Geometric and Physical Fusion Method for Assembly Deviation Prediction of Deformable Structures

Abstract

The present application proposes a geometric and physical fusion method for predicting assembly deviation of deformable structures, belonging to the field of aviation engineering manufacturing technology, and comprising the following steps: decomposing the deformable structure to obtain a spatial vector point set, and characterizing and calculating the consistent manufacturing deviation, assembly positioning deviation, and assembly deformation deviation; constructing an assembly deviation transfer graph, and mapping it into an assembly state space graph by using these three multi-source deviations; performing finite element analysis on the assembly accuracy of the deformable structure by using the assembly state space graph, and converting the obtained assembly deviation nephogram into an assembly deviation contour map; constructing an initial generative adversarial network model, and training and verifying it by using the data in the assembly deviation contour map to obtain a final generative adversarial network model; inputting the actual deviation image of the deformable structure into the final generative adversarial network model for assembly deviation prediction. The present application can improve the assembly accuracy and assembly efficiency of deformable structures.

Description

Technical Field

[0001] This application relates to the technical field of aerospace engineering manufacturing, and particularly relates to a geometric and physical fusion method for predicting assembly deviation of deformable structures. Background Art

[0002] With the iterative development of aerospace engineering, higher requirements have been put forward for the dimensions and accuracies of deformable structures in various aerospace products. For example, the current size of deformable structures has increased from the original 1 - 2 meters to 5 - 10 meters or even larger; at the same time, the assembly accuracy of deformable structures has changed from the millimeter level to the sub - millimeter level or even a more microscopic level. To meet the assembly requirements of large size and high precision, aerospace manufacturing enterprises usually adopt assembly deviation prediction methods such as repeated adjustment, process compensation, rigid analysis, and flexible analysis. However, these traditional assembly deviation prediction methods often have obvious limitations, as follows:

[0003] First, when using repeated adjustment and process compensation methods for assembly deviation prediction, the prediction credibility is low, the calculation cost is high, and it often relies on on - site repeated adjustment and subsequent process compensation, etc. Therefore, it is difficult to meet the requirements of production schedule and quality control.

[0004] Second, the rigid analysis method is mainly based on kinematics, and the flexible analysis method mainly relies on statics. However, there are incompatible problems between the two in terms of mathematical thinking and expression systems, resulting in a large deviation between the simulation calculation results and the actual predicted values.

[0005] Third, due to the large size span, weak structural rigidity, and non - linear factors in deviation transfer of deformable structures, the assembly deviation field is too complex and difficult to accurately predict.

[0006] Finally, traditional assembly deviation prediction methods are often inefficient in processing large - scale data and identifying complex patterns, which limits their application in the field of modern aerospace manufacturing.

[0007] Therefore, it is necessary to propose a solution to improve one or more problems existing in the above - mentioned related technical solutions.

[0008] It should be noted that the information disclosed in the above background art section is only used to strengthen the understanding of the background of this application. Therefore, it may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0009] The embodiment of this application provides a geometric and physical fusion method for predicting assembly deviation of deformable structures, and this method includes the following steps:

[0010] Decompose the deformable structure, extract all key features at each assembly level respectively, and discretize all the key features at the part level into a set of spatial vector points;

[0011] According to the set of spatial vector points, characterize the part manufacturing deviation by using the part warping deviation and the part fluctuation deviation, and define the part manufacturing deviation that conforms to the tolerance specification as the consistent manufacturing deviation;

[0012] Adopt a deterministic assembly method to characterize the assembly positioning deviation, and use finite element analysis to calculate the assembly deformation deviation;

[0013] According to the structure decomposition, process the assembly information of the deformable structure, and construct an assembly deviation transfer diagram; and use the consistent manufacturing deviation, the assembly positioning deviation and the assembly deformation deviation to map the assembly deviation transfer diagram into an assembly state space diagram;

[0014] Use the assembly state space diagram to perform finite element analysis on the assembly accuracy of the deformable structure, obtain an assembly deviation cloud diagram, and convert the assembly deviation cloud diagram into an assembly deviation contour diagram, and the assembly deviation contour diagram includes a training data set and a test data set;

[0015] Construct an initial generative adversarial network model, train the initial generative adversarial network model by using the training data set, and verify the trained initial generative adversarial network model by using the test data set to obtain a final generative adversarial network model;

[0016] Input the actual deviation image of the deformable structure into the final generative adversarial network model for assembly deviation prediction, and generate an assembly deviation prediction image.

[0017] In an exemplary embodiment of the present application, the types of the assembly levels include component levels, sub-assembly levels and the part level; the set of spatial vector points includes: the dimension information, shape information, position information and waviness information of the part.

[0018] In an exemplary embodiment of the present application, the step of characterizing the part manufacturing deviation by using the part warping deviation and the part fluctuation deviation according to the set of spatial vector points, and defining the part manufacturing deviation that conforms to the tolerance specification as the consistent manufacturing deviation includes:

[0019] Superimpose the part warping deviation and the part fluctuation deviation on the set of spatial vector points, and perform deviation statistics on all sampling points on the part surface;

[0020] The result of the deviation statistics is characterized as the part manufacturing deviation by using geometric covariance, and the part manufacturing deviation includes the part warping deviation constructed by using Legendre polynomials and the part fluctuation deviation constructed by using sine polynomials;

[0021] Check whether the part manufacturing deviation conforms to the tolerance specification;

[0022] If the part manufacturing deviation conforms to the tolerance specification, define the part manufacturing deviation as the consistent manufacturing deviation; if the part manufacturing deviation does not conform to the tolerance specification, iterate the process of deviation statistics until the constructed part manufacturing deviation conforms to the tolerance specification.

