With the rapid development of laser weapon technology, predicting the damage behavior and failure process of laser protective coatings plays a key role in understanding the reliability of coatings. However, current models have not fully studied the thermal response process of multi-layer composite coatings and heavily rely on data samples such that their stability and applicability still require further consideration. To tackle these problems, in this work, a multidimensional prediction framework combining finite element simulation, SHAP quantitative analysis and deep learning was proposed. Firstly, through thermal-structural coupled finite element simulation and the SHAP quantitative method, the surface reflectivity was identified as the dominant factor in suppressing temperature rise, revealing its significant negative correlation with the peak temperature; when the reflectivity was increased from 87% to 97%, the peak temperature under 3000 W laser irradiation was decreased by approximately 73.1%. Subsequently, experiments on the Y2O3/8YSZ/NiCrAlY multilayer coating system further validated the finite element model. The results indicated that no obvious damage occurred on the coating surface under low-power laser irradiation. As the laser power increased, significant microstructural evolution, such as ablation rings and elemental enrichment from the bond coat, appeared on the coating surface, showing good agreement between the experimental phenomena and simulation results. Finally, the constructed deep learning framework achieved high-precision prediction of thermal damage, where the deep neural network demonstrated high prediction accuracy for transient temperature curves (R²>0.95) with a failure time prediction error of less than 10%. Furthermore, the Pix2PixHD network successfully realized high-fidelity inversion of the temperature field contour maps. This study provides a systematic reference for the structural design, performance evaluation and lifetime prediction of anti-laser coatings.
Tianyu Fang, Kairui Yu, Lingling Xie, Ziyu Wang, Du Hong, Yaran Niu, Xuebin Zheng.
Damage Failure Process Prediction of Laser Protective Coatings Based on Finite Element Simulation and Deep Learning.
Extreme Materials 10043 DOI:10.1016/j.exm.2026.100043
With the rapid development of laser technology, its high energy density and powerful destructive power have been widely applied in military and industrial fields [1], [2], [3]. However, this also poses a severe survival challenge to structural materials. Currently, surface coating technology is considered one of the most effective methods for improving the laser protection performance of structural materials. The existing forms of laser protection mainly include thermal insulation protection [4], [5], ablation protection [6], [7] and reflective protection [8], [9].
It is well known that 8% yttria-stabilized zirconia (8YSZ) is widely used in the field of thermal barrier coatings on the surfaces of nickel-based high-temperature alloys due to its extremely low thermal conductivity and relatively high coefficient of thermal expansion [10], [11], [12]. Due to the excellent thermal insulation properties, the protective capability of 8YSZ under extreme thermal loads has also attracted the attention as a laser protection coating.
Nevertheless, the protective performance of a single material is often insufficient when facing high-power laser irradiation. In recent years, many efforts such as surface modification, multilayer composite coatings and multi-ceramic coatings have been made to enhance the resistance of the coating [13], [14], [15]. This includes the design of high-reflection surface layers and thermal insulation layers to achieve multifunctional collaborative protection through reflection and thermal insulation. For example, Yang et al. [16] introduced a ceramic-modified component design and prepared a silicone resin-based composite coating and studied its optical conversion behavior under high-energy laser ablation. Their found that the ZrSi2-modified coating exhibited the best improvement in reflectivity under high-energy laser ablation. In another work, Yang et al. [17] designed and prepared a resin-based composite coating consisting of an Al2O3 high-reflection layer, a BN thermal conduction layer and hollow Al2O3 insulation layer. The results showed that the synergistic effects of reflection, thermal conduction and insulation could effectively alleviate heat concentration and significantly enhance the resistance of the coating to high-energy laser ablation.
