Method for calculating transient production capacity of aircraft final assembly system based on pulsating production mode

Abstract

The application discloses a method for calculating transient production capacity of an aircraft assembly system based on a pulsation production mode, comprising the following steps: S1, constructing an aircraft assembly system model, and dividing the aircraft assembly into a plurality of installation units and test units; S2, determining total station positions, assembly unit station positions and test unit station positions of the aircraft assembly; S3, establishing an assembly path set of an installation task, and determining a critical path according to the earliest start time and the latest start time of the assembly path; S4, linearly adding actual installation execution durations, and calculating actual production cycles of the assembly units; S5, linearly adding actual test execution durations, and calculating actual production cycles of the test units; and S6, solving a transient production delivery cycle of the actual aircraft assembly; the method can fully consider actual production, can calculate the production capacity of the aircraft assembly system in real time, can accurately solve the transient production capacity of the aircraft assembly system, can greatly improve the calculation precision of the result, and is suitable for the actual production process of the aircraft.

Description

Technical Field

[0001] This invention relates to the field of aircraft manufacturing technology, and in particular to a method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode. Background Technology

[0002] The pulsed production mode for aircraft final assembly is a rhythm-based assembly line that utilizes lean manufacturing principles to design, optimize, and balance the aircraft final assembly process. This enables station-based final assembly operations at set rhythms, shortening delivery cycles, improving production efficiency, ensuring product quality, and meeting customer requirements. The pulsed production mode is characterized by "assembly without movement, movement without assembly," where each station completes its corresponding final assembly tasks according to the process flow and division of labor, achieving specialized production. Currently, aircraft final assembly operations rely heavily on manual labor and the experience of skilled operators, remaining labor-intensive. The aircraft final assembly process is a complex system integration process. In the operation of such a complex system, the elements of "man, machine, material, method, and environment" in each work unit influence each other. It is particularly constrained by personnel capabilities and experience, tooling and equipment support, effective material supply, process technology changes, final assembly working conditions, and testing tools and methods, which exacerbate fluctuations in production rhythms. This leads to uncertainty and chaos in the calculation of production capacity for the pulsed production line. Therefore, the research and analysis of aircraft final assembly system production capacity based on multiple constraints is the most complex and more in line with actual engineering needs.

[0003] Intelligent decision-making is a key element in building a digital and intelligent final assembly line, and accurately grasping the real-time operating status of the final assembly system is a prerequisite for making intelligent decisions. Researching and analyzing the real-time production capacity of the final assembly system is a key technology for improving the state perception capability of the aircraft final assembly system in a digital and intelligent context. The ability to perceive the state of the aircraft final assembly system's production capacity in real time will lay a crucial foundation for intelligent and accurate decision-making in aircraft final assembly. The transient performance of the aircraft final assembly system describes the relatively constant steady-state performance of the system at any given time; it truly reflects the dynamic changes in system performance over time.

[0004] For decades, scholars both domestically and internationally have conducted extensive research on the production capacity of discrete manufacturing systems. However, most research methods focus on the steady-state performance of these systems, with relatively little research on the transient production capacity calculation of complex systems. The problem of transient analysis and calculation of complex systems, such as aircraft final assembly lines, urgently needs to be solved. Currently, research on the production capacity of pulsed production lines in aircraft final assembly is limited. Methods for solving the production capacity of continuous industrial production lines with large production batches generally employ empirical prediction methods and linear programming methods from operations research. Xin Bo et al. from Northwestern Polytechnical University proposed a method (CN104123672A) for calculating the production capacity of aircraft assembly line personnel, which decomposes the aircraft component assembly process to the operational level. Based on the decomposition results, the theoretical working hours consumed by each assembly unit are calculated. Using the effective working hours of personnel as the standard, the theoretical working hours are quantitatively corrected based on three dominant factors affecting personnel production capacity: assembly accuracy level, learning effect, and assembly intensity. Finally, other key production capacity parameters are solved by the effective working hours of personnel in each process, and the production capacity of the entire assembly line per unit time is calculated. Hou Yukan, Li Yuan et al. also established a station reliability model based on information entropy theory and cognitive reliability model. By constructing the instantaneous state set of workstations and buffers, they completed the inverse modeling of the transient behavior of workstations during system operation, and realized the calculation of real-time production capacity during the transient phase of system operation. These studies, when calculating the production capacity of complex systems such as aircraft final assembly lines, neglect the real-world factors that affect production capacity during mass production. Their solution models and calculation results are either difficult to guarantee in terms of accuracy or are too idealistic, resulting in a large deviation from the actual production capacity of aircraft final assembly lines and making them unsuitable for practical engineering applications. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies that cannot be applied to actual engineering, and to provide a method for calculating the transient production capacity of an aircraft assembly system based on a pulsed production mode. Taking the aircraft assembly system as the object, this method fully considers actual production, quantifies relevant factors of actual production into influencing parameters, constructs a mathematical model of production capacity, and can calculate the production capacity of the aircraft assembly system in real time. It accurately solves the transient production capacity of the aircraft assembly system, greatly improves the accuracy of the calculation results, and is applicable to the actual production process of aircraft.

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0007] The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode includes the following steps:

[0008] S1. Construct an aircraft final assembly system model, describing the aircraft final assembly system as a final assembly system module DT. fas Personnel Module DT person Equipment Module DTequipment Product Module DT product Process Method Module DT method and Environment Module DT equipment The set of units, based on the aircraft's final assembly work surface i and final assembly station j, divides the aircraft final assembly into several installation units and testing units. According to actual production conditions, each installation unit has N... a There are N assembly unit stations, and the test unit has N t Each test unit station has i assembly units and one test unit. Each assembly unit and test unit includes the corresponding required modules.

[0009] S2. Calculate the total number of assembly stations N for aircraft final assembly based on the annual workload, production cycle, and production process cycle. c Number of assembly unit stations N a and the number of test unit stations N t N a +N t =N c Then, the assembly units and testing units are numbered according to their positions. Assembly unit A ij The test unit T is located at the j-th installation unit station on the production line of the i-th working face. j The j-th test unit station is located on the production line of the test unit.

[0010] S3, according to A ij Based on the location of each assembly unit and the assembly relationship on the production line, a set of assembly paths (AOs) for the installation task is established. According to the assembly relationship and theoretical execution time, a weighted directed graph of complex multi-assembly tasks based on graph theory is established. Each assembly path (AO) is numbered according to the topological order of the weighted directed graph. The earliest start time and the latest start time that do not affect the task execution cycle are calculated one by one after all the preceding AOs of each assembly path (AO) are completed. All assembly path (AO) with the earliest start time and the latest start time equal are found and identified as critical path (AO).