[0023] In an exemplary embodiment of the present application, the expression of the consistent manufacturing deviation is:

[0024] (1)

[0025] Wherein, represents the consistent manufacturing deviation of the deformable structure at the th assembly station, represents the ideal value of the part manufacturing deviation of the deformable structure at the th assembly station, represents the geometric covariance of the part surface, represents the normal of the discrete vector points in the spatial vector point set;

[0026] The expression of the geometric covariance of the part surface is:

[0027] (2)

[0028] Wherein, represents the weight coefficient of the part warping deviation, , represents the weight coefficient of the part fluctuation deviation, , represents the range of the part warping deviation, represents the range of the part fluctuation deviation, represents the part warping deviation, , represents the first transformation matrix, , represents the th order Legendre polynomial, represents the th order of the Legendre polynomial, represents the order of the Legendre polynomial, represents the number of sampling points on the part surface, Represents the weight coefficient of the th order of the Legendre polynomial, Represents the index of the th sampling point on the part surface, Represents the index of the th sampling point on the part surface, Represents the variance matrix of the deviation variation of the sampling points, Represents the part fluctuation deviation, , Represents the second transformation matrix, , , Represents the weight coefficient of the frequency curve of the th order in the sine polynomial, Represents the weight coefficient of the th order of the sine polynomial, Represents the th order frequency of the sine polynomial, Represents the column to which the sampling point on the part surface belongs, Represents the row to which the sampling point on the part surface belongs, Represents the th order of the sine polynomial, Represents the order of the sine polynomial.

[0029] In an exemplary embodiment of the present application, the expression of the assembly positioning deviation is:

[0030] (3)

[0031] Wherein, Represents the assembly positioning deviation of the deformable structure at the th assembly station, Represents the Jacobian matrix, Represents the transfer matrix related to the coordinates and control directions of the deformable structure at the th assembly station, Represents the th deviation generated during the assembly process at the assembly station;

[0032] The expression of the assembly deformation deviation is:

[0033] (4)

[0034] Wherein, Represents the assembly deformation deviation of the deformable structure when subjected to the external load at the th assembly station, Represents the external load Mapping function for deformation of the deformable structure during operation Indicates the overall displacement generated during the positioning process of the deformable structure at the th assembly station Indicates the flexible deformation caused during the clamping and riveting processes of the deformable structure at the th assembly station Indicates the springback deformation caused after the release of the tooling or fixture of the deformable structure at the th assembly station

[0035] In an exemplary embodiment of the present application, the step of processing the assembly information of the deformable structure according to the structural decomposition, constructing an assembly deviation transfer diagram; and mapping the assembly deviation transfer diagram into an assembly state space diagram by using the consistency manufacturing deviation, the assembly positioning deviation, and the assembly deformation deviation includes:

[0036] According to the structural decomposition, the deformable structure is successively subjected to assembly unit division, assembly sequence adjustment, assembly reference identification, and mating constraint definition to construct the assembly deviation transfer diagram;

[0037] All part nodes in the assembly deviation transfer diagram are mapped to corresponding state nodes in the assembly state space diagram;

[0038] All tooling constraint nodes in the assembly deviation transfer diagram are mapped to input variables of the corresponding state nodes in the assembly state space diagram;

[0039] All mating constraint nodes in the assembly deviation transfer diagram are mapped to transfer relationships between the corresponding state nodes in the assembly state space diagram;

[0040] Among them, the mapping of various nodes in the assembly deviation transfer diagram is carried out in the order from top to bottom and from left to right, and the consistency manufacturing deviation, the assembly positioning deviation, and the assembly deformation deviation are respectively incorporated into the corresponding nodes to construct the assembly state space diagram.

[0041] In an exemplary embodiment of the present application, the expression of the assembly deviation transfer diagram is:

[0042] (5)

[0043] Wherein, represents the assembly deviation transfer diagram, represents the set of part nodes during the assembly process, , represents the set of tooling constraint nodes during the assembly process, , represents the set of mating constraint nodes during the assembly process, , represents the set of node transfer directions during the assembly process, ;

[0044] The expression of the assembly state space diagram is:

[0045] (6)

[0046] where, represents the assembly accuracy of the deformable structure after completion of the th assembly station, represents the assembly accuracy of the deformable structure after positioning is completed at the previous assembly station of the th assembly station, represents the first deviation coefficient matrix, represents the second deviation coefficient matrix, represents the third deviation coefficient matrix, represents the fourth deviation coefficient matrix, represents the fifth deviation coefficient matrix, represents the consistency manufacturing deviation of the deformable structure at the th assembly station, represents the assembly deviation of the deformable structure obtained by measurement at the th assembly station, represents the measurement error caused by the measurement equipment during the measurement of the deformable structure at the th assembly station.

[0047] In an exemplary embodiment of the present application, the steps of performing finite element analysis on the assembly accuracy of the deformable structure using the assembly state space diagram, obtaining an assembly deviation cloud diagram, and converting the assembly deviation cloud diagram into an assembly deviation contour diagram include:

[0048] In the finite element analysis software, perform finite element analysis on the assembly accuracy of the deformable structure using the assembly state space diagram to obtain the assembly deviation cloud diagram;

[0049] Successively use the cubic spline interpolation algorithm, the deviation normalization algorithm, and the color mapping algorithm to convert the assembly deviation cloud diagram into the assembly deviation contour diagram;

[0050] Divide the data set reflected by the assembly deviation contour diagram into the training data set and the test data set, and the ratio of the training data set to the test data set is 4:1.

