A laser cladding molten pool morphology prediction method and system based on VMD and improved DA-RNN

Abstract

The application provides a laser cladding process molten pool morphology information prediction method and system based on VMD and improved DA-RNN, comprising the following steps: S1: continuously collecting molten pool morphology information in the molten pool dynamic video to obtain molten pool morphology information data; S2: pre-processing the molten pool morphology information data by VMD (variational mode decomposition) to decompose the original data into K different subsequences; S3: taking the decomposed different subsequences as data characteristic variables to construct a VMD data set, and dividing the VMD data set into a training set, a validation set and a test set; S4: establishing a DA-RNN prediction network model, and training and predicting on the data set; S5: quantitatively evaluating the DA-RNN prediction network model by using mean absolute percentage error and mean square error; and S6: predicting the laser cladding molten pool morphology information by using the prediction network model. The application can not only effectively extract data characteristics and reduce the complexity of data, but also effectively improve the molten pool morphology prediction model precision.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of laser cladding additive manufacturing, and particularly relates to a laser cladding molten pool morphology prediction method based on VMD and improved DA-RNN. BACKGROUND

[0002] Laser cladding is an additive manufacturing technology for manufacturing or repairing metal parts by powder melting and deposition. It can manufacture parts with homogeneous or heterogeneous structures for various purposes, and can produce metal parts with high quality and strength. Its application scope and application fields are very wide, and it can almost cover the entire mechanical manufacturing industry, including part manufacturing, petroleum, aviation, shipbuilding and other industries. In the process of laser cladding forming processing, the substrate material or deposition layer is irradiated by a laser energy source, which will produce thermal deformation and thermal stress at the intersection and inside of the laser and the workpiece. The heat generated is difficult to dissipate in time, and the thermal deformation accumulates layer by layer, eventually leading to shape errors and defects in the formed cladding layer. A large number of studies have shown that the molten pool information in the cladding process can reflect the quality of the final formed part to some extent. Therefore, predicting the molten pool morphology information in the cladding process can help to judge the forming quality in advance and improve the processing precision, which is of great importance to the quality of the additive manufacturing cladding layer.

[0003] In the prior art, EMD decomposition is used for preprocessing of molten pool morphology processing, and a traditional LSTM or other recurrent neural network model is used for prediction of molten pool dynamic morphology information. However, EMD decomposition has end effect and mode mixing phenomenon, and the decomposition result is poor. In addition, the traditional LSTM or other recurrent neural network model has poor prediction performance on molten pool dynamic morphology information. Therefore, other model methods are needed to effectively predict the molten pool dynamic morphology information. SUMMARY

[0004] To solve the above technical problems, one of the purposes of one embodiment of the present application is to provide a laser cladding molten pool morphology prediction method based on VMD and improved DA-RNN. VMD uses iterative search variational model to determine the center frequency and bandwidth of each decomposition component, and belongs to a completely non-recursive model. The mode mixing and end effect phenomena in the decomposition result are effectively avoided. DA-RNN is introduced with a two-stage attention mechanism, and GRU units are used instead of the original LSTM units. The present application can not only effectively extract data features and reduce data complexity, but also effectively improve the precision of the molten pool morphology prediction model.

[0005] One of the objects of one embodiment of the present application is to provide a laser cladding molten pool morphology prediction system based on VMD and improved DA-RNN, which introduces a two-stage attention mechanism DA-RNN and replaces the original LSTM unit with a GRU unit. The present application can not only effectively extract data features and reduce data complexity, but also effectively improve the accuracy of the molten pool morphology prediction model.

[0006] Note that the recitation of these objects does not preclude the existence of additional objects. One embodiment of the present application does not need to achieve all the above-mentioned objects. The objects other than the above-mentioned objects can be extracted from the recitations of the specification, drawings, and claims.

[0007] The present application achieves the above technical objects through the following technical means.

[0008] A laser cladding molten pool morphology prediction method based on VMD and improved DA-RNN, comprising the following steps:

[0009] Step S1: data acquisition: analyzing the molten pool dynamic video in the additive manufacturing process using a high-speed camera, continuously collecting the molten pool morphology information in the molten pool dynamic video, and obtaining molten pool morphology information data;

[0010] Step S2: data preprocessing: preprocessing the molten pool morphology information data by variational mode decomposition VMD, and decomposing the original data sequence signal into K different subsequences;

[0011] Step S3: constructing a data set: constructing a VMD data set by taking the decomposed different subsequences as data feature variables, and dividing the VMD data set into a training set, a validation set, and a test set;

[0012] Step S4: establishment and training of DA-RNN prediction network model: establishing an improved DA-RNN prediction network model by replacing the original LSTM unit with a GRU unit, and training and predicting on the data set constructed by VMD;

[0013] Step S5: DA-RNN prediction network model evaluation: quantitatively evaluating the prediction ability of the improved DA-RNN prediction network model by using the mean absolute percentage error MAPE index and the mean square error MSE index;

[0014] Step S6: laser cladding molten pool morphology prediction: predicting the laser cladding molten pool morphology information using the DA-RNN prediction network model.

