Pivot rail contact pressure prediction method and system based on DNN and CGAN

Abstract

The invention discloses a pivot rail contact pressure prediction method and system based on DNN and CGAN, and the method comprises the steps: building armature models with different structure parameters, and obtaining contact pressure values under different structure parameters and corresponding contact pressure field diagrams under different structure parameters; training a DNN model based on the contact pressure value; training a CGAN based on the contact pressure field map; and on the basis of the pre-trained DNN model and the CGAN, respectively predicting the total contact pressure and the field graph of the contact pressure distribution. Through the processing scheme disclosed by the invention, rapid prediction from the structure parameters to the total contact pressure and the contact pressure distribution can be realized.

Description

Technical Field

[0001] The present invention relates to the field of pressure prediction technology, and in particular to a method and system for predicting pivot rail contact pressure based on DNN and CGAN. Background Art

[0002] During the launch of the electromagnetic rail launcher, the field distribution on the contact surface of the pivot rail is extremely uneven, especially the peak intensity in the local area is close to or reaches the material bearing limit. In the initial state, the current distribution on the contact surface of the pivot rail is mainly affected by the contact resistance. This contact resistance is regulated by the contact pressure distribution, and its change will directly affect the current distribution, thereby further affecting the field distribution. The precise design of the contact pressure of the pivot rail at the initial moment is of great significance to the "maximum use" of the electromagnetic rail gun under the existing material parameters.

[0003] The armature of the electromagnetic rail launcher mostly adopts C-type armature. The armature is driven by the electromagnetic force generated by the closed circuit. Good electrical contact is the guarantee of efficient launch of the electromagnetic device. The lack of contact pressure will cause the instability of electrical contact, which will cause melting and arcing of the contact surface, and then cause the transition from metal-metal contact to metal arc contact. Studies have shown that most transitions are caused by insufficient contact pressure. The initial preload between the armature and the rail is provided by the elastic deformation of the armature. The study of the initial contact state is important for understanding the change of contact state during the entire launch process.

[0004] Numerical simulation methods represented by the finite element method have the problems of large amount of calculation, long calculation time and non-reusability. The simulation calculation time of some complex simulation models is tens or hundreds of hours. The high calculation cost makes it difficult to carry out subsequent optimization work smoothly.

[0005] It can be seen that the above existing pressure prediction methods are still inconvenient and defective in use, and are in urgent need of further improvement. How to create a new method for predicting the contact pressure of the pivot rail has become a goal that the industry urgently needs to improve. Summary of the invention

[0006] In view of this, an embodiment of the present disclosure provides a method for predicting the contact pressure of a pivot rail based on DNN and CGAN, which at least partially solves the problems existing in the prior art.

[0007] In a first aspect, an embodiment of the present disclosure provides a method for predicting the contact pressure of a pivot rail based on a DNN and a CGAN, the method comprising the following steps:

[0008] Establish armature models with different structural parameters, and obtain contact pressure values ​​under different structural parameters and corresponding contact pressure field diagrams under different structural parameters;

[0009] Training a DNN model based on the contact pressure value;

[0010] Training the CGAN based on the contact pressure field map;

[0011] The total contact pressure and the field map of contact pressure distribution are predicted based on the pre-trained DNN model and CGAN, respectively.

[0012] According to a specific implementation method of an embodiment of the present disclosure, the structural parameters include: parameter A, parameter B, parameter C, parameter D and parameter E; wherein parameter A is half of the track spacing; parameter B is the interference; parameter C is the tail thickness; parameter D is the armature tail length; and parameter E is the armature curvature.

[0013] According to a specific implementation of the embodiment of the present disclosure, establishing armature models with different structural parameters and obtaining contact pressure values ​​under different structural parameters and corresponding contact pressure field diagrams under different structural parameters include:

[0014] The total contact pressure and contact pressure distribution of the pivot rail contact surface after assembly are calculated by numerical simulation method;

[0015] The total contact pressure and contact pressure distribution are calculated using the parametric sweep method for the specified parameter combination.

[0016] According to a specific implementation of the embodiment of the present disclosure, the training of the DNN model based on the contact pressure value includes: a training phase and an inference phase;

[0017] Based on the parameterized model of the armature and the interference fit model of the electromagnetic rail launcher, the contact pressure in the initial contact situation is numerically simulated to obtain a data set for training;

[0018] The total contact pressure under the initial contact condition is divided into a training set and a test set. The training set is used to train the DNN model, and the test set is used to test the generalization ability of the DNN model.

[0019] According to a specific implementation of the embodiment of the present disclosure, training CGAN based on the contact pressure field map includes:

[0020] The tensor with the same size as the contact pressure field distribution is superimposed with the contact pressure field map channel as the input image of the discriminator D;

[0021] The input image is downsampled by four convolution operations, and each convolution operation is followed by a batch normalization operation and a LeakyReLU activation;

[0022] Use the fully connected layer to expand the output of the convolutional network and output a scalar value. Use the Sigmoid function to limit the result between (0,1), which indicates the probability of judging that the image is a real image.

[0023] According to a specific implementation of the embodiment of the present disclosure, the objective function of CGAN is:

[0024]

[0025] Among them, G * is the objective function of CGAN; λ is the weight of L1 loss function; G is the generator; D is the discriminator; L cGAN (G,D) is the objective function of CGAN; L1(G) is the absolute error loss function;

[0026] L1(G)=E||G(y)-x||1

[0027] Among them, E is the expectation operator, which means averaging all data; G(y) is the contact pressure field map generated by the generator under given condition y; x is the actual contact pressure field map.