[0051] In an exemplary embodiment of the present application, the steps of constructing an initial generative adversarial network model, training the initial generative adversarial network model using the training dataset, and validating the trained initial generative adversarial network model using the test dataset to obtain a final generative adversarial network model include:

[0052] The initial generative adversarial network model includes a finite element module, a generator, and a discriminator that are communicatively connected to each other;

[0053] In the process of training and validating the initial generative adversarial network model to obtain the final generative adversarial network model, a generative adversarial loss function is used, and the generative adversarial loss function includes a loss function and a feature matching loss function;

[0054] The expression of the generative adversarial loss function is:

[0055] (7)

[0056] Wherein, represents the generative adversarial loss function, represents the generator, represents the discriminator, represents the type of the discriminator, represents the loss function, , represents the expected value of the difference between the input image and the real image by the discriminator, represents the input image, represents the real image corresponding to the input image, represents the synthesized image, represents the expected value of the difference between the input image and the synthesized image by the discriminator, represents the generated image, represents the probability that the real image is judged as true by the discriminator, represents the probability that the generated image is judged as true by the discriminator, represents the feature matching loss function, , represents the extractor of the th layer of the discriminator, represents the total number of layers of the discriminator, represents the th layer of the discriminator, represents a random variable, represents a given sample generated by the random variable, represents the expected value of the difference between the given sample and the input image, represents The proportion of the loss function and the feature matching loss function represents the 1-norm.

[0057] Beneficial effects:

[0058] The present application provides a geometric and physical fusion method for predicting assembly deviation of deformable structures, which has at least the following beneficial effects:

[0059] (1) The present application uses part warping deviation and part fluctuation deviation to characterize part manufacturing deviation, defines consistent manufacturing deviation, uses a deterministic assembly method to characterize assembly positioning deviation, and uses finite element analysis to calculate assembly deformation deviation. By introducing these three types of multi-source deviations, aviation manufacturing enterprises do not need to frequently perform on-site repeated calibration and subsequent process compensation, improving the first-pass success rate of product assembly, saving time and resource waste caused by repeated calibration, and thus reducing production costs;

[0060] (2) The present application constructs an assembly deviation transfer diagram and maps the assembly deviation transfer diagram into an assembly state space diagram using multi-source deviations, realizing the simultaneous fusion of geometric information and physical information in the process of predicting assembly deviation and improving the assembly accuracy of deformable structures;

[0061] (3) The present application performs finite element analysis on the assembly accuracy of deformable structures using the assembly state space diagram, obtains an assembly deviation cloud diagram, and converts the assembly deviation cloud diagram into an assembly deviation contour diagram, thereby integrating the advantages of rigid analysis and flexible analysis, overcoming the calculation deviation problems existing in traditional methods, making the results of assembly deviation prediction closer to the actual situation, and thus meeting the accuracy requirements of aviation manufacturing enterprises at the sub-millimeter level or even more microscopic level;

[0062] (4) The present application constructs an initial generative adversarial network model, trains and validates the initial generative adversarial network model to obtain a final generative adversarial network model, which is used as the final model for predicting assembly deviation of the actual deviation image of deformable structures, so as to be able to efficiently process complex assembly deviation prediction tasks. Compared with traditional methods, it can significantly improve the speed and accuracy of assembly deviation prediction, thus meeting the needs of efficient production of aviation manufacturing enterprises. Description of the drawings

[0063] The drawings here are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present application, and are used together with the specification to explain the principles of the present application. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0064] Figure 1Schematic diagram of steps of a geometric and physical fusion method for predicting assembly deviation of deformable structures in an exemplary embodiment of the present application;

[0065] Figure 2 Schematic diagram of the process of a geometric and physical fusion method for predicting assembly deviation of deformable structures in an exemplary embodiment of the present application;

[0066] Figure 3 Schematic diagram of the structure of an aircraft wing box in an exemplary embodiment of the present application;

[0067] Figure 4 Schematic diagram of decomposing a deformable structure in an exemplary embodiment of the present application;

[0068] Figure 5 Schematic diagram of the process of constructing consistent manufacturing deviations in an exemplary embodiment of the present application;

[0069] Figure 6 Schematic diagram of the process of constructing consistent manufacturing deviations of an aircraft thin-walled structure in an exemplary embodiment of the present application;

[0070] Figure 7 Schematic diagram of mapping an assembly deviation transfer diagram to an assembly state space diagram in an exemplary embodiment of the present application;

[0071] Figure 8 Schematic diagram of an assembly deviation cloud map in an exemplary embodiment of the present application;

[0072] Figure 9 Schematic diagram of an assembly deviation contour map in an exemplary embodiment of the present application;

[0073] Figure 10 Schematic diagram of the structure of an initial generative adversarial network model in an exemplary embodiment of the present application;

[0074] Figure 11 Schematic diagram of the structure of a generator in an exemplary embodiment of the present application;

[0075] Figure 12 Schematic diagram of the structure of a discriminator in an exemplary embodiment of the present application;

[0076] Figure 13 Schematic diagram of training an initial generative adversarial network model in an exemplary embodiment of the present application;

[0077] Figure 14 Schematic diagram of the generated assembly deviation prediction image in an exemplary embodiment of the present application. Detailed implementation manners

[0078] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this application will be more complete and comprehensive, and will fully convey the concept of the example embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0079] In addition, the accompanying drawings are only schematic illustrations of the present application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus repeated descriptions thereof will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0080] To this end, the present example embodiment provides a geometric and physical fusion method for predicting assembly deviations of deformable structures, as Figure 1 and Figure 2 shown. The method can include the following steps:

[0081] Step S101: Decompose the deformable structure, extract all key features of each assembly level respectively, and discretize all key features at the part level into a spatial vector point set;

[0082] Step S102: According to the spatial vector point set, characterize the part manufacturing deviation using part warping deviation and part fluctuation deviation, and define the part manufacturing deviation that meets the tolerance specification as the consistent manufacturing deviation;

[0083] Step S103: Use a deterministic assembly method to characterize the assembly positioning deviation, and calculate the assembly deformation deviation using finite element analysis;

[0084] Step S104: According to the structure decomposition, process the assembly information of the deformable structure, construct an assembly deviation transfer diagram, and map the assembly deviation transfer diagram into an assembly state space diagram using the consistent manufacturing deviation, assembly positioning deviation, and assembly deformation deviation;

[0085] Step S105: Use the assembly state space diagram to perform finite element analysis on the assembly accuracy of the deformable structure, obtain an assembly deviation cloud diagram, and convert the assembly deviation cloud diagram into an assembly deviation contour map. The assembly deviation contour map contains a training data set and a test data set;

[0086] Step S106: Construct an initial generative adversarial network model, train the initial generative adversarial network model using the training dataset, and verify the trained initial generative adversarial network model using the test dataset to obtain the final generative adversarial network model;

[0087] Step S107: Input the actual deviation image of the deformable structure into the final generative adversarial network model for assembly deviation prediction to generate an assembly deviation prediction image.

