CN112149335A - Multilayer arc additive manufacturing process thermal history prediction method based on machine learning - Google Patents

Multilayer arc additive manufacturing process thermal history prediction method based on machine learning Download PDF

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CN112149335A
CN112149335A CN202011174760.6A CN202011174760A CN112149335A CN 112149335 A CN112149335 A CN 112149335A CN 202011174760 A CN202011174760 A CN 202011174760A CN 112149335 A CN112149335 A CN 112149335A
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沈洪垚
周泽钰
谈学锋
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Zhejiang University ZJU
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Abstract

The invention discloses a method for predicting the thermal history of a multilayer arc additive manufacturing process based on machine learning, which comprises the following steps: 1) establishing a multilayer arc additive manufacturing process thermal analysis simulation model, performing finite element simulation analysis, extracting manufacturing state data and temperature data at each simulation step moment, and establishing a multilayer arc additive manufacturing process thermal history database; 2) establishing an integrated learning model based on a bidirectional long-time and short-time memory network and training; 3) and after the training and the testing of the integrated learning model are completed and stored, predicting the thermal history of the new arc additive manufacturing process. The method adopts an integrated learning model based on a plurality of base learners mainly based on a bidirectional long-time and short-time memory network to fit the mapping relation between the unit set activation sequence data and the unit set temperature data, and the obtained actual output data and ideal output data have high goodness of fit, high prediction precision, high prediction speed and small occupied memory.

Description

Multilayer arc additive manufacturing process thermal history prediction method based on machine learning
Technical Field
The invention relates to the technical field of arc additive manufacturing, in particular to a multilayer arc additive manufacturing thermal history prediction method based on machine learning.
Background
The electric arc additive manufacturing is a rapid forming technology, and the technology takes welding electric arcs as heat sources and welding wires as raw materials to form parts through a welding deposition process. This technique may improve manufacturing efficiency, reduce design constraints, and reduce material waste as compared to conventional subtractive manufacturing techniques. The thermal history of the arc additive manufacturing process has a significant impact on the residual stress distribution, substrate deformation, etc. of the final part. Therefore, in order to perform quality control on the part, accurate and rapid prediction of the thermal field variation in the arc additive manufacturing process is required to guide the selection of the manufacturing parameters in a feedback manner.
The common thermal history prediction method for the multilayer arc additive manufacturing process comprises a finite element method, an analytic method and a semi-analytic method. The finite element method adopts a living and dead unit technology to simulate the accumulation of materials in the additive manufacturing process, the prediction precision is high, but the high energy density of a heat source causes the temperature gradient around the current deposition area to be large, so that fine space-time discretization is needed to ensure the accuracy of the result, and the calculation cost is high.
Some analytical methods avoid the high computational cost of the mesh and are more efficient than finite element methods, but these methods are often based on many assumptions and simplifications, such as assuming that the substrate is semi-infinite, simplifying the material thermophysical parameters and temperature independence, etc., which will affect the final prediction accuracy.
Some analytical methods or semi-analytical methods discretize the entire additive manufacturing process into a series of discrete point manufacturing processes or a series of continuous line segment manufacturing processes, and obtain the thermal field of each sub-manufacturing process based on the analytical methods, where the temperature field of the entire additive manufacturing process is the result of the sequential action of the temperature fields of each sub-manufacturing process. Compared with the analysis methods in the prior art, the method has better prediction precision and wider application range, but the iterative computation corresponding to the process discretization inevitably increases the time cost.
The patent specification with the publication number of CN110363289A discloses an industrial steam amount prediction method based on machine learning, which is based on historical working condition data and actually-discharged steam amount collected by a boiler sensor, obtains two characteristic data of the internal trend and the period information of the historical working condition data by performing time series decomposition on the historical working condition data, learns the internal trend and the period information of the historical working condition data and the actual discharge amount corresponding to the historical working condition data through a long-time memory network (LSTM) algorithm, finally trains and constructs an LSTM algorithm prediction model, inputs the newly-collected working condition data of the boiler sensor into the LSTM algorithm prediction model after the time series decomposition, and outputs the predicted steam amount of the boiler.
The data-driven method is based on a database comprising a number of data pairs, each data pair consisting of deposition process description data and corresponding thermal field data, and selecting a model, for example, the relationship between the agent model (J.Li, R.jin, H.Z.Yu, Integration of physical-based and data-driven protocols for Thermal field prediction in additive manufacturing, mater.Des.139(2018) 473-485 https:// doi.org/10.1016/j.mattes.2017.11.028.) and the neural network model (K.ren, Y.Chew, Y.F.Zhang, J.Y.H.Fuh, G.J.Bi, Thermal field prediction for channels in laser aided manufacturing by graphics-based mapping, computer-based mapping, emissive/35362. mapping between the agent model (J.Li, R.jin, H.Y.J.Bi, H.J.R.J.11.31) and the neural network model (K.Ren, Y.T.R.D.A. and D.D.A. mapping between the agent model (J.R.R.R.H.J.P.P.I, H.Y.J.S.S.S.D.I.), this type of method performs well in terms of prediction accuracy and prediction efficiency, but currently, there is only research on a data-driven method for thermal field prediction in a single-layer additive process.
Disclosure of Invention
The invention provides a method for predicting the thermal history of a multilayer arc additive manufacturing process based on finite element data and a bidirectional long-short-term memory (BilSTM) machine learning model, which can be used for rapidly and accurately predicting the thermal history of the multilayer arc additive manufacturing process.
A multilayer arc additive manufacturing process thermal history prediction method based on machine learning comprises the following steps:
1) establishing a multilayer arc additive manufacturing process thermal analysis simulation model, performing finite element simulation analysis, extracting manufacturing state data and temperature data at each simulation step moment, and establishing a multilayer arc additive manufacturing process thermal history database;
2) establishing a BilSTM-based ensemble learning model and training;
3) and after the training and the testing of the integrated learning model are completed and stored, predicting the thermal history of the new arc additive manufacturing process.
The invention discloses a method for predicting the thermal history of an arc additive manufacturing process, which is characterized in that a data driving method is used for the multilayer arc additive manufacturing process, and the difficulty lies in designing a proper data structure to represent the manufacturing state and the corresponding temperature field of the arc additive manufacturing process, and designing a model based on physical significance to mine the mapping relation between the manufacturing state data and the corresponding temperature field data.
In the step 1), a thermal history database of the multilayer arc additive manufacturing process is established, and the specific process is as follows:
1.1) generating a multilayer arc additive manufacturing process comprising: setting parameters of an arc additive manufacturing process, establishing a multilayer arc additive manufacturing part model and selecting a multilayer arc additive manufacturing path mode. Under the set parameters of the arc additive manufacturing process, a multilayer arc additive manufacturing part model is combined with a multilayer arc additive manufacturing path mode to form a multilayer arc additive manufacturing process.
The arc additive manufacturing process parameters include: arc parameters, wire parameters, substrate parameters, etc.
Under the set parameters of the electric arc additive manufacturing process, a single-pass electric arc additive manufacturing experiment is carried out to measure the width w of the welding beadweldAnd height hweld,hweldNamely the layer height of the electric arc additive manufacturing process.
1.2) determining an arc additive manufacturing space: in the electric arc additive manufacturing space, the position of the substrate model is fixed, and the relative position of the workpiece model and the substrate model is the same as the relative position of the workpiece and the substrate in the actual manufacturing process.
1.3) establishing an arc additive manufacturing thermal analysis simulation model: establishing a thermal analysis simulation model for each multilayer arc additive manufacturing process in the arc additive manufacturing space, which comprises the following specific steps:
1.3.1) determining a rectangular enveloping body which can envelop all multi-layer arc additive manufacturing part models: dimension l of rectangular enveloping body in x directionenvelopeAnd a dimension w in the y-directionenvelopeAre all wweldIntegral multiple of, dimension h in z-directionenvelopeIs hweldInteger multiples of. The left surface and the right surface of the rectangular enveloping body are both perpendicular to the x axis; the front and back surfaces are both perpendicular to the y-axis; both the upper and lower surfaces are perpendicular to the z-axis, and the lower surface coincides with the upper surface of the base. The position of the rectangular enveloping body in the arc additive manufacturing space is fixed for different part models.