Finite element simulation, on the other hand, as an effective numerical computation method, has been widely applied to solve engineering problems [18], [19], [20]. Through finite element simulation, the interaction between laser and materials can be analyzed and the thermal damage behavior of coatings can be elucidated [21], [22], [23]. For examples, Liang et al. [24] established a thermal-stress coupled simulation model for laser-induced micro-pits on a Ni60 substrate with a WC coating under nanosecond laser irradiation. The effects of different laser process parameters on the micro-pit diameter, depth and residual stress were investigated. Shen et al. [25] established a macro-micro scale finite element model to simulate the ablation mechanism of Al2O3/Al2O3 ceramic matrix composites under continuous laser irradiation. They found that the molten Al2O3 changed the laser transmission behavior and led to the formation of elliptical ablation pits. The established model could accurately characterize the ablation evolution process. Li et al. [26] developed a three-dimensional transient model for single-pulse laser ablation under multi-beam coupling conditions, simulating the evolution of surface morphology and temperature field during the laser ablation process. However, the existing studies on finite element simulations of laser protective coatings still have some shortcomings. As a result, the synergistic effects between the functional layers in multilayer composite coatings are not yet clear. As such, the relationship between the surface reflection layer and the intermediate insulation layer requires further investigation. However, conventional finite element simulations still have limitations in rapid prediction and multi-parameter optimization. The behaviors of multilayer coatings are affected by laser power, reflectivity, irradiation time, interlayer structure, and other factors, requiring repeated calculations under different parameter combinations and resulting in high computational cost. This limits the ability to rapidly predict the evolution of temperature fields under different operating conditions.
The rapid application of machine learning and neural network technology in complex thermophysical problems provides a new approach for predicting the ablation behavior of laser protective coatings [27], [28]. Deep learning is not only widely used to directly predict physical properties such as effective thermal conductivity of microstructures [29], [30], but also shows significant advantages in capturing transient thermal conductivity behavior under extreme loads [31]. For examples, Hao et al. [32] developed a machine learning regression model based on historical experimental datasets. They compared different models for predicting the oxidation and ablation resistance of ultrahigh-temperature ceramic coatings. The results showed that the random forest regression model accurately predicted the ablation resistance of coatings, thereby accelerating the coating development process. Zhang et al. [33] proposed a machine learning framework based on a physical model to optimize the laser-induced plasma micro-machining process. By combining variables from the physical model with process parameters, this method significantly improved the machining depth and material removal rate. The genetic algorithm was further integrated to optimize the multidimensional process parameters, effectively accelerating the optimization of the machining process. Li et al. [34] proposed an innovative approach based on machine learning and multi-objective optimization to predict and co-optimize the heat-affected zone (HAZ) and material removal rate (MRR) during groove machining. The results demonstrated significant improvements in both HAZ and MRR, effectively avoiding issues such as fiber thinning or fracture. However, current models have not fully studied the thermal response process of multi-layer composite coatings. Additionally, these models heavily rely on data samples and their stability and applicability still require further consideration.
To tackle the above problems, a multidimensional prediction method that combines finite element simulation with deep learning was innovatively proposed in this paper. A systematic study is conducted on the failure and ablation behavior of laser protective coatings. Firstly, a laser ablation finite element model is established to analyze the impact of laser power (500~3000 W), surface reflectivity (87%~97%) and irradiation time (0~10 s) on the evolution of the temperature field of the coating. The SHapley Additive explanations (SHAP) method is introduced to quantitatively reveal the contribution weights of each parameter to the temperature rise and their interaction effects. Experimentally, the Y₂O3/8YSZ/NiCrAlY multilayer laser protective coating is prepared on a Ni625 substrate and the simulation results are verified through laser ablation experiments. Based on this, a deep learning-based multidimensional prediction framework for coatings is further developed. A deep neural network is employed to achieve high-precision prediction of transient temperature curves and the Pix2PixHD generative adversarial network is used to reconstruct the 2D transient temperature field rapidly. As we will show in the following sections, this method significantly reduces the finite element computation costs while ensuring prediction accuracy, providing a theoretical support and methodological guidance for the optimization design of laser protective coatings.
2. Experimental procudure
2.1. Finite element model
The finite element model in this paper consists of four layers: the surface layer, insulation layer, bond layer and substrate. The surface layer is a Y₂O3 coating with high reflectivity, with a thickness of 0.1 mm. The insulation layer is made of 8% yttria-stabilized zirconia (8YSZ) material, with a thickness of 0.2 mm. The bond layer is a NiCrAlY coating, with a thickness of 0.1 mm. The substrate material is Ni625, with a thickness of 3.0 mm. The finite element model is a disc-shaped model with a height of 3.4 mm and a diameter of 25 mm, as shown in Fig. 1(a).
