CN111738369A - Weld penetration state and penetration depth real-time prediction method based on visual characteristics of molten pool - Google Patents
Weld penetration state and penetration depth real-time prediction method based on visual characteristics of molten pool Download PDFInfo
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Abstract
The invention discloses a weld penetration state and fusion depth real-time prediction method based on weld pool visual characteristics. The area, the length and the width of a molten pool are used as input, the penetration state of a welding seam is used as output, a GMAW welding penetration state real-time prediction model is established based on a Support Vector Machine (SVM), and experimental results show that the model can effectively predict the penetration state of the welding seam in the welding process in real time. And similarly, the area, the length and the width of a molten pool are used as input, the penetration of a welding seam is used as output, a GMAW welding penetration real-time prediction model is established based on a BP neural network, and experimental results show that the model can effectively predict the penetration of the welding seam in the welding process in real time. The invention has simple design and simple and convenient operation; the calculation result of the constructed model is verified, and the accuracy is high.
Description
Technical Field
The invention relates to a weld penetration state and weld penetration depth real-time prediction method based on visual characteristics of a molten pool, and belongs to the technical field of welding.
Background
In the welding process, the penetration depth of the welding seam is an important parameter concerned by many scholars, so that the real-time accurate prediction and control of the penetration state and the penetration depth of the welding seam are always hot spots of research in the welding field. Much of the previous research has focused on detecting the penetration and penetration changes of welds under different welding conditions.
In the prediction of the penetration state of a weld, the visual sensing method is the most widely used detection method. In the prior art, a set of simple and flexible visual sensing system is provided, multiple frames of keyhole images on the back of a workpiece are collected under different welding conditions, the area and the inclination angle of a keyhole are extracted as characteristic parameters, and a particle swarm optimization and a self-adaptive network fuzzy inference system are combined to establish the relation between the keyhole characteristic and a weld penetration state. Some also use a near-infrared vision sensing method to acquire a plurality of frames of molten pool images of the aluminum alloy twin-wire welding in different penetration states, obtain characteristic parameters such as the area, the perimeter, the half length, the fusion width, the parabolic coefficient and the like of the molten pool by extracting the outline of the molten pool, and establish an aluminum alloy twin-wire welding penetration state identification model based on a neural network. The method also comprises a GTAW penetration state prediction method based on a data-driven method, wherein key characteristics of the surface of the molten pool are extracted by using a computer vision method, a database is established by performing tests under various welding conditions, the database is tested by using two monitoring machine learning methods such as linear regression and the like, and finally importance analysis of the characteristics of the surface of the molten pool is performed. But the calculation accuracy of the methods has higher promotion space.
In the aspect of weld penetration prediction, the visual expression of weld penetration in the welding process is the deepest part of the lower surface of a molten pool, so that many scholars at home and abroad can measure the penetration of the weld through the depth of the molten pool directly detected by various detection means, and the weld penetration can be divided into the following parts according to the difference of sensing technology: a molten pool oscillation method, an ultrasonic sensing method, an infrared sensing method, an X-ray method, and the like. However, these detection methods all have corresponding disadvantages, and the molten pool oscillation method has time delay, so that it is difficult to perform real-time detection. The ultrasonic, infrared and X-ray detection methods generally have the defects of complex structure, high cost and the like, and cannot be popularized and applied to actual welding production.
Therefore, a real-time prediction method for the penetration state and penetration depth of the weld based on the visual characteristics of the weld pool is needed.
Disclosure of Invention
In order to solve the technical problems, the invention provides a real-time prediction method of the penetration state and the penetration depth of a weld pool based on visual characteristics of the weld pool, which has the following specific technical scheme: comprises that
The method comprises the following steps: building a GMAW welding penetration state and penetration prediction experiment system;
step two: starting a test system to obtain visual characteristic parameters of a molten pool;
step three: establishing a weld penetration state and penetration prediction model;
step four: and predicting the weld penetration state and the penetration prediction model.
Further, the weld penetration state and penetration prediction experiment system comprises a welding platform, a welding base metal, a molten pool vision sensing system and a laser positioning system; the molten pool vision sensing system comprises a color CCD, an FPGA and a computer which are connected; the color CDD is fixed on a welding gun of the welding robot by using a clamp, and the FPGA sends out a fixed frequency signal to trigger the color CCD to acquire a molten pool image.
