Aviation composite material hot press molding productivity evaluation method considering interval grey number and working hours

Abstract

The invention discloses an aeronautical composite material hot press molding productivity evaluation method considering interval grey number working hours, which comprises the following steps: determining the interval grey number working hours of each workpiece through historical production data and an uncertain working hour generation algorithm; on the basis, the maximum completion time is obtained as an evaluation index by a mixed integer linear programming model and a heuristic method with the purpose of minimizing the maximum completion time of a production task, and a productivity evaluation result is generated by comparing the maximum completion time with the available time of a machine. On the premise that constraint conditions are met, according to the method, the production capacity evaluation method aiming at the working procedure is designed by comprehensively considering the production characteristics of the aviation composite material hot-press forming working procedure aiming at the uncertain working hours in the actual production process, so that the production capacity is reflected more accurately; the productivity evaluation result provided by the method can provide guidance for the design of an actual production plan and the configuration of production resources, the production delay is reduced, and the production efficiency is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of scheduling of hot pressing forming process of aviation composite materials, and in particular relates to a method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours. Background Art

[0002] Composite materials have become key materials in modern aircraft manufacturing due to their high specific strength, excellent thermal conductivity, high and low temperature resistance, corrosion resistance and heat insulation, and their usage has increased significantly. As the core process of aviation composite manufacturing, hot pressing molding has the typical characteristics of multi-variety, small batch and flexible manufacturing. Improving its production efficiency is the key path to alleviate the contradiction between supply and demand of aviation composite materials. However, the traditional capacity assessment method usually calculates by simply comparing the total processing time with the single-piece processing time, and fails to fully consider the characteristics of batch production in the hot pressing molding process. This method is prone to deviation in the evaluation results, which in turn affects the effective formulation of production plans and the rational allocation of production resources. At the same time, considering the uncertainty of the actual production system, the processing time required for the hot pressing molding process of aviation composite materials is often unable to be accurately determined before actual completion. How to effectively characterize this uncertain working time before capacity assessment has become an important technical problem that needs to be solved urgently. Therefore, a capacity assessment method for hot pressing molding of aviation composite materials considering interval gray number working time is invented to reduce the impact of uncertain working time on capacity assessment and improve the accuracy of capacity assessment results. The application of this method will provide important support for improving the overall production efficiency of aviation composite materials, and has broad engineering application prospects and practical significance. Summary of the invention

[0003] In view of the problems existing in the above-mentioned prior art, the present invention proposes a method for evaluating the capacity of hot pressing molding of aviation composite materials taking into account interval gray number working hours, so as to obtain an evaluation result with higher accuracy by comprehensively considering the batch production characteristics of the hot pressing molding process of aviation composite materials and the influence of uncertain processing time in actual production.

[0004] In order to achieve the above technical objectives, the present invention provides the following technical solutions: A method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours specifically comprises the following steps: S1. Conduct a detailed production mode analysis for the hot pressing molding process of aviation composite materials; the production mode analysis includes: identifying the definite working hours and the indefinite working hours, and determining the calculation method of the completion time; S2. Carry out data preparation for the production task of hot pressing of aviation composite materials; the data preparation work includes: clarifying the working hours and machine availability time of all workpieces; S3, constructing a mixed integer linear programming model with the goal of minimizing the maximum completion time, obtaining the maximum completion time for model evaluation, and judging whether the production task can be completed according to the model evaluation criteria; if an accurate result is obtained, directly output the evaluation result; if an accurate evaluation result cannot be obtained, proceed to step S4; S4. Design a heuristic method based on the production model, obtain the maximum completion time corresponding to the optimal production plan for heuristic evaluation, and obtain the final evaluation result based on the heuristic evaluation standard.

[0005] Furthermore, in step S1, the calculation method for determining the completion time includes a calculation method for determining the maximum completion time of the production task and a calculation method for determining the interval gray number completion time of each batch, which are respectively: Maximum completion time of production tasks The calculation formula is: ; in, Indicates the maximum completion time of a production task; Indicates the interval gray number completion time of each batch; Respectively represent the index and total number of batches; The calculation formula is: ; in, Indicates batch The preparation time, i.e. the time required to load and unload all workpieces in a batch, is characterized by interval gray number; Indicates batch The processing time, that is, the time required for a batch of workpieces to complete processing on a batch processing machine, is represented by a real number.