[0088] Figure 2 In the FEM (Finite Element Method, FEM), it represents the finite element.

[0089] The embodiment of the present application proposes a geometric and physical fusion method for assembly deviation prediction of deformable structures, which has at least the following beneficial effects:

[0090] (1) In the embodiment of the present application, the part manufacturing deviation is characterized by the part warping deviation and the part fluctuation deviation, the consistent manufacturing deviation is defined, the assembly positioning deviation is characterized by the deterministic assembly method, and the assembly deformation deviation is calculated by finite element analysis. By introducing these three multi-source deviations, aviation manufacturing enterprises do not need to frequently perform on-site repeated calibration and subsequent process compensation, improving the first-pass success rate of product assembly, saving time and resource waste caused by repeated calibration, and thus reducing production costs;

[0091] (2) In the embodiment of the present application, by constructing an assembly deviation transfer graph and mapping the assembly deviation transfer graph into an assembly state space graph using multi-source deviations, the geometric information and physical information are fused simultaneously during the assembly deviation prediction process, improving the assembly accuracy of the deformable structure;

[0092] (3) In the embodiment of the present application, by performing finite element analysis on the assembly accuracy of the deformable structure using the assembly state space graph, an assembly deviation nephogram is obtained, and the assembly deviation nephogram is converted into an assembly deviation contour map, thus integrating the advantages of rigid analysis and flexible analysis, overcoming the calculation deviation problem existing in traditional methods, making the result of assembly deviation prediction closer to the actual situation, and thus meeting the accuracy requirements of aviation manufacturing enterprises at the sub-millimeter level or even more microscopic level;

[0093] (4) In the embodiment of the present application, by constructing an initial generative adversarial network model, training and verifying the initial generative adversarial network model, a final generative adversarial network model is obtained as the final model for assembly deviation prediction of the actual deviation image of the deformable structure, so that complex assembly deviation prediction tasks can be efficiently processed. Compared with traditional methods, the speed and accuracy of assembly deviation prediction can be significantly improved, thus meeting the high-efficiency production requirements of aviation manufacturing enterprises.

[0094] Next, a geometric and physical fusion method for predicting assembly deviations of deformable structures proposed in this exemplary embodiment will be described in more detail.

[0095] In step S101 of this embodiment, the deformable structure is decomposed, all key features of each assembly level are extracted respectively, and all key features at the part level are discretized into a spatial vector point set.

[0096] Furthermore, as Figure 3 shown, in this embodiment, the wing box of an aircraft is taken as an example for illustration. In this embodiment, the structure is decomposed in a top-down order, and the wing box of the aircraft is decomposed into components, sub-assemblies, parts, key features, and spatial vector point sets. Figure 3 In a of, the decomposition of the wing box of the aircraft into components and sub-assemblies is shown, that is, it is decomposed into an upper panel, a front beam, ribs, a rear beam, and a lower panel; Figure 3 In b of, the further decomposition of the upper panel into parts including a stopper, a suction cup, a positioning device, and a tooling skeleton is shown.

[0097] Furthermore, as Figure 4 shown, the types of assembly levels include component level, sub-assembly level, and part level. This spatial vector point set includes relevant information such as the dimensional information of the part, the shape information of the part, the position information of the part, and the waviness information of the part, that is, the spatial vector point set contains not only the dimensional deviations and geometric deviations of the part at the macroscopic scale, but also the waviness information at the mesoscopic scale.

[0098] In step S102 of this embodiment, according to the spatial vector point set, the part manufacturing deviation is characterized by the part warping deviation and the part fluctuation deviation, and the part manufacturing deviation that conforms to the tolerance specification is defined as the consistent manufacturing deviation. As Figure 5 and Figure 6 shown, step S102 of this embodiment may include the following sub-steps:

[0099] Sub-step S1021: Superimpose the part warping deviation and the part fluctuation deviation on the spatial vector point set, and perform deviation statistics on all sampling points on the part surface.

[0100] Sub-step S1022: Use geometric covariance to characterize the result of the deviation statistics as the part manufacturing deviation, and the part manufacturing deviation includes the part warping deviation constructed using Legendre polynomials and the part fluctuation deviation constructed using sine polynomials.

[0101] Furthermore, in this embodiment, according to the part length and the deviation wavelength in the spatial vector point set, the deformable structure is decomposed into three basic modes: surface warping ( ), surface fluctuation ( ), and surface roughness ( ), which represents the ratio of the part length to the deviation wavelength. During the process of predicting the assembly deviation of the deformable structure, surface warping and surface fluctuation play a major role, while the influence of surface roughness on the prediction of assembly deviation is very small and can be ignored. Therefore, in this embodiment, only the part warping deviation and the part fluctuation deviation are considered to be introduced.

[0102] Furthermore, in this embodiment, the upper wall panel of the aircraft wing box is modeled.

[0103] Sub-step S1023: Check whether the part manufacturing deviation conforms to the tolerance specification.

[0104] Furthermore, according to different production stages of the product, during the design stage, the inspection to be carried out depends on whether the part manufacturing deviation conforms to the tolerance specification; during the product manufacturing stage, the inspection to be carried out needs to see whether the part manufacturing deviation conforms to the measurement data.

[0105] Sub-step S1024: If the part manufacturing deviation conforms to the tolerance specification, define the part manufacturing deviation as the consistent manufacturing deviation; if the part manufacturing deviation does not conform to the tolerance specification, iterate the process of deviation statistics until the constructed part manufacturing deviation conforms to the tolerance specification.