To limit the rigid body motion of the model and avoid unreasonable displacement and rotation during the finite element simulation process, a three-point constraint is applied to the bottom of the model, as shown in Fig. 1(b). The laser heat source is applied to the surface of the coating through the DFLUX subroutine, with the surface heat flux q(x) represented by Eq. (1).
In Eq. (1), x is the distance from the center of the laser irradiation spot; r is the radius of the laser (the laser radius in this paper is 5 mm); P is the laser power; and R is the reflection coefficient of the coating surface.
To reduce the influence of interfacial temperature gradients in the multilayer coating on mesh calculation, local mesh refinement was applied to the surface layer, bonding layer, interlayer interfaces and laser irradiation region. A relatively coarser mesh was adopted in regions far from the irradiation zone to balance accuracy and computational efficiency. The transient thermal-structural coupled analysis was performed using C3D8RT elements, namely eight-node thermally coupled brick elements. The final finite element model contained 53,040 elements. Mesh independence was verified by comparing the peak surface temperatures under different mesh densities, as shown in Table 1.
This paper considers the temperature-dependent physical properties of different coating layers and substrate materials. The material properties include thermal conductivity K, specific heat capacity C, coefficient of thermal expansion α, elastic modulus E, Poisson's ratio v and density ρ. The specific material parameters are shown in Table2.
2.2. Preparation and characterization of the coating
A combination of plasma spraying and slurry methods is adopted to prepare multilayer composite laser protective coatings. Firstly, the NiCrAlY bond layer and the 8YSZ insulation layer were sequentially sprayed onto the surface of the Ni625 substrate using the plasma spraying method. The thickness of the NiCrAlY bond layer was 0.1 mm and the thickness of the 8YSZ insulation layer was 0.2 mm. Then, the slurry method was used to prepare a Y₂O3 high-reflection layer on the surface of the 8YSZ insulation layer. Through multiple coating and curing processes, the thickness of the coating was precisely controlled to ensure its reflection performance and thermal insulation effect. Finally, a fiber laser with a wavelength of 1070 nm and a spot size of ϕ10mm was used to conduct laser irradiation tests on the coating.
To characterize the microstructure and properties of the prepared coatings, scanning electron microscopy (SEM) was used to observe their surface morphology and microstructure. Particular attention was paid to ablation, cracking and other damage forms generated during laser irradiation. Combined with energy-dispersive spectroscopy (EDS), a qualitative and semi-quantitative analysis of the element distribution in each layer of the coating was performed, revealing the migration and enrichment of elements in the coating after laser irradiation.
2.3. Establishment of deep learning models
The performance of feedforward, shallow, medium and deep neural networks was compared. The feedforward neural network has a simple structure, consisting of an input layer, hidden layer and output layer, with unidirectional data flow, as shown in Fig. 2(a). The other networks are mainly distinguished by the number of hidden layers [35], [36], [37], as shown in Fig. 2(b). The parameters of each network are shown in Table 3.
For predicting the 2D temperature field, the Pix2PixHD generative adversarial network was used. The network, with its multi-scale generator and discriminator structure, can effectively capture the heat diffusion trend and local high-temperature gradient features of the temperature field. Compared to traditional convolutional neural networks, it has stronger expressive power in high-resolution field predictions. Through learning from simulation data, the model can achieve pixel-level temperature reconstruction while ensuring high consistency in spatial continuity and physical rationality. It can be used as an efficient surrogate model for finite element calculations and applied to the prediction of temperature fields in coatings under different laser conditions, as shown in Fig. 2(c).
In the temperature-curve prediction task, laser power, surface reflectivity and irradiation time were used as inputs, while the temperature of the corresponding coating layer was used as the output. The rectified linear unit (ReLU) activation function was adopted in the hidden layers and a linear activation function was used in the output layer to accommodate continuous temperature prediction. Before training, the data were normalized and the generalization ability of the model was evaluated through the division of training and test sets, thereby reducing the risk of overfitting.