[0006] Furthermore, batch Preparation time The calculation formula is: ; in Indicates batch The number of artifacts included in the Representation of workpiece The preparation time is represented by interval grey number. batch Processing time The calculation formula is: ; in Indicates batch The number of artifacts included in the Representation of workpiece The processing time is represented by a real number.

[0007] Furthermore, the working hours and machine available time of all workpieces in step S2 specifically include: The workpiece interval gray number preparation time generation algorithm is used to determine the workpiece Preparation time ; The artifact is generated by the following mathematical formula Processing time: ; in, Indicates that artifacts are included The number of historical batches; Indicates that artifacts are included The historical batch processing time set of ; The machine available time is expressed by the following mathematical formula: ; in, Indicates the available time of the machine, and uses interval gray number to characterize the uncertain working time; → indicates the mapping relationship; represents the true value of the machine available time; Indicates the ideal availability time of the machine; Indicates the shortest available time of the machine; Indicates the utilization rate of the equipment.

[0008] Furthermore, the construction of a mixed integer linear programming model with the goal of minimizing the maximum completion time in step S3 specifically includes: The constructed model is represented using three-field notation as: ; Among them, 1 means that the machine environment is a single machine environment; Indicates that the objective function is to minimize the maximum completion time, which is also an indicator used for capacity evaluation; Indicates that the processing task characteristic is batch processing; is used as a constraint for the model; where Index the artifacts; Indicates the size of the workpiece; Indicates the total capacity of the machine, which is used to constrain the total size of workpieces accommodated in a batch; , They represent the preparation time and processing time of the workpiece respectively; The optimization objective of the model is set as: ; in, represents the objective function of the scheduling model, Indicates batch The interval gray number completion time, represents the index of a single batch, represents a batch set; the optimization goal is to minimize the maximum completion time of the production task .

[0009] Furthermore, the constraints of the constructed mixed integer linear programming model specifically include: (1) ; (2) ; (3) ; (4) ; (5) ; in, A collection of artifacts, indexed by Represents a single artifact, and the set satisfies the condition ; is a collection of batches, indexed by Represents a single batch; Constraints (1) Ensure that the workpiece Can only be assigned to one batch Processing in The indexes of workpieces and batches must meet the conditions ; is a decision variable, if the workpiece Assign to batch Then , otherwise 0; Constraint (2) ensures that the workpiece Assigned to batch When, batch Allow other conditions to be met Workpiece The workpieces are assigned to this batch. The index of the artifact satisfies ; This constraint is also used to enforce the linear relaxation of the model; Constraint (3) ensures that the size of the workpieces in each batch cannot exceed the total capacity of the batch processing machine; Constraint (4) ensures that the batch The interval gray number completion time is not less than the sum of the batch preparation time and the batch processing time; Constraint (5) ensures that the decision variables are within the feasible range.

[0010] Furthermore, the model evaluation in step S3 specifically includes: The model is evaluated by calculating the probability that the machine available time is greater than the maximum completion time. The model evaluation criteria are divided into three categories: P1. The model can find the optimal solution within the set time range. The maximum completion time at this time is : P1.1: If , it is considered that the production task cannot be completed within the specified production cycle; P1.2: If , it is considered that the possibility of completing the production task within the specified production cycle is low; P1.3: If , it is considered that the possibility of completing the production task within the specified production cycle is high; P1.4: If , it is considered that the production task can be completed within the specified production cycle; P2: The model fails to find the optimal solution within the set time range, but returns the upper and lower bounds. The upper and lower bounds are recorded as : P2.1: If , it is considered that the production task cannot be completed within the specified production cycle; P2.2: Otherwise, a heuristic evaluation is required in step S4 for further judgment; P3, if the model does not return any results within the set time range, a heuristic evaluation is performed; in, is the upper bound of the objective function value found, that is, the objective function value of the current optimal feasible solution, represented by interval gray number; is the theoretical lower bound of the optimal solution, that is, the relaxed solution obtained by relaxing the problem in the process of solving the model, and is represented in the form of real numbers; is the uncertain machine available time represented by interval grey number, are the shortest available time and the most ideal available time of the machine, respectively, which are real numbers.