The laser positioning system comprises a laser, a black-and-white CCD and a computer; the black-and-white CCD is fixed on the welding platform, the laser is fixed on a welding gun of the welding robot, and laser irradiates the upper edge part of the welding wire; in the welding process, the FPGA sends out a synchronizing signal to trigger the color CCD and the black and white CCD to acquire images.
Further, the visual characteristics include a molten pool area, length, and width; the definition of the molten pool area is the sum of the number of all pixel points in the molten pool image outline, and the calculation formula is as follows:
in the formula (1), the reaction mixture is,
the line coordinate value of the pixel point on the left edge of the jth line when the molten pool profile is scanned line by line,
and (3) a row coordinate value of a right edge pixel point of the j-th row is represented, and n represents the column number of the molten pool profile.
The length of the molten pool is defined as the number of pixel points contained between two edge points of the contour of the molten pool with the largest distance in the x-axis direction, and the calculation formula is as follows:
in the formula (2), the reaction mixture is,
a line coordinate value representing an edge point of the front portion of the molten pool,
and a line coordinate value representing an edge point of the tail of the molten pool.
Definition of the molten pool width:
the width of the molten pool is defined as the number of pixel points contained between two edge points of the profile of the molten pool with the largest distance in the y-axis direction, and the specific calculation formula is as follows:
in the formula (3), the reaction mixture is,
row coordinate values indicating the uppermost edge point of the molten pool,
and row coordinate values representing the lowermost edge point of the molten pool.
Further, the extracting of the visual characteristic parameter comprises
And (a) selecting the first frame of color molten pool image of each CMT period basic value stage.
And (b) carrying out binarization processing on the color molten pool image, and extracting the contour of the molten pool.
Filling a cavity in the outline of the molten pool; and filling internal holes by using a morphological treatment method, wherein MATLAB self-contained function treatment is used in actual treatment.
And (d) calculating the two-dimensional characteristics of the molten pool.
Further, in the third step:
the weld penetration state and penetration prediction model comprises a weld penetration state model and a penetration prediction model;
the weld penetration state model is a model established by taking the area, the length and the width of a molten pool as input characteristic parameters, taking the penetration state of a welding seam as output and based on a Support Vector Machine (SVM); the method comprises the steps of taking data acquired at a welding current of 90A as a training set, taking data acquired at welding currents of 100A and 70A as a test set, and verifying the prediction accuracy of an established model;
the fusion depth prediction model is a model established based on a BP neural network by taking the surface, the length and the width of the molten pool as input characteristic parameters and taking the fusion depth of a welding seam as output; the neural network comprises two hidden layers, wherein the number of neurons is respectively set to 6 and 3; and welding two welding seams by each set of welding parameters, wherein the data acquired in the first welding seam is used as training data of the model, and the data acquired in the second welding seam is used as test data.
Further, before model training, input characteristic parameters are normalized, and all numbers in the input characteristic parameter data set are mapped to [0,1]]In the formula of
(4)
Wherein neutralization is carried out
Respectively represent the values before and after the normalization,
and
representing the maximum and minimum values in the original data set, respectively.
The invention has the beneficial effects that:
the invention designs a set of molten pool vision sensing system based on the color CCD, and can extract the two-dimensional characteristics of the molten pool in real time in the welding process. The area, the length and the width of a molten pool are used as input, the penetration state of a welding seam is used as output, a GMAW welding penetration state real-time prediction model is established based on a Support Vector Machine (SVM), and experimental results show that the model can effectively predict the penetration state of the welding seam in the welding process in real time. And similarly, the area, the length and the width of a molten pool are used as input, the penetration of a welding seam is used as output, a GMAW welding penetration real-time prediction model is established based on a BP neural network, and experimental results show that the model can effectively predict the penetration of the welding seam in the welding process in real time. The invention has simple design and simple and convenient operation; the calculation results of the two constructed models are verified respectively, and compared with the prior art, the accuracy is improved.