[0011] S4. Determine the theoretical installation execution time h of the critical path AO based on the installation tasks of the installation unit production line. jpk The theoretical assembly time H of the critical path AO at each station is obtained by summarizing. jp The theoretical assembly time H is adjusted based on the actual production process time. jp Make corrections to obtain the actual installation execution time T. AOp Substituting p = r, where r is the set of critical paths AO, and then the actual installation execution time T... AOr Linear summation to calculate the actual production cycle T of the assembly unit. ij ;

[0012] S5. Determine the theoretical test execution time T of test path AO based on the test tasks of the test unit production line. jq The theoretical test execution time T is determined based on the actual test procedure time. jq Make corrections to obtain the actual test execution time T. AOt Then, the actual test execution time T AOt Linear summation to calculate the actual production cycle T of the test unit. j ;

[0013] S6. By summing the maximum value of the total actual production cycle of the assembly units on each production line of the installation unit with the total actual testing cycle of the testing unit, the transient production and delivery cycle C of the actual aircraft final assembly can be obtained. tm .

[0014] By describing the aircraft final assembly system, this approach more closely reflects actual production conditions, considering all factors involved in each stage of aircraft final assembly production. Dividing the production process into installation and testing units allows for adaptation to real-world situations, simplifying the problem into calculations for installation and testing units. By specifying the number of workstations and assembly units, the problem is further refined into assembly relationships and task execution times along assembly paths. This transforms the actual production problem into a mathematical calculation model, resulting in calculations closer to reality. By identifying the critical path (AO), the production cycle problem is transformed into the time consumed by the critical path AO, allowing for the identification of key factors affecting production capacity. Calculations are then performed on the installation and testing units, and considering the influencing factors in actual production, the production capacity of the installation and testing units is adjusted. Finally, the transient production capacity of the aircraft final assembly is obtained through comprehensive and thorough consideration of actual production, quantifying relevant factors into influencing parameters. This enables real-time calculation of the aircraft final assembly system's production capacity, accurately solving for the transient production capacity of the aircraft final assembly system and significantly improving the accuracy of the calculation results.

[0015] In a preferred embodiment of the present invention, in step S2 above:

[0016] N c =T tc *A c / T fc

[0017] Among them, T tc The production process design cycle for aircraft final assembly is in days, A c For the annual task volume, T fc The factory calendar time for final aircraft assembly is in days;

[0018] N a =Tta *A a / T fa

[0019] Among them, T ta The production process design cycle for the installation unit is in days, A. a T represents the number of installation units required to cover the annual workload. fa The factory calendar time for the installation unit, in days;

[0020] N t =T tt *A t / T ft

[0021] Among them, T tt The production process design cycle for the test unit is in days, A t T represents the number of test unit tasks corresponding to the annual task volume. ft The factory calendar time for the test unit is in days.

[0022] Production cycle time reflects capacity demand. The number of workstations is determined by annual task volume, process design cycle, and production cycle time. The required installation unit and testing unit workstations can be determined based on the pulsed production demand and can be adjusted according to the actual situation.

[0023] In a preferred embodiment of the present invention, the specific steps for calculating the earliest start time of assembly path AO in step S3 are as follows:

[0024] S31, according to section A ij Based on the location of each assembly unit and the assembly relationship on the production line, establish a set of assembly paths AO for the installation task. Let the label set of the installation task be N = {1, 2, ..., P}. The priority relationship of the assembly path AO is represented by a directed graph G = {V, E}, where V is the vertex set, representing all assembly paths AO, and E is the set of directed edges, representing the priority assembly relationship between assembly paths AO. The weight of each edge is set to represent the theoretical execution time of the assembly path AO.

[0025] S32. Find all nodes with an in-degree of 0 in the weighted directed graph. After the search is completed, record the results in the topology sequence number set. If there are multiple nodes with an in-degree of 0, record the node with the smaller number first. Delete the nodes and their adjacent edges that have been recorded in the topology sequence number set. After updating the weighted directed graph, repeat the step until all points are recorded in the topology sequence number set.

[0026] S33. Based on the order obtained from the topological sequence number set, renumber each assembly path AO, and use this number as the search order for the dynamic programming algorithm. Solve for the earliest start time using the dynamic programming algorithm. The dynamic programming algorithm formula 1 is:

[0027] first[u] = max{first[v] + edge[v][u]}, the set of neighbors of v∈u.

[0028] Where first[u] represents the earliest start time of the u-th assembly path AO, and edge[v][u] represents the weight of the directed edge from v to u, i.e., the theoretical execution time t of the assembly path AO numbered v. v .

[0029] By transforming the problem into a weighted directed graph, the complex production process can be simplified. The relationships between assembly units and tasks are intricate. Since each assembly unit may affect the subsequent production process, the production processing time on each assembly path cannot be intuitively obtained, and the calculation of production capacity is also difficult to calculate explicitly. This step simplifies the problem of mutual influence between production links. Through the weighted directed graph, the critical path of assembly can be clearly obtained, and the mutual influence of assembly units can be quantitatively sorted. The algorithm's thinking direction is from complex to simple, while the algorithm design is from simple to complex, which can perform calculations more quickly and significantly improve the calculation accuracy.

[0030] In a preferred embodiment of the present invention, the specific steps for solving the dynamic programming algorithm in step S33 are as follows:

[0031] S331. Given the initial values ​​of all assembly paths AO, the earliest start time of the source point in the search order is dist[1] = 0, and other values ​​are set to -∞.

[0032] S332. Solve the earliest start time of assembly path AO one by one according to the search order and dynamic programming algorithm formula 1.

[0033] By setting initial values ​​and iterative calculations, the earliest start time of all assembly paths (AO) can be determined, so as to determine the production capacity of the installation unit.

[0034] In a preferred embodiment of the present invention, the specific steps for calculating the latest start time of assembly path AO in step S3 are as follows:

[0035] S34. Starting from the last sink, generate the reverse topology sequence of the assembly path AO. Calculate the latest possible start time for each node based on the reverse topology sequence, and solve for the latest start time using dynamic programming formula 2:

[0036] last[u] = min{T – (last[v] + edge[v][u])}, the set of neighbors of v∈u.

[0037] Where last[u] represents the latest start time of the u-th assembly path AO, last[v] represents the latest start time of the v-th assembly path AO, and edge[v][u] represents the weight of the directed edge from v to u, i.e., the theoretical execution time t of the assembly path AO numbered v. v T is the maximum value of the earliest start time of all assembly paths AO obtained from the data.

[0038] By using reverse topology, the latest start time of each assembly path AO can be determined from the opposite calculation direction, so as to determine the production capacity of the installation unit.