1.3.2) unitizing the rectangular enveloping body to obtain a unit set of the thermal analysis simulation model: dimension d of the cell in the x-directionxIs equal to wweldDimension d in y-directionyIs equal to wweldDimension d in the z directionzIs equal to hweld. Unitizing to obtain a unit set, namely the unit set of the thermal analysis simulation model, wherein the unit set has the unit number n in the x directionxIs equal to lenvelope/wweldNumber of cells n in y-directionyIs equal to wenvelope/wweldNumber of cells n in z-directionzIs equal to henvelope/hweld。
1.3.3) judging whether the unit is an entity unit: for each unit in the unit set, judging whether the volume of the intersection area of the unit and the part model exceeds 50% of the volume of the unit, if so, the unit is a solid unit; otherwise, the cell is a void cell.
1.3.4) determining a heat source of a thermal analysis simulation model: considering the influence of arc movement on heat input distribution, a double-ellipsoid heat source is selected as the heat source of the thermal analysis simulation model, and the energy distribution density q of the front part and the rear part of the double-ellipsoid heat source isfAnd q isbCalculated by the following formula, respectively:
Figure BDA0002748388020000031
Figure BDA0002748388020000032
wherein a, b, cf,cbThe shape parameters are determined by the shape of the molten pool; q and eta are respectively welding power and welding thermal efficiency; f. offAnd fbEnergy distribution coefficients of the front and rear heat sources, respectively, ff+fb＝2。
1.3.5) generating a simulation step sequence of the thermal analysis simulation model: and generating a simulation step sequence based on the multilayer arc additive manufacturing process, and judging the entity unit which needs to be activated in each simulation step in the simulation step sequence.
In step 1.3.5), the generation of the simulation step sequence includes the following steps:
approximately dispersing the multilayer arc additive manufacturing process into a plurality of linear segment additive manufacturing processes, and ensuring that the maximum distance deviation between the additive manufacturing path formed by all the linear segment additive manufacturing processes and the original additive manufacturing path is smaller than a distance threshold value dthresholdUnder the premise of (2), each linear segment additive manufacturing process is as long as possible. And setting a distance interval delta d, dividing the path corresponding to each linear segment arc additive manufacturing process from the starting point based on the distance interval, and stopping the dividing process if the length of the residual path does not exceed delta d. The segmentation results in one or more sub-paths, each sub-path corresponding to one sub-straight segment additive manufacturing process.
Each sub-straight line segment additive manufacturing process corresponds to one simulation step, and the time length of the sub-straight line segment additive manufacturing process is the time length t of the corresponding simulation steptime(ii) a The starting time of the sub-straight-line segment additive manufacturing process in the whole multilayer electric arc additive manufacturing process is the starting time t of the corresponding simulation stepbeginAll simulation steps are performed in the whole additive manufacturing process according to the corresponding sub-straight line segment additive manufacturing processThe sequence positions of the simulation steps form a simulation step sequence.
In step 1.3.5), the method for determining the activation unit in the simulation step is as follows:
calculating an envelope region R formed by the movement of the first half part of the heat source in the current simulation stepfrontAnd an envelope region R formed by moving the latter half heat source in the current simulation steprearActivation of the judgment region RactivationDefined as the intersection of two envelope regions:
Ractivation＝Rfront∩Rrear
for each inactive entity unit, determining whether its center point is in the region RactivationIf yes, the simulation step is an activated unit of the current simulation step and marked as an activated unit; if not, the unit is not activated.
1.4) establishing a thermal analysis finite element model and calculating: and in the finite element software, establishing a thermal analysis finite element model for each thermal analysis simulation model and calculating to obtain a temperature field corresponding to each simulation step of the thermal analysis simulation model, namely a finite element calculation result of the thermal history in the multilayer arc additive manufacturing process.
1.5) designing a data structure: manufacturing state data and temperature field data at each simulation step time of the thermal analysis simulation model are extracted, and the manufacturing state data and the temperature field data are represented by activation sequence data of a unit set of the thermal simulation analysis model and temperature data of the unit set.
The data structure is designed as follows:
1.5.1) defining the activation time t of a cellactivation: activation time t of the cellactivationStarting time t of simulation step for activating the unitbeginThe activation times of all the cells are represented by a three-dimensional matrix P, with the order nx×ny×nz。
1.5.2) define Unit set activation sequence data and Unit set temperature data: the unit set activation sequence data and the unit set temperature data of the mth simulation step are respectively composed of a three-dimensional matrix SmAnd a three-dimensional matrix TmIs represented by the order nx×ny×nzI, j, k is the index of the unit located at the ith in the x-direction, the jth in the y-direction and the kth in the z-direction in the unit set, SmAnd TmIs defined as follows:
activation sequence data S of unit set of mth simulation stepmIs calculated as follows:
Figure BDA0002748388020000041
for an activated unit, the element value is the start time of the current simulation step minus the activation time of the unit; for inactive cells, the element value is positive infinity.
Reading a finite element model calculation result file to obtain temperature values of eight vertexes of each unit in each simulation step, and using a three-dimensional matrix N for temperature data of all unit vertexes of the mth simulation stepmIs represented by the order of (n)x+1)×(ny+1)×(nz+1)。
Temperature data T of cell set in mth simulation stepmIs calculated as follows:
Figure BDA0002748388020000042
for the activated unit, the temperature data is the average value of the temperature data of the eight vertexes of the activated unit; for the inactive cells, the temperature data is 0.
Analysis shows that, for an activated unit, if the activation sequence data of the unit is smaller or a unit with smaller activation sequence data exists around the activated unit, that is, the unit is in an activated or reheated state, the temperature data of the unit is often higher. That is, there is also some correlation of the spatial signature of the unit activation data with its temperature data.
1.6) constructing a thermal history data pair set of a thermal analysis simulation model: based on the design data structure in the step 1.5), extracting unit set activation sequence data and unit set temperature data of each simulation step, and constructing a thermal history data pair set of the thermal analysis simulation model (S)m,Tm)}。
1.7) extracting and combining the thermal history data pairs of the thermal analysis simulation models of all the arc additive manufacturing processes to obtain a multilayer arc additive manufacturing process thermal history database.
In step 2), an ensemble learning model is established and trained based on a multilayer arc additive manufacturing process thermal history database, and the steps are as follows:
2.1) establishing an ensemble learning model database: the ensemble learning model database is generated based on a multilayer arc additive manufacturing process thermal history database, and is further divided into a training set and a test set, and the method specifically comprises the following steps:
2.1.1) defining the ensemble learning model database input data and the label data: the ensemble learning model predicts the temperature data of each unit based on the activation sequence data of the unit set at a certain stage of the additive manufacturing process, namely the temperature field at the stage. Therefore, the integrated learning model database is established by taking the unit set activation sequence data as input data I and taking the unit set temperature data as label data L.
2.1.2) dividing the integrated learning model database to obtain a training set and a testing set: all input data and label data corresponding to a part of the multilayer arc additive manufacturing process are used as a training set, and all input data and label data corresponding to the rest of the multilayer arc additive manufacturing process are used as a test set.
2.2) designing an ensemble learning model, which specifically comprises the following steps:
2.2.1) the ensemble learning model consists of a normalization layer, three basis learners, a convolution layer and a filter layer, wherein each basis learner consists of a BilSTM and a plurality of Fully Connected (FC) layers.
2.2.2) normalization of the input data I: in order to avoid the occurrence of singular data, facilitate the subsequent data processing and accelerate the network learning speed, the input data I is normalized. Since the elements of the input data I are not negative, the following exponential expression is selected to carry out normalization processing on the input data I, so that the activation sequence data of the unit sets of the multilayer arc additive manufacturing process thermal history database are mapped to the interval of [0,1 ]. As shown in the following equation:
Hnormalization＝exp(-knormalization×I)
wherein k isnormalizationIs a normalized coefficient; hnormalizationIs the output of the normalization layer.