For the Pix2PixHD model, the multi-scale generator was used to reconstruct the two-dimensional temperature field, while the multi-scale discriminator was employed to constrain the generated results at different spatial scales. In this way, both the global heat diffusion trend and local temperature-gradient features could be learned by the model and the spatial continuity of the predicted temperature field was improved.
3. Analysis of finite element simulation results
3.1. Effect of different laser powers on the temperature field
Fig. 3 shows the temperature field distribution contour maps of different layers in the 87% reflectivity coating under 500 W laser irradiation for 10 seconds. It was observed that the temperature field of the coating exhibited a significant central concentration effect and a gradient decrease along the direction of thickness. The peak surface temperature of the coating reached 553°C. In contrast, the temperature at the substrate interface decreased significantly to 350°C, forming a prominent temperature gradient between the coating surface and the substrate. This is due to the Y₂O3 layer on the surface, which has 87% reflectivity and greatly reduces the initial deposition of laser energy. Additionally, the intermediate 8YSZ layer has low thermal conductivity, which reduces the downward diffusion of residual heat flow and provides protection to the bond layer and substrate.
To explore the lateral heat conduction behavior on the coating surface, five characteristic nodes along the radial centerline of the model were selected for analysis, as shown in Fig. 4(a). Fig. 4(b) shows the temperature variation curves of the coating with 87% reflectivity under 500 W laser irradiation for 10 seconds. It can be observed that the temperature at each node increases with the duration of laser irradiation, but significant differences in response characteristics are observed due to varying heat-affected locations. The node at the center of the laser spot (D=12.5 mm) is directly exposed to the laser, with a rapid temperature rise from 0 to 3 seconds. Afterward, the rate of temperature rise slowly due to heat dissipation by conduction and the final temperature reaches about 580°C. The nodes at the spot edges (D=7.5 mm and D=17.5 mm) exhibit a highly symmetric and gradual growth trend, with the temperature reaching 250°C after 10 seconds. Meanwhile, the model edge region far from the spot (D=0 mm and D=25 mm) shows a slow temperature increase at the beginning. As the heat flow continuously spread from the center to the periphery, the temperature rise accelerates in the later stages, reaching only about 95°C at 10 seconds, which is much lower than in the central region.
Fig. 5 shows the temperature field of the 87% reflectivity coating after 10 seconds of irradiation at different laser powers. As the laser power increases from 500 W to 3000 W, the peak surface temperature of the coating increases sharply. Specifically, the peak temperature rises from 553°C at 500 W to 2765°C at 3000 W, corresponding to an increase of 2212°C, or approximately 400%. From the temperature field distribution, it can be seen that at lower power, the temperature is relatively low and the heat-affected area is confined to the central region of the laser irradiation. As the laser power increases, the temperature rises significantly and the heat-affected area expand considerably, forming a steeper temperature gradient and a wider radial diffusion.
As shown in Fig. 6(c), the peak temperatures of the 87% and 97% reflectivity coatings increase monotonically with the increase in laser power. At different laser powers, the reflectivity of the coating exhibits a significant difference in temperature suppression. The high reflectivity coating can effectively reduce the temperature rise at low power, but as the power increases, the temperature suppression effect gradually weakens. Starting from 75.2% at 500 W, the temperature suppression effect gradually weakens and tends to stabilize in the range of 2500 W to 3000 W, at about 73.1%. This indicates that the high-reflectivity coating has a more significant temperature-rise suppression effect under low-power conditions. However, under high-power conditions, the temperature suppression rate remains relatively stable.
3.2. Influence of different laser reflectivity on the temperature field
To study the temperature distribution along the surface and thickness directions of different coatings, two curves along the surface center direction and the thickness center direction were selected. A schematic diagram of the selected curves is shown in Fig. 7.
Fig. 8 shows the temperature distributions along the surface and thickness directions for different reflectivity coatings under 500 W and 3000 W laser irradiation. Fig. 8(a) and (c) indicate that the coating surface temperature follows a Gaussian distribution. The high-temperature region is concentrated between distances of 7.5 mm and 17.5 mm and it decays outward symmetrically with respect to the center of the laser spot. Under 3000 W laser irradiation, as the reflectivity increases from 87% to 97%, the peak temperature drops significantly from 2765°C to 744°C. At this point, the temperature curve becomes flatter, indicating that high reflectivity not only effectively reduces the peak temperature but also improve the distribution of surface thermal stress.