[0011] Furthermore, the heuristic method in step S4 includes: a batching heuristic method based on workpiece processing time and a batching heuristic method based on workpiece size.

[0012] Furthermore, the heuristic evaluation in step S4 specifically includes: The maximum completion time of obtaining a better production plan through heuristic method is ,Combined with the model evaluation criteria, the heuristic evaluation criteria are divided into two categories: I1. Meet the model evaluation standard P2.2. At this time, the upper and lower bounds found within the set time range are , the maximum completion time of the optimal production plan obtained by heuristic method is : I1.1: If , it is considered that the production task cannot be completed within the specified production cycle; I1.2: If , it is considered that the possibility of completing the production task within the specified production cycle is low; I1.3: If , it is considered that the possibility of completing the production task within the specified production cycle is high; I1.4: If , it is considered that the production task can be completed within the specified production cycle; I2. Satisfying the model evaluation criteria P3, the maximum completion time of the optimal production plan obtained by the heuristic method is : I2.1: If , it is considered that the production task cannot be completed within the specified production cycle; I2.2: If , it is considered that the possibility of completing the production task within the specified production cycle is low; I2.3: If , it is considered that the possibility of completing the production task within the specified production cycle is high; I2.4: If , it is considered that the production task can be completed within the specified production cycle.

[0013] Based on the above technical solution, the present invention has at least the following beneficial effects: 1. For the hot pressing molding process of aviation composite materials, the method proposed in the present invention comprehensively considers the influence of production characteristics and uncertain working hours in the actual production process on the production capacity evaluation results, and constructs a production capacity evaluation method for this process. Through the mixed integer linear programming model and heuristic method with the goal of minimizing the maximum completion time, the maximum completion time is obtained as an evaluation indicator, and the production capacity evaluation result is generated by comparing it with the machine available time. The obtained production capacity evaluation results can provide guidance for the design of actual production plans and the configuration of production resources, reduce production delays, and improve production efficiency.

[0014] 2. The method proposed in the present invention also uses interval gray numbers to characterize the uncertain batch completion time in actual production, and defines the uncertain batch completion time according to the actual processing conditions and production characteristics; it combines the processing characteristics with historical production data to design a specific uncertain working time generation algorithm, which can better fit the actual production and reduce the deviation of the evaluation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1A flowchart of a method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours proposed by the present invention; Figure 2 A specific process framework diagram for capacity evaluation of the present invention; Figure 3 This is an example diagram of the relationship between the interval gray number completion time of a batch and the workpiece working time in the present invention. DETAILED DESCRIPTION

[0016] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0018] In order to overcome the limitations of the existing methods for evaluating the production capacity of aviation composite materials by hot pressing molding, in this embodiment, Figure 1 As shown, the present invention proposes a method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours, which specifically includes the following steps: S1. Conduct a detailed production mode analysis for the hot pressing molding process of aviation composite materials; the production mode analysis includes: identifying the definite working hours and the indefinite working hours, and determining the calculation method of the completion time; As a preferred implementation, in step S1, the calculation method for determining the completion time includes a calculation method for determining the maximum completion time of the production task and a calculation method for determining the interval gray number completion time of each batch, which are respectively: Maximum completion time of production tasks The calculation formula is: ; in, Indicates the maximum completion time of a production task; Indicates the interval gray number completion time of each batch; Respectively represent the index and total number of batches; The calculation formula is: ; in, Indicates batch The preparation time, i.e. the time required to load and unload all workpieces in a batch, is characterized by interval gray number; Indicates batch The processing time is the time required for a batch of workpieces to complete processing on a batch processing machine. The specific time composition is as follows: Figure 3 As shown in the figure, it should be noted that , Only the loading time and unloading time are distinguished. In the specific implementation process of the method proposed in the present invention, the loading time and unloading time are directly used in batches. Preparation time express;

[0019] In this embodiment, batch Preparation time The calculation formula is: ; in Indicates batch The number of artifacts included in the Representation of workpiece The preparation time is represented by interval grey number. batch Processing time The calculation formula is: ; in Indicates batch The number of artifacts included in the Representation of workpiece The processing time is represented by a real number.