[0039] In a preferred embodiment of the present invention, the specific steps for solving the dynamic programming algorithm in step S34 are as follows:

[0040] S341. Given the initial values ​​of all assembly paths AO, the latest start time of the sink in the reverse topology order last[1] = T, and other values ​​are set to +∞.

[0041] S342. Solve the latest start time of assembly path AO one by one according to the reverse topology order and dynamic programming algorithm formula 2.

[0042] By setting initial values ​​and iterative calculations, the earliest start time of all assembly paths (AO) can be determined, so as to determine the production capacity of the installation unit.

[0043] In a preferred embodiment of the present invention, determining the critical path AO in step S3 above specifically involves:

[0044] The start-up fluctuation value of assembly path AO is calculated based on the earliest and latest start-up times obtained from S3. The calculation formula is as follows:

[0045] Δ p =LT p -ET p

[0046] Where, represents the start-up fluctuation value of the i-th assembly path AO, represents the latest start-up time of the i-th assembly path AO, and represents the earliest start-up time of the p-th assembly path AO.

[0047] If Δ p =0, then the assembly path AO is the critical path AO, i.e., C j ={r|If Δ p =0, then r∈C j}

[0048] By using floating calculations, the earliest start time and the latest start time can be correlated, avoiding situations where the two calculations are not equal. The time of all critical path AOs is included and considered, and the calculation results match the actual situation and are consistent with reality.

[0049] In a preferred embodiment of the present invention, the actual installation execution time T is obtained by correcting the result in step S4 above. AOp for:

[0050]

[0051] Among them, T m Material waiting time; T res For employee rest time; T q For quality loss time; T t Preparation time for tooling and equipment adjustment; T tec Adjustment time for process changes; η mn Let λ be the operational difficulty coefficient of the p-th assembly path AO. r Let r be the capability coefficient or labor productivity of the personnel or team performing a certain assembly task, and r be the set of critical paths (AO).

[0052] η mn The calculations include: establishing the task assembly difficulty level matrix A for the assembly path AO. M×N =[η mn ], where M∈{1,2,3,4,5,6} represents different assembly postures of assembly path AO, and N∈{1,2,3,4} represents the openness level of the compartment, then η mn =η m *η n , where η m η represents the labor productivity corresponding to different assembly postures. n This indicates the labor productivity corresponding to different cabin openness levels.

[0053] λ r The calculation formula is:

[0054]

[0055] Among them, t s The assembly time for each operator / team is given by R, where R represents the total number of testers / team members, and t represents the assembly time for each operator / team. r This refers to the assembly time for the r-th person / team whose capability coefficient will be calculated.

[0056] Based on the key factors involved in each final assembly and installation unit, the production capacity is calculated by considering factors such as the work tasks of aircraft final assembly, employee capabilities, and quality losses. This comprehensive approach is more consistent with the actual situation, allowing for the correction of theoretical calculations and actual results. The calculation results are more practical and can be applied to real-world situations, resulting in a high level of practical effectiveness.

[0057] In a preferred embodiment of the present invention, the actual test execution time T is obtained by correcting the method in step S5 above. AOt for:

[0058] T AOt =R mp -1 *ρ -1 *T jq +T m +T res +T q +T t +T tec

[0059] Among them, T m Material waiting time; T res For employee rest time; T q For quality loss time; T t Preparation time for tooling and equipment adjustment; T tec Adjusting the time for process changes, R mp ρ represents the reliability of the human-machine system, and ρ represents the reliability of the testing technology.

[0060] R mp The calculation formula is:

[0061] R mp =R m *R p

[0062] Among them, R m For equipment reliability, R m =e -λt t is the fault handling time, and λ is the reciprocal of the average fault occurrence time; R p Employee reliability is defined as the number of times the equipment was operated accurately divided into the total number of times the equipment was operated.

[0063] Based on the key factors involved in each final assembly and installation unit, the production capacity is calculated by considering factors such as the work tasks of aircraft final assembly, employee capabilities, and quality losses. This comprehensive approach is more consistent with the actual situation, allowing for the correction of theoretical calculations and actual results. The calculation results are more practical and can be applied to real-world situations, resulting in a high level of practical effectiveness.

[0064] In a preferred embodiment of the present invention, in step S6 above, the actual transient production and delivery cycle C of the final aircraft assembly is... tm for:

[0065]

[0066] Among them, T m Material waiting time; T res For employee rest time; T q For quality loss time; T t Preparation time for tooling and equipment adjustment; T tec Adjustment time for process changes; η mn Let λ be the operational difficulty coefficient of the p-th assembly path AO. r Let R be the capability coefficient or labor productivity of the personnel or team performing a certain assembly task, and r be the set of critical paths (AO). mp ρ represents the reliability of the human-machine system, and ρ represents the reliability of the testing technology.

[0067] By considering factors such as personnel uncertainties, task requirements, process cycle disturbances, and factory calendar time on the aircraft final assembly line from a holistic perspective, the complex aircraft final assembly line is broken down into assembly units. This fully considers various constraints and conditions in the actual final assembly engineering, quantitatively describes these conditions and factors, and performs corrective calculations, which significantly improves calculation accuracy and reduces errors.

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0069] This method constructs an aircraft final assembly system model, calculates the number of assembly stations, determines the critical path of installation units, calculates the production capacity of installation units, calculates the production capacity of testing units, and integrates these calculations to determine the transient production capacity of aircraft final assembly. First, it treats the aircraft final assembly process as a complex system for comprehensive analysis, breaking it down from top to bottom to identify the key factors actually restricting aircraft final assembly production capacity. Then, it performs calculations from bottom to top, calculating the number of assembly unit stations based on aircraft final assembly capacity requirements and pulsating cycle time. Next, considering the key factors involved in each assembly station, it calculates the production capacity of each station by taking into account factors such as the annual workload, employee capabilities, and quality losses. Finally, from the perspective of the entire aircraft final assembly system, it considers the uncertainties of personnel on the pulsating production line and makes adjustments, transforming the theoretical execution time of tasks into actual execution time, and calculating the transient production capacity of the pulsating production line. Attached Figure Description

[0070] Figure 1 This is a flowchart illustrating the steps of the transient production capacity calculation method for aircraft final assembly systems based on a pulsed production mode, as described in this invention.