2.2.3) reacting said HnormalizationThe decomposition yields the input matrix sequence of three basis learners:
all elements in a single X dimension are taken as an input matrix, and an input matrix sequence X of the first base learner is formed according to the sequence of the first y dimension and the second z dimension [ X ═ X [ ]1,X2,…,Xi,…]The number of the matrices is (n)y×nz) The order of each matrix is nxX 1; all elements in a single Y dimension are taken as an input matrix, and an input matrix sequence Y of the second base learner is formed according to the sequence of the x dimension and the z dimension [ Y ═ Y-1,Y2,…,Yi,…]The number of the matrices is (n)x×nz) The order of each matrix is nyX 1; all elements in a single Z dimension are used as input matrixes, and an input matrix sequence Z ═ Z of a third base learner is formed according to the sequence of the x dimension and the y dimension1,Z2,…,Zi,…]The number of the matrices is (n)x×ny) The order of each matrix is nz×1。
2.2.4) all the base learners are composed of a BilSTM and a plurality of FC layers, the input matrix sequence of the base learners passes through the BilSTM and the FC layers to obtain the output matrix sequence of the base learners, and the specific steps are as follows:
2.2.4.1) number of layers of BilSTM of the first base learner is nxbilstmlayerEach layer comprising (n)y×nz) A forward memory unit and (n)y×nz) A plurality of backward memory units, each memory unit having n hidden layer nodesxbilstmnodeOutputting an order of nxbilstmnodeMatrix of x 1. Sequentially inputting the matrix in the X to obtain a BiLSTM output sequence matrix sequence
Figure BDA0002748388020000051
The number of the matrixes is (n)y×nz) The order of each matrix is (2 × n)y×nz)×1。
2.2.4.2) BilSTM output matrix sequence HxbilstmEach matrix in (1) passes through nxfclayerObtaining the output matrix sequence of the first base learner after the nonlinear transformation of the FC layer
Figure BDA0002748388020000052
The number of the matrix is (n)y×nz) The order of each matrix is nx×1。
2.2.4.3) number of layers of BilSTM of the second base learner nybilstmlayerEach layer comprising (n)x×nz) A forward memory unit and (n)x×nz) A plurality of backward memory units, each memory unit having n hidden layer nodesybilstmnodeOutputting an order of nybilstmnodeThe matrix of x 1 is input in sequence to obtain the BiLSTM output sequence matrix sequence
Figure BDA0002748388020000053
The number of the matrixes is (n)x×nz) The order of each matrix is (2 × n)x×nz)×1。
2.2.4.4) BilSTM output matrix sequence HybilstmEach matrix in (1) passes through nyfclayerObtaining the output matrix sequence of the second base learner after the nonlinear transformation of the FC layer
Figure BDA0002748388020000054
The number of the matrix is (n)x×nz) The order of each matrix is ny×1。
2.2.4.5) number of layers of BilSTM of the third base learner nzbilstmlayerEach layer comprising (n)x×ny) A forward memory unit and (n)x×ny) A plurality of backward memory units, each memory unit having n hidden layer nodeszbilstmnodeOutputting an order of nzbilstmnodeThe matrix of x 1 is input in the matrix sequence in Z to obtain the BiLSTM output sequence matrix sequence
Figure BDA0002748388020000055
The number of the matrixes is (n)x×ny) The order of each matrix is (2 × n)x×ny)×1。
2.2.4.6) BilSTM output matrix sequence HzbilstmEach matrix in (1) passes through nzfclayerObtaining the output matrix sequence of the third base learner after the nonlinear transformation of the FC layer
Figure BDA0002748388020000061
The number of the matrix is (n)x×ny) The order of each matrix is nz×1。
The output of each BilSTM unit is obtained based on the input of the BilSTM unit and the output of the front and rear BilSTM units of the unit, thereby realizing the capture of the spatial characteristics of 1.5.2) and accurate information prediction; three input data sequences containing different spatial features are learned through three base learners, and a plurality of FC layers are connected behind the BilSTM, so that the fitting capability of the integrated learning model is enhanced.
2.2.5) for the output matrix sequence of each base learner, setting each output matrix in H according to the corresponding input matrixnormalizationThe three-dimensional matrix obtained by connecting the three-dimensional matrix sequences of the single-base learner is used as the input of a single channel of the convolutional layer, and the average value of the output matrixes of the three convolutional layer channels is the output matrix of the convolutional layer, and the method specifically comprises the following steps:
will output matrix sequence HxEach matrix of
Figure BDA0002748388020000062
According to its corresponding input matrix XiAt HnormalizationThe dimensional position relations are connected to obtain a three-dimensional matrix Iconv1Order of nx×ny×nz，Iconv1Namely the input of the first channel of the convolution layer; will output matrix sequence HyEach matrix of
Figure BDA0002748388020000063
According to its corresponding input matrix YiAt HnormalizationThe dimensional position relations are connected to obtain a three-dimensional matrix Iconv2Order of nx×ny×nz，Iconv2The input of the second channel of the convolution layer; will output matrix sequence HzEach matrix of
Figure BDA0002748388020000064
According to its corresponding input matrix ZiAt HnormalizationThe dimensional position relations are connected to obtain a three-dimensional matrix Iconv3Order of nx×ny×nz，Iconv3I.e. the input of the convolutional layer third channel. The convolutional layer comprises a three-dimensional convolution kernel, inputs I for three channelsconv1、Iconv2、Iconv3Respectively carrying out convolution operation to obtain output H of three channelsconv1、Hconv2、Hconv3The average value of the outputs of the three channels is the output H of the convolutional layerconvOrder of nx×ny×nz。
The convolutional layer has the function of averaging after carrying out convolution operation on each base learner by adopting convolution kernel, and compared with the method of directly averaging the output of each base learner, the convolutional layer can better capture 1.5.2) the spatial characteristics and improve the fitting capability of the ensemble learning model.
2.2.6) obtaining the output O of the integrated learning model after the output matrix of the convolution layer is filtered by a filter layer: from the description of the data structure, it can be seen that the value of the co-located element in the final output matrix corresponding to the positive infinite element in the input matrix I should be 0, so that the output H to the convolutional layer based on the input I of the ensemble learning modelconvThe following filtration was performed: for HconvIf the value of its co-located element in the input matrix I is positive infinity, then the element is set to 0, otherwise, it is retained. Filtering to obtain the input of the integrated learning modelO is out, the order is nx×ny×nz。
The filter layer is used for forcibly setting the output values of all the inactivated units to be 0, so that the correctness of the corresponding outputs of the units is ensured, and the accuracy of prediction is improved.
2.3) after the building of the ensemble learning model and the building of the database thereof are completed, training the ensemble learning model, and specifically comprising the following steps:
2.3.1) selecting mini-batch method for training, setting batch size as nbatchsize。
2.3.2) establish the loss function: in the multilayer arc additive manufacturing process, the high temperature state experienced by the part has an important influence on the final residual stress distribution, substrate deformation and the like. Therefore, in the loss function of the back propagation process, higher weight is given to the loss values of the units with higher label values, the attention of the training process to the units is improved, and the accuracy of the ensemble learning model for predicting the high-temperature region is further improved. Specifically, the loss function is defined as follows:
2.3.2.1) element division: setting a temperature threshold TthresholdThe temperature threshold should be slightly lower than the minimum of the largest elements of all temperature data matrices. Dividing a label element set { L } corresponding to the label matrix L, wherein the label value is less than TthresholdThe elements of (a) constitute a low temperature tag element set { llowN number of elementslow(ii) a The rest elements form a high-temperature label element set lhighN number of elementshighAccording to the grouping of the corresponding label elements, the element set { O } corresponding to the output matrix O is divided, and the output element set { O } corresponding to the low-temperature label element set is correspondingly obtainedlowSet of output elements { o } corresponding to the set of high temperature tag elementshigh}。
2.3.2.2) calculating { l }lowAnd { o }lowObtaining the prediction Loss function value Loss of the low-temperature unit according to the average absolute error between the two unitslow(ii) a Calculation of { lhighAnd { o }highObtaining the prediction Loss function value Loss of the high-temperature unit according to the average absolute error between the two unitshigh. Computing LosslowAnd LosshighThe Loss function value Loss of all units is obtained, and the calculation formula is as follows:
Figure BDA0002748388020000071
Figure BDA0002748388020000072
Figure BDA0002748388020000073
2.3.3) calculating the loss function value of the batch data, setting the learning rate, and realizing the iterative optimization of the model by a self-adaptive matrix estimation method.
2.3.4) the training process is stopped after a certain number of training sessions, and all parameters of the model are saved locally.
Preferably, to further evaluate the performance of the ensemble learning model, its prediction accuracy and prediction efficiency are verified on the test set: the prediction Accuracy is evaluated by an Accuracy function, which is defined as the average absolute error Accuracy between the output matrix O and the label matrix L, and the calculation formula is as follows:
Figure BDA0002748388020000074
the prediction accuracy of the integrated learning model on the whole test set exceeds 0.94, and the prediction accuracy achieves the expected effect.
In the step 3), after the training of the ensemble learning model is completed and the ensemble learning model is stored, the step of predicting the thermal history of the new arc additive manufacturing process is as follows:
3.1) generating a thermal analysis simulation model of the new arc additive manufacturing process by the same thermal analysis simulation model building process.
3.2) extracting to obtain a unit set activation sequence state data set: extraction thermal analysis simulation modelThe unit set of each simulation step of (1) activates the sequential state data SiAnd obtaining an activation sequence state data set { S } of the unit set.