[0015] In the above scheme, the specific steps of the step S2 variational mode decomposition VMD for preprocessing data are:

[0016] The specific steps of the step S2 variational mode decomposition VMD for preprocessing data are:

[0017] Step S2.1: Constructing a variational problem, the original signal F is decomposed into K components, to ensure that the decomposition sequence is a modal component IMF with a center frequency and a limited bandwidth, while the sum of the estimated bandwidths of each mode is minimized, the constraint condition is that the sum of all modes is equal to the original signal, and the VMD constraint variational model is constructed using the following steps:

[0018] Step S2.1.1 defines the intrinsic mode function as an amplitude-frequency-modulation (AM-FM) signal, and its expression is:

[0019]

[0020] Where, u k (t) is the k modal components after decomposition, A k (t) is the amplitude of the k modal components, is the phase of the k modal components;

[0021] Step S2.1.2 Hilbert transform to get the marginal spectrum of each modal function, and the one-sided spectrum of the component is:

[0022]

[0023] Where, δ(t) is the impulse function, j is the imaginary part, t represents time, "*" represents convolution operation, and k is the total number of modal components;

[0024] Step S2.1.3: For each modal function, the exponential term corresponding to the center frequency w k is mixed, and the signal is shifted to the baseband:

[0025]

[0026] Where, is the phasor description of the center frequency of the modal function on the complex plane, w k is the center frequency corresponding to the Kth modal component;

[0027] Step S2.1.4: Estimate the bandwidth of the signal using Gaussian smoothness: that is, the square of the 2-norm of the gradient is converted into a VMD constraint variational model;

[0028] Step S2.2: Solving the variational problem

[0029] Further, the VMD constraint variational model of step S2.1.4 is as follows:

[0030]

[0031]

[0032] where {u k} = {u1, …, u k} are the K decomposed modal function components; {w k} = {w1, …, w k} are the center frequencies of each modal function IMF, δ(t) is the impulse function, j is the imaginary unit, t represents time, and f is the original input signal, is the partial derivative with respect to t, min represents the minimum value, and s.t. represents the constraint condition.

[0033] In the above scheme, the specific process of step S2.2 is as follows:

[0034] Step S2.2.1: Introduce a quadratic penalty term α and a Lagrange multiplier λ to obtain the optimal solution of the variational model, convert the formula in 2.2 into an unconstrained variational problem to solve, and augment the Lagrange expression as follows:

[0035]

[0036] where L({u k}, {w k}, λ) is the augmented Lagrange function, λ(t) is the Lagrange multiplier, {u k} = {u1, …, u k} are the K decomposed modal function components; {w k} = {w1, …, w k} are the center frequencies of each modal function IMF, δ(t) is the impulse function, j is the imaginary unit, t represents time, and f is the original input signal, is the partial derivative with respect to t;

[0037] Step S2.2.2: Initialize λ 1 , the iteration number n, and continuously update each component u k and the center frequency w k and λ by using the alternating multiplier direction algorithm;

[0038] Step S2.2.2.1: Update each modal component u k by using the alternating multiplier direction algorithm;

[0039] Step S2.2.2.2: Update each component corresponding center frequency w k by using the alternating multiplier direction algorithm;

[0040] Step S2.2.2.3: Continuously update the Lagrange multiplier λ by using the alternating multiplier direction algorithm;

[0041] Step S2.2.3: stop iteration by setting threshold value ε until the following formula is met:

[0042]

[0043] wherein, respectively represent the modal function components after Fourier transform in the n+1th, nth iteration;

[0044] Step S2.2.4: at this time, K modal components IMF of limited bandwidth are obtained, namely u k (t).

[0045] In the above scheme, the data set construction in step S3 divides the features extracted in step S2 into training set and test set [X tw , Y tw ]t1, [X tw , Y tw ]t2 in the ratio of 7:3, wherein X tw represents input variable, Y tw represents label, i.e. molten pool morphology information, and t1 and t2 are the time lengths of training set and test set respectively.