Drawings
FIG. 1 is a weld penetration state prediction experiment system;
FIG. 2 is a weld penetration prediction experiment system;
FIG. 3 is a schematic view of a molten bath;
FIG. 4 is a welding current waveform;
FIG. 5 is a molten pool image acquired in a CMT period;
FIG. 6 shows the results of weld pool image processing: (a) processing results of the original color molten pool image (b);
fig. 7 is an image of a weld at a welding current of 100A: (a) the front side of the welding seam (b) the back side of the welding seam;
fig. 8 is an image of a weld at a welding current 90A: (a) the front side of the welding seam (b) the back side of the welding seam;
fig. 9 is an image of a weld at a welding current of 70A: (a) the front side of the welding seam (b) the back side of the welding seam;
fig. 10 is an image of a weld cut along the welding direction: (a) the welding seam metallographic picture (b) a welding seam profile picture;
FIG. 11 is a BP neural network structure;
FIG. 12 shows the predicted result of penetration at a welding current of 100A;
FIG. 13 shows predicted results of penetration at a welding current of 70A;
FIG. 14 shows the prediction results of weld penetration at different welding currents: (a) 140A, (b) 150A.
In the figure: 1-welding platform, 2-welding parent metal, 3-welding gun of welding robot, 4-color CCD, 5-FPGA, 6-computer, 7-laser and 8-black and white CCD.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic views illustrating only the basic structure of the present invention in a schematic manner, and thus show only the constitution related to the present invention.
Step 1: and (4) building a GMAW welding penetration state and penetration prediction experiment system.
1.1 establishing GMAW welding penetration state prediction experiment system
As shown in the figure, in the experiment performed under the CMT welding process, the welding base metal 1 is a steel plate with the size of 100mm multiplied by 50mm multiplied by 2mm, and the welding wire material is stainless steel with the diameter of 1.2 mm. The molten pool vision sensing system consists of a color CCD4, an FPGA5 and a computer 6, as shown in figure 1, the color CCD4 is fixed on a welding gun 3 of the welding robot by a clamp, and the FPGA5 sends a fixed frequency signal to trigger the color CCD4 to acquire a molten pool image along with the movement of the welding gun.
1.2, establishing a GMAW welding depth prediction experiment system;
the experiment is carried out under the CMT welding process, the welding base metal is a steel plate with the size of 100mm multiplied by 50mm multiplied by 5mm, and the welding wire material is stainless steel with the diameter of 1.2 mm. The whole system comprises a molten pool vision sensing system and a laser positioning system, as shown in fig. 2, the molten pool vision sensing system also comprises a color CCD4, an FPGA5 and a computer 6, and the laser positioning system comprises a laser 7, a black-and-white CCD8 and the computer 6. The laser positioning system has the effects that a molten pool image acquired by the color CCD4 corresponds to the position of a welding seam, the central wavelength of the laser 7 is 450nm, the laser is fixed on a welding gun of the welding robot 3, the laser irradiates the upper edge part of the welding wire, the black and white CCD is fixed on a welding platform to capture the coordinate of a laser spot, and the FPGA sends out a synchronous signal to trigger the color CCD and the black and white CCD to acquire the image in the welding process.
Step 2: and starting a test system to obtain visual characteristic parameters of the molten pool.
2.1 protocol
In the experiment of GMAW welding penetration state prediction, welding current is the main parameter that influences the welding seam penetration state, and the welding current setting of this application is in 70~100A within ranges, and the step length is 10A, and welding speed is 3mm/s, and welding parameter is as shown in Table 1. In the welding process, the FPGA sends out a signal with the frequency of 1000Hz to trigger the color CCD to acquire a molten pool image, the area, the length and the width of the molten pool are extracted as characteristic parameters, and training and testing data are provided for a GMAW welding penetration state prediction model.