[0071] Figure 2 This is a model of the aircraft final assembly system in an embodiment of the present invention;

[0072] Figure 3 This is a production capacity hierarchy model based on the aircraft final assembly system model in this embodiment of the invention;

[0073] Figure 4 This is a weighted directed graph based on priority assembly relationships in an embodiment of the present invention;

[0074] Figure 5 This is a comparison chart of transient production capacity calculations for aircraft final assembly systems in embodiments of the present invention;

[0075] Figure 6 This is a comparison chart showing the accuracy of the calculation of transient production capacity of the aircraft final assembly system in this embodiment of the invention. Detailed Implementation

[0076] The present invention will be further described in detail below with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0077] Example 1

[0078] Please refer to Figure 1 This embodiment provides a method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode. In this embodiment, the aircraft final assembly is divided into 4 working surfaces (i=4) based on the tooling, indicating that the aircraft final assembly is divided into 4 working surfaces: upper left, upper right, lower left, and lower right. The specific calculation method includes the following steps:

[0079] S1. Construct an aircraft final assembly system model. In the intelligent aircraft final assembly model, the five core elements of the final assembly system—"people, machines, materials, methods, and environment"—need to be identified by computers and transformed into data for full-scale, full-element connection and real-time feedback via the Internet of Things and the Internet. This requires data to connect and interact in both the information space and physical space, necessitating that we model the aircraft final assembly process as a complex system and digitally represent it to achieve a digital twin. Please refer to... Figure 2 The aircraft final assembly system is described as the final assembly system module DT. fas Personnel Module DT person Equipment Module DT equipment Product Module DT product Process Method Module DT method and Environment Module DT equipmentThe set of units, based on the aircraft's final assembly work surface i and final assembly station j, divides the aircraft final assembly into several installation units and testing units. According to actual production conditions, each installation unit has N... a There are N assembly unit stations, and the test unit has N t There are 1 test unit station, each installation unit station has i assembly units, and each test unit station has 1 test unit. Each assembly unit and test unit includes the corresponding required modules.

[0080] S2, please refer to Figure 3 Production capacity is calculated using a top-down and bottom-up approach. Based on the aircraft final assembly system model, the production capacity model is divided into three hierarchical frameworks: resource capacity, assembly unit capacity, and production line capacity. Within this hierarchical framework, the production capacity of resources and similar resource groups is calculated first. Then, the production capacity of assembly units is calculated based on assembly tasks and resource allocation. Finally, the production capacity of production lines is calculated based on the aircraft final assembly system. Based on the aircraft final assembly system, a transient capacity calculation model is constructed. Within a defined measurement period, this model provides a comprehensive measure of the time, speed, and quality of aircraft final assembly, forming an indicator that can effectively assess the time-dimensional energy efficiency of the aircraft final assembly system.

[0081] First, assembly unit calculations are performed based on the aircraft final assembly capacity requirements and the pulse cycle time. In the construction of a pulse production line for a certain type of aircraft in this embodiment, the assembly unit capacity is broken down into specialized assembly paths such as wiring harness installation, conduit installation, large component assembly, engine installation, flight control testing, and avionics and weapon testing, according to a professional approach. Aircraft final assembly is then carried out according to the process flow requirements.

[0082] Based on the 3-5 year aircraft final assembly plan quantity targets and constraints, the annual task volume is determined, and the production takt time is set. The production takt time is set based on historical output data and the company's development needs, combined with effective working time. Based on the production takt time and production process cycle, the total number of assembly stations N for aircraft final assembly is calculated. c Number of assembly unit stations N a and the number of test unit stations N t N a +N t =N c Then, the assembly unit and testing unit are numbered according to their positions. Assembly unit A is numbered according to the order of working face i and position j. ij The test unit T is located at the j-th installation unit station on the production line of the i-th working face. j The j-th test unit station is located on the production line of the test unit. The test unit is specialized according to the process flow.

[0083] The total number of stations N in aircraft final assembly c for:

[0084] N c =T tc *C c =T tc *A c / T fc

[0085] Among them, T tc The production process design cycle for aircraft final assembly is in days, C c To maintain the production cycle, C c =A c / T fc A c For the annual task volume, T fc The factory calendar time for final aircraft assembly is in days;

[0086] In this embodiment, aircraft annual production plan task A c For 120 aircraft, the process design cycle T for a certain type of aircraft tc If the production time is 1 month (30 days), then the monthly production capacity of the final assembly line is 120 / 12*1 = 10 aircraft / month, and its aircraft final assembly cycle time C c =Aircraft final assembly process design cycle T tc The monthly production capacity of the final assembly line = 30 / 10 = 3 days. Based on the final assembly cycle time and the aircraft final assembly process flow, the number of final assembly units N can be set. c =Aircraft final assembly process design cycle T tc Aircraft assembly rhythm C c =30 / 3=10.

[0087] Similarly, the number of assembly unit stations N a for;

[0088] N a =T ta *A a / T fa

[0089] Among them, T ta The production process design cycle for the installation unit is in days, A. a T represents the number of installation units required to cover the annual workload. fa The factory calendar time for the installation unit, in days;

[0090] Similarly, the number of test unit stations N t for:

[0091] N t =T tt *A t / T ft

[0092] Among them, T tt The production process design cycle for the test unit is in days, A t T represents the number of test unit tasks corresponding to the annual task volume. ft The factory calendar time for the test unit is in days.

[0093] Production cycle time reflects capacity demand. The number of workstations is determined by annual task volume, process design cycle, and production cycle time. The required installation unit and testing unit workstations can be determined based on the pulsed production demand and can be adjusted according to the actual situation.

[0094] S3, according to A ij Based on the location of each assembly unit and its assembly relationships on the production line, an assembly path (AO) set for the installation task is established. Then, based on the assembly relationships and theoretical execution time, a weighted directed graph of complex multi-assembly tasks is constructed using graph theory. Please refer to [reference needed]. Figure 4 According to the topological order of the weighted directed graph, each assembly path AO is numbered. The earliest start time and the latest start time that will not affect the task execution cycle are calculated one by one after all the preceding AOs of each assembly path AO are completed. All assembly path AOs with the same earliest start time and latest start time are found and identified as critical path AOs. The critical path AO is the sequence of production schedule activities AOs that determines the delivery cycle of the whole machine. The total duration of this sequence is the shortest completion cycle of the entire assembly activity.

[0095] The above steps require calculating the earliest start time and the latest start time, which will be explained below.

[0096] The specific steps for calculating the earliest start time of assembly path AO are as follows:

[0097] S31, according to section A ij Based on the location of each assembly unit and the assembly relationship on the production line, establish a set of assembly paths AO for the installation task. Let the label set of the installation task be N = {1, 2, ..., P}. The priority relationship of the assembly path AO is represented by a directed graph G = {V, E}, where V is the vertex set, representing all assembly paths AO, and E is the set of directed edges, representing the priority assembly relationship between assembly paths AO. The weight of each edge is set to represent the theoretical execution time of the assembly path AO.

