JP7759142B2 - Prediction method and program - Google Patents

Description

The present invention relates to a prediction method and program for predicting plastic strain distribution (intrinsic strain distribution), residual stress distribution or deformation.

Numerical analysis using thermo-elastic-plastic analysis is commonly used to calculate residual stresses generated by welding. Using thermo-elastic-plastic analysis, it is possible to consider the welding conditions when welding the target steel material in a digital space. However, with thermo-elastic-plastic analysis, it is necessary to input time-series data of the temperature distribution that changes from moment to moment, from heating to the end of cooling. This results in a huge amount of calculation and long analysis times. Furthermore, when analyzing an object with a complex shape, the analysis time becomes even longer.
The inherent strain method is known as a method for shortening the analysis time (see, for example, Patent Document 1).

Japanese Patent Application Laid-Open No. 2020-144425

However, when the deformations obtained by the inherent strain method are compared with those obtained by the thermo-elastic-plastic analysis method, the analysis results often deviate.Furthermore, when the deformations obtained by the inherent strain method are compared with those of welded components, the deformations often deviate.
The present invention has been made in view of the above circumstances, and provides a prediction method that can predict plastic strain distribution, deformation distribution, or residual stress distribution in a short time with high accuracy.

The present invention provides a prediction method for predicting the plastic strain distribution (inherent strain distribution), residual stress distribution, or deformation of a target object, which includes a step of outputting prediction output data corresponding to the plastic strain distribution from prediction input data including heating conditions using a machine learning model trained with training data including learning input data including heating conditions and training output data corresponding to the plastic strain distribution (inherent strain distribution) calculated from the heating conditions using a numerical analysis method.

According to the present invention, it is possible to predict the plastic strain distribution (inherent strain distribution), deformation or residual stress distribution in a short time with high accuracy. Furthermore, it is possible to predict the plastic strain distribution, deformation or residual stress distribution of a complex target object in a short time.
The prediction method of the present invention does not require the tedious task of creating an element mesh, thereby reducing the workload of the analyst.

FIG. 1 is an explanatory diagram of a prediction method according to an embodiment of the present invention. FIG. 10 is an explanatory diagram of geometric conditions showing the heating position on the input side. FIG. 10 is an explanatory diagram of geometric conditions showing the heating position on the input side. FIG. 10 is an explanatory diagram of input items required for fillet welding. This is the relationship between inherent deformation and inherent strain. FIG. 1 is a schematic diagram of an analytical model of a target object used in a thermo-elastic-plastic analysis. 10A is the plastic strain distribution in the x direction created from the results of the thermo-elastic-plastic analysis, and FIG. 10B is the plastic strain distribution in the x direction created from the prediction output data. 10A is the plastic strain distribution in the x direction created from the results of the thermo-elastic-plastic analysis, and FIG. 10B is the plastic strain distribution in the x direction created from the prediction output data. (a) is the plastic strain distribution in the y direction created from the analysis results of the thermo-elastic-plastic analysis, and (b) is the plastic strain distribution in the y direction created from the prediction output data. 6A to 6D are graphs comparing the inherent deformation calculated using the relational expressions in FIG. 5 with the inherent deformation calculated using thermo-elastic-plastic analysis. 10A is the plastic strain distribution in the x direction created from the results of the thermo-elastic-plastic analysis, and FIG. 10B is the plastic strain distribution in the x direction created from the prediction output data. (a) is the plastic strain distribution in the y direction created from the analysis results of the thermo-elastic-plastic analysis, and (b) is the plastic strain distribution in the y direction created from the prediction output data. 6A to 6D are graphs comparing the inherent deformation calculated using the relational expressions in FIG. 5 with the inherent deformation calculated using thermo-elastic-plastic analysis. (a) is the plastic strain distribution in the x direction created from the results of the thermo-elastic-plastic analysis, and (b) is the plastic strain distribution in the x direction created from this prediction output data. (a) is the residual stress distribution in the x direction created from the results of the thermo-elastic-plastic analysis, and (b) is the residual stress distribution in the x direction created from data calculated by elastically analyzing the prediction output data. 6A and 6B are graphs comparing the inherent deformation calculated using the relational expression in FIG. 5 with the inherent deformation calculated using thermo-elastic-plastic analysis. This is the angular distortion distribution along the heating direction created from the prediction output data. This is the angular distortion distribution along the heating direction created from the prediction output data. This is the angular distortion distribution along the heating direction created from the prediction output data. This is the angular distortion distribution along the heating direction created from the prediction output data. This is a distribution of transverse shrinkage along the heating direction created from the prediction output data. This is a distribution of transverse shrinkage along the heating direction created from the prediction output data. This is a distribution of transverse shrinkage along the heating direction created from the prediction output data. This is a distribution of transverse shrinkage along the heating direction created from the prediction output data. This is a longitudinal shrinkage distribution along the heating direction created from the prediction output data. This is a longitudinal shrinkage distribution along the heating direction created from the prediction output data. This is a longitudinal shrinkage distribution along the heating direction created from the prediction output data. This is a longitudinal shrinkage distribution along the heating direction created from the prediction output data. This is a vertical bending distribution along the heating direction created from the prediction output data. This is a vertical bending distribution along the heating direction created from the prediction output data. This is a vertical bending distribution along the heating direction created from the prediction output data. This is a vertical bending distribution along the heating direction created from the prediction output data.