[0020] S2. Carry out data preparation for the production task of hot pressing of aviation composite materials; the data preparation work includes: clarifying the working hours and machine availability time of all workpieces; As a preferred implementation, in this embodiment, step S2 uses the workpiece interval gray number preparation time generation algorithm to determine the workpiece Preparation time ; The specific details are shown in Algorithm 1: ; ; in, is the coefficient of volatility; is the weight coefficient; is the resolution coefficient; To predetermine the evaluation criteria; The artifact is generated by the following mathematical formula Processing time: ; in, Indicates that artifacts are included The number of historical batches; Indicates that artifacts are included The historical batch processing time set of ; The machine available time is expressed by the following mathematical formula: ; in, represents the available time of the machine, and uses interval gray number to represent the uncertain working time; → represents the mapping relationship; where The true value of the machine's available time, which cannot be determined in advance; It represents the ideal available time of the machine, which is a determined value when equipment failure is not considered; Indicates the shortest available time of the machine; Indicates the utilization rate of the equipment.

[0021] S3, constructing a mixed integer linear programming model with the goal of minimizing the maximum completion time, obtaining the maximum completion time for model evaluation, and judging whether the production task can be completed according to the model evaluation criteria; if an accurate result is obtained, directly output the evaluation result; if an accurate evaluation result cannot be obtained, proceed to step S4; It should be noted that the establishment of the model in this method needs to be based on the following assumptions: all workpiece and machine information is known at time zero; the start time defaults to time zero, and machine interruptions and failures are not considered; each workpiece has the same priority, and processing will not be interrupted; workpieces cannot be split or overlapped in the machine; the total size of workpieces in each batch must be less than or equal to the machine capacity; the index of the workpiece is defined by the non-decreasing order of its operation time. Based on these assumptions, as a preferred implementation, the mixed integer linear programming model constructed in step S3 with the goal of minimizing the maximum completion time specifically includes: The constructed model is represented using three-field notation as: ; Among them, 1 means that the machine environment is a single machine environment; Indicates that the objective function is to minimize the maximum completion time, which is also an indicator used for capacity evaluation; Indicates that the processing task characteristic is batch processing; is used as a constraint for the model; where Index the artifacts; Indicates the size of the workpiece; Indicates the total capacity of the machine, which is used to constrain the total size of workpieces accommodated in a batch; , They represent the preparation time and processing time of the workpiece respectively; The optimization objective of the model is set as: ; in, represents the objective function of the scheduling model, Indicates batch The interval gray number completion time, represents the index of a single batch, represents a batch set; the optimization goal is to minimize the maximum completion time of the production task .

[0022] The constraints of the constructed mixed integer linear programming model specifically include: (1) ; (2) ; (3) ; (4) ; (5) ; in, A collection of artifacts, indexed by Represents a single artifact, and the set satisfies the condition ; is a collection of batches, indexed by Represents a single batch; Constraints (1) Ensure that the workpiece Can only be assigned to one batch Processing in The indexes of workpieces and batches must meet the conditions ; is a decision variable, if the workpiece Assign to batch Then , otherwise 0; Constraint (2) ensures that the workpiece Assigned to batch When, batch Allow other conditions to be met Workpiece The workpieces are assigned to this batch. The index of the artifact satisfies ; This constraint is also used to enforce the linear relaxation of the model; Constraint (3) ensures that the size of the workpieces in each batch cannot exceed the total capacity of the batch processing machine; Constraint (4) ensures that the batch The interval gray number completion time is not less than the sum of the batch preparation time and the batch processing time; Constraint (5) ensures that the decision variables are within the feasible range.