[0046] wherein, respectively represent the modal function components after Fourier transform in the n+1th, nth iteration;

[0047] In the above scheme, the specific implementation process of the improved DA-RNN prediction network model in step S4 is as follows:

[0048] Step S4.1: the improved DA-RNN prediction network is a recurrent neural network with double-stage attention mechanism, the sliding window length is selected as W, the time in the sliding window is represented as tw, tw=T-W+1, T-W+2, …, T, wherein T is the current time, and different weight factors a tw are designed through attention mechanism to represent the influence degree of feature X tw on target variable Y tw , and the reconstruction thereof is taken as the input of the encoder;

[0049] Step S4.2: multiple GRU gate recurrent units are used to replace the original multiple LSTM units as the encoder of the network, the input of each GRU unit is the reconstruction related variable at one time in the sliding window, and the output part of the encoder is hidden vector h;

[0050] Step S4.3: different weight factors b tw are designed through attention mechanism to allocate the hidden vectors h t at different times in the sliding window to target variable Y twthe influence degree of each feature, to obtain a semantic vector C, and using a linear regression model to integrate the semantic vector and the historical value of the target variable as the input of the decoder;

[0051] Step S4.4: The decoder part is a plurality of GRU gate units, and the output is the hidden state d of the current time T t , and the estimated value of the target variable at the future time is obtained through a full connection layer.

[0052] Further, the GRU update formula for replacing the original LSTM unit in the improved DA-RNN network in step S4.2 comprises:

[0053] Reset gate: r t = σ (x t W xr + H t-1 W hr + b r )

[0054] Update gate: z t = σ (x t W xz + H t-1 W hz + b z )

[0055] Candidate hidden layer state:

[0056] Final hidden layer state:

[0057] wherein r t represents the information of the reset gate at time t, z t represents the information of the update gate at time t, represents the information of the hidden gate at time t, H t-1 is the GRU hidden state at the previous time, is the element-wise multiplication, σ is the sigmoid function, W xr , W hr , W xz , W hz , W hx , W hh are the weight matrices in the calculation process, b r , b z , b h are the biases, x t is the input at time t, H t-1 is the GRU hidden state at the previous time, and H t is the current final hidden layer state.

[0058] ​In the above scheme, the learning rate of the improved DA-RNN network in step S4 is set to 0.001, the training period epoch is 200, the activation function of the GRU unit is LeakyReLU, and the optimizer is Adam.

[0059] In the above scheme, the mathematical expressions of the mean absolute percentage error MAPE index and the mean square error MSE index in step S5 are as follows:

[0060]

[0061]

[0062] where y i is the actual target molten pool morphology information value, is the predicted target molten pool morphology information value, n is the number of samples, and i represents each sample data.

[0063] A laser cladding molten pool morphology prediction system based on VMD and improved DA-RNN, comprising a data acquisition module, a data preprocessing module, a data set construction module and a network model module;

[0064] The data acquisition module is used to analyze the molten pool dynamic video in the additive manufacturing process by using a high-speed camera, continuously acquire the molten pool morphology information in the molten pool dynamic video, and obtain molten pool morphology information data;

[0065] The data preprocessing module is used to preprocess the molten pool morphology information data by using VMD, and decompose the original data sequence signal into K different sub-sequences;

[0066] The data set construction module is used to construct a VMD data set by taking the decomposed different sub-sequences as data feature variables, and divide the VMD data set into a training set, a validation set and a test set;

[0067] The network model module is used to replace the original LSTM unit with a GRU unit, establish an improved DA-RNN prediction network model, train the improved DA-RNN prediction network model on the VMD constructed data set, use the MAPE index and the MSE index to quantitatively evaluate the prediction ability of the improved DA-RNN prediction network model, and finally predict the laser cladding molten pool morphology information.

[0068] Compared with the prior art, the present application has the following advantages:

[0069] According to one mode of the present application, a pretreatment method is proposed for raw data, taking VMD as an iterative search update and completely non-recursive modal variation method, which effectively suppresses the modal aliasing phenomenon of other decomposition methods such as EMD, so that the model is more robust to sampling noise.

[0070] According to one mode of the present application, the improved DA-RNN is used as a variable estimation model, the influence of related variables and historical information is considered comprehensively, and the different influence weights of the related variables on the target variable estimation are determined through a double-layer attention mechanism, and GRU is used as an encoding and decoding unit, thereby improving the reliability and accuracy of the original DA-RNN model

[0071] Note that the description of these effects does not hinder the existence of other effects. One mode of the present application does not necessarily have all the above effects. Effects other than the above can be clearly seen and extracted from the description, drawings, claims, etc. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 is the algorithm flowchart of the VMD combined with the improved DA-RNN model of one embodiment of the present application.