The prediction method of the present invention is a prediction method for predicting the plastic strain distribution (intrinsic strain distribution), residual stress distribution, or deformation of a target object, and includes a step of outputting prediction output data corresponding to the plastic strain distribution from prediction input data including heating conditions using a machine learning model trained with training data including learning input data including heating conditions and training output data corresponding to the plastic strain distribution calculated from the heating conditions using a numerical analysis method.

The prediction method of the present invention preferably includes a step of calculating a deformation or residual stress distribution from the prediction output data, thereby making it possible to predict the deformation or residual stress distribution in a short time with high accuracy.
It is preferable that the heating conditions included in the learning input data include at least one of bead-on welding, groove welding, fillet welding, plug welding, slot welding, multi-layer welding, metal additive manufacturing, strain relief by heating, cutting by heating, and bending by heating.
The present invention also provides a prediction method for predicting the inherent deformation distribution along the heating direction of a target object, the prediction method including a step of outputting prediction output data corresponding to the inherent deformation distribution along the heating direction from prediction input data including heating conditions using a machine learning model trained with teacher data including learning input data including heating conditions and learning output data corresponding to the inherent deformation distribution along the heating direction calculated from the heating conditions using a numerical analysis method.
The present invention also provides a program configured to cause a computer to execute the prediction method of the present invention.

An embodiment of the present invention will be described below using the drawings. The configurations shown in the drawings and the following description are examples, and the scope of the present invention is not limited to those shown in the drawings and the following description.

First Embodiment FIG. 1 is an explanatory diagram of a prediction method according to this embodiment.
The prediction method of the first embodiment is a prediction method for predicting the plastic strain distribution (inherent strain distribution), residual stress distribution, or deformation of a target object. The prediction method of this embodiment includes a step of outputting prediction output data corresponding to the plastic strain distribution from prediction input data including heating conditions using a machine learning model trained with teacher data including training input data including heating conditions and training output data corresponding to the plastic strain distribution (inherent strain distribution) calculated from the heating conditions using a numerical analysis method. The prediction method of this embodiment may also include a step of calculating the deformation or residual stress distribution from the prediction output data.
The prediction method of this embodiment is a prediction method for predicting the plastic strain distribution, residual stress distribution, or deformation of a target object caused by, for example, bead-on welding, groove welding, fillet welding, plug welding, slot welding, multi-layer welding, metal additive manufacturing, strain relief by heating, cutting by heating, and bending by heating.
The program of this embodiment is provided to cause a computer to execute the prediction method of this embodiment.

First, the creation of a machine learning model used in the prediction method of this embodiment will be described.
Numerical analysis is used to create the training data. Examples of numerical analysis methods include thermo-elastic-plastic analysis, elasto-plastic analysis, and elastic analysis, and it is preferable to use thermo-elastic-plastic analysis. Furthermore, thermo-elastic-plastic analysis can include heat conduction analysis. Idealized explicit FEM can be used for thermo-elastic-plastic analysis. In the following explanation, the training data is created using thermo-elastic-plastic analysis.
Specifically, as shown in Figure 1, analysis is performed using shape data (mesh data, etc.) (analysis model) of the target object, information on the target object's material (specific heat, density, thermal conductivity coefficient, Young's modulus, yield stress, Poisson's ratio, linear expansion coefficient, work hardening coefficient, etc.), and heating conditions (specifically, heat input, heat source distribution parameters, heating rate, coordinates of the heating start point, coordinates of the heating end point, etc.), and data corresponding to the plastic strain distribution (intrinsic strain distribution) is calculated. Furthermore, residual stress distribution or inherent deformation can be calculated as necessary. The "heat source distribution parameters" correspond to the standard deviation σ when the heat source distribution is assumed to be a normal distribution.
"Plastic strain" includes strain that occurs when a target object is cooled after being locally melted or locally heated by welding, etc. "Plastic strain" may be "intrinsic strain" or "permanent strain.""Plasticstrain" may also be "strain" that results from a numerical analysis.
The heating conditions may also include at least one of bead-on welding, groove welding, fillet welding, seam welding, plug welding, slot welding, multi-layer welding, multi-pass welding, metal additive manufacturing (e.g., 3D printer, 3D metal additive manufacturing), strain relief by heating, cutting by heating (e.g., melt cutting), bending by heating (e.g., linear heating), and thermal spraying.
In addition, the shape data (analysis model) of the target object can be shape data of any one of a butt joint, lap joint, double-sided pad joint, single-sided pad joint, corner joint, T-joint, cross joint, edge joint, metal additive manufacturing, strain relief, and bending.