From Fig. 8(b) and Fig. 8(d), it can be seen that the four-layer structure of the coating causes the temperature variation along the thickness direction to follow a nonlinear trend. The relatively high thermal conductivity of the Y₂O3 surface layer (0~0.1 mm) causes the temperature to decrease more gradually. In contrast, the intermediate 8YSZ layer (0.1~0.4 mm) causes the temperature to decrease rapidly due to its lower thermal conductivity. The high reflectivity of the Y₂O3 layer reflects a large amount of laser energy and combine with the insulating effect of the 8YSZ layer, it effectively protects the substrate from high-temperature damage.
To further investigate the nonlinear influence mechanism of laser reflectivity and power on the coating temperature field, SHAP dependence plots and interaction effect plots were used for analysis. The SHAP dependence plots reveal the marginal effects between individual features and the prediction target, clarifying the positive and negative impact trends of feature value changes on temperature. The interaction effect plots further explain the synergistic effects between features [38], [39], [40]. Fig. 9 shows the SHAP dependency relationship between laser power and reflectivity, as well as the interaction effect analysis between them.
Fig. 9(a) and (b) show that laser power has a positive effect on temperature. As the power increases from 500 W to 3000 W, the temperature rises significantly. Reflectivity exhibits a negative suppression effect. As reflectivity increases, the temperature decreases and the SHAP value drops sharply. The vertical dispersion in the figure indicates that there is a significant coupling effect between laser power and reflectivity. When low reflectivity is combined with high power, the system has the highest energy absorption rate and the temperature shows the greatest sensitivity to parameter changes.
The interaction effect plot in Fig. 9(c) and the temperature heat map in Fig. 9(d) further validates the coupling mechanism between laser power and laser reflectivity. Under the combination of high power (3000 W) and low reflectivity (87%), the coating surface temperature increases significantly, reaching 2765°C. In contrast, under the combination of low power (500 W) and high reflectivity (97%), the coating surface temperature is only 137°C, with a significant difference. Furthermore, the SHAP method was used to quantitatively analyze the importance weights of laser power and reflectivity on the coating surface temperature. Feature importance was measured by calculating the absolute average SHAP value of that feature across all samples. This metric reflects the average influence of the feature on model predictions, with a larger value indicating a more significant global impact of that parameter on temperature change [41], [42]. As shown in Fig. 9(e), the average SHAP value of reflectivity is 435, which is higher than that of laser power at 380. This indicates that reflectivity plays a dominant role in the coating temperature variation within the parameter range considered in this study.
3.3. Effect of different laser times on the temperature field
Fig. 10 shows the effect of 87% and 97% reflectivity on the coating temperature field under 500 W laser power. From the spatial dimension of heat diffusion, it can be seen that the diffusion radius of the heat-affected zone is similar under both laser powers. At t = 3 s, 5 s and 10 s, the heat diffusion diameters for the two reflectivity are 12.65 mm, 14.9 mm and 16.17 mm, respectively. This phenomenon indicates that, with thermal properties of the material remaining unchanged, the speed of heat propagation is primarily determined by the thermal diffusivity of the material. From the time dimension, at 3 s, the high-temperature heat-affected zone expands to 12.65 mm, which is 2.65 mm larger than the original laser spot radius. From 3 s to 5 s, the diffusion radius increases by 2.25 mm and from 5 s to 10 s, it only increases by 1.27 mm. This indicates that as heat dissipates into the far field and the temperature gradient becomes gentler, the surface heat diffusion boundary is gradually stabilized.