[0028] In a second aspect, an embodiment of the present disclosure provides a pivot rail contact pressure prediction system based on DNN and CGAN, the system comprising:

[0029] A data acquisition module is configured to establish armature models with different structural parameters, and obtain contact pressure values ​​under different structural parameters and corresponding contact pressure field diagrams under different structural parameters;

[0030] A training module is configured to train a DNN model based on the contact pressure value; and train a CGAN based on the contact pressure field map;

[0031] The prediction module is configured to predict the field map of the total contact pressure and the contact pressure distribution based on the pre-trained DNN model and CGAN, respectively.

[0032] According to a specific implementation of the embodiment of the present disclosure, the system further includes:

[0033] The DNN model training module is configured to optimize the entire network by calculating the gradient of the loss function using the back-propagation mechanism;

[0034] The CGAN training module is configured to superimpose a tensor of the same size as the contact pressure field distribution and the contact pressure field map channel as an input image of the discriminator D; downsample the input image through four convolution operations, perform batch normalization and LeakyReLU activation after each convolution operation; and use a fully connected layer to expand the output of the convolution network, output a scalar value, and use a Sigmoid function to limit the result between (0,1), indicating the probability of judging that the image is a real image.

[0035] The DNN and CGAN-based method for predicting the contact pressure of the pivot rail in the disclosed embodiment simulates different armature structures and rails to study the influence of different armature structural parameters on the contact pressure distribution of the pivot rail contact surface. Furthermore, the calculation results of the above model are formed into a data set to use DNN and CGAN to predict the total contact pressure and field map respectively. At this point, a rapid prediction from structural parameters to total contact pressure and contact pressure distribution is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The above is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0037] Figure 1 A schematic flow chart of a method for predicting pivot rail contact pressure based on DNN and CGAN provided in an embodiment of the present disclosure;

[0038] Figure 2 Interference fit diagram;

[0039] Figure 3 is a schematic diagram of boundary conditions;

[0040] Figure 4 Schematic diagram of contact pressure field of typical size;

[0041] Figure 5 This is a schematic diagram of contact pressure distribution after the armature is assembled;

[0042] Figure 6 This is a schematic diagram of the distribution of the contact area between the armature surface and the track and the area above the half-peak value after assembly;

[0043] Figure 7 Schematic diagram of the effect of A parameter change on the non-uniformity coefficient and total contact pressure;

[0044] Figure 8 Schematic diagram of the effect of B parameter change on the non-uniformity coefficient and total contact pressure;

[0045] Fig. 9 Schematic diagram of the effect of C parameter change on the non-uniformity coefficient and total contact pressure;

[0046] Fig.10 Schematic diagram of the effect of D parameter change on the non-uniformity coefficient and total contact pressure;

[0047] Fig.11 Schematic diagram of the effect of E parameter change on the non-uniformity coefficient and total contact pressure;

[0048] Fig.12 Schematic diagram of the deep neural network structure;

[0049] Fig.13 Schematic diagram of the GAN model structure;

[0050] Fig.14 Schematic diagram of the CGAN model structure;

[0051] Fig.15 Schematic diagram of the network structure of the discriminator D;

[0052] Fig.16 is a flow chart of the initial contact pressure prediction method;

[0053] Fig.17 Schematic diagram of the CGAN contact pressure field map prediction model;

[0054] Fig.18 Schematic diagram of the convergence effect of the training process;

[0055] Fig.19 It is a schematic diagram of contact pressure prediction effect;

[0056] Fig. 20 This is a schematic diagram of the absolute error percentage of the contact pressure prediction effect;

[0057] Fig.21 This is a schematic diagram of the training and testing convergence diagram;

[0058] Fig. 22 It is a schematic diagram of the prediction results of the contact pressure field diagram of the pivot-rail contact surface;

[0059] Fig.23 A schematic diagram of the structure of a pivot rail contact pressure prediction system based on DNN and CGAN provided in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0060] The embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.

[0061] The following describes the embodiments of the present disclosure through specific examples, and those skilled in the art can easily understand other advantages and effects of the present disclosure from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all of the embodiments. The present disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present disclosure.

[0062] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described in the present invention may be embodied in a wide variety of forms, and any specific structure and / or function described in the present invention is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described in the present invention may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described in the present invention may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described in the present invention may be used to implement this device and / or practice this method.

[0063] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects described may be practiced without these specific details.

[0064] The existing technology uses the finite element method to analyze the contact pressure after interference fit of armatures with different geometric structures, but has the problems of long calculation time, large workload and non-reusability.

[0065] In order to solve the problems existing in the prior art, the embodiment of the present invention provides a method for predicting the contact pressure of the armature rail based on a deep neural network (DNN) and a conditional generative adversarial network (CGAN). First, the C-type armature is taken as the research object, and the armature model with different structural parameters is established by using a parametric modeling method. The total contact pressure and contact pressure distribution of the contact surface of the armature rail after assembly are calculated by a numerical simulation method. The influence of different structural parameter changes on the total contact pressure and contact pressure distribution is analyzed. Then, the total contact pressure and contact pressure distribution of the specified parameter combination are calculated by a parametric scanning method. The armature structural parameters are matched with the field diagrams of the total contact pressure and contact pressure distribution respectively to form two data sets. Finally, the DNN model and CGAN are used to predict the field diagrams of the total contact pressure and contact pressure distribution. By comparing the prediction results of the test set with the actual simulation results, it can be found that the mean absolute percentage error (MAPE) of the total contact pressure and contact pressure distribution prediction results and the actual simulation results in the test set are less than 1% and 0.78%, respectively. The model prediction can meet the actual engineering needs and realize efficient exploration in the design domain. The rapid prediction model established by the present invention has a reference significance for optimizing the armature structure and carrying out refined design of the overall system.