Such thermo-elastic-plastic analysis is repeated while randomly changing heating conditions, etc. For example, thermo-elastic-plastic analysis can be repeated more than 1,000 times. For example, thermo-elastic-plastic analysis can be repeated while randomly changing the heat input, heating rate, coordinates of the heating start point, and coordinates of the heating end point. The same shape data of the target object, information about the material of the target object, etc. can be used in repeated thermo-elastic-plastic analyses. Thermo-elastic-plastic analysis can also be repeated while changing the shape data of the target object or information about the material of the target object.

The geometric conditions indicating the heating position on the input side can be set as follows:
The set of variables for a one-dimensional problem can be set as shown in Figure 2 (the unit of length is unified to [mm]). The basic information of the heating conditions can be expressed as follows: Qnet: net heat per unit length [kJ/s], Qhh: heat input parameter [J/ ^mm3 ], Speed: heating rate [mm/s], thickness: plate thickness [mm], sigma: heat source parameter σ [mm], and SE_length: heating length. The stiffness at the target point P can be expressed as P_L1: shortest distance (parallel) to the edge of the target point P, and P_L2: shortest distance (perpendicular) to the edge of the target point P. The influence of the heating direction can be expressed as PS_vector: signed distance between the target point P and the start point S, and PE_vector: signed distance between the target point P and the end point E. This allows the diversity of strain distribution to be characterized by geometric distances, etc.
The heat input parameter is a parameter that represents the magnitude of heat input determined by the relationship between the heat input, heating rate, and plate thickness, and is expressed as (Q/v)/ ^h2 , where Q is the heat input (W), v is the heating rate (mm/s), and h is the plate thickness (mm).

The variables for a three-dimensional problem can be set as shown in Figure 3 (the unit of length is unified as [mm]). The basic information for heating conditions can be expressed as follows: Qnet: net heat per unit length [kJ/s], Qhh: heat input parameter [J/ ^mm³ ], Speed: heating rate [mm/s], thickness: plate thickness [mm], sigma: heat source parameter σ [mm], and SE_length: heating length. The stiffness at target point P can be expressed as follows: P_L1: shortest distance to the edge of target point P (horizontal), P_L2: shortest distance to the edge of target point P (perpendicular), and P_L3: shortest distance to the edge of target point P (depth). The influence of heating direction can be expressed as follows: PS_vector: signed distance between target point P and start point S, and PE_vector: signed distance between target point P and end point E. To express the thermal impact near the start and end points, the following can be used: S_L1: shortest distance (parallel) to the edge of start point S, S_L2: shortest distance (perpendicular) to the edge of start point S, E_L1: shortest distance (parallel) to the edge of end point E, E_L2: shortest distance (perpendicular) to the edge of end point E, TH_length: maximum possible length of construction. As distances from the heating center, the following can be used: P_heatline_L2: shortest distance (perpendicular) to the heated part of target point P, P_heatline_R: radius of the heated part of target point P (≠ L2), P_depth: depth of target point P from the heated surface (≠ L3).

The input items (entered by the user) required for fillet welding as shown in Figure 4 are: Qnet: net heat per unit length [kJ/s], Speed: heating rate [mm/s], sigma: heat source parameter σ [mm], Xs, Ys, Zs: coordinates of the welding start point (x, y, z) [mm], Xe, Ye, Ze: coordinates of the welding end point (x, y, z) [mm], CAD data for the model, Thickness_plate: base material plate thickness [mm], Thickness_web: web plate thickness [mm], plate dimensions [mm]. These user-entered items are converted internally into geometric explanatory variables for machine learning.