TABLE 1 penetration State prediction Experimental welding parameters
| Welding current (A) | Welding speed (mm/s) | Plate thickness (mm) | Flow of protective gas（L/min） |
| 70~100 | 3 | 2 | 25 |
In an experiment of GMAW welding penetration prediction, welding current is set within the range of 130A-150A, step length is 10A, welding speed is 5mm/s, and welding parameters are shown in table 2. In the welding process, the FPGA synchronously sends out a signal with the frequency of 1000Hz to trigger the color CCD and the black-and-white CCD, the color CCD is used for collecting a molten pool image, and the black-and-white CCD is used for collecting the position of a laser spot, so that the position of a welding seam corresponding to the molten pool image is determined. And similarly, extracting the area, the length and the width of the molten pool as characteristic parameters, and welding two welding seams by each group of welding parameters, wherein the data acquired in the first welding seam is used as training data of the model, and the data acquired in the second welding seam is used as test data of the model.
TABLE 2 penetration prediction experiment welding parameters
2.2 definition of two-dimensional characteristics of the weld pool
The method comprises the steps of acquiring a molten pool image by a color CCD, subsequently extracting a molten pool contour, and calculating to obtain the area, the length and the width of the molten pool, wherein FIG. 3 is a schematic diagram of the molten pool image, an x axis is a row coordinate axis, a y axis is a column coordinate axis, and the x axis is consistent with the welding direction.
Definition of molten pool area:
the area of the molten pool is defined as the sum of the number of all pixel points in the image contour of the molten pool, and the specific calculation formula is as follows:
in the formula (1), the reaction mixture is,
the line coordinate value of the pixel point on the left edge of the jth line when the molten pool profile is scanned line by line,
and (3) a row coordinate value of a right edge pixel point of the j-th row is represented, and n represents the column number of the molten pool profile.
Definition of the length of the molten pool:
the length of the molten pool is defined as the number of pixel points contained between two edge points of the contour of the molten pool with the largest distance in the x-axis direction, and the specific calculation formula is as follows:
in the formula (2), the reaction mixture is,
a line coordinate value representing an edge point of the front portion of the molten pool,
and a line coordinate value representing an edge point of the tail of the molten pool.
Definition of the molten pool width:
the width of the molten pool is defined as the number of pixel points contained between two edge points of the profile of the molten pool with the largest distance in the y-axis direction, and the specific calculation formula is as follows:
in the formula (3), the coordinate values of the rows representing the uppermost edge point of the molten pool,
and row coordinate values representing the lowermost edge point of the molten pool.
The cycle of the CMT is about 14ms, and as can be seen from fig. 5, the acquired molten pool image is strongly influenced by the electric arc in the peak value stage of the CMT, and the acquired molten pool image is hardly influenced by the electric arc in the base value stage of the CMT, so that the signal-to-noise ratio is high. In the CMT penetration state and penetration prediction experiment, the first frame image of each CMT period basic value stage is selected to extract the two-dimensional characteristics of a molten pool.
According to the acquired color molten pool image, firstly, binarization processing is carried out, the contour of the molten pool is extracted, then, a cavity in the contour of the molten pool is filled, as shown in fig. 6, the result of the molten pool image processing of a certain frame is obtained, and finally, the two-dimensional characteristic parameter of the molten pool is calculated.
And step 3: and establishing a weld penetration state and penetration prediction model.
3.1 establishing a penetration weld state model
According to the welding parameters in table 1, the length of each welding line is set to be 8cm, the experimental results are shown in fig. 7, 8 and 9, when the welding current is 100A, the welding line is not completely melted when the moving length of the welding gun is less than 7mm, and the welding line begins to be completely melted when the moving length of the welding gun is greater than 7 mm. When the welding current is 90A, the welding seam is not completely melted when the moving length of the welding gun is less than 14mm, and the welding seam begins to be completely melted when the moving length of the welding gun is greater than 14 mm. When the welding current is 70A, the welding seam is in an unmelted state in the whole welding process.
The color CCD collects a molten pool image at the frequency of 1000Hz, selects the collected first frame color molten pool image of each CMT period, extracts the area, the length and the width of a molten pool as input characteristic parameters, takes the penetration state of a welding seam as output, and establishes a real-time detection model of the penetration state of the welding seam based on a Support Vector Machine (SVM). The weld joint at the welding current of 90A comprises two states of non-penetration and penetration, the data acquired at the welding current of 90A is used as a training set, the data acquired at the welding currents of 100A and 70A is used as a test set, and the prediction accuracy of the established model is verified.