[0073] Figure 2 is the algorithm flowchart of the VMD of one embodiment of the present application.

[0074] Figure 3 is the principle diagram of the improved DA-RNN model of one embodiment of the present application.

[0075] Figure 4 is the GRU unit structure diagram in the improved DA-RNN of one embodiment of the present application. DETAILED DESCRIPTION

[0076] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference signs represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application.

[0077] In the description of the present application, it needs to be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "front", "back", "left", "right", "up", "down", "axial", "radial", "vertical", "horizontal", "inner", "outer" and the like are based on the orientation or positional relationship shown in the drawings, which is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. In addition, the terms "first", "second" are only for description purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first", "second" can be explicitly or implicitly included one or more of the features. In the description of the present application, the meaning of "a plurality of" is two or more, unless otherwise explicitly specified and limited.

[0078] In the present application, unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connection", "fixing" and the like should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0079] Figure 1 The preferred embodiment of the laser cladding molten pool morphology prediction method based on VMD and improved DA-RNN is shown, and the laser cladding molten pool morphology prediction method based on VMD and improved DA-RNN comprises the following steps:

[0080] Step S1: data acquisition: analyzing the molten pool dynamic video in the additive manufacturing process by using a high-speed camera, continuously collecting the molten pool morphology information in the molten pool dynamic video, and obtaining the molten pool morphology information data;

[0081] Step S2: data preprocessing: preprocessing the molten pool morphology information data by using a variational mode decomposition VMD, and decomposing the original data sequence signal into K different sub-sequences;

[0082] Step S3: constructing a data set: constructing a VMD data set by using the decomposed different sub-sequences as data characteristic variables, and dividing the VMD data set into a training set, a validation set and a test set;

[0083] Step S4: Establishment and training of DA-RNN prediction network model: an improved DA-RNN prediction network model is established by using GRU units instead of original LSTM units, and is trained and predicted on the data set constructed by VMD;

[0084] Step S5: Evaluation of DA-RNN prediction network model: the prediction ability of the improved DA-RNN prediction network model is quantitatively evaluated by using the mean absolute percentage error MAPE index and the mean square error MSE index;

[0085] Step S6: Prediction of laser cladding molten pool morphology: the DA-RNN prediction network model is used to predict the morphology information of the laser cladding molten pool.

[0086] As shown in Figure 2 , the VMD in step S2 converts the decomposition method of the signal into a variational problem, and the VMD determines the center frequency and bandwidth of each decomposed component by searching for the global optimal solution of the variational model through iterative calculation, thereby realizing the decomposition of the signal and obtaining K narrow-band intrinsic mode components; the specific implementation process of the data preprocessing is as follows:

[0087] S2.1 Construct a variational problem, the original signal F is decomposed into K components, and ensure that the decomposition sequence is a modal component IMF with a center frequency and a limited bandwidth, and the sum of the estimated bandwidths of each mode is minimized, and the constraint condition is that the sum of all modes is equal to the original signal.

[0088] The VMD constraint variational model construction steps are as follows:

[0089] 1) Define the intrinsic mode function as an amplitude-frequency-modulation (AM-FM) signal, and its expression is:

[0090]

[0091] Where, u k (t) is the k modal components after decomposition, A k (t) is the amplitude of the k modal components, is the phase of the k modal components.

[0092] 2) Hilbert transform to get the marginal spectrum of each modal function, and the one-sided spectrum of the component is:

[0093]

[0094] Where, δ(t) is the impulse function, j is the imaginary part, t represents time, "*" represents convolution operation, and k is the total number of modal components.

[0095] 3) For each modal function, the center frequency w kExponential term aliasing, shift the signal to baseband:

[0096]

[0097] where, is the phasor description of the center frequency of the mode function on the complex plane, w k is the corresponding center frequency of the Kth mode component.