Training data can be created from the input data and analysis results used in the repeated thermo-elastic-plastic analysis. For example, the training input data items for this training data include the shape data of the target object, heat source distribution parameters, heat input amount, heating rate, and coordinates of the heating start point and the heating end point, and the training output data (correct answer data) includes data corresponding to the plastic strain distribution (intrinsic strain distribution). The training data includes many pairs of training input data and training input data (correct answer data). The training input data may also include information about the material of the target object.
Furthermore, if the shape data of the target object is the same in all thermo-elastic-plastic analyses, this shape data can be excluded from the training input data.If the heat source distribution parameters are the same in all thermo-elastic-plastic analyses, this heat source distribution parameters can be excluded from the training input data.

Next, a machine learning model can be created by training a machine learning framework using the created training data.

Next, the prediction input data is input to the machine learning model, and prediction output data is output. The prediction input data is input data for which the correct answer data is unknown, and the machine learning model is used to predict the correct answer data (prediction output data) from this input data. The data items of the prediction input data can be the same as the data items of the training input data.
The prediction input data includes, for example, shape data of the target object, heat source distribution parameters, heat input, heating rate, coordinates of the heating start point, and coordinates of the heating end point. These input data are input into a machine learning model, and data corresponding to the plastic strain distribution (intrinsic strain distribution) is output as prediction output data. By creating a plastic strain distribution from this data, it is possible to know the plastic strain distribution predicted when heating is performed under the heating conditions of the prediction input data.

For example, many candidate heating conditions can be created, and a machine learning model can be used to create a predicted plastic strain distribution (intrinsic strain distribution) from each heating condition. The most appropriate plastic strain distribution can then be selected, and overheating, such as welding, can be performed using the heating conditions corresponding to the selected plastic strain distribution. The prediction method of this embodiment can create a predicted plastic strain distribution in a short period of time, allowing for the setting of many candidate heating conditions and the identification of more appropriate heating conditions. Furthermore, even if the target object has a complex shape, a predicted plastic strain distribution can be created in a short period of time.

The prediction method of this embodiment can also include a step of calculating deformation from prediction output data (data corresponding to plastic strain distribution). Deformation can be calculated by integrating the plastic strain distribution (intrinsic strain distribution). For example, the inherent deformation (longitudinal shrinkage, longitudinal bending, lateral shrinkage, lateral bending) can be calculated from data corresponding to the plastic strain distribution using the relationship shown in Figure 5. This makes it possible to know the inherent deformation predicted when heated under the heating conditions of the prediction input data. The prediction method of this embodiment can calculate the predicted inherent deformation in a short time, allowing for the setting of many candidate heating conditions and the identification of more appropriate heating conditions. Furthermore, even if the target object has a complex shape, the predicted inherent deformation can be calculated in a short time.

The prediction method of this embodiment may also include a step of performing elastic analysis using prediction output data (data corresponding to the plastic strain distribution) to calculate data corresponding to the residual stress distribution. A residual stress distribution can be created from the data corresponding to this residual stress distribution. For example, data corresponding to the plastic strain distribution (inherent strain distribution) (output data of the machine learning model) can be provided to a stress-free analytical model and elastic analysis can be performed to calculate data corresponding to the residual stress distribution. The prediction method of this embodiment can create a predicted residual stress distribution in a relatively short time, allowing for the setting of many candidate heating conditions and the identification of more appropriate heating conditions. Furthermore, even when the target object has a complex shape, a predicted residual stress distribution can be created in a short time.
The prediction method of the first embodiment is effective when a comprehensive judgment is desired because it is possible to predict the plastic strain distribution, the inherent deformation distribution, and the residual stress distribution.

Second Embodiment A prediction method of the second embodiment is a prediction method for predicting the inherent deformation distribution along the heating direction of a target object, and includes a step of outputting prediction output data corresponding to the inherent deformation distribution along the heating direction from prediction input data including heating conditions using a machine learning model trained with teacher data including training input data including heating conditions and training output data corresponding to the inherent deformation distribution along the heating direction calculated from the heating conditions using a numerical analysis method.