[0098] S32. In the weighted directed graph, find all nodes with an in-degree of 0. After the search is complete, record the results in the topological sequence index set. If multiple nodes have an in-degree of 0, record the node with the smaller index first. Delete the nodes already recorded in the topological sequence index set and their adjacent edges. Update the weighted directed graph and repeat this step until all points are recorded in the topological sequence index set. Figure 4The arrowhead of a directed edge represents the immediate preceding AO, and the tail of the arrow represents the immediate following AO. The directed edge e ij The weight is t i , representing the theoretical execution time of the i-th AO;

[0099] S33. Based on the order obtained from the topology sequence number set, renumber each assembly path AO, such as... Figure 4 The numbers in the inner circle are used as the search order for the dynamic programming algorithm. The earliest start time is determined by the dynamic programming algorithm. Formula 1 of the dynamic programming algorithm is as follows:

[0100] first[u] = max{first[v] + edge[v][u]}, the set of neighbors of v∈u.

[0101] Where first[u] represents the earliest start time of the u-th assembly path AO, and edge[v][u] represents the weight of the directed edge from v to u, i.e., the theoretical execution time t of the assembly path AO numbered v. v This formula transforms the problem into finding the earliest start time of the assembly path AO labeled v, making it a smaller subproblem. The earliest execution time problem of all assembly path AOs can be transformed and reduced, ultimately resulting in the simplest problem.

[0102] The specific steps for solving the problem using the dynamic programming algorithm are as follows:

[0103] S331. Given the initial values ​​of all assembly paths AO, the earliest start time of the source point in the search order is dist[1] = 0, and other values ​​are set to -∞.

[0104] S332. Solve the earliest start time of assembly path AO one by one according to the search order and dynamic programming algorithm formula 1.

[0105] By setting initial values ​​and iterative calculations, the earliest start time of all assembly paths (AO) can be determined, so as to determine the production capacity of the installation unit.

[0106] The specific steps for calculating the latest start time of assembly path AO are as follows:

[0107] S34. Starting from the last sink, generate the reverse topology sequence of the assembly path AO. Calculate the latest possible start time for each node based on the reverse topology sequence, and solve for the latest start time using dynamic programming formula 2:

[0108] last[u] = min{T – (last[v] + edge[v][u])}, the set of neighbors of v∈u.

[0109] Where last[u] represents the latest start time of the u-th assembly path AO, last[v] represents the latest start time of the v-th assembly path AO, and edge[v][u] represents the weight of the directed edge from v to u, i.e., the theoretical execution time t of the assembly path AO numbered v. v T is the maximum value of the earliest start time of all assembly paths AO obtained from the data.

[0110] By using reverse topology, the latest start time of each assembly path AO can be determined from the opposite calculation direction, so as to determine the production capacity of the installation unit.

[0111] The specific steps of solving the problem using the dynamic programming algorithm in step S34 are as follows:

[0112] S341. Given the initial values ​​of all assembly paths AO, the latest start time of the sink in the reverse topology order last[1] = T, and other values ​​are set to +∞.

[0113] S342. Solve the latest start time of assembly path AO one by one according to the reverse topology order and dynamic programming algorithm formula 2.

[0114] By setting initial values ​​and iterative calculations, the earliest start time of all assembly paths (AO) can be determined, so as to determine the production capacity of the installation unit.

[0115] When determining the critical path (AO), it is necessary to compare the earliest start time and the latest start time mentioned above. The specific method is as follows:

[0116] Based on the earliest and latest start times of AO obtained in this step, the AO start-up fluctuation value is calculated using the following formula:

[0117] Δ p =LT p -ET p

[0118] Where, represents the start-up fluctuation value of the i-th assembly path AO, represents the latest start-up time of the i-th assembly path AO, and represents the earliest start-up time of the p-th assembly path AO.

[0119] If Δ p =0, then the assembly path AO is the critical path AO, i.e., C j ={r|If Δ p =0, then r∈C j}

[0120] By using floating calculations, the earliest start time and the latest start time can be correlated, avoiding situations where the two calculations are not equal. The time of all critical path AOs is included and considered, and the calculation results match the actual situation and are consistent with reality.

[0121] By transforming the problem into a weighted directed graph, the complex production process can be simplified. The relationships between assembly units and tasks are intricate. Since each assembly unit may affect the subsequent production process, the production processing time on each assembly path cannot be intuitively obtained, and the calculation of production capacity is also difficult to calculate explicitly. This step simplifies the problem of mutual influence between production links. Through the weighted directed graph, the critical path of assembly can be clearly obtained, and the mutual influence of assembly units can be quantitatively sorted. The algorithm's thinking direction is from complex to simple, while the algorithm design is from simple to complex, which can perform calculations more quickly and significantly improve the calculation accuracy.

[0122] S4. Based on the key factors involved in each assembly unit of the aircraft final assembly, consider factors such as the work tasks (task objectives), dynamic assessment of employee capabilities (employee capabilities), and final assembly quality control (quality losses) to solve for the production capacity T. ij It equals the linear sum of the actual assembly task times of the critical path AO, calculated as follows:

[0123]

[0124] Where T AOr C represents the actual assembly time of the critical path AO. j Let r be the set of critical paths AO for the assembly unit, and let r be the set C. j In the middle element. At this point, according to step S1, a total of N are set. a Let there be an installation unit, and let any assembly unit j (j = 1, 2, ..., N) be an assembly unit. a The assembly path AO contains p installation tasks (assembly paths AO), and the p-th assembly path AO mainly contains k (k = 1, 2, ..., N). jp ( ) processes.

[0125] The theoretical installation execution time h of the critical path AO is determined based on the installation tasks of the installation unit production line. jpk Let represent the operation time of the k-th process of the p-th assembly path AO at the j-th station; sum up to obtain the theoretical assembly time H of the critical path AO at each station. jp :

[0126]

[0127] The theoretical assembly time H is calculated based on the actual production process time. jpMake corrections to obtain the actual installation execution time T. AOp Substituting p = r, where r is the set of critical paths AO, and then the actual installation execution time T... AOr Linear summation to calculate the actual production cycle T of the assembly unit. ij .