3.3) sequentially inputting the data of the cell set activation sequence state data set into the ensemble learning model to obtain a prediction result of the thermal history: activating a set of cells sequential state data SiInputting the ensemble learning model to obtain output data OiAnd sequentially inputting the data in the { S } into the trained ensemble learning model to obtain an output set { O }:
Oi＝Ensembling(Si)
the Ensembling function is nonlinear transformation corresponding to the integrated learning model, and the { O } function is a thermal history prediction result of the multilayer arc additive process.
The prediction space of the integrated learning model is a rectangular enveloping space of the thermal analysis simulation model establishing process, and all predictable multilayer arc additive manufacturing part models are located in the space. But the space of the rectangular enveloping body is variable, namely the maximum size of the predictable multilayer arc additive manufacturing part model is variable, and the method specifically comprises the following steps:
(1) changing the size of a rectangular enveloping body when the thermal analysis simulation model is established, correspondingly, changing the number of units in a unit set of the thermal analysis simulation model, and changing the order of an activation sequence state matrix and a temperature state matrix of the corresponding unit set;
(2) changing some structural parameters of the ensemble learning model, including: the number of the memory units of the BilSTM, the number of nodes of a hidden layer of the memory units, the number of nodes of a full connection layer, the size of a convolution kernel and the like;
(3) reestablishing a thermal history database of the multilayer arc additive manufacturing process;
(4) and reestablishing, training and storing the ensemble learning model.
The steps do not influence the architectural nature of the ensemble learning model.
Compared with the prior art, the invention has the beneficial effects that:
the method realizes the discrete representation of the manufacturing state and the corresponding temperature field in the multilayer arc additive manufacturing process, can be used for a machine learning model, fully considers the associated information between discrete input data, adopts an integrated learning model based on a plurality of base learners mainly based on a bidirectional long-and-short-term memory network to fit the mapping relation between the unit set activation sequence data and the unit set temperature data, and obtains higher actual output data and ideal output data.
When the method is used for predicting the thermal history of a new arc additive manufacturing process, only the unit set activation sequence data set corresponding to the process needs to be generated, and the data set is sequentially input into the integrated learning model to carry out forward propagation, so that the prediction result of the thermal history of the process can be obtained.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a flow chart for building a thermal history database for a multi-layer arc additive manufacturing process.
Fig. 3 is a diagram of 5 arc additive manufacturing path patterns selected by a multi-layer arc additive manufacturing process in an embodiment.
Fig. 4 is a structural diagram of a machine learning model in the embodiment.
Fig. 5 is a schematic diagram of an input sequence of the first base learner in the embodiment.
Fig. 6 is a diagram showing an input sequence of the second base learner in the embodiment.
Fig. 7 is a diagram showing an input sequence of the third base learner in the embodiment.
FIG. 8 is a diagram of 28 part models corresponding to the training set in the example.
FIG. 9 is a diagram of 3 part models corresponding to the test set in the example.
FIG. 10 is a graph of the visualization of a portion of the tag data and corresponding output data for a test set in an example.
Fig. 11 is a flow chart for predicting a new multi-layer arc additive manufacturing process thermal history through an integrated learning model.
Detailed Description
The present invention is further described below in conjunction with the following specific embodiments and the attached drawings, it is to be noted that the described embodiments are only intended to facilitate the understanding of the present invention, and do not have any limiting effect thereon.
Fig. 1 is a flow chart of a method for predicting thermal history of a multi-layer arc additive manufacturing process based on machine learning, comprising the steps of:
1) establishing a multilayer arc additive manufacturing process thermal analysis simulation model, performing finite element simulation analysis, extracting manufacturing state data and temperature data at each simulation step moment, and establishing a multilayer arc additive manufacturing process thermal history database, wherein the process is shown in fig. 2 and comprises the following steps:
1.1) generating a number of multi-layer arc additive manufacturing processes comprising:
1.1.1) determining arc additive manufacturing process parameters including arc parameters, wire parameters, substrate parameters, and the like. Specifically, the electric arc power is 1500w, the electric arc moving speed is 10mm/s, and the electric arc thermal efficiency is 75%; the diameter of the welding wire is 1.2mm, the feeding rate of the welding wire is 11mm/s, and the material of the welding wire is ER 308L; the geometric shape of the substrate is a disc, the diameter of the substrate is 300mm, the thickness of the substrate is 20mm, and the material of the substrate is ER 308L; the interlayer cooling time was 0 s.
1.1.2) establishing 31 multilayer arc additive manufacturing part models, and selecting 5 arc additive manufacturing path modes, wherein the arc additive manufacturing path modes are shown in fig. 3.
1.1.3) respectively combining each multi-layer arc additive manufacturing part model and each arc additive manufacturing path mode under the set arc additive manufacturing process parameters to obtain 155 multi-layer arc additive manufacturing processes.
And (3) carrying out a single-pass arc additive manufacturing experiment under the set parameters of the arc additive manufacturing process, and measuring to obtain that the width of a welding bead is 4mm and the height of the welding bead is 1mm, namely the layer height of the arc additive manufacturing process is 1 mm.
1.2) determining an electric arc additive manufacturing space, wherein the position of the substrate model is fixed, and the relative position of the part model and the substrate model in the space is the same as that of the part and the substrate in the actual manufacturing process.
1.3) establishing an arc additive manufacturing thermal analysis simulation model, and establishing the thermal analysis simulation model for each multilayer arc additive manufacturing process in an arc additive manufacturing space. The method comprises the following steps:
1.3.1) determining a rectangular enveloping body which can envelop all multi-layer arc additive manufacturing part models: its dimension in the x-direction is 40mm, in the y-direction 40mm and in the z-direction 5 mm. The left surface and the right surface of the rectangular enveloping body are both perpendicular to the x axis; the front and back surfaces are both perpendicular to the y-axis; the upper surface and the lower surface are both perpendicular to the z-axis, and the lower surface coincides with the upper surface of the base. The positions of the different part models in the arc additive manufacturing space are fixed.
1.3.2) unitizing the rectangular enveloping body: since the width of the weld bead is 4mm and the depth is 1mm, the dimension of the cell in the x direction is set to 2mm, the dimension in the y direction is set to 2mm, and the dimension in the z direction is set to 1 mm. The unit set obtained by unitization is the unit set of the thermal analysis simulation model, the unit number of the unit set in the x direction is 20, the unit number in the y direction is 20, and the unit number in the z direction is 5.
1.3.3) judging whether the unit is an entity unit: for each unit in the unit set, judging whether the volume of the intersection area of the unit and the part model exceeds 50% of the unit volume, if so, the unit is an entity unit; otherwise, the cell is a void cell.
1.3.4) determining a heat source of a thermal analysis simulation model: considering the influence of arc movement on heat input, a double-ellipsoid heat source is selected as the heat source of the thermal analysis simulation model, and the energy distribution density q of the front part and the rear part of the heat sourcefAnd q isbCalculated by the following formula, respectively:
Figure BDA0002748388020000091
Figure BDA0002748388020000092
wherein a, b, cf,cbRespectively the shape parameters, observing the shape of the molten pool, wherein a is 2mm, b is 1mm, cf＝2mm，cb4 mm; q and eta are respectively welding power and welding thermal efficiency, Q is 1500kw, eta is 75%; f. offAnd fbEnergy distribution coefficients of the front and rear heat sources, respectively, ff＝0.6，fb＝1.4。
1.3.5) generating a simulation step sequence of the thermal analysis simulation model: generating a simulation step sequence based on a multilayer arc additive manufacturing process, and judging an entity unit needing to be activated in each simulation step in the simulation step sequence, wherein the generation of the simulation step sequence comprises the following steps:
1.3.5.1) discretizing a multi-layer arc additive manufacturing process into a plurality of straight-line segment additive manufacturing processes: approximately dispersing the multilayer arc additive manufacturing process into a plurality of linear segment additive manufacturing processes, and ensuring that the maximum distance deviation between the additive manufacturing path formed by all the linear segment additive manufacturing processes and the original additive manufacturing path is smaller than a distance threshold value dthresholdEach straight line section additive manufacturing process is as long as possible under the premise of 0.5 mm. And setting the distance interval delta d to be 2mm, dividing the path corresponding to each straight-line-section arc additive manufacturing process from the starting point based on the distance interval, and stopping the dividing process if the length of the rest path does not exceed the delta d. The segmentation results in one or more sub-paths, each sub-path corresponding to one sub-straight segment additive manufacturing process. Each sub-straight line segment additive manufacturing process corresponds to one simulation step. The time length of the sub-straight line segment additive manufacturing process is the time length t of the corresponding simulation steptime(ii) a The starting time of the sub-straight-line segment additive manufacturing process in the whole multilayer electric arc additive manufacturing process is the starting time t of the corresponding simulation stepbeginAnd forming a simulation step sequence according to the sequence positions of the corresponding sub-straight line segment additive manufacturing process in the whole additive manufacturing process.