Before training, preprocessing a data set is needed, wherein the preprocessing process of the data is mainly normalization processing, all data in the data set are mapped to [0,1], and a specific calculation formula is as follows:
wherein neutralization is carried out
Respectively represent the values before and after the normalization,
and
representing the maximum and minimum values in the original data set, respectively.
3.2 establishing a penetration prediction model
According to the welding parameters in the table 2, the length of each welding line is set to be 8cm, after welding is completed, the welding line is evenly cut into two halves along the welding direction, one half of the welding line is selected to be polished, corroded and the like, and then the penetration change condition of the welding line along the welding direction is observed by using a body microscope. As shown in fig. 10 (a), a certain section of a weld metal phase diagram observed by using a body type microscope at the welding current 110A is shown, fig. 10 (b) is an extracted weld outline, a reference line on the upper surface of a base material in an image is calculated and determined according to a purple reference line on the lower surface of the base material in fig. 10 (a) and a scale, and the distance between the reference line and the lower surface outline of the weld is the weld penetration, so that the actual weld penetration of the weld can be calculated, and then the weld penetration corresponding to each frame of weld pool image acquired by a color CCD can be determined according to a laser positioning system in an experiment.
And selecting the collected first frame of color molten pool image of each CMT period, and extracting characteristic parameters of the area, the length and the width of the molten pool. The weld penetration real-time prediction model is established based on a BP neural network by taking the area, the length and the width of a molten pool as input and the weld penetration as output, wherein the weld penetration real-time prediction model comprises two hidden layers, the number of neurons is respectively set to be 6 and 3, and the model structure is shown in figure 11. And welding two welding seams by each set of welding parameters, wherein the data acquired in the first welding seam is used as training data of the model, and the data acquired in the second welding seam is used as test data. Also prior to training, all data in the dataset needs to be normalized according to equation (4).
And 4, step 4: and predicting the weld penetration state and the penetration prediction model.
Prediction results and analysis of GMAW welding penetration state:
when the welding current is 90A, the critical point of the weld penetration state corresponds to the first frame image of the 304 th CMT cycle acquired by the color CCD, when the welding current is 100A, the critical point of the weld penetration state corresponds to the first frame image of the 144 th CMT cycle acquired by the color CCD, 0 represents the non-penetration state, 1 represents the penetration state, and the prediction model is trained by using the data acquired at the welding current of 90A as a training set, and the prediction result of the weld penetration state at the welding current of 100A is shown in fig. 12. It can be seen that the prediction accuracy of the weld penetration state is 95.7031%.
The weld penetration state prediction result at the welding current 70A is shown in fig. 13: the prediction accuracy of the weld penetration state is 100%, so that the built GMAW weld penetration state prediction model can effectively predict the penetration state of the weld in the welding process in real time.
Prediction results and analysis of GMAW welding penetration depth:
according to table 2, two welds were welded for each set of welding parameters, with the data collected in the first weld as training data for the model and the data collected in the second weld as test data. The results of weld penetration prediction at both welding currents are shown in fig. 14.
The prediction accuracy of the established model can be evaluated by using the mean absolute error MAE, and the calculation formula of the mean absolute error MAE is as follows:
wherein
It is shown that the predicted penetration depth,
representing the actual penetration depth, and m representing the total data set number in the test data set.
The prediction error of the model is shown in table 3:
TABLE 3 model prediction error
| Welding current (A) | 140 | 150 |
| MAE（mm） | 0.1235 | 0.1083 |
| Ratio of | 7.54% | 6.53% |
Therefore, the built GMAW welding penetration prediction model can effectively predict the penetration of the welding seam in the welding process in real time.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The meaning of "and/or" as used herein is intended to include both the individual components or both.
The term "connected" as used herein may mean either a direct connection between components or an indirect connection between components via other components.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.