[0128] During the correction process, in aircraft final assembly units primarily operated by personnel, the reliability of installation is mainly determined by key factors such as the difficulty of the task and the skill level of the operators, ultimately reflected in the operation time of the assembly path AO. The correction yields the actual installation execution time T. AOp for:

[0129]

[0130] Among them, T m Material waiting time; T res For employee rest time; T q For quality loss time; T t Preparation time for tooling and equipment adjustment; T tec Adjustment time for process changes; η mn Let η be the operation difficulty coefficient of the p-th assembly path AO, and let η be the assembly task. m and η n The two influencing factors are divided into categories, and the assembly difficulty coefficient λ for each assembly path (AO) is determined after classification. r r is the capability coefficient or labor productivity of the personnel or team performing a certain assembly task, used to evaluate the skill / operation level of the personnel / team, and r is the set of critical path AO;

[0131] η mn The calculations include: establishing the task assembly difficulty level matrix A for the assembly path AO. M×N =[η mn ], where M∈{1,2,3,4,5,6} represents different assembly postures of assembly path AO, and N∈{1,2,3,4} represents the openness level of the compartment, then η mn =η m *η n , where η m η represents the labor productivity corresponding to different assembly postures. n This indicates the labor productivity corresponding to different cabin openness levels.

[0132] Labor productivity η corresponding to different working / assembly postures m As shown in the table below:

[0133]

[0134]

[0135] The labor productivity η corresponding to the degree of openness of the cabin n As shown in the table below:

[0136] Openness level Labor productivity Final Assembly Test Case Remark Zone I: The narrowest operating space <![CDATA[b1]]> 25％ Zone II: Limited operating space <![CDATA[b2]]> 60％ Zone III: Operating space is slightly narrow <![CDATA[b3]]> 90％ Zone IV: No spatial constraints <![CDATA[b4]]> 100％ Such as ground-level accessories

[0137] The data from the aircraft final assembly test cases in the two tables above were set based on test results, historical data verification, and expert opinions. For example, if the assembly posture of a certain assembly path AO is "semi-squatting posture, operating directly in front of the assembly object", and the openness level is "the operating space is relatively narrow", then the difficulty coefficient of this assembly path AO is 95% * 60% = 0.57, that is, the overall output rate is 57%.

[0138] Installation execution time T Aop In the calculation parameters, λ r The calculation formula is:

[0139]

[0140] Among them, t s The assembly time for each operator / team is given by R, where R represents the total number of testers / team members, and t represents the assembly time for each operator / team. r This refers to the assembly time for the r-th person / team whose capability coefficient will be calculated.

[0141] In this embodiment, three people / teams perform the same standard assembly task. Person A (person / team) needs 10 hours, Person B needs 8 hours, and Person C needs 6 hours. Therefore, Person A's ability coefficient = 10*3 / (10+8+6) = 1.25, Person B's ability coefficient = 8*3 / 10+8+6 = 1, and Person C's ability coefficient = 6*3 / (10+8+6) = 0.75.

[0142] Based on the key factors involved in each final assembly and installation unit, the production capacity is calculated by considering factors such as the work tasks of aircraft final assembly, employee capabilities, and quality losses. This comprehensive approach is more consistent with the actual situation, allowing for the correction of theoretical calculations and actual results. The calculation results are more practical and can be applied to real-world situations, resulting in a high level of practical effectiveness.

[0143] S5. Based on the key factors involved in each test unit, consider factors such as the aircraft final assembly test tasks (task objectives), human-machine reliability, and technical reliability to solve for the production capacity, T of the test unit. j It equals the linear sum of the actual test times for the critical path:

[0144]

[0145] Where T AOtThis indicates the actual test duration after AO correction for each test path in the test unit. At this point, N is set according to step one. t Let there be *j* test units, each containing *Q* test tasks (test paths *AO*), and the theoretical operation time of each test task be *T*. jp .

[0146] The theoretical test execution time T of test path AO is determined based on the test tasks of the test unit production line. jq The theoretical test execution time T is determined based on the actual test procedure time. jq Make corrections to obtain the actual test execution time T. AOt Then, the actual test execution time T AOt Linear summation to calculate the actual production cycle T of the test unit. j .

[0147] During the correction, the reliability of the aircraft assembly test unit, which is mainly guaranteed by equipment, is determined primarily by the reliability of personnel, test equipment, and test processes. The correction yields the actual test execution time T. AOt for:

[0148] T AOt =R mp -1 *ρ -1 *T jq +T m +T res +T q +T t +T tec

[0149] Among them, T m Material waiting time; T res For employee rest time; T q For quality loss time; T t Preparation time for tooling and equipment adjustment; T tec Adjusting the time for process changes, R mp ρ represents the reliability of the human-machine system, and ρ represents the reliability of the testing technology.

[0150] During aircraft final assembly testing, multiple people typically operate a single piece of equipment. Equipment reliability is one dimension, while personnel operational reliability is another. Therefore, human-machine system reliability (Rreliability) is required. mp To express it, R mp The calculation formula is:

[0151] R mp =R m *R p

[0152] Among them, Rm For equipment reliability, R m =e -λt Let t be the fault handling time, and λ be the reciprocal of the average fault duration. For example, if a flight control device is used for an average of 1 hour per day and experiences an average of 0.5 faults per year, after 4 years of use, the mean time between failures (MTBF) of the device is: MTBF = total working time / total number of faults = 4 * 365 * 24 / 0.5 = 70080 hours. The reliability of the flight control device is R = e^(-1 / 70080 * 1 * 4 * 365 * 24) = 0.61. p Employee reliability is calculated as the number of times the equipment was operated accurately divided by the total number of times the equipment was operated. For example, if an employee / team operates the flight control equipment 100 times and makes 2 mistakes, then the employee / team's reliability is 98 / 100 = 0.98.

[0153] The reliability ρ of the testing technology is calculated as follows: ρ = theoretical design time of the benchmark production line process / theoretical design time of the production line process. For example, if the theoretical test design time of a certain aircraft production line is 2 days / aircraft, while the theoretical test design time of a certain type of aircraft production line of a benchmark enterprise is 1 day / aircraft, then the technical reliability = 1 / 2 = 0.5. If, through production line optimization or technological progress, the theoretical test design time of a certain aircraft production line is 1 day / aircraft, then the technical reliability is 1 / 1 = 1.

[0154] Based on the key factors involved in each final assembly and installation unit, the production capacity is calculated by considering factors such as the work tasks of aircraft final assembly, employee capabilities, and quality losses. This comprehensive approach is more consistent with the actual situation, allowing for the correction of theoretical calculations and actual results. The calculation results are more practical and can be applied to real-world situations, resulting in a high level of practical effectiveness.

[0155] S6. By summing the maximum value of the total actual production cycle of the assembly units on each production line of the installation unit with the total actual testing cycle of the testing unit, the transient production and delivery cycle C of the actual aircraft final assembly can be obtained. tm .

[0156] Exploring and constructing a transient capacity calculation model for aircraft final assembly systems involves comprehensively measuring the time, speed, and quality of aircraft final assembly within a defined measurement period, thus forming an indicator that can more timely assess the time-dimensional energy efficiency of aircraft final assembly systems.