[0023] After the model is built, the maximum completion time is obtained to evaluate the model and analyze whether the production task can be completed. The specific process includes: The model is evaluated by calculating the probability that the machine available time is greater than the maximum completion time. The model evaluation criteria are divided into three categories: P1. The model can find the optimal solution within the set time range. The maximum completion time at this time is : P1.1: If , it is considered that the production task cannot be completed within the specified production cycle; P1.2: If , it is considered that the possibility of completing the production task within the specified production cycle is low; P1.3: If , it is considered that the possibility of completing the production task within the specified production cycle is high; P1.4: If , it is considered that the production task can be completed within the specified production cycle; P2: The model fails to find the optimal solution within the set time range, but returns the upper and lower bounds. The upper and lower bounds are recorded as : P2.1: If , it is considered that the production task cannot be completed within the specified production cycle; P2.2: Otherwise, a heuristic evaluation is required in step S4 for further judgment; P3, if the model does not return any results within the set time range, a heuristic evaluation is performed; in, is the upper bound of the objective function value found, that is, the objective function value of the current optimal feasible solution, represented by interval gray number; is the theoretical lower bound of the optimal solution, that is, the relaxed solution obtained by relaxing the problem in the process of solving the model. This solution does not satisfy all the constraints of the model and is therefore an infeasible solution, and is represented in real number form; is the uncertain machine available time represented by interval grey number, are the shortest available time and the most ideal available time of the machine, respectively, which are real numbers.

[0024] When the model evaluation cannot obtain accurate results, step S4 is required to perform further heuristic evaluation.

[0025] S4. Design a heuristic method based on the production model, obtain the maximum completion time corresponding to the optimal production plan for heuristic evaluation, and obtain the final evaluation result according to the heuristic evaluation standard; As a preferred embodiment, the heuristic method in step S4 includes a batching heuristic method based on workpiece processing time and a batching heuristic method based on workpiece size; The batching heuristic method based on workpiece processing time is shown in Algorithm 2 below, specifically: ; in represents the index of the batch, Indicates batch The collection of artifacts contained in Indicates the remaining available capacity of the machine for the batch.

[0026] The batching heuristic method based on workpiece size is shown in Algorithm 3 below, specifically: ; ; in, , and It is a subset of the artifact set obtained by filtering according to certain rules; The maximum completion time of the optimal production plan is obtained by heuristic method, which is recorded as ; It should be noted that, in this embodiment, the batch heuristic method based on workpiece processing time and the batch heuristic method based on workpiece size each return a production plan, which is a feasible solution; the one with the smaller maximum completion time is selected as the better production plan, and its corresponding maximum completion time is , using interval gray number representation; then combined with the model evaluation criteria for heuristic evaluation, the heuristic evaluation criteria are divided into two categories: I1. Meet the model evaluation standard P2.2. At this time, the upper and lower bounds found within the set time range are , the maximum completion time of the optimal production plan obtained by heuristic method is : I1.1: If , it is considered that the production task cannot be completed within the specified production cycle; I1.2: If , it is considered that the possibility of completing the production task within the specified production cycle is low; I1.3: If , it is considered that the possibility of completing the production task within the specified production cycle is high; I1.4: If , it is considered that the production task can be completed within the specified production cycle; I2. Satisfying the model evaluation criteria P3, the maximum completion time of the optimal production plan obtained by the heuristic method is : I2.1: If , it is considered that the production task cannot be completed within the specified production cycle; I2.2: If , it is considered that the possibility of completing the production task within the specified production cycle is low; I2.3: If , it is considered that the possibility of completing the production task within the specified production cycle is high; I2.4: If , it is considered that the production task can be completed within the specified production cycle.

[0027] At this point, after the entire process of the method proposed in the present invention, this embodiment will further illustrate the effectiveness and feasibility of the method for evaluating the hot pressing forming capacity of aviation composite materials considering the interval gray working hours proposed in the present invention through the following numerical tests and simulation experiments.

[0028] In this example, 10 cases were first selected for numerical experiments, and then 2 cases of different scales were selected for simulation experiments. All experiments were implemented using Python 3.9 programming and conducted on a computer running the macOS 14.0 operating system, equipped with an Apple M1 MAX chip, and equipped with 32GB of memory.

[0029] 1. Numerical experiments The present invention selects 10 cases to test the performance of model evaluation and heuristic evaluation. Table 1 lists the completion time and running time of each case obtained by using the mixed integer linear programming model (G-MILP) in model evaluation and the batch heuristic method based on workpiece processing time (P-BPA) or the batch heuristic method based on workpiece size (S-BPA) in heuristic evaluation, where the set time range of G-MILP is 60 seconds. In the completion time column of model evaluation, are the upper and lower bounds, where represents the lower bound, Indicates the upper bound. Specifically, for Case 3 (i.e., Case-3), the lower bound is 287.80 and the upper bound is [262.07, 317.57].