4. Experimental verification
To verify the accuracy of the finite element simulation, coating samples were fabricated according to the geometric model and the failure process of the laser protective coating was analyzed in detail through laser testing. Fig. 11 shows the microstructure of the surface area under 500 W laser irradiation. It can be seen that after 10 seconds of 500 W laser irradiation, the coating structure remains intact, indicating that the damage threshold of Y₂O3 is not reached. In the center of the laser irradiated area (area b) and the area far from the laser ablation zone (area c), the microstructure remains consistent with the as-fabricated state. The characteristics are represented by needle-like poly-sodium silicate (Na₂O•nSiO₂), effectively encapsulating Y₂O3 particles. At this point, the heat generated by laser irradiation does not cause the coating to melt. The finite element simulation shows that, under this laser power, the surface temperatures of each layer in the coating are 444°C, 432°C, 265°C and 239°C, respectively. None of these temperatures reached the melting point of material, which corresponds with the experimental observation.
Fig. 12 shows the microstructure of the surface area under 2500 W laser irradiation at different times. It can be observed that within 0-5 s, during high-energy laser exposure at 3 s and 5 s, ablation rings appear on the coating surface while the coating structure remains intact. EDS results indicate that the ablated area underwent a reaction between Y₂O3 and Y₂Si₂O₇ is formed. When the laser irradiation reached 10 s, the laser energy exceeds the damage threshold of the sample. The surface of the sample shows a molten morphology and the coating structure has been destroyed. At this point, the finite element simulation shows the surface temperatures of each layer in the coating, from top to bottom, to be 2341°C, 2281°C, 1340°C and 1280°C, respectively. Although the surface temperature does not reach the melting point of the material, the shockwave stress accompanying the high-power laser causes stress accumulation in the coating, leading to the failure of the surface layer. The bond layer rapidly oxidized under high-energy laser exposure.
Fig. 13 (a-c) shows the microstructural morphology of the coating surface at different regions after 3 s of 3000 W laser irradiation. Affected by the Gaussian distribution of laser energy, the coating surface displays significant regional differences. In the center region, where the energy is most concentrated (Fig. 13(a)), the original needle-like structure almost disappears. It is replaced by the melting and decomposition of the poly-silicate binder, as well as the sintering and agglomeration of Y₂O3 particles at high temperatures. In the ablation transition zone (Fig. 13(b)), the boundary between ablated and non-ablated areas is clearly defined. The region directly exposed to the laser irradiation exhibits smooth and dense molten features. In the edge region far from the center (Fig. 13(c)), the coating is affected by heat to a lesser extent, and the randomly oriented needle-like Y₂O3 structure and clear crystal boundaries are still preserved.
Fig. 13(d-g) shows the microstructure and composition distribution of the surface after 5 seconds of 3000 W laser irradiation. Under these conditions, the finite element simulation indicates that the surface temperatures of each layer in the coating are 2497°C, 2425°C, 1295°C, and 1223°C, from top to bottom. The EDS results at the ablation center (Fig. 13(d)) reveal significant Cr enrichment on the surface after 5 seconds of 3000 W laser irradiation. The regions of Cr and O enrichment highly overlap, indicating the formation of chromium oxide. Since Cr only exists in the NiCrAlY bond layer in the as-prepared coating, the chromium oxide likely originates from the oxidation of Cr in the bond layer. Moreover, a significant amount of Zr and a small amount of Y are found around the Cr-enriched area. No signals of Si, Na, or other related elements are detected, indicating that the area surrounding the chromium oxide is mainly composed of YSZ. Based on the phase distribution of the as-prepared coating and the temperature field data obtained from the finite element simulation, the surface temperature at the ablation center is found to exceed the melting point of Y₂O3 after 5 s of 3000 W irradiation. As a result, the surface layer melted. Under the stress induced by laser irradiation, the surface layer peeled off, the YSZ layer and the bond layer are exposed. Meanwhile, the bond layer rapidly oxidized under the high temperature conditions induce by high-energy laser irradiation, leading to coating failure.
5. Prediction of ablation behavior of laser protective coatings based on deep learning
From a physical perspective, the evolution of the temperature field inside the coating during laser ablation is governed by the transient heat conduction equation. Therefore, the temperature field exhibits significant nonlinear characteristics and complex spatial gradient distributions. The coupling effects of parameters such as laser power, reflectivity and irradiation time cause the temperature field of the coating to change rapidly in the time dimension while also displaying distinct localized concentration features in the spatial dimension. Therefore, predicting the laser ablation temperature field is essentially a spatiotemporal field reconstruction problem driven by multiple parameters, rather than a simple point-value regression or interpolation problem.
