , The process recursively degenerates into a single active compressed state at each stage, with a constant merging ratio of 2.0. Mission reliability decreases monotonically with each stage, with the maximum reliability loss occurring in the later stage (stage 11), due to the cumulative aging of the UAV.

[0128] 2. Optimized multi-machine allocation: Although the multi-machine phase generates multiple combinations of local failures (such as phase 5: Phase 6: Phase 8: The projection and state merging mechanism effectively compresses the state space, merging most of the extended successor states into a small number of unique compressed states, thus preserving the total number of active compressed states throughout the process. Minimal (maximum value 5). The probability of failure in critical stages is significantly reduced, resulting in a significant improvement in reliability.

[0129] This invention studies the reliability assessment and optimization problem of a multi-stage inspection system subjected to stage-dependent environmental stresses, where UAVs are unrepairable and have arbitrarily distributed failure times. An efficient assessment algorithm is proposed, capable of quantifying stage reliability and overall mission reliability under single-UAV and multi-UAV allocation schemes. The proposed assessment algorithm significantly reduces practical computational complexity through three techniques: 1. Activation-based compression: reducing the state space dimension to a small-scale cardinality of related sets. The correlation is based on the total number of drones, not the total number M. 2. Feasibility pruning: Remove compressed states that will inevitably lead to task failure, and eliminate a large number of meaningless state paths in recursion; 3. State merging: Eliminate duplicate and compress states, reducing the size of the active state set.

[0130] Furthermore, a genetic algorithm is employed as an optimization tool to search for a drone allocation scheme that maximizes task reliability. An example based on actual reservoir inspection parameters demonstrates this: In the test cases, multi-machine allocation can improve task reliability by up to 1.8%; In large-scale problems with more stages and more drones, the optimized allocation obtained by the genetic algorithm can improve reliability by up to 9.7%.

[0131] The recursive evaluation and genetic optimization combination framework proposed in this invention provides an effective solution for the design and reliability improvement of multi-stage UAV inspection tasks.

[0132] The above description is merely a preferred embodiment of the present invention and does not limit the scope of the present invention. All equivalent changes and modifications made in accordance with the claims of the present invention should still fall within the scope of the present invention.