1.3.5.2) for each simulation step, the judgment method of the activation unit is as follows:
1.3.5.2.1) calculating the envelope region R formed by the movement of the heat source in the first half part in the current simulation stepfrontAnd an envelope region R formed by moving the latter half heat source in the current simulation steprear. Activation determination region RactivationDefined as the intersection of two envelope regions:
Ractivation＝Rfront∩Rrear
1.3.5.2.2) for each inactive entity unit, determine if its center point is in the region RactivationIf yes, the simulation step is an activated unit of the current simulation step and marked as an activated unit; if not, the cell is still inactive.
1.4) establishing a thermal analysis finite element model and calculating: in the Abaqus software, a thermal analysis finite element model is established for each thermal analysis simulation model and calculated to obtain a temperature field corresponding to each simulation step of the thermal analysis simulation model, namely a finite element calculation result of the thermal history in the multilayer arc additive manufacturing process. The method comprises the following steps:
1.4.1) taking a geometric model formed by all entity units of the thermal analysis simulation model as a simulation entity model, and exporting the simulation entity model into an STP format file; the geometric model of the substrate is exported as an STP format file.
1.4.2) a model is newly built in Abaqus software, then STP files of a simulation entity model and a substrate geometric model are imported, and a simulation entity part and a substrate part are generated. And the positions of the simulation solid model and the substrate geometric model in the coordinate system of the Abaqus model are the same as the positions of the simulation solid model and the substrate geometric model in the coordinate system of the thermal analysis simulation model, and the relative positions of the simulation solid component and the substrate component are the same as the relative positions of the workpiece and the substrate in the actual arc additive manufacturing process.
1.4.3) creating a homogeneous solid cross section on the simulated solid part and the substrate part.
1.4.4) creating and partitioning the mock-up body part using a series of reference planes, one cell for each partitioned area. The unitization process and parameters of the unitization and the thermal analysis simulation model building process are completely the same.
1.4.5) creating a material, the material properties including density, specific heat and conductivity, all related to temperature, the specific values being shown in table 1. The created materials are assigned to homogeneous solid sections created on the mock-up real body part and the substrate part, respectively.
TABLE 1 Density, specific Heat and conductivity
Figure BDA0002748388020000101
Figure BDA0002748388020000111
1.4.6) assembling the simulated solid part and the substrate part according to the current relative position to generate an example.
1.4.7) creating an analysis step sequence of the finite element model based on the simulation step sequence of the thermal analysis simulation model, each simulation step corresponding to an analysis step. The first analysis step is an initial analysis step set by software and can not be changed, and the subsequent analysis steps are self-created transient analysis steps. Specifically, the first transient analysis step corresponds to the inactivation process of all the units, the time length is 1E-008, the maximum increment step number is 100000, the initial increment step size is 1E-009, the minimum increment step size is 1E-013, the maximum increment step size is 1E-008, the maximum temperature change allowed for each load step is 200, and the maximum radiation change allowed for each load step is 0.1. The second transient analysis step and each subsequent analysis step correspond to each simulation step sequence of the simulation step sequence, the time length of the transient analysis step is the duration of the corresponding simulation step, the maximum increment step number is 100000, the size of the initial increment step is 0.001, the size of the minimum increment step is 1E-008, the size of the maximum increment step is 0.1, the allowed maximum temperature change value of each load step is 150, and the allowed maximum radiation change value of each load step is 0.1.
1.4.8) create multiple interactions for each transient analysis step:
1.4.8.1) for the first transient analysis step, creating an interaction of type change in which all units are inactivated; creating an interaction of the type of surface heat exchange conditions in which the heat dissipation coefficient of all the free surfaces currently in contact with air is set to 0.04 and the ambient temperature is set to 20 ℃; an interaction of the type surface radiation is created in which the emissivity of all free surfaces currently in contact with air is set to 0.00016 and the ambient temperature to 20 ℃.
1.4.8.2) for each transient analysis step later, if there is an activation unit in the simulation step corresponding to the analysis step, creating an interaction with the type of model change, and reactivating the units in the interaction; creating an interaction of the type of surface heat exchange conditions in which the heat dissipation coefficient of all the free surfaces currently in contact with air is set to 0.04 and the ambient temperature is set to 20 ℃; an interaction of the type surface radiation is created in which the emissivity of all free surfaces currently in contact with air is set to 0.00016 and the ambient temperature to 20 ℃. Meanwhile, the transient analysis step before inactivation corresponds to the type of interaction of surface heat exchange conditions and the type of interaction of surface radiation.
1.4.9) define initial constants including the boltzmann constant, absolute zero degrees.
1.4.10) to create a load of the type body heat flux, acting from the second load analysis step. The heat flow density distribution of the moving load is defined by writing a user subroutine DFLUX.
1.4.11) creates a predefined field of the type temperature, which acts from the initial analysis step, predefining the whole instance to have an initial temperature value of 20 c.
1.4.12) to divide the entire instance into hexahedral meshes, the mesh type being DC3D 8. The grid division is respectively carried out on each unit and the substrate, and finally the grid of the whole example is obtained through integration.
1.4.13) checking whether a currently established finite element model has Bug, completing the modeling process of the thermal analysis finite element model in the whole arc additive manufacturing process, newly establishing Job, writing in an INP file, and calculating. The calculation results are stored in the ODB file.
1.5) designing a data structure: and designing a data structure to extract the unit set activation sequence data and the unit set temperature data of each simulation step moment of all the thermal analysis simulation models so as to establish a multilayer arc additive manufacturing process thermal history database. The method comprises the following steps:
1.5.1) the design of the data structure is as follows:
1.5.1.1) defines the activation time t of the cellactivation: activation time t of the cellactivationStart time t defined as the simulation step activating the cellbeginThe activation times of all the cells are represented by a three-dimensional matrix P, with the order of 20 × 20 × 5.
1.5.1.2) define the order of activation of the unit sets and the temperature data of the unit sets: the unit set activation sequence data and the unit set temperature data of the mth simulation step are respectively composed of a three-dimensional matrix SmAnd a three-dimensional matrix TmThe numbers of the steps are 20X 5. i, j, k are indices of cells located at the ith in the x-direction, the jth in the y-direction, and the kth in the z-direction in the cell set. SmAnd TmIs defined as follows:
1.5.1.2.1) Unit set activation sequence data S for the mth simulation stepmIs calculated as follows:
Figure BDA0002748388020000121
for an activated unit, the element value is the start time of the current simulation step minus the activation time of the unit; for inactive cells, the element value is positive infinity.
1.5.1.2.2) the meshing is performed on each cell, so that the eight vertices of the cell are mesh nodes, containing temperature information. And reading the ODB file of the finite element model of the current multilayer arc additive manufacturing process by using a script file written by the Python language by using the secondary development technology of the Abaqus to obtain the temperature data of all the unit vertexes of each analysis step. Three-dimensional matrix N for unit vertex temperature data of analysis step corresponding to mth simulation stepmThe number of the order is 21X 6.
1.5.1.2.3) Unit set temperature data T of the mth simulation stepmIs calculated as follows:
Figure BDA0002748388020000122
for the activated unit, the temperature data is the average value of the temperature data of the eight vertexes of the unit; for the inactive cells, the temperature data is 0.
Analysis shows that, for an activated unit, if the activation sequence data of the unit is smaller or a unit with smaller activation sequence data exists around the activated unit, that is, the unit is in an activated or reheated state, the temperature data of the unit is often higher. I.e. the spatial characteristics of the unit activation data, also have a certain correlation with its temperature data.
1.6) constructing a thermal history data pair set of a thermal analysis simulation model: based on the data structure, extracting unit set activation sequence data and unit set temperature data of each simulation step to form a thermal history data pair set { (S) of the thermal analysis simulation modelm,Tm)}。
1.7) extracting and combining the thermal history data pairs of the thermal analysis simulation models of all the arc additive manufacturing processes to obtain a multilayer arc additive manufacturing process thermal history database, wherein the total number of the thermal history data pairs is 98585.