Claims (4)
1. A weld penetration state and penetration depth real-time prediction method based on visual characteristics of a molten pool is characterized by comprising the following steps: comprises that
The method comprises the following steps: building a GMAW welding penetration state and penetration prediction experiment system;
step two: starting an experimental system to obtain visual characteristic parameters of a molten pool;
step three: establishing a weld penetration state and penetration prediction model;
step four: predicting a weld penetration state and a penetration prediction model;
the experimental system for predicting the penetration state and the penetration depth of the weld comprises a welding platform (1), a welding parent metal (2), a welding gun (3) of a welding robot, a molten pool vision sensing system and a laser positioning system;
the molten pool visual sensing system comprises a color CCD (4), an FPGA (5) and a computer (6) which are connected with each other; the color CCD (4) is fixed on a welding gun (3) of the welding robot by using a clamp, and the FPGA (5) sends a fixed frequency signal to trigger the color CCD (4) to acquire a molten pool image;
the laser positioning system comprises a laser (7), a black-and-white CCD (8) and a computer (6); the black-and-white CCD (8) is fixed on the welding platform (1), the laser (7) is fixed on a welding gun (3) of the welding robot, and laser irradiates the upper edge part of the welding wire; in the welding process, the FPGA (5) sends out a synchronous signal to trigger the color CCD (4) and the black and white CCD (8) to acquire images;
the visual characteristics include a melt pool area, length, and width; the definition of the molten pool area is the sum of the number of all pixel points in the molten pool image outline, and the calculation formula is as follows:
in the formula (1), the reaction mixture is,
the line coordinate value of the pixel point on the left edge of the jth line when the molten pool profile is scanned line by line,
a row coordinate value of a pixel point at the right edge of the jth row is represented, and n represents the number of columns of the molten pool profile;
the length of the molten pool is defined as the number of pixel points contained between two edge points of the contour of the molten pool with the largest distance in the x-axis direction, and the calculation formula is as follows:
in the formula (2), the reaction mixture is,
a line coordinate value representing an edge point of the front portion of the molten pool,
a line coordinate value representing an edge point at the tail of the molten pool;
the width of the molten pool is defined as the number of pixel points contained between two edge points of the profile of the molten pool with the largest distance in the y-axis direction, and the calculation formula is as follows:
in the formula (3), the reaction mixture is,
row coordinate values indicating the uppermost edge point of the molten pool,
and row coordinate values representing the lowermost edge point of the molten pool.
2. The weld penetration state and penetration depth real-time prediction method based on the visual characteristics of the weld pool as claimed in claim 1, wherein: the second step of acquiring visual characteristic parameters of the molten pool comprises
Selecting a first frame of color molten pool image of each CMT period basic value stage;
performing binarization processing on the color molten pool image to extract a molten pool contour;
filling a cavity in the outline of the molten pool;
and (d) calculating the two-dimensional characteristics of the molten pool by using the formulas (1), (2) and (3).
3. The weld penetration state and penetration depth real-time prediction method based on the visual characteristics of the weld pool as claimed in claim 1, wherein: in the third step:
the weld penetration state and penetration prediction model comprises a weld penetration state model and a penetration prediction model;
the weld penetration state model is a model established by taking the area, the length and the width of a molten pool as input characteristic parameters, taking the penetration state of a welding seam as output and based on a Support Vector Machine (SVM); the method comprises the steps of taking data acquired at a welding current of 90A as a training set, taking data acquired at welding currents of 100A and 70A as a test set, and verifying the prediction accuracy of an established model;
the fusion depth prediction model is a model established based on a BP neural network by taking the surface, the length and the width of the molten pool as input characteristic parameters and taking the fusion depth of a welding seam as output; the neural network comprises two hidden layers, wherein the number of neurons is respectively set to 6 and 3; and welding two welding seams by each set of welding parameters, wherein the data acquired in the first welding seam is used as training data of the model, and the data acquired in the second welding seam is used as test data.
4. The weld penetration state and penetration depth real-time prediction method based on the visual characteristics of the weld pool as claimed in claim 1, wherein: before model training, input characteristic parameters are normalized, and all data in an input characteristic parameter data set are mapped to [0,1]]In the formula of
(4)
Wherein
And
respectively represent the values before and after the normalization,
and
representing the maximum and minimum values in the original data set, respectively.
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| CN114905116A (en) * | 2022-06-02 | 2022-08-16 | 南京理工大学 | Groove weld penetration monitoring method based on feature learning |
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| CN115456982A (en) * | 2022-09-05 | 2022-12-09 | 武汉理工大学 | Weld penetration determination method, weld penetration determination device, electronic device, and storage medium |
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