In the second embodiment, training data is created from input data and analysis results used in repeated thermo-elastic-plastic analyses, similar to the first embodiment, except that in the thermo-elastic-plastic analyses, training output data corresponding to the inherent deformation distribution along the heating direction is calculated.
Next, a machine learning model can be created by training a machine learning framework using the created training data.
Next, input data for prediction is input to the machine learning model, and output data for prediction is output.
The input data for prediction include, for example, shape data of the target object, heat source distribution parameters, heat input, heating rate, coordinates of the heating start point, and coordinates of the heating end point. These input data are input to a machine learning model, and data corresponding to the intrinsic deformation distribution along the heating direction (angular distortion distribution, lateral shrinkage distribution, longitudinal shrinkage distribution, longitudinal bending distribution) is output as output data for prediction. By creating an intrinsic deformation distribution from this data, it is possible to know the intrinsic deformation distribution predicted when heating is performed under the heating conditions of the input data for prediction.
The prediction method of the second embodiment is effective when only the inherent deformation distribution is required. Since the inherent deformation distribution has only four components (longitudinal shrinkage, longitudinal bending, transverse shrinkage, and transverse bending) for each cross section, there is little freedom in obtaining the distribution in the heating line direction (approximately 100 components), and prediction is relatively easy.

Creating a machine learning model 1
A machine learning model was created using training data obtained by performing a thermal elastic-plastic analysis. The idealized explicit FEM method was used for the thermal elastic-plastic analysis.
FIG. 6 is a schematic diagram of the analytical model (shape data of the target object) used in the thermo-elastic-plastic analysis. The target object is a steel plate with a length of 400 mm, a width of 400 mm, and a thickness of 16 mm. The longitudinal direction of the analytical model is defined as the x-direction, the lateral direction of the analytical model is defined as the y-direction, and the thickness direction of the analytical model is defined as the z-direction. The analytical model is divided into a plurality of elements (mesh), and each vertex of each element is a node. In addition, the analytical model has a region with a width of 80 mm and a length of 400 mm, centered on a line (a line extending in the x-direction) connecting the midpoints of two sides of the analytical model extending in the y-direction. The region is divided into elements with a mesh size of 2.5 mm.

Using this analytical model, 3,900 thermo-elastic-plastic analyses were performed under various heating conditions (gas heating), and data corresponding to the plastic strain distribution was calculated for each analysis. In all analyses, the thermal efficiency was set to 1.0, and the heat source distribution parameter σ was set to 20 mm. The starting and ending points of the heating lines in each analysis were randomly set on a line connecting the midpoints of two edges extending in the y direction of the analytical model (a line extending in the x direction). The heat input in each analysis was randomly set within a range of 2,000 W to 40,000 W (2 kW to 40 kW). The heating rate in each analysis was randomly set within a range of 1 mm/sec to 20 mm/sec.
In addition, to represent the start point and end point of the heating line on a line connecting the midpoints of two sides extending in the y direction of the analytical model, an x-coordinate is used in which one end of the line connecting the midpoints is 0 and the other end is 400 (0 → 400 is the x-direction).

Based on the results of 3,900 thermal elastic-plastic analyses, training data was created in which the data items for the learning input data were the shape data of the target object, heat source distribution parameters, heat input, starting and ending points of the heating line, and heating rate, and the learning output data was data corresponding to the plastic strain distribution.This training data was used to train a machine learning framework and create a machine learning model.

Calculation and prediction of plastic strain distribution and inherent strain Input data for prediction (shape data of the target object, heat source distribution parameter σ: 20 mm, heat input: 10,000 W (10 kW), x-coordinate of starting point: 0, x-coordinate of ending point: 400, heating rate: 2 mm/sec) was input into the created machine learning model, and prediction output data (data corresponding to the plastic strain distribution) was output. Figure 7 (b) shows the plastic strain distribution (predicted distribution) in the x-direction (vertical direction) created from this prediction output data.
FIG. 7(a) shows the plastic strain distribution in the x direction created from the results of a thermo-elastic-plastic analysis (heat source distribution parameter σ: 20 mm, heat input: 10,000 W (10 kW), x-coordinate of starting point: 0, x-coordinate of ending point: 400, heating rate: 2 mm/sec, analysis model: same as above).
In addition, prediction input data (shape data of the target object, heat source distribution parameter σ: 20 mm, heat input: 10,000 W (10 kW), x-coordinate of starting point: 0, x-coordinate of ending point: 400, heating rate: 4 mm/sec) was input into the created machine learning model, and prediction output data (data corresponding to plastic strain distribution) was output. Figure 8(b) is the plastic strain distribution (predicted distribution) in the x-direction (vertical direction) created from this prediction output data. Also, Figure 9(b) is the plastic strain distribution (predicted distribution) in the y-direction (horizontal direction) created from this prediction output data.
8(a) shows the plastic strain distribution in the x direction created from the results of a thermo-elastic-plastic analysis (heat source distribution parameter σ: 20 mm, heat input: 10,000 W (10 kW), x-coordinate of starting point: 0, x-coordinate of ending point: 400, heating rate: 4 mm/sec, analytical model: same as above). Also, FIG. 9(a) shows the plastic strain distribution in the y direction created from the results of this thermo-elastic-plastic analysis.
As shown in Figures 7 to 9, it was found that the plastic strain distribution (predicted distribution) created from the output data of the machine learning model was in good agreement with the plastic strain distribution created from the results of the thermo-elastic-plastic analysis.