[0066] Figure 1 A schematic diagram of the process of the pivot rail contact pressure prediction method based on DNN and CGAN provided in an embodiment of the present disclosure.

[0067] like Figure 1 As shown, at step S110, armature models with different structural parameters are established, and contact pressure values ​​under different structural parameters and corresponding contact pressure field diagrams under different structural parameters are obtained.

[0068] In an embodiment of the present invention, the structural parameters include: parameter A, parameter B, parameter C, parameter D and parameter E; wherein parameter A is half of the track spacing; parameter B is the interference; parameter C is the tail thickness; parameter D is the armature tail length; and parameter E is the armature curvature.

[0069] In an embodiment of the present invention, the establishment of armature models with different structural parameters and the acquisition of contact pressure values ​​under different structural parameters and corresponding contact pressure field diagrams under different structural parameters include: calculating the total contact pressure and contact pressure distribution of the armature-rail contact surface after assembly by numerical simulation; and calculating the total contact pressure and contact pressure distribution of a specified parameter combination by parametric scanning.

[0070] More specifically, the process proceeds to step S120.

[0071] In step S120, a DNN model is trained based on the contact pressure value.

[0072] In an embodiment of the present invention, the training of the DNN model based on the contact pressure value includes: based on the parameterized model of the armature and the interference fit model of the electromagnetic rail launcher, numerically simulating the contact pressure under the initial contact condition to obtain a data set for training; dividing the total contact pressure under the initial contact condition into a training set and a test set, using the training set to train the DNN model, and using the test set to test the generalization ability of the DNN model.

[0073] Next, go to step S130.

[0074] In step S130 , a CGAN is trained based on the contact pressure field map.

[0075] In an embodiment of the present invention, training a CGAN based on the contact pressure field map includes: superimposing a tensor with the same size as the contact pressure field distribution and the contact pressure field map channel as an input image of the discriminator D; downsampling the input image through four convolution operations, and performing a batch normalization operation and a LeakyReLU activation after each convolution operation; using a fully connected layer to expand the output of the convolution network, outputting a scalar value, and using a Sigmoid function to limit the result between (0,1), indicating the probability of judging that the image is a real image.

[0076] In this embodiment of the present invention, the objective function of CGAN is:

[0077]

[0078] Among them, G * is the objective function of CGAN; λ is the weight of L1 loss function; G is the generator; D is the discriminator; L cGAN (G,D) is the objective function of CGAN; L1(G) is the absolute error loss function;

[0079] L1(G)=E||G(y)-x||1

[0080] Among them, E is the expectation operator, which means averaging all data; G(y) is the contact pressure field map generated by the generator under given condition y; x is the actual contact pressure field map.

[0081] Next, go to step S140.

[0082] At step S140, the field map of the total contact pressure and the contact pressure distribution are predicted based on the pre-trained DNN model and CGAN, respectively.

[0083] The present invention is described below in conjunction with embodiments:

[0084] 1 Armature assembly simulation modeling

[0085] 1.1 Armature geometric parameters

[0086] The C-type solid armature used in the study. The deformation of the armature before and after interference fit is as follows Figure 2 Parameters A, B, C, D, and E represent half of the track spacing, interference, tail thickness, armature tail length, and armature curvature, respectively. c Represents the total contact pressure generated by the armature and rail in the vertical direction.

[0087] 1.2 Model Setup

[0088] The calculation of the contact pressure of the electromagnetic track in the initial state is a problem involving contact nonlinearity. The present invention uses finite element software to establish a contact surface contact pressure calculation model and solve it. During the numerical simulation process, the following basic assumptions are made:

[0089] (1) Ignore the material wear of the armature and rail during assembly.

[0090] (2) The armature undergoes only elastic deformation during the deformation process, and the track is approximately a rigid body.

[0091] (3) The physical processes experienced by the two contact surfaces of the armature during assembly are symmetrical, so a 1 / 2 model is used for ease of calculation.

[0092] The material parameters of the armature interference fit model established in the present invention are shown in Table 1. The material parameters are the values ​​of the ETP copper alloy and the A6061 aluminum alloy at room temperature.

[0093] Table 1 Material parameters

[0094]

[0095] like Figure 3 As shown in the figure, select the prescribed displacement in the Solid Mechanics module. The position of the rail contact surface is specified so that it is parallel to the symmetry plane of the armature after the armature is fully in contact. To prevent the armature from being ejected due to deformation, a fixed constraint is applied to the armature mid-axis surface so that it cannot move in any direction. The contact method is set to penalty function.

[0096] The model is solved using a steady-state solver. The solution mode is set to fully coupled, and the dependent variables in the model are the node displacements of the mesh.

