Abstract
According to the spatial distribution pattern of melt pool size features, a prediction method of melt pool width based on edge iterative model was proposed. In order to obtain accurate melt pool width, mathematical morphological method was used to denoise the melt pool image and coarse segmentation was conducted on the melt pool image by manual thresholding method. The Canny algorithm was then employed to extract the melt pool edge. Finally, the edge iterative model was used for edge iteration and the melt pool width after fine segmentation was obtained. Comparison experiment results show that this algorithm has good accuracy and robustness, and it is simple and efficient.
Laser-directed energy deposition (LDED) is a unique manufacture technique, which uses high-energy laser beam to form melt pool in the deposition area. The laser beam moves at high speed, and the to-be-deposited material is directly fed into the high-temperature melt zone in the powder form and deposited layer by layer after melting. LDED technique has the advantages of high material utilization, fast part forming, and no mold fixtures, which is suitable for the manufacture of complex parts and the repair and remanufacture of valuable part
Laser processing exhibits high-energy characteristics, and its non-contact visual detectio
With the development of physical model for LDED process and the improvement in computing capability of hardware, the prediction methods of melt pool characteristics based on simulation data and machine learning are increasingly value

Fig.1 Representative image of melt pool captured by coaxial camera
In this research, a melt pool width extraction algorithm based on edge iterative model coupled with morphology characteristics of melt pool region and processing efficiency of image algorithms was proposed. This algorithm provided practical guidance for the development of stable melt pool edge extraction algorithm with high accuracy and high robustness.

Fig.2 Schematic diagram of coaxial monitoring system
During the experiment, the melt pool was a relatively small part of the whole image, and the image was cropped to improve the image processing efficiency. The raw image resolution was 1024×768, and the resolution of cropped image was 200×192. Fe101 alloy powder was used in the experiment, and its powder particle size ranged from 20 μm to 53 μm. The composition of Fe101 alloy powder is shown in
C | Mn | Si | Ni | Mo | Cr | N | P | Fe |
---|---|---|---|---|---|---|---|---|
0.03 | 0.35 | 7.86 | 0.77 | 14.55 | 0.12 | 0.045 | 0.42 | Bal. |
The melt pool width extraction process is shown in

Fig.3 Schematic diagram of melt pool width extraction process

Fig.4 Pre-processing of melt pool image: (a) raw image; (b) binary image; (c) Canny edge extraction result
During the deposition process, the melt pool formed by laser-melted powder is theoretically circular, which is determined by the light spot. However, the slow cooling rate at the end of melt pool often results in “trailing” phenomenon, leading to the elliptical melt pool, as shown in

Fig.5 Melt pool width extraction process by algorithm method (a); calculation durations of algorithm in melt pool width extraction process (b)
(1) The pixel point in the melt pool image is set as ai,j with i, j∈[image width, image high].
(2) Define the set of contour points in
(3) Calculate the distances gi,j between the points in set Q and the point ai,j, and then calculate the sum of all distances.
(4) Loop through
(1) |
where gmax is the historical maximum distance and gi, j is the current iterative distance.
(5) The coordinates of the pixel point corresponding to gmax are the center of the maximum inner tangent circle, and the diameter of the inner tangent circle is the width of melt pool.
The edge iterative model can be described as follows.
(1) As shown in

Fig.6 Schematic diagrams of edge iterative model of melt pool width extraction process: (a) set of contour points; (b) initial width extraction; (c) iterative width extraction
firstly counted. Three points (P1, P2, P3) with point-to-point distances of one-third of the contour length are selected. The purpose of averaging sampling is to effectively avoid loops falling into the local optimum solution. Take one point as the intersection and connect it to other two points, as shown in
(2) |
(2) If ΔP1P2P3 is not an acute triangle, the point should be re-selected until △P1P2P3 is an acute triangle.
(3) |
(3) Find the edge point Pmin in the circle with the smallest distance to point O1 and replace the nearest point (P1, P2, or P3) with Pmin while still satisfying
(4) |
(4) Repeat the abovementioned step until there is no edge point Pmin inside the circle Oi. At this time, the point Oi is the center of the circle inside the melt pool shape, and the distance OiPi1 is the radius R of the circle.
As shown in
(5) |
where (X1, Y1), (X2, Y2), and (X3, Y3) are the coordinates of point P1, P2, and P3, respectively.
The radius of the circle can be calculated by
(6) |
The results of optimized algorithm extraction method are shown in