[0098] 4) Estimate the bandwidth of the signal using Gaussian smoothness: i.e. the squared transform of the 2-norm of the gradient into a VMD constrained variational model as follows:

[0099]

[0100]

[0101] where {u k} = {u1,..., u k} are the K mode function components of the decomposition; {w k} = {w1,..., w k} are the center frequencies of the mode functions IMFs, δ(t) is the impulse function, j is the imaginary part, t represents time f is the original input signal, is the partial derivative with respect to t, min denotes the minimum value, s.t. denotes the constraint condition;

[0102] S2.2 Variational problem solution

[0103] S2.2.1 In order to obtain the optimal solution of the variational model, first introduce the quadratic penalty term α and the Lagrange multiplier λ, convert the formula in 2.2 into an unconstrained variational problem to solve, the augmented Lagrange function L expression is as follows:

[0104]

[0105] where, L({u k}, {w k}, λ) is the augmented Lagrange function, λ(t) is the Lagrange multiplier, {u k} = {u1,..., u k} are the K mode function components of the decomposition; {w k} = {w1,..., w k} are the center frequencies of the mode functions IMFs, δ(t) is the impulse function, j is the imaginary part, t represents time f is the original input signal, is the partial derivative with respect to t;

[0106] S2.2.2 Initialization λ 1The algorithm iteratively updates each component u n times using the alternating multiplier direction algorithm. k and its center frequency w k And the Lagrange multiplier λ, and the number of iterations n;

[0107] Furthermore, as shown in the formula of step 2.2.1, the iteration is equivalent to minimizing the following equation:

[0108]

[0109]

[0110]

[0111] Where argmin represents the value of the variable when the objective function is minimized, and α is a quadratic penalty term. These represent the modal function components in the (n+1)th iteration. λ represents the center frequency of the modal function component in the (n+1)th iteration. n+1 This represents the Lagrange multiplier in the (n+1)th iteration, where τ is the time constant. for The Fourier transform form;

[0112] S2.2.2.1 Due to the equivalence of the Fourier transform, we use Parseval's theorem to transform Equation 1 in 2.2.2 to the frequency domain, and then use ww k Instead of w, we convert it to an integral form in the non-negative frequency range for solving:

[0113]

[0114] in u i (w), λ(w), f(t) and u are respectively i (t), λ(t), The Fourier transform form of argmin represents the value of the variable when the objective function is minimized;

[0115] At this point, each component is obtained from the frequency domain space by the following formula:

[0116]

[0117] in u i (w), λ(w), f(t) and u are respectively i (t), λ(t), The Fourier transform form of α, where α is the quadratic penalty term;

[0118] Similarly, Equation 2 in S2.2.2 is transformed into the frequency domain for solution:

[0119]

[0120] Where argmin represents the value of the variable when the objective function is minimized. For u k Fourier transform of (w);

[0121] get:

[0122]

[0123] In the formula: The center frequency of the current modal function. For {u k Fourier transform (t)}

[0124] Similarly, λ is updated using the following formula:

[0125]

[0126] S2.2.3 By setting a threshold ε, repeat the above steps until the following equation is satisfied to complete the iteration.

[0127]

[0128] in, These represent the modal function components after the Fourier transform in the (n+1)th and nth iterations, respectively;

[0129] S2.2.4 At this point, we obtain K finite-bandwidth modal components IMFs, i.e., u k (t);

[0130] Step S3 involves constructing the dataset by dividing the features extracted in step S2 into a training set and a test set in a 7:3 ratio. tw Y tw ]t1, [X tw Y tw ]t2, where X tw Y represents the input variable. tw The label represents the melt pool topography information, and t1 and t2 are the time lengths of the training set and the test set, respectively.

[0131] like Figure 3 and Figure 4 As shown, the specific implementation process of the improved DA-RNN prediction network model described in step S4 is as follows:

[0132] The improved DA-RNN prediction network in S4.1 is a recurrent neural network with a two-stage attention mechanism. The sliding window length is selected as W, and the time within the sliding window is represented as tw, where tw = T-W+1, T-W+2, ..., T, and T is the current time. Different weight factors α are designed using the attention mechanism. tw To represent feature X tw For the target variable Y tw The degree of influence is determined, and the reconstructed data is used as the input to the encoder.

[0133] Furthermore, the attention mechanism weight factor α in the encoder part tw The calculation process is as follows:

[0134]

[0135]

[0136] in, W represents the attention score during the encoder phase. en V en U en For the parameters that need to be learned, Indicates input features, represents the hidden state of the encoder at the previous time step, and tanh represents the tanh activation function.

[0137] S4.2 replaces the original multiple LSTM units with multiple GRU gated recurrent units as the encoder of the network. The input of each GRU unit is the reconstruction-related variables at one time step within the sliding window, and the encoder output is the hidden vector h.