2) Establishing an integrated learning model and a database thereof based on a bidirectional long-short-term memory (BilSTM) based on the multilayer arc additive manufacturing process thermal history database, and training: the ensemble learning model was built and trained using a PyTorch library. The method comprises the following steps:
2.1) establishing an ensemble learning model database: the ensemble learning model database is generated based on a multi-layer arc additive manufacturing process thermal history database and is further divided into a training set and a test set, and the method comprises the following steps:
2.1.1) defining the ensemble learning model database input data and the label data: the ensemble learning model predicts the temperature data of each unit based on the activation sequence data of the unit set at a certain stage of the additive manufacturing process, namely the temperature field at the stage. Therefore, the integrated learning model database is established by taking the unit set activation sequence data as input data I and taking the unit set temperature data as label data L.
2.1.2) dividing the integrated learning model database to obtain a training set and a testing set: dividing an ensemble learning model database to obtain a training set and a test set: selecting all input data and label data corresponding to the 28 part models as shown in fig. 8 as a training set, wherein 88460 data pairs are obtained in total; all input data and label data corresponding to the remaining part models as shown in fig. 9 were selected as a test set, for a total of 10125 data pairs.
2.2) designing an ensemble learning model, which specifically comprises the following steps:
2.2.1) the ensemble learning model is composed of a normalization layer, three basis learners, a convolution layer and a filter layer. The specific structure is shown in fig. 4, each base learner is composed of a BilSTM and a plurality of Full Connected (FC) layers, each layer of the BilSTM is composed of two single-layer long-term memory networks (LSTMs) in opposite order
2.2.2) input data I normalization: since the input data I element is not negative, it is normalized by the following exponential:
Hnormalization＝exp(-knormalization×I)
wherein k isnormalizationIs a normalized coefficient, with a value of 0.12; hnormalizationThe order is 20 × 20 × 5 for the output of the normalization layer.
2.2.3) reacting said HnormalizationThe decomposition yields the input matrix sequence of three basis learners: all elements in a single X dimension are taken as an input matrix, and an input matrix sequence X of a first base learner is formed according to the sequence of a y dimension and a z dimension1,X2,…,X100]The rank of each input matrix is 20 × 1, as shown in fig. 5; using single Y-dimension element as an input matrix, and forming an input matrix sequence Y-Y of a second base learner according to the sequence of x-dimension and then z-dimension1,Y2,…,Y100]Each input ofThe order of the matrix is 20 × 1, as shown in fig. 6; forming an input matrix sequence Z ═ Z of a third base learner according to the sequence of the x dimension and the y dimension by taking the element of the single Z dimension as an input matrix1,Z2,…,Z400]The order of each input matrix is 5 × 1, as shown in fig. 7.
2.2.4) all the basis learners are composed of one BilSTM and a plurality of FC layers, and after the input matrixes in the input matrix sequence are sequentially input into the basis learners, the output matrix sequence of the basis learners is obtained, and the specific structure is as follows:
2.2.4.1) the number of levels of the BilSTM of the first base learner is 1, including 100 forward memory cells and 100 backward memory cells. The number of hidden layer nodes in each memory unit is 60, and a matrix with the order of 60 multiplied by 1 is output. Inputting the matrix sequence in X to obtain the output sequence matrix sequence
Figure BDA0002748388020000131
Wherein the ith input matrix XiCorresponding output
Figure BDA0002748388020000132
The calculation formula of (A) is as follows:
Figure BDA0002748388020000133
Figure BDA0002748388020000134
Figure BDA0002748388020000135
wherein the content of the first and second substances,
Figure BDA0002748388020000136
is the output of the forward memory cell and,
Figure BDA0002748388020000137
is in a reverse directionThe output of the memory unit, LSTM (,) represents the nonlinear transformation of the LSTM network, CONCAT (,) represents an operation in which two-dimensional matrices are connected in columns,
Figure BDA0002748388020000138
the order of (2) is 120 × 1.
2.2.4.2) BilSTM output matrix sequence HxbilstmEach output matrix in the first base learner obtains an output matrix sequence of the first base learner after nonlinear transformation of two FC layers
Figure BDA0002748388020000141
2.2.4.3) output the matrix with the ith BilSTM
Figure BDA0002748388020000142
For example, the number of neurons in the first FC layer is 45, the
Figure BDA0002748388020000143
Connected thereto, output
Figure BDA00027483880200001431
The calculation formula of (A) is as follows:
Figure BDA0002748388020000145
wherein Relu () is the activation function, Wxfc1Is a weight matrix with the order of 45 × 120, Bxfc1The order is 45 x 1 for the offset matrix. All first FC layers of the first base learner share a weight matrix and a bias matrix.
2.2.4.4) the number of neurons in the second FC layer is 20, will
Figure BDA0002748388020000146
And is connected to, outputs of
Figure BDA0002748388020000147
The calculation formula of (A) is as follows:
Figure BDA0002748388020000148
wherein Relu () is the activation function, Wxfc2Is a weight matrix with the order of 20 × 45, Bxfc2The order is 20 x 1 for the offset matrix. All second FC layers of the first base learner share the weight matrix and the bias matrix.
Figure BDA0002748388020000149
I.e. the ith output matrix of the first basis learner
Figure BDA00027483880200001410
2.2.4.5) the number of levels of the BilSTM of the second base learner is 1, including 100 forward memory cells and 100 backward memory cells. The number of hidden layer nodes in each memory unit is 60, and a matrix with the order of 60 multiplied by 1 is output. Inputting the matrix sequence in Y to obtain the output sequence matrix sequence
Figure BDA00027483880200001411
Wherein the ith input matrix YiCorresponding output
Figure BDA00027483880200001412
The calculation formula of (A) is as follows:
Figure BDA00027483880200001413
Figure BDA00027483880200001414
Figure BDA00027483880200001415
wherein the content of the first and second substances,
Figure BDA00027483880200001416
is the output of the forward memory cell and,
Figure BDA00027483880200001417
for the output of the inverse memory unit, LSTM (,) represents the nonlinear transformation of the LSTM network, CONCAT (,) represents an operation in which two-dimensional matrices are connected in columns,
Figure BDA00027483880200001418
the order of (2) is 120 × 1.
2.2.4.6) BilSTM output matrix sequence HybilstmEach output matrix in the first base learner obtains an output matrix sequence of the first base learner after nonlinear transformation of two FC layers
Figure BDA00027483880200001419
2.2.4.7) output the matrix with the ith BilSTM
Figure BDA00027483880200001420
For example, the number of neurons in the first FC layer is 45, the
Figure BDA00027483880200001421
Connected thereto, output
Figure BDA00027483880200001422
The calculation formula of (A) is as follows:
Figure BDA00027483880200001423
wherein Relu () is the activation function, Wyfc1Is a weight matrix with the order of 45 × 120, Byfc1The order is 45 x 1 for the offset matrix. All first FC layers of the second base learner share a weight matrix and a bias matrix.
2.2.4.8) the number of neurons in the second FC layer is 20, will
Figure BDA00027483880200001424
And is connected to, outputs of
Figure BDA00027483880200001425
The calculation formula of (A) is as follows:
Figure BDA00027483880200001426
wherein Relu () is the activation function, Wyfc2Is a weight matrix with the order of 20 × 45, Byfc2The order is 20 x 1 for the offset matrix. All second FC layers of the second base learner share the weight matrix and the bias matrix.
Figure BDA00027483880200001427
I.e. the ith output matrix of the second basis learner
Figure BDA00027483880200001428
2.2.4.9) the number of levels of the BilSTM of the third base learner is 1, and includes 400 forward memory cells and 400 backward memory cells. The number of hidden layer nodes in each memory cell is 15, and a matrix with the order of 15 multiplied by 1 is output. Inputting the matrix sequence in Z to obtain the output sequence matrix sequence
Figure BDA00027483880200001429
Wherein the ith input matrix ZiCorresponding output
Figure BDA00027483880200001430
The calculation formula of (A) is as follows:
Figure BDA0002748388020000151
Figure BDA0002748388020000152
Figure BDA0002748388020000153
wherein the content of the first and second substances,
Figure BDA0002748388020000154
is the output of the forward memory cell and,
Figure BDA0002748388020000155
for the output of the inverse memory unit, LSTM (,) represents the nonlinear transformation of the LSTM network, CONCAT (,) represents an operation in which two-dimensional matrices are connected in columns,
Figure BDA0002748388020000156
the order of (2) is 30X 1.