Fig.7 Melt pool width extraction process by optimized algorithm method: (a) the first iteration, (b) the second iteration, and (c) final iteration; calculation durations of optimized algorithm in melt pool width extraction process (d)
The algorithm calculation was conducted by Intel Core I5 1135 CPU with frequency of 2.40 GHz and 16 G RAM. The experiment parameters were as follows: powder feeding rate of 0.16 g/s, scanning speed of 10 mm/s, and laser power of 600 W. A circular deposition trajectory was selected for the printing scheme with an interlayer lift of 0.3 mm. Although machine learning methods are superior in the melt pool feature extraction in recent year

Fig.8 Schematic diagram with captured melt pool images (a) and appearances (b–d) of deposition sample and interference points: (b) overall appearance; (c) cross-section A; (d) cross-section B
Hence, the microscopic-measured width of cross-section of the deposition layer is considered as the actual pixel width of the detected melt pool image. After measuring the melt pool width, the number of melt pool pixels was calculated from the pixel ratio, which was calibrated as 0.118 68 mm/pixel in this research. The algorithms predict the width by the number of image pixels.
Under each interference level condition, two groups of melt pool detection were conducted, and the L1, L2, M1, M2, H1, and H2 represent the detection groups under low, medium, and high interference level. For comparison, the raw images, FD algorithm results, MBR algorithm results, and optimized algorithm results are shown in

Fig.9 Melt pool image processing results under low interference condition: (a, e) raw images; (b, f) FD algorithm; (c, g) MBR algorithm; (d, h) optimized algorithm

Fig.10 Melt pool image processing results under medium interference condition: (a, e) raw images; (b, f) FD algorithm; (c, g) MBR algorithm; (d, h) optimized algorithm

Fig.11 Melt pool image processing results under high interference condition: (a, e) raw images; (b, f) FD algorithm; (c, g) MBR algorithm; (d, h) optimized algorithm
Interference level | Measurement | FD algorithm | MBR algorithm | Optimized algorithm |
---|---|---|---|---|
L1 | 16.3 | 16.5 | 17.9 | 16.6 |
L2 | 15.3 | 16.3 | 14.9 | 14.8 |
M1 | 15.7 | 21.3 | 21.5 | 14.9 |
M2 | 15.5 | 20.4 | 19.4 | 14.9 |
H1 | 15.6 | 22.3 | 17.5 | 15.4 |
H2 | 16.0 | 23.8 | 20.8 | 16.3 |

Fig.12 Error (a) and time consumption (b) of three algorithms for melt pool width detection
Notably, the melt pool identification area is located at the rear of the scanning direction, as shown in
Briefly, the optimized algorithm can accurately identify the width of melt pool under different working conditions and has good robustness against various types of noise.
Deposition experiments were conducted to validate the feasibility and adaptability of the proposed approach. Single-track deposition was chosen as the experiment method. On the one hand, single-track deposition can avoid variable introduction, such as overlap ratio and interlayer lift, which can affect the accuracy of deposition width measurement. On the other hand, single-track deposition can reduce the deposition time and material consumption.
Based on the single-track deposition experiments, the process range was determined: laser power of 400–800 W, powder feeding rate of 0.25–0.35 g/s, and scanning speed of 9–11 mm/s. In this case, the formation quality can be ensured. An orthogonal experiment design was devised based on this parameter range: the interval of laser power was 200 W, the interval of scanning speed was 1 mm/s, and the interval of powder feeding rate was 0.05 g/s. The experiment parameters and results are shown in
Specimen No. | Laser power, P/W | Scanning speed, V/mm·mi | Powder feeding rate, G/g· | Melt pool width/mm |
---|---|---|---|---|
1 | 300 | 480 | 0.25 | 1.41 |
2 | 300 | 600 | 0.35 | 1.22 |
3 | 300 | 720 | 0.30 | 1.16 |
4 | 500 | 480 | 0.35 | 1.81 |
5 | 500 | 600 | 0.30 | 1.69 |
6 | 500 | 720 | 0.25 | 1.58 |
7 | 700 | 480 | 0.30 | 2.22 |
8 | 700 | 600 | 0.25 | 2.12 |
9 | 700 | 720 | 0.35 | 2.00 |

Fig.13 Overall morphologies as well as melt pool images and metallographic results at point A of different single-track deposition specimens
Non-uniform powder accumulation can be observed in the cross-section along the deposition track. This phenomenon may be attributed to the non-vertical alignment between the processing head and the substrate, or the uneven powder distribution, which causes uneven powder aggregation at the laser focus and thereby affects the deposition morphology. However, this influence has a relatively minor effect on the melt pool width and can be ignored during measurement.