[0030] Table 1 Maximum completion time and running time of the cases in the model evaluation and heuristic evaluation process

[0031] As can be seen from Table 1, most simple production tasks can quickly obtain clear evaluation results in model evaluation, and the remaining production tasks can obtain high-quality evaluation indicators and reliable evaluation results through heuristic evaluation. Specifically, for simple production tasks such as Case-1, Case-2, and Case-4 with a small number of workpieces or a large range of workpiece sizes, the G-MILP used in the model evaluation can find the optimal completion time in a very short time, indicating that for simple production tasks, the model evaluation can efficiently give clear evaluation results. For general production tasks with a moderate number of workpieces such as Case-3, Case-5, Case-6, and Case-8, the performance of G-MILP is often relatively unstable. At this time, P-BPA and S-BPA used in the heuristic evaluation can quickly obtain the maximum completion time of the same size or even smaller, which can be used as a supplementary evaluation indicator. For complex production tasks such as Case-7, Case-9, and Case-10 with a small range of workpiece sizes and a large number of workpieces, although the running time of G-MILP increases significantly, the heuristic method can still find a better solution with a smaller maximum completion time in a relatively short time.

[0032] The following simulation experiments are used to further analyze the effectiveness and feasibility of specific cases; (II) Simulation experiment Capacity assessment for Case-1: The production task in this case includes 20 workpieces, all of which need to be processed on a machine with a capacity of 10. The maximum daily machine usage time is 22 hours, and the normal machine utilization rate is 96%. Figure 2 As shown, data preparation is first performed, and the historical preparation time and machine usage data of each workpiece are retrieved from the database (the historical processing time and machine available time can be obtained through the machine usage data, as shown in Table 2 and Table 3 below; and the workpiece working hours for capacity evaluation are obtained by the working hour generation method shown in step S2, as shown in Table 4 below; ; ; ; Then, according to the machine available time generation method described in step S2, the machine available time within a given production cycle (n days) is calculated as: ; The data preparation is now complete, and Case-1 is evaluated. Based on the mixed integer linear programming model constructed in step S3, the optimal solution is obtained within the set time range of 60 seconds, that is, the optimal solution for workpiece-batch allocation and the maximum completion time of the production task. , as shown in Table 5 below. At this time, the maximum completion time To evaluate the indicators, perform model evaluation: ; It should be noted that, in the present invention, the purpose of the batch index and workpiece index is to solve the mixed integer linear programming model, which is determined after non-sequential sorting according to the processing time; and the purpose of the workpiece number and batch number here is to show the optimal solution for workpiece-batch allocation; other places where the index and number are mentioned in the present invention refer to the explanation here; the following is a capacity analysis based on a given production cycle: If the given production cycle is 4 days, the machine availability time is , the probability that the machine available time is greater than the maximum completion time of the production task is: ; According to evaluation criteria P1.1, the production task cannot be completed within 4 days; If we relax the production cycle and set it to 6 days, the machine availability time is , the probability that the machine available time is greater than the maximum completion time of the production task is: ; According to evaluation criterion P1.3, the production task is more likely to be completed within 6 days; Since the optimal solution for Case-1 is found within the set time range, the evaluation result can be obtained during the model evaluation process, and there is no need to perform heuristic evaluation. The evaluation ends here. The evaluation result is that the production task cannot be completed within 4 days, but there is a high possibility that it can be completed within 6 days.

[0033] Then select Case-3 for capacity assessment; the production task in this case includes 50 workpieces, all of which need to be processed on a machine with a capacity of 10. The maximum daily machine usage time is 18 hours, and the normal machine utilization rate is 90%. The machine available time within a given production cycle (n days) is: ; Similarly, the model evaluation is first performed, and the upper and lower bounds are obtained within the set time range of 60 seconds, as shown in Table 6: ; The following boundaries Evaluation indicators are used to evaluate the model. If the given production cycle is 18 days, the machine availability time is , the probability that the machine available time is greater than the maximum completion time of the production task is: ; According to the model evaluation standard P2.2, since the model evaluation failed to obtain a clear evaluation result, heuristic evaluation is required; the optimal production plan and the corresponding maximum completion time of Case-3 are obtained through the heuristic method, that is, the optimal feasible solution, as shown in Table 7: ; At this time, the probability that the machine available time is greater than the maximum completion time of the production task is: ; According to evaluation criteria I1.3, the final result is that there is a high possibility that the production task can be completed within 18 days.