[0138] Furthermore, the relevant variables are reconstructed as follows:

[0139]

[0140] S4.3 Design different weighting factors β through a time attention mechanism tw To assign the hidden vector h at different times within the sliding window t For the target variable Y tw The degree of influence is determined to obtain a semantic vector C. A linear regression model is then used to integrate the semantic vector with the historical values ​​of the target variable as input to the decoder.

[0141] Furthermore, the temporal attention mechanism weight factor β in the decoder part tw The calculation process is as follows:

[0142]

[0143]

[0144] in is the attention score of the encoder stage, v de is the input of the encoder, W de is the output of the encoder, U de is the parameter to be learned, h i is the hidden state of the encoder, d tw-1 is the hidden state of the decoder at the previous time, the hidden state is reconstructed based on the weight β to obtain the semantic vector, denoted as:

[0145]

[0146] wherein, is the reconstructed variable as the input of the decoder, h T-W+1 …h T denotes the hidden state of the encoder at different times, is the attention weight factor corresponding to the hidden state of the encoder at different times.

[0147] Further, a linear regression model is used to integrate the historical semantic vector C and the historical value of the target variable as the input of the decoder, denoted as:

[0148]

[0149] wherein denotes and the input of the decoder, is the parameter to be learned, is the historical variable value, is the historical semantic vector, is the bias.

[0150] S4.4 The decoder part is a plurality of GRU gate units, and the output is the hidden state d T of the current time T, and then the future time target variable is estimated by a fully connected layer for regression.

[0151]

[0152] wherein W T is the parameter to be learned, d T is the output of the decoder, b T is the regression bias.

[0153] According to the embodiment, preferably, the learning rate of the improved DA-RNN network in step S4 is set to 0.001, the training period epoch is 200, the activation function of the GRU unit is LeakyReLU, the optimizer is Adam, the neural network is regularized by using the Dropout method, some weight connections between neurons are randomly discarded with a probability of 0.2, and the generalization ability of the model is improved.

[0154] The specific implementation of the improved DA-RNN network in step S4 is to replace the original LSTM unit with a GRU unit, and the GRU update formula includes:

[0155] Reset gate: r t =σ(x t W xr +H t-1 W hr +b r )

[0156] Update gate: z t =σ(x t W xz +H t-1 W hz +b z )

[0157] Candidate hidden layer state:

[0158] Final hidden layer state:

[0159] Wherein r t represents the information of the reset gate at time t, z t represents the information of the update gate at time t, represents the information of the hidden gate at time t, H t-1 is the GRU hidden state at the previous moment, and is the element-wise multiplication; σ is the sigmoid function, W xr , W hr , W xz , W hz , W hx , W hh are weight matrices in the calculation process, b r , b z , b h are biases, x t is the input at time t, H t-1 is the GRU hidden state at the previous moment, and H t is the final hidden layer state at the moment.

[0160] The mean absolute percentage error MAPE index and the mean square error MSE index in step S5 have mathematical expressions as follows:

[0161]

[0162]

[0163] wherein y i is the actual target molten pool topography information value, is the predicted target molten pool topography information value, n is the number of samples, and i represents each sample data.

[0164] A laser cladding molten pool topography prediction system based on VMD and improved DA-RNN, comprising a data acquisition module, a data preprocessing module, a data set construction module and a network model module;

[0165] The data acquisition module is used to analyze the molten pool dynamic video in the additive manufacturing process by using a high-speed camera, continuously acquire the molten pool topography information in the molten pool dynamic video, and obtain molten pool topography information data;

[0166] The data preprocessing module is used to preprocess the molten pool topography information data by VMD, and decompose the original data sequence signal into K different sub-sequences;

[0167] The data set construction module is used to construct a VMD data set by taking the decomposed different sub-sequences as data feature variables, and divide the VMD data set into a training set, a validation set and a test set;

[0168] The network model module is used to replace the original LSTM unit with a GRU unit to establish an improved DA-RNN prediction network model, train the improved DA-RNN prediction network model on the VMD constructed data set, use the MAPE and MSE indexes to quantitatively evaluate the prediction ability of the improved DA-RNN prediction network model, and finally predict the laser cladding molten pool topography information.

[0169] It should be understood that although the present specification is described in terms of various embodiments, not every embodiment contains only one independent technical solution, and the description of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that those skilled in the art can understand.

[0170] The above series of detailed descriptions are only specific descriptions of feasible embodiments of the present application, and are not intended to limit the protection scope of the present application, and any equivalent embodiments or changes made without departing from the spirit of the present application should be included in the protection scope of the present application.