[0106] Furthermore, the expression of the consistent manufacturing deviation is:

[0107] (1)

[0108] where, represents the consistent manufacturing deviation of the deformable structure at the th assembly station, represents the ideal value of the part manufacturing deviation of the deformable structure at the th assembly station, represents the geometric covariance of the part surface, represents the normal direction of the discrete vector points in the spatial vector point set.

[0109] Furthermore, after the part manufacturing deviation is constructed, it needs to be inspected to ensure that the consistent manufacturing deviation conforms to the tolerance specification. Here, conforming to the tolerance specification means that it should be within the tolerance range of the key features. Only the part manufacturing deviation that meets this requirement can be defined as the consistent manufacturing deviation, that is , represents the upper limit of the tolerance range, represents the lower limit of the tolerance range.

[0110] Furthermore, the expression of the geometric covariance of the part surface is:

[0111] (2)

[0112] Among them, represents the weight coefficient of the part warpage deviation, , represents the weight coefficient of the part fluctuation deviation, , represents the range of the part warpage deviation, represents the range of the part fluctuation deviation, represents the part warpage deviation, , represents the first transformation matrix, , represents the th order Legendre polynomial, represents the th order of the Legendre polynomial, represents the order of the Legendre polynomial, represents the number of sampling points on the part surface, represents the th order weight coefficient of the Legendre polynomial, represents the th index of the sampling point on the part surface, represents the th index of the sampling point on the part surface, represents the variance matrix of the deviation change of the sampling points, represents the part fluctuation deviation, , represents the second transformation matrix, , , represents the weight coefficient of the frequency curve of the th order in the sine polynomial, represents the th order weight coefficient of the sine polynomial, represents the th order frequency of the sine polynomial, represents the column to which the sampling point on the part surface belongs, represents the row to which the sampling point on the part surface belongs, represents the th order of the sine polynomial, represents the order of the sine polynomial.

[0113] Furthermore, in this embodiment, the part manufacturing deviation is characterized by the part warping deviation and the part fluctuation deviation, the consistent manufacturing deviation is defined, the assembly positioning deviation is characterized by the deterministic assembly method, and the assembly deformation deviation is calculated by finite element analysis. By introducing these three multi-source deviations, the aviation manufacturing enterprise does not need to frequently perform on-site repeated calibration and subsequent process compensation, improving the one-time success rate of product assembly, saving time and resource waste caused by repeated calibration, and thus reducing the production cost.

[0114] In step S103 of this embodiment, the assembly positioning deviation is characterized by the deterministic assembly method, and the assembly deformation deviation is calculated by finite element analysis.

[0115] Furthermore, the expression of the assembly positioning deviation is:

[0116] (3)

[0117] Wherein, represents the assembly positioning deviation of the deformable structure at the th assembly station, represents the Jacobian matrix, represents the transfer matrix related to the coordinates and control directions of the deformable structure at the th assembly station, represents the deviation generated during the assembly process at the th assembly station.

[0118] Furthermore, the expression of the assembly deformation deviation is:

[0119] (4)

[0120] Wherein, represents the assembly deformation deviation generated when the deformable structure at the th assembly station is subjected to the external load , represents the mapping function of the deformation of the deformable structure when the external load acts, represents the overall displacement generated during the positioning process of the deformable structure at the th assembly station, represents the flexible deformation caused during the clamping and riveting processes of the deformable structure at the th assembly station, represents the springback deformation caused after the release of the tooling or fixture of the deformable structure at the th assembly station.

[0121] In step S104 of this embodiment, as Figure 7As shown, according to the above structural decomposition, the assembly information of the deformable structure is processed to construct an assembly deviation transfer diagram; and using the consistent manufacturing deviation, assembly positioning deviation, and assembly deformation deviation, the assembly deviation transfer diagram is mapped into an assembly state space diagram. Step S104 of this embodiment may include the following sub-steps:

[0122] Sub-step S1041: According to the structural decomposition, the deformable structure is successively subjected to assembly unit division, assembly sequence adjustment, assembly reference identification, and mating constraint definition to construct an assembly deviation transfer diagram.

[0123] Sub-step S1042: Map all the part nodes in the assembly deviation transfer diagram to the corresponding state nodes in the assembly state space diagram.

[0124] Sub-step S1043: Map all the tooling constraint nodes in the assembly deviation transfer diagram to the input variables of the corresponding state nodes in the assembly state space diagram.

[0125] Sub-step S1044: Map all the mating constraint nodes in the assembly deviation transfer diagram to the transfer relationship between the corresponding state nodes in the assembly state space diagram.

[0126] Among them, mapping of various nodes in the assembly deviation transfer diagram is carried out in the order from top to bottom and from left to right, and the consistent manufacturing deviation, assembly positioning deviation, and assembly deformation deviation are respectively incorporated into the corresponding nodes to construct an assembly state space diagram.

[0127] Furthermore, the expression of the assembly deviation transfer diagram is:

[0128] (5)

[0129] Among them, represents the assembly deviation transfer diagram, represents the set of part nodes in the assembly process, , represents the set of tooling constraint nodes in the assembly process, , represents the set of mating constraint nodes in the assembly process, , represents the set of node transfer directions in the assembly process, .

[0130] Furthermore, based on the above product assembly hierarchical relationship, combined with the assembly process information and the interaction relationship in the assembly process, an assembly deviation transfer diagram is constructed. This assembly deviation transfer diagram is a tree diagram structure reflecting the assembly deviation transfer, as Figure 7As shown in the figure, the part nodes in the tree diagram structure are mapped to the state nodes in the assembly state space diagram, the tooling constraint nodes in the tree diagram structure are mapped to the input variables of the corresponding state nodes in the assembly state space diagram, and the mating constraint nodes in the tree diagram structure are mapped to the transfer relationships between the corresponding state nodes in the assembly state space diagram.