[0097] 1.3 Contact pressure unevenness coefficient

[0098] The uneven distribution of contact pressure is reflected by the contact pressure on the contact surface. Take a typical example, in which the parameters A, B, C, D, and E are 15mm, 0.2mm, 1.4mm, 25mm, and 11° respectively. The contact pressure distribution after assembly is as follows: Figure 47 parameters are defined, and the meaning of each parameter is shown in Table 2. Some parameters are shown in Figure 5 As shown. The contact area between the armature surface and the track after assembly is Figure 6 The red area and the blue area. The red and blue parts together constitute the actual contact area A c The blue part is the area A2 above the half peak after assembly. The actual contact area and the gray area together constitute the total surface area A1 of the outer surface of the armature tail.

[0099] Table 2 Parameter definition

[0100]

[0101]

[0102] At the same time, four non-uniform coefficients are defined, and their expressions and physical meanings are shown in Table 3. The value range of the four parameters is between 0 and 1, and the closer to 1, the more uniform the distribution.

[0103] Table 3 Definition of non-uniformity coefficient

[0104]

[0105] 2. Characteristics of uneven contact pressure distribution

[0106] 2.1 Effect of A parameter changes on non-uniform characteristics

[0107] Fixed B = 0.2mm, C = 1.4mm, D = 25mm, E = 11°, and took A = 15mm, 16mm, 17mm, 18mm, 19mm. When changing the A parameter, the non-uniformity coefficient changes as follows Figure 7 shown.

[0108] Depend on Figure 7 It can be seen that when the other structural parameters of the armature remain unchanged and only the A parameter is changed, the change of the uneven coefficient is inconsistent. c / d s and A c / A1 shows a downward trend overall. p2 / p1 shows an oscillating trend. A2 / A c This is because as the A parameter increases, the actual contact length L c The overall maximum contact pressure p1 and the local maximum contact pressure p2 both show a downward trend. The difference in the rate of decline causes p2 / p1 to show an oscillating trend. The increase in the A parameter will directly lead to a decrease in the actual contact area, thereby affecting A2 / A. c and A c / A1.

[0109] Therefore, appropriately increasing the railgun track spacing can reduce the local unevenness and increase the unevenness of the lateral distribution and overall distribution. At the same time, it should be noted that increasing the railgun track spacing will reduce the total contact pressure and the maximum contact pressure. The actual situation needs to be comprehensively considered when designing the bore width.

[0110] 2.2B Effect of parameter changes on inhomogeneous characteristics

[0111] Fix A = 15mm, C = 1.4mm, D = 25mm, E = 11°, and take B = 0.2mm, 0.3mm, 0.4mm, 0.5mm and 0.6mm. When changing the B parameter, the non-uniformity coefficient changes as follows Figure 8 shown.

[0112] Depend on Figure 8 It can be seen that when the other structural parameters of the armature remain unchanged and only the B parameter is changed, as the interference B increases, the total contact pressure F c Rapidly increase. Among the geometric parameters of the armature, the size of the interference B plays an almost decisive role in the total contact pressure. As the interference B increases, the unevenness of the longitudinal distribution and the unevenness of the local distribution deteriorate to a certain extent. However, the unevenness of the lateral distribution and the unevenness of the overall distribution do not change significantly. The main reason for these phenomena is that the increase in the interference B does not lead to an increase in the actual contact length L. c The significant increase in p1 will lead to a rapid increase in p1. The rapid increase in p1 will cause a rapid increase in the half-peak value, and A2 will decrease slightly.

[0113] Since the interference of the armature plays a leading role in the total contact pressure at the initial moment, the size of the interference should be determined first when the total contact pressure is given. Excessive interference will aggravate the longitudinal and local unevenness. This may aggravate the damage to the track in the early stage of launch.

[0114] 2.3 Effect of C parameter changes on inhomogeneous characteristics

[0115] Fix A = 15mm, B = 0.2mm, D = 25mm, E = 11°, and take C = 1.4mm, 1.5mm, 1.6mm, 1.7mm and 1.8mm. When changing the C parameter, the non-uniformity coefficient changes as follows Fig. 9 shown.

[0116] Depend on Fig. 9 It can be seen that when the other structural parameters of the armature remain unchanged and only the C parameter is changed, A2 / A c and the total contact pressure gradually increases, L c / d s and A c / A1 hardly changes, and p2 / p1 shows an oscillating trend. When the thickness C of the tail wing gradually increases, although the maximum value p1 at the waist will also increase, the growth rate is slower. The increased contact pressure will be more evenly distributed in other areas, partially improving the degree of local uneven distribution.

[0117] The thickness of the armature tail wing mainly provides space for friction and wear between the armature and the track, melting wear and the armature mass. Therefore, the overall flexibility of the tail wing should be considered when selecting the value.

[0118] 2.4 Effect of D parameter changes on inhomogeneous characteristics

[0119] Fix A = 15mm, B = 0.2mm, C = 1.4mm, E = 11°, and take D = 25mm, 26mm, 27mm, 28mm and 29mm. When changing the D parameter, the non-uniformity coefficient changes as follows Fig.10 shown.

[0120] Depend on Fig.10 It can be seen that when the D parameter is increased, the L c / d s Except for the decreasing trend, the other parameters all show an increasing trend. As the D parameter increases, the armature tail length d s The actual contact length L c will also increase, but not as much as d s , so it leads to L c / d s The overall trend is downward. As the D parameter increases, p1 gradually decreases, and p2, A1, A2, A c and F c Overall, increasing parameter D is beneficial to improving the uneven distribution of contact pressure.