Claims

1. A multi-stage unmanned aerial vehicle (UAV) inspection method, characterized in that, Includes the following steps: S1: For an inspection task involving M drones and H stages, construct an M×H stage conditional reliability matrix R and a conditional unreliability matrix Q; set up For the lifetime of UAV i, its cumulative failure distribution is as follows: ； in, For the drone's serial number, , Let i be the Weibull distribution parameters of UAV i; The reliability function for UAV i is: ； To identify whether drone i is assigned to participate in phase k, where k is the phase of the inspection task, Define a binary assignment indicator variable. , : Drone i is assigned to execution phase k; Drone i is not assigned execution phase k; The cumulative equivalent working time of drone i at the end of stage k is defined as: ； In the formula, For the stage acceleration factor, For the stage The actual execution time; The recursive form of the cumulative equivalent working time is: ； Will Substitution The cumulative failure probability of drone i at the end of stage k can be written as: ； For UAV i, the conditional reliability of stage k is defined as: ； Using conditional probability relations, we get: ； The conditional unreliability of drone i in stage k is: ;when At that time, the cumulative equivalent working time is updated to The conditional reliability is satisfied: ； when At that time, the cumulative equivalent working time remains unchanged. The conditional reliability is satisfied: ; For an inspection task involving M drones and H stages, an M×H stage conditional reliability matrix R and a conditional unreliability matrix Q can be constructed: ； S2: Using the reliability matrix R and the conditional unreliability matrix Q as inputs, the compressed state forward recursive algorithm is used to evaluate the mission reliability of the UAV inspection system. S2.1: Define the compression state and feasible pruning; Three types of drone sets are defined for each mission phase: The collection has been activated. , including the deadline phase All drones that have been assigned to perform at least one phase; Future demand set , including stages All drones will then be assigned to perform the subsequent phases; Related sets, It only includes drones that are already activated and needed in the future; Based on relevant sets ,stage Compression state vector Defined as a full-state vector In the relevant set Limitations on: ； set up For the stage The set of all possible compressible states at the end; for Each compression state Define the future feasibility function ; From the current compression state Setting off will complete the mission; Starting from this compressed state, the task will inevitably fail; based on Feasibility pruning is used to remove invalid states that cannot guarantee the success of subsequent tasks, thereby reducing the number of states involved in recursion. Single drone allocation scheme: if there is a phase satisfy , And the drone i is in a compressed state If it fails, then ; Multi-drone allocation scheme: if there is a phase satisfy ,and All drones in the compressed state If both fail, then ; The status is passed to the next stage; S2.2: Forward recursive evaluation based on compression state; Two types of explicit operators are defined: expansion operators and projection operators, to realize the mutual mapping between the compressed state and its expanded state, which contains all relevant UAVs in the current stage; Extension operator: ； Compressed state Mapped to extended state , included All drones in China; phase Newly activated drone Set the state to 1; Projection operator: ； Extended state Mapped to compressed state Only keep The drone in the middle, namely ; No drones were activated before the start of the first phase; the initial set of activated drones was already in place. Initial compression state Set as dimension A vector of all 1s, i.e. This indicates that all drones assigned to the first phase at the initial moment of the mission are functioning perfectly. Definition phase The system is in a compressed state at the end. and stage 1 to The probability of all joint operations being successfully completed is: Initial compression state The probability mass is set as: At the start of the task, there is only one possible state, namely... ; For the set of compressed states Each compression state in ( Perform forward recursion as follows: S2.2.1 State expansion and activation set update; For compression state Apply the extension operator to obtain the extended state. ; included in the allocation set All drones in the group will have their activation sets updated to... ; S2.2.2 Generate extended successor states; definition For the stage At the beginning, in The allocation set that works normally All drones inside: ； Based on the independence of UAV failures, enumerate all possible failure subsets. For each subset of failures, the extended state will be... The corresponding state variable of the UAV flips from 1 to 0, forming a phase. Extended successor state at the end ; S2.2.3 Calculate the transition probability of the stage; For each extended successor state Calculation of extended state based on component-level conditional reliability parameters arrive Conditional transition probability: In the formula: The joint failure probability of the UAVs within the failure subset; The combined survival probability of the remaining normal drones; S2.2.4 Cumulative extended state probability quality; Through accumulated compression state The product of the probability quality of the phase transition and the phase success factor achieves the cumulative extended state probability quality. ； Introduction of success factors Ensure that only the corresponding stage is retained. Successfully executed extended successor state; S2.2.5 State compression and probabilistic quality merging; Calculation phase Future demand set With related sets For each extended successor state Applying the projection operator, it is mapped to a compressed state. Projecting to the same compression state Multiple extended successor states Sum their probabilities and masses to obtain the compressed state. Probability mass: S2.2.6 Feasibility pruning and forming the next stage of the compressed state set; For all compression states Only retain those that meet the requirements. and The state, constituting the stage The set of compressed states at the end Used for the next stage of recursion: ； After completing the forward recursion for all H stages using the steps described above, compress the state set for the final stage. The final mission reliability is obtained by summing the probabilistic masses of all compressed states: S4 Based on task reliability The corresponding drone allocation scheme dispatches drones to carry out inspections of multi-stage inspection tasks.

2. The multi-stage UAV inspection method according to claim 1, characterized in that, It also includes the following steps: S3: Optimize task reliability using a genetic algorithm; S3.1: The UAV allocation scheme is encoded into a string using integer set encoding; the encoded string is defined as follows: The string length is the total number of task stages. , For the stage The drone allocation set; S3.2: The fitness function is the task reliability of the UAV allocation scheme corresponding to the encoded string U. ; S3.3: Genetic operations: Selection: The roulette wheel selection method is used, and the selection probability is set according to the fitness value to ensure that superior genes are inherited. Crossover: Single-point crossover is used, with crossover probability... Retain the best allocation schemes from the parent generation and introduce new combinations; Mutation: Random mutation is used, with mutation probability... To prevent the population from converging to a local optimum prematurely; S3.4: The genetic algorithm terminates when it meets the dual conditions of convergence in both the number of iterations and the fitness level. Apply to step S4; Number of iterations: The number of iterations the algorithm has completed to reach the preset maximum number of iterations. ; Fitness convergence: The change in the optimal fitness value of the population is less than a threshold for 20 consecutive generations. .

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