[0131] Furthermore, the expression of the assembly state space diagram is:

[0132] (6)

[0133] Wherein, represents the assembly accuracy of the deformable structure after positioning at the th assembly station, represents the assembly accuracy of the deformable structure after positioning at the previous assembly station of the th assembly station, represents the first deviation coefficient matrix, represents the second deviation coefficient matrix, represents the third deviation coefficient matrix, represents the fourth deviation coefficient matrix, represents the fifth deviation coefficient matrix, represents the consistency manufacturing deviation of the deformable structure at the th assembly station, represents the assembly deviation of the deformable structure obtained by measurement at the th assembly station, represents the measurement error caused by the measurement of the measurement equipment for the deformable structure at the th assembly station.

[0134] Furthermore, the assembly accuracy here refers to the cumulative assembly deviation of the deformable structure after positioning at the th assembly station.

[0135] Furthermore, in this embodiment, by constructing an assembly deviation transfer diagram and mapping the assembly deviation transfer diagram to an assembly state space diagram using multi-source deviations, the geometric information and physical information are simultaneously fused in the process of predicting the assembly deviation, and the assembly accuracy of the deformable structure is improved. The multi-source deviations here include part manufacturing deviations, assembly positioning deviations, and assembly deformation deviations.

[0136] In step S105 of this embodiment, the assembly accuracy of the deformable structure is analyzed by finite element using the assembly state space diagram to obtain an assembly deviation cloud diagram, and the assembly deviation cloud diagram is converted into an assembly deviation contour map. The assembly deviation contour map includes a training data set and a test data set. Step S105 of this embodiment may include the following steps:

[0137] Sub-step S1051: As shown in Figure 8 , in the finite element analysis software, the assembly accuracy of the deformable structure is analyzed by using the assembly state space diagram to obtain the assembly deviation nephogram.

[0138] Sub-step S1052: As shown in Figure 9 , the assembly deviation nephogram is converted into an assembly deviation contour map by using the cubic spline interpolation algorithm, the deviation normalization algorithm, and the color mapping algorithm in sequence;

[0139] In this embodiment, the resolution of the generated assembly deviation contour map is .

[0140] Sub-step S1053: The data set reflected by the assembly deviation contour map is divided into a training data set and a test data set, and the ratio of the training data set to the test data set is 4:1.

[0141] Further, in this embodiment, the data set reflected by the assembly deviation contour map is divided into 2000 groups of training data sets and 500 groups of test data sets.

[0142] Further, in this embodiment, the assembly accuracy of the deformable structure is analyzed by using the assembly state space diagram to obtain the assembly deviation nephogram, and the assembly deviation nephogram is converted into an assembly deviation contour map, thereby integrating the advantages of rigid analysis and flexible analysis, overcoming the calculation deviation problem existing in the traditional method, making the result of assembly deviation prediction closer to the actual situation, and thus meeting the accuracy requirements of aviation manufacturing enterprises at the sub-millimeter level or even more microscopic level.

[0143] In step S106 of this embodiment, an initial generative adversarial network model is constructed, the initial generative adversarial network model is trained by using the training data set, and the trained initial generative adversarial network model is verified by using the test data set to obtain the final generative adversarial network model. Step S106 of this embodiment may include the following sub-steps:

[0144] Sub-step S1061: The constructed initial generative adversarial network model includes a finite element module, a generator, and a discriminator that are communicatively connected to each other.

[0145] Further, as shown in Figure 10 , Figure 10 shows the overall structure of the initial generative adversarial network model. It can be seen that the finite element module is responsible for performing finite element analysis on the assembly accuracy of the deformable structure to generate an assembly deviation nephogram.

[0146] Further, as shown in Figure 11As shown, the generator adopts a coarse-to-fine design strategy. The low-resolution image is generated by the coarse generator to ensure the continuity of the image, while capturing the overall structure and key features of the image. Then, the fine generator is used to focus on enhancing the subtle local key features of the high-resolution image, improving the detail quality and realism of the image. This process is connected by multiple residual blocks to enhance the transmission of key features, improve the training stability, and maintain the information integrity of key features. The network architecture includes a convolutional layer for extracting initial key features, residual blocks for processing deep key features, and a transposed convolutional layer for image upsampling. In terms of the working mechanism, first, the image is downsampled by a factor of 2 in the fine generator. Then, the low-resolution image is generated based on the downsampled image on the coarse generator. Finally, the low-resolution image is sent back to the fine generator and fused with the image downsampled by a factor of 2 at the pixel level to generate a high-quality image, thus achieving the efficient generation of high-resolution images from low-resolution images.

[0147] Further, as Figure 12 shown, the designed discriminator adopts a multi-scale architecture to evaluate the authenticity of high-resolution images. It contains discriminators at two scales, which process the original resolution image and the downsampled (reduced by a factor of 2 in resolution) image respectively, enabling the model to analyze at different levels of detail, focusing on the authenticity of image details while evaluating global consistency. The inputs include the "fake" images synthesized by the generator and the "real" images generated by the finite element module. These images are fed into discriminators at different scales to extract key features, and the model is trained by calculating the element-wise loss. This design effectively avoids the problems of overfitting and increased storage space caused by deepening the network or increasing the convolutional kernel.

[0148] Sub-step S1062: As Figure 13 shown, in the process of training and validating the initial generative adversarial network model to obtain the final generative adversarial network model, the generative adversarial loss function is utilized. The generative adversarial loss function includes the loss function and the feature matching loss function.

[0149] Further, the initial generative adversarial network model mentioned in this embodiment is a High Resolution-Precision Generative Adversarial Networks (HiRes-PreciGAN) model, which consists of Figure 13It can be seen that the loss changes of the generator and discriminator during the training process of the HiRes-PreciGAN model. As the number of training epochs increases, the loss of the generator rapidly decreases and tends to be stable, indicating that the generator is continuously learning and improving the quality of the generated images. At the same time, the loss of the discriminator remains at a low level, showing its stable high discrimination ability. Figure 13 It also emphasizes through arrows and example images how the quality of the generated images gradually improves as training progresses, from initially blurred to finally clear and accurately structured. This demonstrates the ability of the HiRes-PreciGAN model in handling warping deviation and fluctuation deviation, as well as its effectiveness in image generation tasks.