[0121] When designing the armature, appropriately increasing the length of the armature tail can effectively improve the uneven coefficient except for the lateral distribution. However, an overly long armature will significantly increase the mass of the armature, thereby affecting the exit speed. The value of parameter D should comprehensively consider the relationship between the length of the armature tail and the overall mass.

[0122] 2.5E Effect of Parameter Variation on Inhomogeneous Characteristics

[0123] Fix A = 15mm, B = 0.2mm, C = 1.4mm, D = 25mm, and take E = 11°, 12°, 13°, 14° and 15°. When changing the E parameter, the non-uniformity coefficient changes as follows Fig.11 shown.

[0124] Depend on Fig.11 It can be seen that with the increase of E parameter L c / d sNo obvious change, A c / A1 has a small increase. p2 / p1, A2 / A c and F c As the parameter E increases, the actual contact length L c Almost no change, p1, p2, A1, A2 and A c All of them increase, and the different increasing rates lead to different trends of different non-uniformity coefficients. It is worth noting that the total contact pressure F c As the E parameter increases, the rate of increase is greater.

[0125] Therefore, it can be considered that the larger the E parameter, the better the overall contact pressure distribution. However, when designing, it is also necessary to consider the ability of the armature throat to carry current and electromagnetic force to determine the actual size of the E parameter.

[0126] 3 Deep Learning Theory

[0127] 3.1 Deep Learning Theory

[0128] A neural network is a computational model that simulates the working principle of the human brain nervous system. It contains multiple neurons, and each layer of the neural network is composed of multiple neurons, and each neuron has a weight value related to the size of the input data of that layer. These neurons are arranged in an orderly manner into a hierarchical structure, in which the neurons in each layer receive the output from the neurons in the previous layer as input. In this way, the neural network completes the transmission and processing of information, forming a complex network structure.

[0129] like Fig.12 As shown in the figure, a neural network usually consists of an input layer, a hidden layer, and an output layer. When a neural network has multiple hidden layers, especially three or more hidden layers, it is called a deep neural network (DNN). The basic structure of a neural network includes an input layer, a hidden layer, and an output layer. In a general neural network, the neurons in the input layer receive external data and pass it to the hidden layer. The neurons in the hidden layer use a specific activation function to weight the input data and pass the output to the output layer, and finally obtain the output result of the model.

[0130] In a deep neural network (DNN), this structure is extended to include multiple hidden layers, and the activation functions in the hidden layers are usually nonlinear, and the weight values ​​are learned through training. Compared with traditional models, deep neural networks (DNNs) have more complex and abstract feature expression capabilities. Through multi-level feature extraction and combination, DNNs can learn higher-order and more abstract features, thereby achieving higher-precision reasoning and classification in various tasks.

[0131] The training of DNN is divided into two stages: training stage and inference stage. In the training stage, the model performance is improved by optimizing the weight values ​​of each layer. These weight values ​​are usually randomly initialized to avoid falling into local minima. In order to adjust the weights of neurons, optimization algorithms such as stochastic gradient descent and more advanced algorithms in recent years, such as Adam and RMSProp, are used. By calculating the gradient of the loss function, the back-propagation mechanism is used to optimize the entire network, and finally the convergence and learning of the model are achieved.

[0132] 3.2CGAN

[0133] Generative Adversarial Network (GAN) is an unsupervised learning model that consists of two parts: generator G and discriminator D. Generator G is responsible for generating synthetic images that are similar to the distribution of real images, while discriminator D is used to distinguish between real images and generated images. Its model structure is as follows Fig.13 As shown. First, fix the parameters of the generator G, train the discriminator D, calculate the discriminant loss and update the parameters of the discriminator D; then fix the parameters of the discriminator D, train the generator G, input random noise z into the generator G to output the generated image, input the generated image into D to obtain the discriminant loss, and back propagate to update the parameters of the generator G. Repeat the above process until a realistic image is generated.

[0134] From the principle of the GAN network, we can know that the generator G and the discriminator D compete with each other, and L(G,D) represents the loss function. The expected error of the discriminator D is minimized, while the expected error of the generator G is maximized.

[0135] The final error function is

[0136]

[0137] Where Ex~p(x), Ez~p(z) represent the expected value of the sample, D(x) represents the probability that the discriminator judges whether x is real data, and D(G(Z)) represents the probability that the discriminator judges whether the generated data G(z) is real data.

[0138] The original GAN ​​can only generate high-dimensional data randomly, and cannot generate data under given conditions, which greatly limits the application scope of GAN. Based on GAN, the Conditional Generative Adversarial Network (CGAN) inputs label information as a constraint condition together with random noise into the generative model, so that the model can generate high-dimensional data under specified conditions. Fig.14 shown.

[0139] CGAN adds additional conditional variables y to the generator G and the discriminator D on the basis of GAN so that the output contains specified information. The objective function of CGAN is

[0140]

[0141] In the formula, D(x|y) represents the output probability of the discriminator D for the real data x under condition y, and G(z|y) represents the data generated by the generator G based on the noise z and condition y.

[0142] In the CGAN model, the architecture of the generator uses a four-layer deconvolution network to effectively generate the target image from the noise vector. The generator first receives random noise z and conditional variables y as input. These inputs first pass through a fully connected layer and are subsequently reshaped into a multi-dimensional feature map (specific resolution can be written). Next, the feature map is fed into four consecutive deconvolution layers, each accompanied by batch normalization and LeakyReLU activation functions. Each deconvolution layer gradually enlarges the spatial dimension of the feature map while reducing its depth, thereby gradually constructing the required image resolution. At the end of the network, an upsampling operation is performed to convert the image to a resolution of 221*201, using the Sigmoid activation function to generate the final output image. Through this design, the generator is able to learn complex data distributions from a low-dimensional latent space and effectively reconstruct high-resolution image details.

