Machine learning and gray relational analysis optimize CO₂ laser cutting of PMMA

Researchers have combined a compact artificial neural network with gray relational analysis to find the best settings for cutting acrylic with a carbon dioxide laser, reporting that a specific combination of high laser power, high cutting speed, and thick material delivered narrower cuts and nearly half the machining time, at the cost of a moderately rougher surface. The study, published in Discover Mechanical Engineering, focused on polymethyl methacrylate, the transparent plastic better known as PMMA or acrylic, and set out to predict and optimize three competing goals at once: kerf width, surface roughness, and cutting time.

Laser cutting is a non-contact manufacturing method prized for its precision, speed, and cost-effectiveness, but its performance depends heavily on the interplay of process parameters. The team identified three control factors: laser power, cutting speed, and material thickness. Using a full factorial design with three factors at three levels, they systematically mapped the design space across all 27 possible parameter combinations, arranged in an L27 orthogonal array for structural convenience. The responses were measured on a Zaiku Laser LS-6040 machine with 100 watts of input power, a 60 by 40 centimeter cutting area, and a flying-optic system, with a nozzle stand-off distance of 8 millimeters, assist gas pressure of 2.9 psi, and a 1.0 millimeter nozzle diameter.

A distinctive feature of the work was its treatment of cutting geometry. Rather than evaluating only isolated straight-line cuts, the researchers assessed edge quality along three distinct paths: straight, diagonal, and curved radius paths. Kerf width was measured separately on all three paths, while surface roughness was recorded on the straight and diagonal paths, each at three distinct points with three replicates to reduce technical and human error. The authors argue that combining these variables into a single macro-metric would obscure the localized effects of CNC interpolation and heat accumulation on complex geometries, so treating them as separate responses allows the machine learning model to capture these localized non-linearities.

Signal-to-noise ratio analysis using the smaller-is-better criterion revealed that cutting speed was the most dominant factor governing both productivity and cut quality. High laser power combined with high cutting speed on thicker materials produced a narrower kerf and shorter cutting time, but reduced surface quality. The researchers explain the physics: a slower cutting speed generates more heat in the workpiece, enlarging the melting area, especially in thin sheets, whereas a faster nozzle movement limits heat input per unit length. Increasing laser power, by contrast, did not significantly change kerf width, leading the team to suggest that power can be set to the minimum level sufficient for full penetration, saving energy and preserving the laser generator.

Path type mattered as well. The radius path produced the narrowest kerf width, with an overall mean signal-to-noise ratio of 10.21 decibels, followed by the diagonal path at 9.73 decibels and the straight path at 8.75 decibels, an effect the authors attribute to the mechanical aspects of nozzle movement on the flying-optic machine. For surface roughness, the optimal single-response combination was the opposite regime: high laser power with slow cutting speed on thinner material. Straight paths yielded significantly better surface roughness than diagonal paths, with a mean signal-to-noise ratio difference of 6.84 decibels, because single-axis movement allows the nozzle to travel more smoothly. Cutting time, meanwhile, was governed almost entirely by cutting speed, with the other two parameters showing no meaningful effect.

To predict performance, the team built three modeling paradigms and compared them: a shallow artificial neural network, a random forest regressor, and an analytical ridge regression baseline chosen for its robustness on small datasets. The neural network used a deliberately compact 3–5–6 architecture, meaning three input neurons for the process parameters, a single hidden layer of five neurons, and six output neurons covering kerf widths on all three paths, surface roughness on straight and diagonal paths, and cutting time. The authors selected this small architecture because the dataset contained only 27 experimental runs, a scale at which ensemble methods like XGBoost and LightGBM or deep networks risk overfitting; the compact multilayer perceptron optimizes only 56 parameters and was trained with the L-BFGS algorithm and five-fold cross-validation.

The comparison produced a nuanced picture. For kerf width along the radius and straight paths, the machine learning models outperformed ridge regression, with the neural network achieving the highest predictive capacity, which the authors link to its ability to model non-linear thermal gradients. The random forest proved more robust for the diagonal kerf, where simultaneous coordinated movement of both CNC axes introduces minor kinematic vibrations and complex heat accumulation. Surface roughness posed a severe challenge for every model, with extremely low and sometimes negative R² values reflecting the stochastic nature of striation formation driven by melt-pool oscillations and assist-gas dynamics; there, ridge regression was the most stable performer. For the deterministic cutting time, the random forest was nearly perfect, while the neural network struggled with the scaling discrepancy between sub-millimeter kerf widths and cutting times of tens of seconds.

Validation against independent experimental runs outside the original 27 combinations showed average error rates of 6.19 percent for the neural network, 7.94 percent for the random forest, and 8.25 percent for ridge regression, which the authors describe as acceptable for initial process estimation. Gray relational analysis then converted the six responses into a single gray relational grade, using a distinguishing coefficient of 0.5 that sensitivity analysis across values from 0.1 to 0.9 confirmed as stable. The balanced optimum was the parameter combination A3B3C3: laser power at 90 percent, cutting speed at 8 millimeters per second, and material thickness of 5 millimeters. This ranking held first place across all five weighting scenarios tested, including quality-focused and productivity-focused weightings, and a two-way analysis of variance attributed 59.25 percent of the multi-response contribution to cutting speed, 15.31 percent to material thickness, and 6.01 percent to laser power, with a statistically significant interaction between laser power and thickness contributing 8.97 percent.

The confirmation experiment compared the initial condition A1B1C1 with the optimum, showing the gray relational grade rising from 0.477 to 0.891, kerf width narrowing across all paths, and cutting time falling from 47.85 to 24.49 seconds, a 48.8 percent reduction achieved while cutting material 66.7 percent thicker. Surface roughness rose moderately from 1.304 to 1.543 micrometers, which the authors consider acceptable for acrylic displays, signage, and mechanical casings without secondary finishing. The predicted grade of 0.785 fell below the experimental value, which the team interprets as an absence of overconfidence in the optimization model. The authors acknowledge limitations: the model was trained on only 27 runs and its generalization is confined to the PMMA and parameter ranges studied, and a residual error contribution of 4.43 percent suggests unidentified technical variables remain. Future work will expand the dataset to more polymer types, wider thickness ranges, and broader process conditions, with the stated aim of enabling deep learning architectures and industrial deployment on laser CNC systems.

Subject of Research: Multi-objective optimization of CO₂ laser cutting parameters for PMMA using machine learning and gray relational analysis

Article Title: Multi-objective optimization of CO₂ laser cutting for PMMA using machine learning and gray relational analysis integration

Article References: Arifin, A., Wijanarka, B. S., Harjanto, C. T., Putri, R. R. M., & Tran, V.-Q. (2026). Multi-objective optimization of CO₂ laser cutting for PMMA using machine learning and gray relational analysis integration. Discover Mechanical Engineering, 5(1), Article 206. https://doi.org/10.1007/s44245-026-00372-y

Image Credits: AI Generated

DOI: 10.1007/s44245-026-00372-y

Keywords: CO₂ laser cutting, PMMA, artificial neural network, gray relational analysis, multi-objective optimization, kerf width, surface roughness, cutting time, machine learning, full factorial design, signal-to-noise ratio, manufacturing