[0150] Furthermore, the expression of the generative adversarial loss function is:

[0151] (7)

[0152] Where, represents the generative adversarial loss function, represents the generator, represents the discriminator, represents the type of discriminator, represents the loss function, , represents the expected value of the difference between the input image and the real image by the discriminator, represents the input image, represents the real image corresponding to the input image, represents the synthesized image, represents the expected value of the difference between the input image and the synthesized image by the discriminator, represents the generated image, represents the probability that the real image is judged as true by the discriminator, represents the probability that the generated image is judged as true by the discriminator, represents the feature matching loss function, , represents the extractor of the th layer of the discriminator, represents the total number of layers of the discriminator, represents the th layer of the discriminator, represents the number of elements in the th layer of the discriminator, represents the random variable, represents the given sample generated by the random variable, represents the expected value of the difference between the given sample and the input image, Represents the 1-norm.

[0153] Furthermore, The loss function is conducive to restoring the low-frequency part of the image; the feature matching loss function is used to reconstruct the high-frequency details of the image.

[0154] Furthermore, The ratio of the loss function and the feature matching loss function can be fine-tuned according to the specific requirements of the synthesized image to achieve the best image quality.

[0155] Furthermore, in this embodiment, by constructing an initial generative adversarial network model, training and validating the initial generative adversarial network model, a final generative adversarial network model is obtained, which is used as the final model for predicting the assembly deviation of the actual deviation image of the deformable structure. Thus, it can efficiently handle complex assembly deviation prediction tasks. Compared with traditional methods, it significantly improves the speed and accuracy of assembly deviation prediction, meeting the high-efficiency production requirements of aerospace manufacturing enterprises.

[0156] In step S107 of this embodiment, as Figure 14 shown, the actual deviation image of the deformable structure is input into the final generative adversarial network model for assembly deviation prediction, and an assembly deviation prediction image is generated.

[0157] Furthermore, it can be seen that after obtaining the final generative adversarial network model, by inputting the actual assembly deviation contour map of any deformable structure into the final generative adversarial network model for assembly deviation prediction, an assembly deviation prediction image as shown in Figure 14 can be obtained. Figure 14 is shown in the figure.

[0158] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of the present application, "a plurality" means two or more unless otherwise specifically defined.

[0159] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of this application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0160] As described above, it is only the specific implementation manner of this application, but the protection scope of this application is not limited thereto. Any person skilled in the art within the technical scope disclosed by this application can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of this application.

[0161] After considering the specification and practicing the invention disclosed herein, those skilled in the art will readily conceive of other embodiments of this application. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include the common general knowledge or conventional technical means in the technical field not disclosed by this application.

Claims

1. A geometric and physical fusion method for predicting assembly deviation of deformable structures, characterized in that The method includes the following steps: Decompose the deformable structure, extract all key features of each assembly level respectively, and discretize all the key features at the part level into a spatial vector point set; According to the spatial vector point set, characterize the part manufacturing deviation by using part warping deviation and part fluctuation deviation, and define the part manufacturing deviation that conforms to the tolerance specification as the consistent manufacturing deviation; Adopt a deterministic assembly method to characterize the assembly positioning deviation, and use finite element analysis to calculate the assembly deformation deviation; According to the structure decomposition, process the assembly information of the deformable structure, construct an assembly deviation transfer diagram; and use the consistent manufacturing deviation, the assembly positioning deviation and the assembly deformation deviation to map the assembly deviation transfer diagram into an assembly state space diagram, including: According to the structure decomposition, perform assembly unit division, assembly sequence adjustment, assembly datum identification and mating constraint definition on the deformable structure in sequence, and construct the assembly deviation transfer diagram; Map all part nodes in the assembly deviation transfer diagram into corresponding state nodes in the assembly state space diagram; Map all tooling constraint nodes in the assembly deviation transfer diagram into input variables of the corresponding state nodes in the assembly state space diagram; Map all mating constraint nodes in the assembly deviation transfer diagram into transfer relationships between the corresponding state nodes in the assembly state space diagram; Among them, mapping various nodes in the assembly deviation transfer diagram is carried out in the order from top to bottom and from left to right, and the consistent manufacturing deviation, the assembly positioning deviation and the assembly deformation deviation are respectively incorporated into the corresponding nodes to construct the assembly state space diagram; Use the assembly state space diagram to perform finite element analysis on the assembly accuracy of the deformable structure to obtain an assembly deviation cloud diagram, and convert the assembly deviation cloud diagram into an assembly deviation contour map, and the assembly deviation contour map contains a training data set and a test data set; Construct an initial generative adversarial network model, train the initial generative adversarial network model by using the training data set, and verify the trained initial generative adversarial network model by using the test data set to obtain a final generative adversarial network model; Input the actual deviation image of the deformable structure into the final generative adversarial network model for assembly deviation prediction to generate an assembly deviation prediction image.

2. The geometric and physical fusion method for predicting the assembly deviation of the deformable structure according to claim 1, wherein The types of the assembly levels include the component level, the sub-assembly level and the part level; The spatial vector point set includes: dimension information, shape information, position information and waviness information of the part.

3. The geometric and physical fusion method for predicting the assembly deviation of the deformable structure according to claim 1, characterized in that The step of characterizing the part manufacturing deviation by using part warping deviation and part fluctuation deviation according to the spatial vector point set and defining the part manufacturing deviation that conforms to the tolerance specification as the consistent manufacturing deviation includes: Superimpose the part warping deviation and the part fluctuation deviation on the spatial vector point set, and perform deviation statistics on all sampling points on the part surface; The result of the deviation statistics is characterized as the part manufacturing deviation by using geometric covariance, and the part manufacturing deviation includes the part warping deviation constructed by using Legendre polynomials and the part fluctuation deviation constructed by using sine polynomials; Check whether the part manufacturing deviation conforms to the tolerance specification; If the part manufacturing deviation conforms to the tolerance specification, define the part manufacturing deviation as the consistent manufacturing deviation; if the part manufacturing deviation does not conform to the tolerance specification, iterate the process of deviation statistics until the constructed part manufacturing deviation conforms to the tolerance specification.