Claims

1. A method for predicting the molten pool morphology of laser cladding based on VMD and improved DA-RNN, Its features include the following steps: Step S1: Data Acquisition: Analyze the dynamic video of the molten pool during the additive manufacturing process using a high-speed camera, continuously acquire the molten pool morphology information in the dynamic video of the molten pool, and obtain molten pool morphology information data; Step S2: Data preprocessing: The melt pool topography information data is preprocessed by variational mode decomposition (VMD) to decompose the original data sequence signal into K different subsequences; Step S3: Construct the dataset: Construct the VMD dataset by using the different subsequences of the decomposition as data feature variables, and divide the VMD dataset into training set, validation set and test set; Step S4: Building and training the DA-RNN prediction network model: Using GRU units to replace the original LSTM units to build an improved DA-RNN prediction network model, and training and predicting on the dataset constructed by VMD. Step S5: Evaluation of DA-RNN prediction network model: The predictive ability of the improved DA-RNN prediction network model is quantitatively evaluated using the mean absolute percentage error (MAPE) and mean squared error (MSE) metrics. Step S6: Prediction of molten pool morphology in laser cladding: Predict the morphology of the molten pool in laser cladding using a DA-RNN prediction network model; The improved DA-RNN prediction network x described in step S4 k The specific implementation process of the model is as follows: Step S4.1: The improved DA-RNN prediction network is a recurrent neural network with a two-stage attention mechanism. The sliding window length is selected as W, and the time within the sliding window is represented as tw, where tw = T-W+1, T-W+2, ..., T, and T is the current time. Different weight factors α are designed using the attention mechanism. tw To represent feature X tw For the target variable Y tw The degree of influence is determined, and the reconstructed data is used as the input to the encoder. Step S4.2: Replace the original multiple LSTM units with multiple GRU gated recurrent units as the encoder of the network. The input of each GRU unit is the reconstruction-related variables at one time step within the sliding window, and the encoder output is the hidden vector h. Step S4.3: Design different weighting factors β through an attention mechanism tw To assign the hidden vector h at different times within the sliding window t For the target variable Y tw The degree of influence is determined to obtain a semantic vector C. A linear regression model is used to integrate the semantic vector with the historical values ​​of the target variable as input to the decoder. Step S4.4: The decoder consists of multiple GRU gate units, and its output is the hidden state d at the current time T. t Then, regression is performed through a fully connected layer to obtain the target variable for future time steps. The estimated value; The GRU update formula in the improved DA-RNN network in step S4.2, which replaces the original LSTM units with GRU units, includes: Reset Gate: r t =σ(x t W xr +H t-1 W hr +b r ) Update Gate: z t =σ(x t W xz +H t-1 W hz +b z ) Candidate hidden layer states: Final hidden layer state: Where r t This indicates the information about resetting the gate at time t, z t This indicates that the gate information is updated at time t. H represents the information about the hidden door at time t. t-1 The previous GRU hidden state is represented by ⊙, which represents element-wise multiplication; σ is the sigmoid function, and W... xr W hr W xz W hz W hx W hh b is the weight matrix used in the calculation process. r b z b h For bias, x t H is the input at time t. t-1 h represents the hidden state of the GRU in the previous moment. t This is the current final hidden layer state.

2. The laser cladding pool morphology prediction method based on VMD and improved DA-RNN according to claim 1, characterized in that, The specific steps of the variational mode decomposition (VMD) preprocessing of the data in step S2 are as follows: Step S2.1: Construct a variational problem. The original signal F is decomposed into K components. To ensure that the decomposed sequence is a mode component (IMF) with a finite bandwidth and a center frequency, and that the sum of the estimated bandwidths of each mode is minimized, the constraint is that the sum of all modes is equal to the original signal. The following steps are used to construct a VMD-constrained variational model: Step S2.1.1 Define the intrinsic mode function as an amplitude-frequency modulation (AM-FM) signal, and its expression is: Among them, u k (t) represents the k modal components after decomposition, A k (t) represents the amplitude of the k modal components. The phases of the k modal components; Step S2.1.2: Use Hilbert transform to obtain the marginal spectrum of each mode function, resulting in the one-sided spectrum of each component: Where δ(t) is the impulse function, j is the imaginary part, t represents time, "*" indicates convolution operation, and k is the total number of modal components; Step S2.1.3 For each modal function, the corresponding center frequency w k The exponential term aliasing shifts the signal to baseband: in, It is a phasor description of the center frequency of the modal function in the complex plane, w k It is the center frequency corresponding to the Kth modal component; Step S2.1.4 uses Gaussian smoothness to estimate the bandwidth of the signal: that is, the square of the 2-norm of the gradient is converted into a VMD-constrained variational model. Step S2.2: Solve the variational problem.