Fig.14 Melt pool width comparison between measured results and algorithm calculation results (a); relative error of different algorithms (b)
Compared with FD and MBR algorithm methods, the detection algorithm of melt pool width based on the edge iterative model shows higher accuracy and better robustness, and its average relative error is only 2.46%. This is mainly due to the numerous interference in the melt pool area and the complicated boundary variation. At the same time, the optimized algorithm has high resistance against the boundary variation and can therefore detect the melt pool edge in more practical situations.
1) In LDED image recognition, interference, such as powder splash and arc light, may lead to inaccurate detection of melt pool width. The traditional algorithm for melt pool width extraction has restrictions due to the boundary features of the melt pool.
2) The optimized algorithm method considers the laser energy distribution and the laws of powder metallurgy forming changes, which thereby exhibits excellent robustness and high extraction accuracy. The detection efficiency can meet the requirements of industrial online detection.
3) The optimized algorithm can effectively extract the melt pool width under various process parameters, and the calculated results and measured results are in good agreement. The average error of the optimized algorithm is only 2.46%.
References
Qin L Y, Wang K, Li X D et al. Chinese Journal of Mechanical Engineering: Additive Manufacturing Frontiers[J], 2022, 1(4): 100052 [Baidu Scholar]
Lin X, Zhu K, Fuh J Y H et al. ISA Transactions[J], 2022, 120: 147 [Baidu Scholar]
McCann R, Obeidi M A, Hughes C et al. Additive Manufactur-ing[J], 2021, 45: 102058 [Baidu Scholar]
Xue Sa, Wang Qingxiang, Liang Shujin et al. Rare Metal Materials and Engineering[J], 2023, 52(5): 1943 (in Chinese) [Baidu Scholar]
Qi X, Chen G, Li Y et al. Engineering[J], 2019, 5(4): 721 [Baidu Scholar]
Tang Z, Liu W, Wang Y et al. The International Journal of Advanced Manufacturing Technology[J], 2020, 108: 3437 [Baidu Scholar]
Tan C L, Li R S, Su J L et al. International Journal of Machine Tools and Manufacture[J], 2023, 189: 104032 [Baidu Scholar]
Liu H, Sun R, Bai R et al. Rare Metal Materials and Engineer-ing[J], 2023, 52(10): 3433 [Baidu Scholar]
Su Y Y, Wang Z F, Xu X et al. Journal of Manufacturing Processes[J], 2022, 82: 708 [Baidu Scholar]
Zheng L P, Zhang Q, Cao H Z et al. Materials & Design[J], 2019, 183: 108110 [Baidu Scholar]
Sun Z, Wei G, Li L. Optics & Laser Technology[J], 2020, 129: 106280 [Baidu Scholar]
Le T N, Lee M H, Lin Z H et al. Journal of Manufacturing Processes[J], 2021, 68: 1735 [Baidu Scholar]
Huang J F, Xue L, Huang J Q et al. Journal of Mechanical Engineering[J], 2019, 55(17): 41 [Baidu Scholar]
Yang Q, Yuan Z J, Zhi X L et al. Optics & Laser Technology[J], 2020, 123: 105925 [Baidu Scholar]
Jeon I, Liu Y, Ryu K et al. Additive Manufacturing[J], 2021, 47: 102295 [Baidu Scholar]
Goossens L R, Hooreweder B V. Additive Manufacturing[J], 2021, 40(5): 101923 [Baidu Scholar]
Liu Y, Sohn H, Ma Z et al. Computers in Industry[J], 2023, 148: 103882 [Baidu Scholar]
Zhu Q M, Liu Z L, Yan J H. Comput Mech[J], 2021, 67: 619 [Baidu Scholar]
Zheng C, Wen J T, Diagne M. Journal of Dynamic Systems Measurement and Control[J], 2020, 142(6): 061001 [Baidu Scholar]
Colodron P, Farina J, Rodriguez-Andina J et al. IEEE International Symposium on Industrial Electronics[C]. Gdnask: IEEE, 2011 [Baidu Scholar]
Ding Y, Warton J, Kovacevic R. Additive Manufacturing[J], 2016, 10: 24 [Baidu Scholar]
Huang Y, Khamesee M B, Toyserkani E. Optics & Laser Technology[J], 2019, 109: 584 [Baidu Scholar]
Chen D J, Li G, Wang P et al. Finite Elements in Analysis and Design[J], 2023, 223: 103971 [Baidu Scholar]
Liu M, Liu Z Q, Li B K et al. Journal of Materials Research and Technology[J], 2023, 26: 5626 [Baidu Scholar]
Song Wei, Cheng Yanhai, Tantai Fanliang et al. Applied [Baidu Scholar]
Laser[J], 2021, 41(1): 183 (in Chinese) [Baidu Scholar]
Shrivastava A, Chakraborty S S, Mukherjee S. Optics & Laser Technology[J], 2021, 144: 107404 [Baidu Scholar]
Liu Jian, Xiang Chaoqian, Wang Fanghua et al. Journal of Mechanical Engineering[J], 2018, 54(5): 166 (in Chinese) [Baidu Scholar]