2.2.4.10) BilSTM output matrix sequence HzbilstmEach output matrix in the first base learner obtains an output matrix sequence of the first base learner after nonlinear transformation of two FC layers
Figure BDA0002748388020000157
2.2.4.11) output the matrix with the ith BilSTM
Figure BDA0002748388020000158
For example, the number of neurons in the first FC layer is 12, the
Figure BDA0002748388020000159
Connected thereto, output
Figure BDA00027483880200001510
The calculation formula of (A) is as follows:
Figure BDA00027483880200001511
wherein Relu () is the activation function, Wzfc1Is a weight matrix with the order of 12 x 30, Bzfc1The order is 12 x 1 for the offset matrix. All first FC layers of the third base learner share a weight matrix and a bias matrix.
2.2.4.12) the number of neurons in the second FC layer is 5, will
Figure BDA00027483880200001512
And is connected to, outputs of
Figure BDA00027483880200001513
The calculation formula of (A) is as follows:
Figure BDA00027483880200001514
wherein Relu () is the activation function, Wzfc2Is a weight matrix with the order of 5 × 12, Bzfc2The order is 5 x 1 for the offset matrix. All second FC layers of the third base learner share the weight matrix and the bias matrix.
Figure BDA00027483880200001515
I.e. the ith output matrix of the second basis learner
Figure BDA00027483880200001516
2.2.5) for the output matrix sequence of each base learner, setting each output matrix in H according to the corresponding input matrixnormalizationThe three-dimensional matrix obtained by connecting the three-dimensional matrix sequences of the single-base learner is used as the input of a single channel of the convolutional layer, and the average value of the output matrixes of the three convolutional layer channels is the output matrix of the convolutional layer, and the method specifically comprises the following steps:
output matrix sequence H of first base learning devicexEach matrix of
Figure BDA00027483880200001517
According to its corresponding input matrix XiAt HnormalizationThe dimension positions are connected to obtain a three-dimensional matrix Iconv1The order is 20X 5, Iconv1Namely the input of the first channel of the convolution layer; output matrix sequence H of second base learning deviceyEach matrix of
Figure BDA00027483880200001518
According to its corresponding input matrix YiAt HnormalizationThe dimension positions are connected to obtain a three-dimensional matrix Iconv2The order is 20X 5, Iconv2The input of the second channel of the convolution layer; output matrix sequence H of the third base learnerzEach matrix H ofz iAccording to its corresponding input matrix ZiAt HnormalizationThe dimension positions are connected to obtain a three-dimensional matrix Iconv3The order is 20X 5, Iconv3I.e. the input of the convolutional layer third channel.
The convolutional layer contains a three-dimensional convolutional kernel with a size of 5 × 5 × 5 and a step size of 1. The number of input channels of the convolutional layer is 3, and the convolutional layer corresponds to three-dimensional output matrixes of the three base learners respectively. Before calculation, the data on each dimension of the input of each channel is supplemented by 0 twice. Performing convolution operation on the inputs of the three channels respectively to obtain an output Hconv1、Hconv2、Hconv3. The average value of the outputs of the three channels is the output H of the convolution layerconvThe calculation process is as follows:
Hconv1＝conv3d(padding(Iconv1,2),Wconv)
Hconv2＝conv3d(padding(Iconv2,2),Wconv)
Hconv3＝conv3d(padding(Iconv3,2),Wconv)
Figure BDA00027483880200001519
wherein, WconvA weight matrix which is a convolution kernel; padding (,) represents the operation of 0 compensation, the first parameter is the object for 0 compensation, and the second parameter is the times of 0 compensation before and after each dimension; conv3d (,) represents the corresponding nonlinear transformation of the three-dimensional convolution kernel.
2.2.6) obtaining the output O of the integrated learning model after filtering by a filter layer: by delineation of data structuresIt can be seen that the value of the co-located element in the final output matrix corresponding to the positive infinite element in the input matrix I should be 0. Thus, based on the input I of the ensemble learning model, the output H to the convolutional layerconvThe following filtration was performed: for HconvIf the value of its co-located element in the input matrix I is positive infinity, then the element is set to 0, otherwise, it is retained. And obtaining the output O of the ensemble learning model after filtering, wherein the order is 20 multiplied by 5. Element O with index (i, j, k)i,j,kIs calculated as follows:
Figure BDA0002748388020000161
2.3) after the building of the ensemble learning model and the building of the database thereof are completed, training the ensemble learning model, and specifically comprising the following steps:
2.3.1) choose mini-batch method for training, set batch size 4000.
2.3.2) establish the loss function: in the multilayer arc additive manufacturing process, the high temperature state experienced by the part has an important influence on the final residual stress distribution, substrate deformation and the like. Therefore, in the loss function of the back propagation process, higher weight is given to the loss values of the units with higher label values, the attention of the training process to the units is improved, and the accuracy of the ensemble learning model for predicting the high-temperature region is further improved. Specifically, the loss function is defined as follows:
2.3.2.1) element division: setting a temperature threshold value to be 1300 ℃, dividing a label element set { L } corresponding to the label matrix L, and forming a low-temperature label element set { L } by label elements with label values smaller than 1300 DEG ClowN number of elementslow(ii) a The rest label elements form a high-temperature label element set lhighN number of elementshigh. According to the grouping of the corresponding label elements, the element set { O } corresponding to the output matrix O is divided, and the output matrix element set { O } corresponding to the low-temperature label element set is correspondingly obtainedlowSet of output matrix elements { o } corresponding to the set of high temperature tag elementshigh}。
2.3.2.2) calculating { l }lowAnd { o }lowObtaining the prediction Loss function value Loss of the low-temperature unit according to the average absolute error between the two unitslow(ii) a Calculation of { lhighAnd { o }highObtaining the prediction Loss function value Loss of the high-temperature unit according to the average absolute error between the two unitshigh. Computing LosslowAnd LosshighThe Loss function value Loss of all units is obtained, and the calculation formula is as follows:
Figure BDA0002748388020000162
Figure BDA0002748388020000163
Figure BDA0002748388020000164
2.3.3) calculating a loss function value of batch data, and realizing iterative optimization of the model by using a self-adaptive matrix estimation method, wherein the initial learning rate is 0.01;
2.3.4) the training process stops after 1000 trains, and then all parameters of the model are saved locally.
To further evaluate the performance of the ensemble learning model, the prediction accuracy and prediction efficiency of the ensemble learning model are verified on a test set:
the prediction Accuracy is evaluated by an Accuracy function, which is defined as the average absolute error Accuracy between the output matrix O and the label matrix L, and the calculation formula is as follows:
Figure BDA0002748388020000165
the prediction accuracy of the integrated learning model on the whole test set exceeds 0.94, and the prediction accuracy achieves the expected effect.
The 'unidirectional straight line filling X' path mode is selected, the finite element method and the method are used for predicting the thermal histories of the three test models shown in the figure 9 respectively, the time consumption is shown in the table 2, and it can be seen that the method can remarkably improve the thermal history prediction efficiency.
TABLE 2 thermal history predicts elapsed time
Figure BDA0002748388020000171
The comparison of the visualized label data of the partial test set and the output data obtained by the integrated learning model is shown in fig. 10, where the left side of each row is the visualized result of the label data, and the right side is the visualized result of the corresponding output data. It can be seen that the simulation result has better consistency with the prediction result.
3) After the training and the saving of the ensemble learning model are completed, in the later use, for a new multilayer arc additive manufacturing process, a prediction result of the thermal history of the multilayer arc additive manufacturing process can be obtained according to the flow shown in fig. 11. The method comprises the following steps:
3.1) generating a thermal analysis simulation model of the arc additive manufacturing process through the same thermal analysis simulation model establishing process;
3.2) extracting to obtain a unit set activation sequence state data set: extracting unit set activation sequence state data S of each simulation step of thermal analysis simulation modeliObtaining a unit set activation sequence state data set { S };
3.3) sequentially inputting the data of the cell set activation sequence state data set into the ensemble learning model to obtain a prediction result of the thermal history: will be data S in { S }iInputting the trained ensemble learning model in sequence to obtain an output set { O }:
Oi＝Ensembling(Si)
wherein Ensembling () is a nonlinear transformation corresponding to the ensemble learning model. And O is the predicted result of the thermal history of the multilayer arc additive process.
The length, the width and the height of the part model corresponding to the predictable multilayer arc additive manufacturing process of the ensemble learning model shown in the above embodiments are not greater than 40mm, not greater than 40mm and not greater than 5mm, that is, the rectangular envelope when the thermal analysis simulation model is built must be enveloped, and the rectangular envelope is the prediction space of the ensemble learning model.