[0143] The discriminator D of the contact pressure distribution prediction model based on CGAN is mainly composed of convolutional layers, and its structure is as follows: Fig.15 As shown in the figure. The conditional variable y is converted into a tensor (batch×1×256×256) of the same size as the contact pressure field distribution, and is superimposed with the contact pressure field map channel as the input of the discriminator D. The input image is downsampled by 4 convolution operations, and each convolution operation is followed by batch normalization and LeakyReLU activation. Finally, the output of the convolutional network is expanded using a fully connected layer to output a scalar value, and the Sigmoid function is used to limit the result between (0,1), indicating the probability of judging that the image is a real image.

[0144] Since the task of the generator G is not only to deceive the discriminator D, but also to generate a contact pressure field map close to the real one, the loss function of the generator G additionally adds the L1 loss function, i.e., the absolute error loss function, which is expressed as

[0145] L1(G)=E||G(y)-x||1 (3)

[0146] The final overall objective function can be written as

[0147]

[0148] Where λ is the weight of the L1 loss function.

[0149] 3.3 Contact pressure size and distribution prediction model

[0150] The contact pressure prediction problem is a typical regression problem, that is, predicting a numerical output by inputting features. DNN usually performs well in regression problems, so a method for predicting the contact pressure of the pivot rail in the initial state based on DNN is established, such as Fig.16 shown.

[0151] (1) Based on the parameterized model of the armature and the interference fit model of the electromagnetic rail launcher, the contact pressure under the initial contact condition is numerically simulated to obtain a data set for training;

[0152] (2) The total contact pressure under the initial contact condition is divided into a training set and a test set. The training set is used to train the DNN model, and the test set is used to test the generalization ability of the DNN model.

[0153] (3) Rapid prediction of total contact pressure under different armature geometries

[0154] In the CGAN model, random noise z and conditional variable y are spliced ​​together as the input of the generator G. Due to the randomness of the noise z, the process of G generating an image can be regarded as a one-to-many mapping under the constraint of a given conditional variable y. The existence of z gives the generated images differences. The present invention establishes a one-to-one mapping from parameters A, B, C, D, E to contact pressure distribution. Therefore, the random noise z is removed and the generator G only takes the conditional variable y as input.

[0155] The contact pressure field map prediction model based on CGAN is as follows Fig.17 As shown, it includes two parts: training phase and testing phase. During the training process, the armature geometric parameters A, B, C, D, and E are first combined into the conditional variable y. After the dimension conversion through the fully connected layer, y is input into the generator G to generate the field distribution G(y) of the contact pressure distribution. Next, the calculated contact pressure value of the actual contact surface is matrixed to form a real image x. Throughout the process, the conditional variable y is spliced ​​and combined with the generated image G(y) or the real image x, and then input into the discriminator D. Finally, the discriminator D evaluates these input data and outputs the probability that the image is a real image.

[0156] During this training process, the generator G and the discriminator D collaborate with each other in an adversarial manner, alternately updating the neural network parameters in the hope that the generated images are closer to the real images, forming a dynamic optimization process.

[0157] The armature geometry established in Section 1.3 is used as a variable, as shown in Table 4. All combinations are calculated using the parametric sweep method, and a total of 1200 sets of data under different structural parameters are obtained. The 1200 sets of sample data are divided into training set and test set according to 8:2.

[0158] Table 4 Armature structure variable values

[0159]

[0160] In the process of comparative analysis of the prediction experiment, the mean square error (MSE) and mean absolute percentage error (MAPE) are used as performance indicators of the model to evaluate the accuracy of the predicted contact pressure distribution field map. The formula is:

[0161]

[0162] In the formula, y i and are the true value and predicted value of the i-th sample, respectively, and N is the number of samples. The value range of MAPE and MSE is [0, +∞). The smaller the value, the better the model prediction effect. The normal value range of R2 is [0, 1]. The closer the result is to 1, the better the fitting effect. The contact pressure numerical prediction results are calculated using MSE, MAPE and R 2 The field map prediction model uses MSE and MAPE.

[0163] 3.4 Numerical prediction results of contact pressure

[0164] 3.4.1 Network training and hyperparameter tuning

[0165] Appropriate hyperparameters can speed up model training, reduce training time, and prevent overfitting, thereby improving prediction accuracy. After a lot of attempts, we finally decided to use 4 hidden layers with 32, 32, 24, and 18 neurons, respectively. We chose 32 for batch size and 1×10 for learning rate. -3 .

[0166] Adaptive Moment Estimation (Adam) optimizer is used to minimize the objective function, which has great advantages in convergence speed and computational efficiency. The iterative process of the Adam optimization algorithm is as follows:

[0167]

[0168] In the formula, t is the number of iterations, and the initial value is 0; f t(w t-1 ) is the loss function; w t is the weight parameter; g t is the gradient of the loss function; m t is the first-order moment estimate, m0 is 0; v t is the second-order moment estimate, v0 is 0; is the corrected first-order moment estimate; is the corrected second-order moment estimate.

[0169] Compare the effects of different optimizers on the model prediction performance. Four optimizers, Adam, AdaGrad, RMSProp, and SGD, are used to compare the prediction effects, as shown in Table 5. It can be seen that Adam is better than the other three in comprehensive aspects, so the Adam optimizer is selected.