3. The laser cladding pool morphology prediction method based on VMD and improved DA-RNN according to claim 2, characterized in that, The VMD-constrained variational model formula in step S2.1.4 is as follows: Where {u k } = {u1, ..., u k } represents the K modal function components of the decomposition; {w k } = {w1, ..., w k } represents the center frequency of each modal function (IMF), δ(t) is the impulse function, j is the imaginary part, t represents time, and f is the original input signal. To find the partial derivative with respect to t, min represents the minimum value, and st represents the constraint condition.

4. The laser cladding pool morphology prediction method based on VMD and improved DA-RNN according to claim 2, characterized in that, The specific process of step S2.2 is as follows: Step S2.2.1: Introduce the quadratic penalty term α and the Lagrange multiplier λ to find the optimal solution of the variational model. Transform the VMD-constrained variational model into an unconstrained variational problem for solution. The augmented Lagrange expression is as follows: Wherein, L({u k },{w k }, λ) is the augmented Lagrange function, λ(t) is the Lagrange multiplier, {u k } = {u1, ..., u k } represents the K modal function components of the decomposition; {w k } = {w1, ..., w k } represents the center frequency of each modal function (IMF), δ(t) is the impulse function, j is the imaginary part, t represents time, and f is the original input signal. To find the partial derivative with respect to t; Step S2.2.2: Initialization λ 1 The iteration count is n, and the solution for each component u is continuously updated using the alternating multiplier direction algorithm. k and its center frequency w k And λ; Step S2.2.2.1: Update the solution for each modal component u using the alternating multiplier direction algorithm. k ; Step S2.2.2.2: Update the center frequency w corresponding to each component using the alternating multiplier direction algorithm. k ; Step S2.2.2.3: Continuously update and solve for the Lagrange multiplier λ using the alternating multiplier direction algorithm; Step S2.2.3: By setting a threshold ε, repeat the above steps until the following equation is satisfied and the iteration stops: in, These represent the modal function components after the Fourier transform in the (n+1)th and nth iterations, respectively; Step S2.2.4: At this point, K finite-bandwidth modal components (IMFs) are obtained, i.e., u k (t).

5. The laser cladding pool morphology prediction method based on VMD and improved DA-RNN according to claim 1, characterized in that, In step S3, the dataset is constructed by dividing the features extracted in step S2 into a training set and a test set in a 7:3 ratio. tw Y tw ]t1, [X tw Y tw ]t2, where X tw Y represents the input variable. tw The label represents the melt pool topography information, and t1 and t2 are the time lengths of the training set and the test set, respectively.

6. The laser cladding pool morphology prediction method based on VMD and improved DA-RNN according to claim 1, characterized in that, In step S4, the learning rate of the improved DA-RNN network is set to 0.001, the training epoch is 200, the activation function of the GRU unit is LeakyReLU, and the optimizer is Adam.

7. The laser cladding pool morphology prediction method based on VMD and improved DA-RNN according to claim 1, characterized in that, The mathematical expressions for the Mean Absolute Percentage Error (MAPE) and Mean Square Error (MSE) in step S5 are as follows: Where y V These are the actual numerical values ​​of the target molten pool morphology. It is the predicted target melt pool morphology information value, n is the number of samples, and i represents each sample data.

8. A system for predicting the morphology of a laser cladding pool based on VMD and an improved DA-RNN according to any one of claims 1-7, characterized in that, It includes a data acquisition module, a data preprocessing module, a dataset construction module, and a network model module; The data acquisition module is used to analyze the dynamic video of the molten pool during the additive manufacturing process using a high-speed camera, and continuously acquire the molten pool morphology information in the dynamic video of the molten pool to obtain molten pool morphology information data. The data preprocessing module is used to preprocess the melt pool topography information data through variational mode decomposition (VMD), decomposing the original data sequence signal into K different subsequences; The dataset construction module is used to construct a VMD dataset by using the different subsequences of the decomposition as data feature variables, and to divide the VMD dataset into a training set, a validation set, and a test set. The network model module is used to replace the original LSTM unit with GRU unit to establish an improved DA-RNN prediction network model, and train it on the dataset constructed by VMD. The prediction ability of the improved DA-RNN prediction network model is quantitatively evaluated by the mean absolute percentage error (MAPE) and mean square error (MSE) indicators. Finally, the morphology information of the laser cladding pool is predicted.

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