[0034] In summary, the present invention proposes a capacity evaluation method that takes into account interval gray working hours for the hot pressing molding process of aviation composite materials. In this evaluation method, a mixed integer linear programming model is first used to perform model evaluation on the production task. If a clear evaluation result cannot be obtained, a heuristic method is used to perform heuristic evaluation. The experimental results show the effectiveness and feasibility of the proposed capacity evaluation method. Through the method proposed in the present invention, capacity evaluation can be performed for production tasks with uncertain working hours, and the obtained evaluation results are helpful to guide the formulation of production plans and the allocation of production resources, improve production efficiency, and reduce production delays.

[0035] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0036] The above-mentioned embodiments only express several implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours, characterized in that: The specific steps include: S1. Conduct detailed production model analysis for the hot pressing process of aviation composite materials; The production mode analysis includes: identifying definite working hours and indefinite working hours, and determining the calculation method of completion time; S2. Carry out data preparation for the production task of hot pressing of aviation composite materials; the data preparation work includes: clarifying the working hours and machine availability time of all workpieces; S3, constructing a mixed integer linear programming model with the goal of minimizing the maximum completion time, obtaining the maximum completion time for model evaluation, and judging whether the production task can be completed according to the model evaluation criteria; if an accurate result is obtained, directly output the evaluation result; if an accurate evaluation result cannot be obtained, proceed to step S4; S4. Design a heuristic method based on the production model, obtain the maximum completion time corresponding to the optimal production plan for heuristic evaluation, and obtain the final evaluation result based on the heuristic evaluation standard.

2. The method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours according to claim 1, characterized in that: In step S1, the calculation method for determining the completion time includes a calculation method for determining the maximum completion time of the production task and a calculation method for determining the interval gray number completion time of each batch, which are respectively: Maximum completion time of production tasks The calculation formula is: ； in, Indicates the maximum completion time of a production task; Indicates the interval gray number completion time of each batch; Respectively represent the index and total number of batches; The calculation formula is: ； in, Indicates batch The preparation time, i.e. the time required to load and unload all workpieces in a batch, is characterized by interval gray number; Indicates batch The processing time, that is, the time required for a batch of workpieces to complete processing on a batch processing machine, is represented by a real number.

3. The method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours according to claim 2, characterized in that: batch Preparation time The calculation formula is: ； in Indicates batch The number of artifacts included in the Representation of workpiece The preparation time is represented by interval grey number. batch Processing time The calculation formula is: ； in Indicates batch The number of artifacts included in the Representation of workpiece The processing time is represented by a real number.

4. The method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours according to claim 1, characterized in that: In step S2, the working hours and machine available time of all workpieces are specifically defined as follows: The workpiece interval gray number preparation time generation algorithm is used to determine the workpiece Preparation time ; The artifact is generated by the following mathematical formula Processing time: ； in, Indicates that artifacts are included The number of historical batches; Indicates that artifacts are included The historical batch processing time set of ; The machine available time is expressed by the following mathematical formula: ； in, Indicates the available time of the machine, and uses interval gray number to characterize the uncertain working time; → indicates the mapping relationship; represents the true value of the machine available time; Indicates the ideal availability time of the machine; Indicates the shortest available time of the machine; Indicates the utilization rate of the equipment.

5. The method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours according to claim 1, characterized in that: The construction of the mixed integer linear programming model with the goal of minimizing the maximum completion time in step S3 specifically includes: The constructed model is represented using three-field notation as: ； Among them, 1 means that the machine environment is a single machine environment; Indicates that the objective function is to minimize the maximum completion time, which is also an indicator used for capacity evaluation; Indicates that the processing task characteristic is batch processing; is used as a constraint for the model; where Index the artifacts; Indicates the size of the workpiece; Represents the total capacity of the machine, which is used to constrain the total size of workpieces accommodated in a batch; , They represent the preparation time and processing time of the workpiece respectively; The optimization objective of the model is set as: ； in, represents the objective function of the scheduling model, Indicates batch The interval gray number completion time, represents the index of a single batch, represents a batch set; the optimization goal is to minimize the maximum completion time of the production task .