The method is scalable in that the maximum size of the part model can be predicted, i.e. the prediction space of the integrated learning model can be varied. Specifically, the prediction of the change in space comprises the steps of:
(1) changing the size of a rectangular enveloping body when the thermal analysis simulation model is established, correspondingly, changing the number of units in a unit set of the thermal analysis simulation model, and changing the order of an activation sequence state matrix and a temperature state matrix of the corresponding unit set;
(2) changing some structural parameters of the ensemble learning model, including: the number of the memory units of the BilSTM, the number of nodes of a hidden layer of the memory units, the number of nodes of a full connection layer, the size of a convolution kernel and the like;
(3) reestablishing a thermal history database of the multilayer arc additive manufacturing process;
(4) and reestablishing, training and storing the ensemble learning model.
The steps do not influence the architectural nature of the ensemble learning model.

Claims (9)

1. A multilayer arc additive manufacturing process thermal history prediction method based on machine learning comprises the following steps:
1) establishing a multilayer arc additive manufacturing process thermal analysis simulation model, performing finite element simulation analysis, extracting manufacturing state data and temperature data at each simulation step moment, and establishing a multilayer arc additive manufacturing process thermal history database;
2) establishing an integrated learning model based on a bidirectional long-time and short-time memory network and training;
3) and after the training and the testing of the integrated learning model are completed and stored, predicting the thermal history of the new arc additive manufacturing process.
2. The method for predicting the thermal history of the multi-layer arc additive manufacturing process according to claim 1, wherein in step 1), a multi-layer arc additive manufacturing process thermal history database is established, and the specific process is as follows:
1.1) generating a multilayer arc additive manufacturing process comprising: setting parameters of an electric arc additive manufacturing process, establishing a multilayer electric arc additive manufacturing part model and selecting a multilayer electric arc additive manufacturing path mode;
1.2) determining an arc additive manufacturing space;
1.3) establishing an arc additive manufacturing thermal analysis simulation model: establishing a thermal analysis simulation model for each multi-layer arc additive manufacturing process in the arc additive manufacturing space;
1.4) establishing a thermal analysis finite element model and calculating: in finite element software, establishing a thermal analysis finite element model for each thermal analysis simulation model and calculating to obtain a temperature field corresponding to each simulation step of the thermal analysis simulation model, namely a finite element calculation result of the thermal history in the multilayer arc additive manufacturing process;
1.5) designing a data structure: extracting manufacturing state data and temperature field data of each simulation step moment of the thermal analysis simulation model, wherein the manufacturing state data and the temperature field data are represented by activation sequence data and temperature data of a thermal analysis simulation model unit set;
1.6) constructing a thermal history data pair set of a thermal analysis simulation model;
1.7) extracting and combining the thermal history data pairs of the thermal analysis simulation models of all the arc additive manufacturing processes to obtain a multilayer arc additive manufacturing process thermal history database.
3. The method for predicting the thermal history of the multi-layer arc additive manufacturing process according to claim 2, wherein in the step 1.3), a thermal analysis simulation model is established for each multi-layer arc additive manufacturing process in the arc additive manufacturing space, and the specific steps are as follows:
1.3.1) determining a rectangular enveloping body enveloping all multi-layer arc additive manufacturing part models;
1.3.2) unitizing the rectangular enveloping body to obtain a unit set of the thermal analysis simulation model;
1.3.3) judging whether the unit is an entity unit;
1.3.4) determining a heat source of the thermal analysis simulation model;
1.3.5) generating a simulation step sequence of the thermal analysis simulation model: and generating a simulation step sequence based on the multilayer arc additive manufacturing process, and judging the entity unit which needs to be activated in each simulation step in the simulation step sequence.
4. The method of claim 2, wherein in step 1.5), the data structure is designed as follows:
1.5.1) defining the activation time t of a cellactivation: activation time t of the cellactivationStarting time t of simulation step for activating the unitbeginThe activation times of all the cells are represented by a three-dimensional matrix P, with the order nx×ny×nz，nx、ny、nzThe unit numbers of the thermal analysis simulation model unit sets in the x dimension, the y dimension and the z dimension are respectively;
1.5.2) define Unit set activation sequence data and Unit set temperature data: the unit set activation sequence data and the unit set temperature data of the mth simulation step are respectively composed of a three-dimensional matrix SmAnd a three-dimensional matrix TmIs represented by the order nx×ny×nzI, j, k is the index of the unit located at the ith in the x-direction, the jth in the y-direction and the kth in the z-direction in the unit set, SmAnd TmIs defined as follows:
activation sequence data S of unit set of mth simulation stepmIs calculated as follows:
Figure FDA0002748388010000021
reading the finite element model calculation result file to obtain the temperature values of eight vertexes of each unit in each simulation step and the temperature values of all the vertexes of the unit in the mth simulation stepThree-dimensional matrix N for datamIs represented by the order of (n)x+1)×(ny+1)×(nz+1)；
Temperature data T of cell set in mth simulation stepmIs calculated as follows:
Figure FDA0002748388010000022
5. the method of claim 1, wherein in step 2), the integrated learning model is designed by the following specific steps:
2.2.1) the integrated learning model consists of a normalization layer, three base learners, a convolution layer and a filter layer, wherein each base learner consists of a bidirectional long-time and short-time memory network and a plurality of full-connection layers;
2.2.2) normalizing the input data I, as shown in the following formula:
Hnormalization＝exp(-knormalization×I)
wherein k isnormalizationIs a normalized coefficient; hnormalizationIs the output of the normalization layer;
2.2.3) reacting said HnormalizationDecomposing to obtain input matrix sequences of three base learners;
2.2.4) all the base learners are composed of a bidirectional long-short time memory network and a plurality of full connection layers, and the input matrix sequence of the base learner obtains the output matrix sequence of the base learner through the bidirectional long-short time memory network and the full connection layers;
2.2.5) connecting the output matrix sequence of the single-basis learner to obtain a three-dimensional matrix as the input of the single channel of the convolutional layer, wherein the average value of the output matrixes of the three convolutional layer channels is the output matrix of the convolutional layer;
2.2.6) filtering the output matrix of the convolution layer by a filter layer to obtain the output O of the integrated learning model.
6. The method for predicting the thermal history of the multi-layer arc additive manufacturing process according to claim 1, wherein in the step 2), the ensemble learning model is trained, and the method specifically comprises the following steps:
2.3.1) selecting a mini-batch method for training;
2.3.2) establish the loss function:
2.3.3) calculating a loss function value of batch data, setting a learning rate, and realizing iterative optimization of the model by a self-adaptive matrix estimation method;
2.3.4) the training process is stopped after a certain number of training sessions and all parameters of the model are saved locally.
7. The method of claim 6, wherein in step 2.3.2) the loss function is defined as follows:
2.3.2.1) setting the temperature threshold TthresholdDividing a label element set { L } corresponding to the label matrix L, wherein the label element set { L } is smaller than TthresholdThe tag elements of (a) constitute a low temperature set of tag elements { l }lowN number of elementslow(ii) a The rest label elements form a high-temperature label element set lhighN number of elementshighAccording to the grouping of the corresponding label elements, the element set { O } corresponding to the output matrix O is divided, and the output element set { O } corresponding to the low-temperature label element set is correspondingly obtainedlowSet of output elements { o } corresponding to the set of high temperature tag elementshigh}；
2.3.2.2) calculating { l }lowAnd { o }lowObtaining the prediction Loss function value Loss of the low-temperature unit according to the average absolute error between the two unitslow(ii) a Calculation of { lhighAnd { o }highObtaining the prediction Loss function value Loss of the high-temperature unit according to the average absolute error between the two unitshigh(ii) a Computing LosslowAnd LosshighThe Loss function value Loss of all the units is obtained.
8. The method of claim 5, wherein the performance of the ensemble learning model is evaluated by verifying the prediction accuracy and prediction efficiency of the ensemble learning model on the test set.
9. The method for predicting the thermal history of the multi-layer arc additive manufacturing process according to claim 1, wherein the specific steps of the step 3) are as follows:
3.1) generating a new thermal analysis simulation model of the arc additive manufacturing process through the same thermal analysis simulation model establishing process;
3.2) extracting to obtain a unit set activation sequence state data set: extracting unit set activation sequence state data S of each simulation step of thermal analysis simulation modeliObtaining a unit set activation sequence state data set { S };
3.3) sequentially inputting the data of the cell set activation sequence state data set into the ensemble learning model to obtain a prediction result of the thermal history: activating a set of cells sequential state data SiInputting the ensemble learning model to obtain output data OiAnd sequentially inputting the data in the { S } into the trained ensemble learning model to obtain an output set { O }:
Oi＝Ensembling(Si)
the Ensembling function is nonlinear transformation corresponding to the integrated learning model, and the { O } function is a thermal history prediction result of the multilayer arc additive process.
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