Next, using the relational equation between inherent deformation and inherent strain shown in Figure 5, the four components of inherent deformation (longitudinal shrinkage, lateral shrinkage, longitudinal bending, and lateral bending) were calculated from the data corresponding to the plastic strain distributions shown in Figures 7(b), 8(b), and 9(b) (output data of the machine learning model).
Furthermore, using thermo-elastic-plastic analysis, the inherent deformations (longitudinal shrinkage, lateral shrinkage, longitudinal bending, lateral bending) corresponding to the plastic strain distributions shown in Figures 7(a), 8(a), and 9(a) were calculated.
10(a) to 10(d) are graphs comparing the inherent deformation calculated using the relational equation in FIG. 5 (labeled "Prediction") with the inherent deformation calculated using thermo-elastic-plastic analysis (labeled "Thermal-elastic-plastic analysis").
As shown in the graphs in Figures 10(a) to 10(d), it was found that the four inherent deformation components calculated from the output data of the machine learning model were in good agreement with the four inherent deformation components calculated using thermal elastic-plastic analysis.

Next, the prediction input data (shape data of the target object, heat source distribution parameter σ: 20 mm, heat input: 10,000 W (10 kW), x-coordinate of the starting point: 200, x-coordinate of the ending point: 400, heating rate: 4 mm/sec) was input into the created machine learning model, and prediction output data (data corresponding to the plastic strain distribution) was output. Figure 11(b) shows the plastic strain distribution (predicted distribution) in the x-direction (vertical direction) created from this prediction output data. Figure 12(b) shows the plastic strain distribution (predicted distribution) in the y-direction (horizontal direction) created from this prediction output data.
11(a) shows the plastic strain distribution in the x direction created from the results of a thermo-elastic-plastic analysis (heat source distribution parameter σ: 20 mm, heat input: 10,000 W (10 kW), x-coordinate of starting point: 200, x-coordinate of ending point: 400, heating rate: 4 mm/sec, analytical model: same as above). Also, FIG. 12(a) shows the plastic strain distribution in the y direction created from the results of this thermo-elastic-plastic analysis.
As shown in Figures 11 and 12, it was found that the plastic strain distribution (predicted distribution) created from the output data of the machine learning model was in good agreement with the plastic strain distribution created from the analysis results of the thermo-elastic-plastic analysis.

Next, using the relational equation between inherent deformation and inherent strain shown in Figure 5, the four components of inherent deformation (longitudinal shrinkage, lateral shrinkage, longitudinal bending, and lateral bending) were calculated from the data corresponding to the plastic strain distribution shown in Figure 11(b) and Figure 12(b) (output data of the machine learning model).
Furthermore, the inherent deformations (longitudinal shrinkage, lateral shrinkage, longitudinal bending, lateral bending) corresponding to the plastic strain distributions shown in Fig. 11(a) and Fig. 12(a) were calculated using a thermo-elastic-plastic analysis.
13(a) to 13(d) are graphs comparing the inherent deformation calculated using the relational equations in FIG. 5 (labeled "Prediction") with the inherent deformation calculated using thermo-elastic-plastic analysis (labeled "Thermal-elastic-plastic analysis").
As shown in the graphs in Figures 13(a) to 13(d), it was found that the four inherent deformation components calculated from the output data of the machine learning model were in good agreement with the four inherent deformation components calculated using thermal elastic-plastic analysis.