[0170] Table 5 Model prediction results under different optimizers

[0171]

[0172] The curve of mean square error changing with the number of iterations is as follows: Fig.18 As shown in Figure 2, it can be seen that when the number of iterations reaches 50, the mean square error hardly changes.

[0173] 3.4.2 Prediction Results

[0174] The above network and the above parameter adjustment method are used to predict the 240 groups of samples in the test set. The predicted values ​​and actual values ​​are as follows Fig.19 As shown in Figure 2, it can be seen that the network has achieved good results in predicting the absolute value of contact pressure. Fig. 20 The absolute error percentage of each prediction sample is shown. It can be seen that the maximum absolute error percentage does not exceed 4.5%, and the average absolute percentage error is 0.81%, which can basically meet engineering requirements. The DNN model used in the present invention can well learn the relationship between contact pressure and armature structural parameters and predict contact pressure with high accuracy.

[0175] 3.5 Contact pressure field map prediction results

[0176] 3.5.1 Network training and hyperparameter tuning

[0177] Based on the Pytorch deep learning contact pressure field map prediction model, GPU is used to accelerate model training. The hardware configuration is: NVIDIA GTX 4090, video memory 24GB.

[0178] The commonly used Adam optimizer is used to minimize the damage function. To further improve the convergence speed, a learning rate adjustment strategy is adopted based on Adam. When the loss function does not decrease for 5 consecutive iterations, the learning rate is returned to the original 0.1.

[0179] Appropriate hyperparameters can improve prediction accuracy, speed up training, prevent model overfitting, and improve model accuracy. Perform hyperparameter tuning on Epoch, Batch-size, initial learning rate, and L1 loss function weight λ. Perform hyperparameter tuning according to the hyperparameter value range shown. Finally, it is determined that when Epoch is 200, Batch-size is 64, initial learning rate is 2e-3, and λ is 50, the comprehensive prediction performance of the model is the best. Under this structural parameter, the change trend of the Loss function with epoch is as follows: Fig.21 shown.

[0180] Too large a data set will increase the cost of data processing, and while it will take time, the prediction accuracy will not be significantly improved. Therefore, the model structure is kept unchanged to verify the impact of the data set on the model performance.

[0181] The prediction results under different sample numbers are shown in Table 6. When the number of training samples is 120 and 240, the training results are poor and do not meet the accuracy requirements. When the number of training samples increases to 360, 480, 600 and 720, the MSE decreases significantly. However, there is a slight increase when the number of samples is 840, and then it decreases again when the number of samples is 960, but it only decreases slightly when the sample data is 720, but the training time is greatly increased. If the data set preparation time is taken into account, each set of data still needs several minutes of calculation time. Therefore, while ensuring the training speed and taking into account the training effect, the number of subsequent training samples is selected as 720.

[0182] Table 6 Prediction error and training time of the model under different training set sample numbers

[0183]

[0184]

[0185] The number of transposed convolution layers in the generator is studied to explore the impact of different numbers of convolution layers on the prediction effect. As can be seen from Table 7, with the increase in the number of convolution layers, the MSE and MAPE of the model continue to decrease, but the time cost is rapidly increasing. When the number of convolution layers reaches 6, the time used has reached 120 hours, and the training results are partially improved compared to 5 layers. It can be inferred that if the number of convolution layers is further increased, the time cost will be unbearable. Therefore, the number of convolution layers is selected to be 6.

[0186] Table 7 Prediction error and training time of different convolutional layer models

[0187]

[0188] 3.5.2 Prediction Results

[0189] The training set samples are predicted using the CGAN network and the above parameter adjustment method. In order to compare the results more intuitively, the predicted field diagram is compared with the field diagram calculated by the finite element method. Five typical groups of results are selected for display. Fig. 22 As shown in the figure. The first column in the figure is the true solution obtained by finite element simulation, the second column is the value predicted by the CGAN method, and the third column is the absolute value of the difference between the true solution and the CGAN predicted value at the corresponding position. It can be observed from the figure that the contact pressure field map predicted by the CGAN model basically coincides with the true solution result obtained by simulation, and the agreement is good. The shape of the actual contact area also matches well with the area where the contact pressure is concentrated. The error is mainly concentrated in the transition area between the non-contact area of ​​the armature head and the actual contact area.

[0190] 4 Conclusion

[0191] The present invention uses a parametric modeling method to study the contact pressure size and distribution characteristics of different structure armatures after interference fit, and uses DNN and CGAN models to predict the contact pressure size and contact pressure field map after assembly. The specific conclusions are as follows:

[0192] 1) Different armature structural parameters have different effects on the contact pressure value and contact pressure distribution in the initial state. The different effects include total contact pressure, lateral non-uniformity coefficient, longitudinal non-uniformity coefficient, overall non-uniformity coefficient and local non-uniformity coefficient.

[0193] 2) A contact pressure magnitude and field map prediction method based on DNN and CGAN is proposed. The armature geometric structure parameters are used as input to directly predict the total contact pressure magnitude and generate the contact pressure distribution field map. The absolute error percentage of the total contact pressure magnitude prediction result does not exceed 4.5%, and the average absolute percentage error is 0.81%, which has good accuracy. The average absolute error percentage of the contact pressure field map is 0.78%, which has good accuracy. The overall prediction result accuracy can meet the actual engineering needs.