4. The geometric and physical fusion method for predicting the assembly deviation of the deformable structure according to claim 3, wherein The expression of the consistent manufacturing deviation is: (1) Among them, represents the consistent manufacturing deviation of the deformable structure at the th assembly station, represents the ideal value of the part manufacturing deviation of the deformable structure at the th assembly station, represents the geometric covariance of the part surface, represents the normal direction of the discrete vector points in the spatial vector point set; The expression of the geometric covariance of the part surface is: (2) Among them, represents the weight coefficient of the part warping deviation, , represents the weight coefficient of the part fluctuation deviation, , represents the range of the part warping deviation, represents the range of the part fluctuation deviation, represents the part warping deviation, , represents the first transformation matrix, , represents the order Legendre polynomial, represents the order of the Legendre polynomial, represents the order of the Legendre polynomial, represents the number of sampling points on the part surface, represents the weight coefficient of the order of the Legendre polynomial, represents the th index of the sampling point on the part surface, represents the th index of the sampling point on the part surface, represents the variance matrix of the deviation change of the sampling points, represents the part fluctuation deviation, , represents the second transformation matrix, , , represents the weight coefficient of the frequency curve of the th order in the sine polynomial, represents the weight coefficient of the th order of the sine polynomial, represents the th order frequency of the sine polynomial, represents the column to which the sampling point on the part surface belongs, represents the row to which the sampling point on the part surface belongs, represents the th order of the sine polynomial, represents the order of the sine polynomial.

5. The geometric and physical fusion method for predicting the assembly deviation of the deformable structure according to claim 1, wherein The expression of the assembly positioning deviation is: (3) Among them, represents the assembly positioning deviation of the deformable structure at the th assembly station, represents the Jacobian matrix, represents the transfer matrix related to the coordinates and control directions of the deformable structure at the th assembly station, represents the deviation generated during the assembly process at the th assembly station; The expression of the assembly deformation deviation is: (4) Among them, represents the assembly deformation deviation generated when the deformable structure is under the action of an external load at the th assembly station, and represents the mapping function of the deformation of the deformable structure when the external load acts. represents the overall displacement generated during the positioning process of the deformable structure at the th assembly station, represents the flexible deformation caused during the clamping and riveting processes of the deformable structure at the th assembly station, and represents the springback deformation caused after the tooling or fixture of the deformable structure is released at the 6. The geometric and physical fusion method for predicting the assembly deviation of the deformable structure according to claim 5, wherein The expression of the assembly deviation transfer diagram is: (5) Among them, represents the assembly deviation transfer diagram, represents the set of part nodes during the assembly process, , represents the set of fixture constraint nodes during the assembly process, , represents the set of mating constraint nodes during the assembly process, , represents the set of node transfer directions during the assembly process, ; The expression of the assembly state space diagram is: （6） Among them, represents the assembly accuracy of the deformable structure after positioning at the th assembly station, represents the assembly accuracy of the deformable structure after positioning at the previous assembly station of the th assembly station, represents the first deviation coefficient matrix, represents the second deviation coefficient matrix, represents the third deviation coefficient matrix, represents the fourth deviation coefficient matrix, represents the fifth deviation coefficient matrix, represents the consistency manufacturing deviation of the deformable structure at the th assembly station, represents the assembly deviation of the deformable structure at the th assembly station obtained by measurement, represents the measurement error caused by the measurement of the measurement equipment at the th assembly station.

7. The geometric and physical fusion method for predicting the assembly deviation of the deformable structure according to claim 1, characterized in that The steps of performing finite element analysis on the assembly accuracy of the deformable structure by using the assembly state space diagram, obtaining an assembly deviation cloud diagram, and converting the assembly deviation cloud diagram into an assembly deviation contour diagram include: In finite element analysis software, perform finite element analysis on the assembly accuracy of the deformable structure by using the assembly state space diagram to obtain the assembly deviation cloud diagram; Successively use the cubic spline interpolation algorithm, the deviation normalization algorithm, and the color mapping algorithm to convert the assembly deviation cloud diagram into the assembly deviation contour diagram; Divide the data set reflected by the assembly deviation contour diagram into the training data set and the test data set, and the ratio of the training data set to the test data set is 4:

1.

8. The geometric and physical fusion method for predicting the assembly deviation of the deformable structure according to claim 1, characterized in that The steps of constructing an initial generative adversarial network model, training the initial generative adversarial network model by using the training data set, and verifying the trained initial generative adversarial network model by using the test data set to obtain a final generative adversarial network model include: The initial generative adversarial network model includes a finite element module, a generator, and a discriminator that are communicatively connected to each other; In the process of training and validating the initial generative adversarial network model to obtain the final generative adversarial network model, a generative adversarial loss function is utilized, and the generative adversarial loss function includes a loss function and a feature matching loss function; The expression of the generative adversarial loss function is: (7) Among them, represents the generative adversarial loss function, represents the generator, represents the discriminator, represents the type of discriminator, represents the loss function, , represents the expected value of the difference between the discriminator's input image and the real image, represents the input image, represents the real image corresponding to the input image, represents the synthesized image, represents the expected value of the difference between the discriminator's input image and the synthesized image, represents the generated image, represents the probability that the real image is judged as true by the discriminator, represents the probability that the generated image is judged as true by the discriminator, represents the feature matching loss function, , represents the extractor of the layer of the discriminator, represents the number of elements in the layer of the discriminator, represents a random variable, represents a given sample generated by the random variable, represents the expected value of the difference between the given sample and the input image, represents the ratio of the loss function and the feature matching loss function.

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