Calculation of plastic strain distribution, inherent strain, and residual stress distribution. Using the analytical model of a T-joint (shape data of the target object) shown in Figures 14(a) and 14(b) and 15(a) and 15(b), thermo-elastic-plastic analyses were performed multiple times under various heating conditions (gas heating for backside strain relief), and data corresponding to the plastic strain distribution were calculated for each analysis. An idealized explicit FEM method was used for the thermo-elastic-plastic analyses. The target object had a steel plate 400 mm long, 400 mm wide, and 16 mm thick, to which another steel plate 400 mm long, 84 mm wide, and 15 mm thick was welded in a T-shape.
In all thermo-elastic-plastic analyses, the thermal efficiency was set to 1.0, and the heat source distribution parameter σ was set to 20 mm. The start and end points of the heating lines in each thermo-elastic-plastic analysis were randomly set on a line (extending in the x-direction) connecting the midpoints of two sides extending in the y-direction of the analysis model. The heat input in each thermo-elastic-plastic analysis was randomly set within a range of 2,000 W to 40,000 W (2 kW to 40 kW). The heating rate in each thermo-elastic-plastic analysis was randomly set within a range of 1 mm/sec to 20 mm/sec.
Based on the results of the thermal elastic-plastic analysis, training data was created in which the data items of the learning input data were the shape data of the target object, heat source distribution parameters, heat input, starting and ending points of the heating line, and heating rate, and the learning output data was data corresponding to the plastic strain distribution.This training data was used to train a machine learning framework and create a machine learning model.

Next, the prediction input data (heat source distribution parameter σ: 20 mm, heat input: 10,000 W (10 kW), x-coordinate of starting point: 0, x-coordinate of ending point: 400, heating rate: 2 mm/sec) was input into the created machine learning model, and prediction output data (data corresponding to the plastic strain distribution) was output. Figure 14(b) shows the plastic strain distribution in the x-direction (vertical direction) created from this prediction output data.
FIG. 14(a) shows the plastic strain distribution in the x direction created from the results of a thermo-elastic-plastic analysis (heat source distribution parameter σ: 20 mm, heat input: 10,000 W (10 kW), x coordinate of starting point: 0, x coordinate of ending point: 400, heating rate: 2 mm/sec, analytical model: the above-mentioned T-joint analytical model).
As shown in Figures 14(a) and (b), even when the target object is a T-joint, it was found that the plastic strain distribution created from the output data of the machine learning model was in good agreement with the plastic strain distribution created from the analysis results of the thermal elastic-plastic analysis.

Next, data corresponding to the plastic strain distribution shown in Fig. 14(b) (output data of the machine learning model) was applied to a stress-free analytical model, and elastic analysis was performed to calculate data corresponding to the residual stress distribution in the x direction. Fig. 15(b) shows the residual stress distribution in the x direction created from the calculated data.
FIG. 15(a) shows the residual stress distribution in the x direction created from the results of a thermo-elastic-plastic analysis (heat source distribution parameter σ: 20 mm, heat input: 10,000 W (10 kW), x coordinate of starting point: 0, x coordinate of ending point: 400, heating rate: 2 mm/sec, analysis model: the above-mentioned T-joint analysis model).
As shown in Figures 15(a) and 15(b), even when the target object is a T-joint, the residual stress distribution created from the output data of the machine learning model was found to be in good agreement with the residual stress distribution created from the analysis results of the thermal elastic-plastic analysis.

Next, using the relational equation between inherent deformation and inherent strain as shown in Figure 5, the inherent deformation (longitudinal shrinkage, lateral bending (angular distortion)) was calculated from the data corresponding to the plastic strain distribution shown in Figure 14(b) (output data of the machine learning model).
Furthermore, the inherent deformation (longitudinal shrinkage and lateral bending (angular distortion)) corresponding to the plastic strain distribution shown in FIG. 14(a) was calculated using a thermo-elastic-plastic analysis.
16(a) and 16(b) are graphs comparing the inherent deformation calculated using the relational equations in FIG. 5 (labeled "Prediction") with the inherent deformation calculated using thermo-elastic-plastic analysis (labeled "Thermal-elastic-plastic analysis").
As shown in the graphs in Figures 16(a) and (b), even when the target object is a T-joint, it was found that the inherent deformation calculated from the output data of the machine learning model is in good agreement with the inherent deformation calculated using thermal elastic-plastic analysis.