[0157] The formula for calculating the production capacity of an aircraft final assembly line is as follows:

[0158]

[0159] In the formula, C tm N represents the aircraft final assembly production capacity, i.e., the actual delivery cycle of aircraft final assembly; a N represents the number of spaces occupied by the assembly unit.c N represents the number of stations in the final assembly of the aircraft. t To test the number of unit stations, N a +N t =N c ;T ij For the Ath ij Installation time per assembly unit; T j Let be the test time for the j-th assembly unit;

[0160] From the perspective of the overall aircraft final assembly system, considering factors such as uncertainties in personnel on the final assembly line (personnel adjustments), customer demands and process changes (state disturbances), and factory calendar time (legal requirements), the production capacity of personnel on the aircraft final assembly line is calculated. Based on the disassembled parameters obtained in steps S1-S5, the T value determined in step S4 is substituted into the parameters. ij and T determined in step S5 j The actual transient production and delivery cycle C of aircraft final assembly tm for:

[0161]

[0162] Where i is the process separation surface (i = 1, 2, 3, 4), T m Material waiting time; T res For employee rest time; T q For quality loss time; T t Preparation time for tooling and equipment adjustment; T tec Adjustment time for process changes; η mn Let λ be the operational difficulty coefficient of the p-th assembly path AO. r Let R be the capability coefficient or labor productivity of the personnel or team performing a certain assembly task, and r be the set of critical paths (AO). mp ρ represents the reliability of the human-machine system, and ρ represents the reliability of the testing technology.

[0163] By describing the aircraft final assembly system, this approach more closely reflects actual production conditions, considering all factors involved in each stage of aircraft final assembly production. Dividing the production process into installation and testing units allows for adaptation to real-world situations, simplifying the problem into calculations for installation and testing units. By specifying the number of workstations and assembly units, the problem is further refined into assembly relationships and task execution times along assembly paths. This transforms the actual production problem into a mathematical calculation model, resulting in calculations closer to reality. By identifying the critical path (AO), the production cycle problem is transformed into the time consumed by the critical path AO, allowing for the identification of key factors affecting production capacity. Calculations are then performed on the installation and testing units, and considering the influencing factors in actual production, the production capacity of the installation and testing units is adjusted. Finally, the transient production capacity of the aircraft final assembly is obtained through comprehensive and thorough consideration of actual production, quantifying relevant factors into influencing parameters. This enables real-time calculation of the aircraft final assembly system's production capacity, accurately solving for the transient production capacity of the aircraft final assembly system and significantly improving the accuracy of the calculation results.

[0164] Please refer to Figure 5 and Figure 6 The calculation method in this embodiment is compared with the calculation method for the production capacity of aircraft assembly line personnel proposed by Xin Bo et al. of Northwestern Polytechnical University (CN104123672A) for aircraft component assembly production lines. This calculation method considers factors such as personnel uncertainty, task requirements, process cycle disturbances, and factory calendar time in the pulsed production line of the aircraft final assembly system from a global perspective. It decomposes the complex pulsed production line of aircraft final assembly into assembly units, fully considers various constraints and conditions in the actual final assembly engineering, and provides quantitative descriptions and corrective calculations for these conditions and factors. This calculation method is triggered from the actual engineering of aircraft final assembly, takes the smallest assembly unit at the AO level of the assembly path as the analysis object, and considers multiple interference factors to evaluate the production capacity of the entire final assembly system, making it closer to the actual engineering. At the same time, compared with the static simplified algorithm, this method is based on dynamic perception and real-time data capture in the context of intelligence, which can realize the calculation of transient production capacity of the production line. Practical tests were conducted using the algorithm of this invention. Calculations showed that the proposed algorithm had a small deviation from the actual delivery cycle, with an average error of 11.1 days, while the WITNESS simulation results showed an average error of 57.2 days. The comparison demonstrates that the calculation method of this invention significantly improves calculation accuracy and reduces error.

[0165] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode, characterized in that, Includes the following steps: S1. Construct an aircraft final assembly system model, describing the aircraft final assembly system as a final assembly system module DT. fas Personnel Module DT person Equipment Module DT equipment Product Module DT product Process Method Module DT method and Environment Module DT equipment The set of units, based on the aircraft's final assembly work surface i and final assembly station j, divides the aircraft final assembly into several installation units and testing units. According to actual production conditions, each installation unit has N... a There are N assembly unit stations, and the test unit has N t Each test unit station has i assembly units and one test unit. Each assembly unit and test unit includes the corresponding required modules. S2. Calculate the total number of assembly stations N for aircraft final assembly based on the annual workload, production cycle, and production process cycle. c Number of assembly unit stations N a and the number of test unit stations N t N a +N t =N c Then, the assembly units and testing units are numbered according to their positions. Assembly unit A ij The test unit T is located at the j-th installation unit station on the production line of the i-th working face. j The j-th test unit station is located on the production line of the test unit. S3, according to A ij Based on the location of each assembly unit and the assembly relationship on the production line, an assembly path (AO) set for the installation task is established. According to the assembly relationship and theoretical execution time, a weighted directed graph of complex multi-assembly tasks based on graph theory is established. Each assembly path (AO) is numbered according to the topological order of the weighted directed graph. The earliest start time and the latest start time that do not affect the task execution cycle are calculated one by one after all the preceding AOs of each assembly path (AO) are completed. All assembly path (AO) with the earliest start time and the latest start time equal to the latest start time are found and identified as critical path (AO). S4. Determine the theoretical installation execution time h of the critical path AO based on the installation tasks of the installation unit production line. jpk The theoretical assembly time H of the critical path AO at each station is obtained by summarizing. jp The theoretical assembly time H is adjusted based on the actual production process time. jp Make corrections to obtain the actual installation execution time T. AOp Substituting p = r, where r is the set of critical paths AO, and then the actual installation execution time T... AOr Linear summation to calculate the actual production cycle T of the assembly unit. ij ; S5. Determine the theoretical test execution time T of test path AO based on the test tasks of the test unit production line. jq The theoretical test execution time T is determined based on the actual test procedure time consumption. jq Make corrections to obtain the actual test execution time T. AOt Then, the actual test execution time T AOt Linear summation to calculate the actual production cycle T of the test unit. j ; S6. By summing the maximum value of the total actual production cycle of the assembly units on each production line of the installation unit with the total actual testing cycle of the testing unit, the transient production and delivery cycle C of the actual aircraft final assembly can be obtained. tm .