6. The method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours according to claim 5, characterized in that: The constraints of the constructed mixed integer linear programming model specifically include: (1) ； (2) ； (3) ； (4) ； (5) ； in, A collection of artifacts, indexed by Represents a single artifact, and the set satisfies the condition ; is a collection of batches, indexed by Represents a single batch; Constraints (1) Ensure that the workpiece Can only be assigned to one batch Processing in The indexes of workpieces and batches must meet the conditions ; is a decision variable, if the workpiece Assign to batch Then , otherwise 0; Constraint (2) ensures that the workpiece Assigned to batch When, batch Allow other conditions to be met Workpiece The workpieces are assigned to this batch. The index of the artifact satisfies ; This constraint is also used to enforce the linear relaxation of the model; Constraint (3) ensures that the size of the workpieces in each batch cannot exceed the total capacity of the batch processing machine; Constraint (4) ensures that the batch The interval gray number completion time is not less than the sum of the batch preparation time and the batch processing time; Constraint (5) ensures that the decision variables are within the feasible range.

7. The method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours according to claim 6, characterized in that: The model evaluation in step S3 specifically includes: The model is evaluated by calculating the probability that the machine available time is greater than the maximum completion time. The model evaluation criteria are divided into three categories: P1. The model can find the optimal solution within the set time range. The maximum completion time at this time is : P1.1: If , it is considered that the production task cannot be completed within the specified production cycle; P1.2: If , it is considered that the possibility of completing the production task within the specified production cycle is low; P1.3: If , it is considered that the possibility of completing the production task within the specified production cycle is high; P1.4: If , it is considered that the production task can be completed within the specified production cycle; P2: The model fails to find the optimal solution within the set time range, but returns the upper and lower bounds. The upper and lower bounds are recorded as : P2.1: If , it is considered that the production task cannot be completed within the specified production cycle; P2.2: Otherwise, a heuristic evaluation is required in step S4 for further judgment; P3, if the model does not return any results within the set time range, a heuristic evaluation is performed; in, is the upper bound of the objective function value found, that is, the objective function value of the current optimal feasible solution, represented by interval gray number; is the theoretical lower bound of the optimal solution, that is, the relaxed solution obtained by relaxing the problem in the process of solving the model, and is represented in the form of real numbers; is the uncertain machine available time represented by interval grey number, are the shortest available time and the most ideal available time of the machine, respectively, which are real numbers.

8. The method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours according to claim 1, characterized in that: The heuristic method in step S4 includes: a batching heuristic method based on workpiece processing time and a batching heuristic method based on workpiece size.

9. The method for evaluating the hot pressing forming capacity of aviation composite materials considering interval gray number working hours according to claim 7, characterized in that: The heuristic evaluation in step S4 specifically includes: The maximum completion time of obtaining a better production plan through heuristic method is ,Combined with the model evaluation criteria, the heuristic evaluation criteria are divided into two categories: I1. Meet the model evaluation standard P2.

2. At this time, the upper and lower bounds found within the set time range are , the maximum completion time of the optimal production plan obtained by heuristic method is : I1.1: If , it is considered that the production task cannot be completed within the specified production cycle; I1.2: If , it is considered that the possibility of completing the production task within the specified production cycle is low; I1.3: If , it is considered that the possibility of completing the production task within the specified production cycle is high; I1.4: If , it is considered that the production task can be completed within the specified production cycle; I2. Satisfying the model evaluation criteria P3, the maximum completion time of the optimal production plan obtained by the heuristic method is : I2.1: If , it is considered that the production task cannot be completed within the specified production cycle; I2.2: If , it is considered that the possibility of completing the production task within the specified production cycle is low; I2.3: If , it is considered that the possibility of completing the production task within the specified production cycle is high; I2.4: If , it is considered that the production task can be completed within the specified production cycle.

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