[0194] Fig.23 The pivot rail contact pressure prediction system 2300 based on DNN and CGAN provided by the present invention is shown, including a data acquisition module 2310, a training module 2320 and a prediction module 2330.

[0195] The data acquisition module 2310 is used to establish armature models with different structural parameters, and obtain contact pressure values ​​under different structural parameters and corresponding contact pressure field diagrams under different structural parameters;

[0196] The training module 2320 is used to train the DNN model based on the contact pressure value; and train the CGAN based on the contact pressure field map;

[0197] The prediction module 2330 is used to predict the field diagram of the total contact pressure and the contact pressure distribution based on the pre-trained DNN model and CGAN respectively.

[0198] In an embodiment of the present invention, the system also includes: a DNN model training module, configured to optimize the entire network by calculating the gradient of the loss function and using a back-propagation mechanism; a CGAN training module, configured to superimpose a tensor of the same size as the contact pressure field distribution and the contact pressure field map channel as an input image of the discriminator D; downsampling the input image through four convolution operations, performing batch normalization and LeakyReLU activation after each convolution operation; and expanding the output of the convolution network using a fully connected layer, outputting a scalar value, and using a Sigmoid function to limit the result to between (0,1), indicating the probability of judging that the image is a real image.

[0199] The above is only a specific implementation of the present disclosure, but the protection scope of the present disclosure is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present disclosure should be included in the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be based on the protection scope of the claims.

Claims

1. A method for predicting the contact pressure of a pivot rail based on DNN and CGAN, characterized in that: The method comprises the following steps: Establish armature models with different structural parameters, and obtain contact pressure values ​​under different structural parameters and corresponding contact pressure field diagrams under different structural parameters; Training a DNN model based on the contact pressure value; Training the CGAN based on the contact pressure field map; The total contact pressure and the field map of contact pressure distribution are predicted based on the pre-trained DNN model and CGAN, respectively.

2. The method for predicting the contact pressure of a pivot rail based on DNN and CGAN according to claim 1, characterized in that: The structural parameters include: parameter A, parameter B, parameter C, parameter D and parameter E; wherein parameter A is half of the track spacing; parameter B is the interference; parameter C is the tail thickness; parameter D is the armature tail length; and parameter E is the armature curvature.

3. The method for predicting the contact pressure of a pivot rail based on DNN and CGAN according to claim 1, characterized in that: The armature models with different structural parameters are established, and the contact pressure values ​​under the different structural parameters and the corresponding contact pressure field diagrams under the different structural parameters are obtained, including: The total contact pressure and contact pressure distribution of the pivot rail contact surface after assembly are calculated by numerical simulation method; The total contact pressure and contact pressure distribution are calculated using the parametric sweep method for the specified parameter combination.

4. The method for predicting hinge rail contact pressure based on DNN and CGAN according to claim 1, characterized in that: The training of the DNN model based on the contact pressure value comprises: Based on the parameterized model of the armature and the interference fit model of the electromagnetic rail launcher, the contact pressure in the initial contact situation is numerically simulated to obtain a data set for training; The total contact pressure under the initial contact condition is divided into a training set and a test set. The training set is used to train the DNN model, and the test set is used to test the generalization ability of the DNN model.

5. The method for predicting the contact pressure of a pivot rail based on DNN and CGAN according to claim 1, characterized in that: Training the CGAN based on the contact pressure field map includes: The tensor with the same size as the contact pressure field distribution is superimposed with the contact pressure field map channel as the input image of the discriminator D; The input image is downsampled by four convolution operations, and each convolution operation is followed by a batch normalization operation and a LeakyReLU activation; Use the fully connected layer to expand the output of the convolutional network and output a scalar value. Use the Sigmoid function to limit the result between (0,1), which indicates the probability of judging that the image is a real image.

6. The method for predicting the contact pressure of a pivot rail based on DNN and CGAN according to claim 5, characterized in that: The objective function of CGAN is: Among them, G * is the objective function of CGAN; λ is the weight of the L1 loss function of the generator; G is the generator; D is the discriminator; L cGAN (G,D) is the objective function of CGAN; L1(G) is the absolute error loss function; L1(G)=E||G(y)-x||1 Among them, E is the expectation operator, which means averaging all data; G(y) is the contact pressure field map generated by the generator under given condition y; x is the actual contact pressure field map.

7. A pivot rail contact pressure prediction system based on DNN and CGAN, characterized in that: The system comprises: A data acquisition module is configured to establish armature models with different structural parameters, and obtain contact pressure values ​​under different structural parameters and corresponding contact pressure field diagrams under different structural parameters; A training module is configured to train a DNN model based on the contact pressure value; and train a CGAN based on the contact pressure field map; The prediction module is configured to predict the field map of the total contact pressure and the contact pressure distribution based on the pre-trained DNN model and CGAN, respectively.

8. The DNN and CGAN-based pivot rail contact pressure prediction system according to claim 7, characterized in that: The system further comprises: The DNN model training module is configured to optimize the entire network by calculating the gradient of the loss function using the back-propagation mechanism; The CGAN training module is configured to superimpose a tensor of the same size as the contact pressure field distribution and the contact pressure field map channel as an input image of the discriminator D; downsample the input image through four convolution operations, perform batch normalization and LeakyReLU activation after each convolution operation; and use a fully connected layer to expand the output of the convolution network, output a scalar value, and use a Sigmoid function to limit the result between (0,1), indicating the probability of judging that the image is a real image.

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