2. The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode according to claim 1, characterized in that, In step S2: N c =T tc *A c / T fc Among them, T tc The production process design cycle for aircraft final assembly is in days, A c For the annual task volume, T fc The factory calendar time for final aircraft assembly is in days; N a =T ta *A a / T fa Among them, T ta The production process design cycle for the installation unit is in days, A. a T represents the number of installation units required to cover the annual workload. fa The factory calendar time for the installation unit, in days; N t =T tt *A t / T ft Among them, T tt The production process design cycle for the test unit is in days, A t T represents the number of test unit tasks corresponding to the annual task volume. ft The factory calendar time for the test unit is in days.

3. The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode according to claim 1, characterized in that, The specific steps for calculating the earliest start time of assembly path AO in step S3 are as follows: S31, according to section A ij Based on the location of each assembly unit and the assembly relationship on the production line, establish a set of assembly paths AO for the installation task. Let the label set of the installation task be N = {1, 2, ..., P}. The priority relationship of the assembly path AO is represented by a directed graph G = {V, E}, where V is the vertex set, representing all assembly paths AO, and E is the set of directed edges, representing the priority assembly relationship between assembly paths AO. The weight of each edge is set to represent the theoretical execution time of the assembly path AO. S32. Find all nodes with an in-degree of 0 in the weighted directed graph. After the search is completed, record the results in the topology sequence number set. If there are multiple nodes with an in-degree of 0, record the node with the smaller number first. Delete the nodes and their adjacent edges that have been recorded in the topology sequence number set. After updating the weighted directed graph, repeat the step until all points are recorded in the topology sequence number set. S33. Based on the order obtained from the topological sequence number set, renumber each assembly path AO, and use this number as the search order for the dynamic programming algorithm. Solve for the earliest start time using the dynamic programming algorithm. The dynamic programming algorithm formula 1 is: first[u] = max{first[v] + edge[v][u]}, the set of neighbors of v∈u. Where first[u] represents the earliest start time of the u-th assembly path AO, and edge[v][u] represents the weight of the directed edge from v to u, i.e., the theoretical execution time t of the assembly path AO numbered v. v .

4. The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode according to claim 3, characterized in that, The specific steps for solving the dynamic programming algorithm in step S33 are as follows: S331. Given the initial values ​​of all assembly paths AO, the earliest start time of the source point in the search order is dist[1] = 0, and other values ​​are set to -∞. S332. Solve the earliest start time of assembly path AO one by one according to the search order and dynamic programming algorithm formula 1.

5. The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode according to claim 3, characterized in that, The specific steps for calculating the latest start time of assembly path AO in step S3 are as follows: S34. Starting from the last sink, generate the reverse topology sequence of the assembly path AO. Calculate the latest possible start time for each node based on the reverse topology sequence, and solve for the latest start time using dynamic programming formula 2: last[u] = min{T – (last[v] + edge[v][u])}, the set of neighbors of v∈u. Where last[u] represents the latest start time of the u-th assembly path AO, last[v] represents the latest start time of the v-th assembly path AO, and edge[v][u] represents the weight of the directed edge from v to u, i.e., the theoretical execution time t of the assembly path AO numbered v. v T is the maximum value of the earliest start time of all assembly paths AO obtained from the data.

6. The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode according to claim 5, characterized in that, The specific steps for solving the dynamic programming algorithm in step S34 are as follows: S341. Given the initial values ​​of all assembly paths AO, the latest start time of the sink in the reverse topology order last[1] = T, and other values ​​are set to +∞. S342. Solve the latest start time of assembly path AO one by one according to the reverse topology order and dynamic programming algorithm formula 2.

7. The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode according to claim 1, characterized in that, The determination of the critical path AO in step S3 is specifically as follows: The start-up fluctuation value of assembly path AO is calculated based on the earliest and latest start-up times obtained from S3. The calculation formula is as follows: Δ p =LT p -AND p Where, represents the start-up fluctuation value of the i-th assembly path AO, represents the latest start-up time of the i-th assembly path AO, and represents the earliest start-up time of the p-th assembly path AO. If Δ p =0, then the assembly path AO is the critical path AO, i.e., C j ={r|If Δ p =0, then r∈C j } 8. The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode according to claim 1, characterized in that, In step S4, the actual installation execution time T is corrected and obtained. AOp for: Among them, T m Material waiting time; T res For employee rest time; T q For quality loss time; T t Preparation time for tooling and equipment adjustment; T tec Adjustment time for process changes; η mn Let λ be the operational difficulty coefficient of the p-th assembly path AO. r Let r be the capability coefficient or labor productivity of the personnel or team performing a certain assembly task, and r be the set of critical paths (AO). η mn The calculations include: establishing the task assembly difficulty level matrix A for the assembly path AO. M×N =[η mn ], where M∈{1,2,3,4,5,6} represents different assembly postures of assembly path AO, and N∈{1,2,3,4} represents the openness level of the compartment, then η mn =η m *η n , where η m η represents the labor productivity corresponding to different assembly postures. n This indicates the labor productivity corresponding to different cabin openness levels. λ r The calculation formula is: Among them, t s The assembly time for each operator / team is given by R, where R represents the total number of testers / team members, and t represents the assembly time for each operator / team. r This refers to the assembly time for the r-th person / team whose capability coefficient will be calculated.

9. The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode according to claim 1, characterized in that, In step S5, the actual test execution time T is obtained by correction. AOt for: T AOt =R mp -1 *ρ -1 *T jq +T m +T res +T q +T t +T tec Among them, T m Material waiting time; T res For employee rest time; T q For quality loss time; T t Preparation time for tooling and equipment adjustment; T tec Adjusting the time for process changes, R mp ρ represents the reliability of the human-machine system, and ρ represents the reliability of the testing technology. R mp The calculation formula is: R mp =R m *R p Among them, R m For equipment reliability, R m =e -λt t is the fault handling time, and λ is the reciprocal of the average fault occurrence time; R p Employee reliability is defined as the number of times the equipment was operated accurately divided into the total number of times the equipment was operated.

10. The method for calculating the transient production capacity of an aircraft final assembly system based on a pulsed production mode according to claim 1, characterized in that, In step S6, the actual transient production and delivery cycle C of the final aircraft assembly tm for: Among them, T m Material waiting time; T res For employee rest time; T q For quality loss time; T t Preparation time for tooling and equipment adjustment; T tec Adjustment time for process changes; η mn Let λ be the operational difficulty coefficient of the p-th assembly path AO. r Let R be the capability coefficient or labor productivity of the personnel or team performing a certain assembly task, and r be the set of critical paths (AO). mp ρ represents the reliability of the human-machine system, and ρ represents the reliability of the testing technology.

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