Creating a machine learning model 2
A machine learning model was created using training data obtained by performing a thermal elastic-plastic analysis. The idealized explicit FEM method was used for the thermal elastic-plastic analysis.
The analytical model used was the same as that used in "Creating a Machine Learning Model 1" (analysis model in Figure 6). Using this analytical model, thermo-elastic-plastic analyses were repeatedly performed under various heating conditions (gas heating), and data corresponding to deformation (angular distortion, transverse shrinkage, longitudinal shrinkage, longitudinal bending) was calculated for each thermo-elastic-plastic analysis. The heating conditions were set in the same way as in "Creating a Machine Learning Model 1."
Based on the results of the thermal elastic-plastic analysis, training data was created in which the data items of the learning input data were the shape data of the target object, heat source distribution parameters, heat input, starting and ending points of the heating line, and heating rate, and the learning output data was data corresponding to the inherent deformation distribution along the heating direction (angular distortion distribution, transverse shrinkage distribution, longitudinal shrinkage distribution, longitudinal bending distribution).This training data was used to train a machine learning framework, and a machine learning model was created.

The prediction input data (shape data of the target object, heat source distribution parameters, heat input: 20,000 W (20 kW), x-coordinate of the starting point, x-coordinate of the ending point, heating rate) was input into the created machine learning model, and the prediction output data (data corresponding to the inherent deformation distribution along the heating direction) was output.
17 to 20 show angular distortion distributions created from the prediction output data. In Fig. 17, the x-coordinate of the start point is 0 and the x-coordinate of the end point is 400. In Fig. 18, the x-coordinate of the start point is 100 and the x-coordinate of the end point is 300. In Fig. 19, the x-coordinate of the start point is 100 and the x-coordinate of the end point is 350. In Fig. 20, the x-coordinate of the start point is 100 and the x-coordinate of the end point is 400. The heat input parameter Qhh [J/ ^mm3 ] and the heating rate Speed [mm/s] are also shown in each figure. Qhh is expressed as (Q/v)/ ^h2 , where Q is the heat input (W), v is the heating rate (mm/s), and h is the plate thickness (mm).

21 to 24 show the distribution of transverse shrinkage amounts created from the prediction output data, with the x-coordinate of the start point being 0 and the x-coordinate of the end point being 400 in Fig. 21, the x-coordinate of the start point being 100 and the x-coordinate of the end point being 300 in Fig. 22, the x-coordinate of the start point being 100 and the x-coordinate of the end point being 350 in Fig. 23, and the x-coordinate of the start point being 100 and the x-coordinate of the end point being 400 in Fig. 24. The heat input parameter Qhh [J/ ^mm3 ] and the heating speed Speed [mm/s] are also shown in each figure.

Figures 25 to 28 show the distribution of transverse shrinkage amounts created from the prediction output data, with the x-coordinate of the start point being 0 and the x-coordinate of the end point being 400 in Figure 21, the x-coordinate of the start point being 100 and the x-coordinate of the end point being 300 in Figure 22, the x-coordinate of the start point being 100 and the x-coordinate of the end point being 350 in Figure 23, and the x-coordinate of the start point being 100 and the x-coordinate of the end point being 400 in Figure 24. The heat input parameter Qhh [J/ ^mm3 ] and the heating rate Speed [mm/s] are also shown in each figure.

29 to 32 show longitudinal shrinkage distributions created from the prediction output data, with the x-coordinate of the start point being 0 and the x-coordinate of the end point being 400 in Fig. 29, the x-coordinate of the start point being 100 and the x-coordinate of the end point being 300 in Fig. 30, the x-coordinate of the start point being 100 and the x-coordinate of the end point being 350 in Fig. 31, and the x-coordinate of the start point being 100 and the x-coordinate of the end point being 400 in Fig. 32. The heat input parameter Qhh [J/ ^mm3 ] and the heating rate Speed [mm/s] are also shown in each figure.
It was found that the inherent deformation distribution along the heating direction can be predicted well from FIGS.

Claims (2)

A prediction method for predicting an angular distortion distribution in a heating line direction, a transverse shrinkage distribution in a heating line direction, a longitudinal shrinkage distribution in a heating line direction, and a longitudinal bending distribution in a heating line direction of an object, comprising:
The prediction method includes a step of outputting prediction output data corresponding to the angular distortion distribution in the heating line direction, the transverse shrinkage distribution in the heating line direction, the longitudinal shrinkage distribution in the heating line direction, and the longitudinal bending distribution in the heating line direction from the prediction input data including the heating conditions including the starting point and the end point of the heating line, using a machine learning model trained with teacher data including training input data including heating conditions including the starting point and the end point of the heating line, and training output data corresponding to the angular distortion distribution in the heating line direction, the transverse shrinkage distribution in the heating line direction, the longitudinal shrinkage distribution in the heating line direction, and the longitudinal bending distribution in the heating line direction, calculated from the heating conditions using a numerical analysis method. A program configured to cause a computer to execute the prediction method according to claim 1 .