To further study the temperature variation trend and melting behavior of the coating within the power and reflectivity ranges set in the simulation, neural networks were used to predict the finite element simulation results of coatings with different laser power and reflectivity. The dataset consists of 24 sets of temperature curves for the surface layer and bonding layer over time, totaling 386 data points and 386 simulation result images.
5.1. Prediction of coating failure time by different neural network models
To achieve the above goal, 21 of the 24 simulation data sets were used as the training set and the remaining 3 were used as test sets. The test set consisted of laser powers of 1500 W, 2000 W and 2500 W with 90% laser reflectivity. Fig. 14(a-d) compares the surface layer temperature curves predicted by four different neural networks with the actual curves. The results show that network depth and structural complexity have a decisive impact on the ability to perform nonlinear mapping. Shallow and medium-depth networks (Fig. 14(a) and Fig. 14(b)) struggle to capture the sharp nonlinear temperature rise of the surface layer due to insufficient feature extraction depth, leading to significant underfitting across the entire time domain. The deep neural network (Fig. 14(c)) maintains higher accuracy during the 0-3 second temperature rise stage, showing the best performance. The feedforward neural network model (Fig. 14(d)), limited by its ability to learn high-frequency sudden changes, shows a noticeable delay in the predicted curve during the rapid temperature rise stage (0-3 s), with a larger error. After 3 seconds, as the temperature change slow, the prediction results gradually converged to the actual values.
Fig. 14(e-f) shows the comparison between the temperature prediction curves of the bond layer using different neural networks and the actual curves. The insulation performance of the 8YSZ layer results in a relatively smooth temperature rise curve for the bond layer. Shallow and medium networks exhibit overfitting in high-power temperature curve predictions, with lower fitting accuracy. The deep neural network (Fig. 14(g)) maintains high accuracy across all power levels and time domains. Unlike the surface layer, the feedforward neural network (Fig. 14(h)) shows progressively improved accuracy when predicting the bond layer temperature.
To quantitatively evaluate the prediction performance of the deep learning models, the coefficient of determination (R2) and mean squared error (MSE) were used as evaluation metrics. The calculation formulas are as follows:
where yi is the true value, ŷi is the predicted value, where ӯ is the mean value of the true values.
Fig. 15 uses the coefficient of determination (R²) to quantitatively compare the prediction accuracy of four different models under different operating conditions. From Fig. 15(a), it can be seen that the surface layer affected by direct laser irradiation exhibits a more intense nonlinear characteristic in the temperature change curve. However, the shallow and medium neural networks exhibit weaker feature extraction capabilities, leading to underfitting in temperature curve predictions, with the lowest accuracy of 0.15. In contrast, using the deep neural network model, the prediction accuracy for all temperature curves exceeds 0.95, demonstrating strong generalization robustness and the ability to effectively capture the nonlinear temperature variations under different conditions. The accuracy of the feedforward neural network in predicting the surface layer is significantly lower than that of the deep neural network.
Based on the above, the deep neural network outperformed all other models, providing relatively accurate temperature predictions over the entire time domain. It particularly demonstrates a clear advantage in handling complex nonlinear problems, such as variations in laser power and rapid temperature rise.
To further validate the accuracy of the model, a deep neural network model was used to predict four coatings: 800 W-88%, 1600 W-92%, 2250 W-87% and 2900 W-87%. Fig. 16 shows the prediction results for the surface and bond layers of the four coatings using the deep neural network. The model demonstrates high prediction accuracy for the four coatings, with a small error between the predicted and actual curves, achieving a prediction accuracy of 95%
Table 4 compares the predicted time to reach the melting point for different layers using the deep neural network model with simulation time. From Table 4, it can be seen that for coatings with 800 W-88%, 1600 W-92% and 2250 W-87%, the surface layer and bond layer do not reach the melting point during 0-10 s of laser irradiation, with the simulation values and predicted values matching closely. However, for the 2900 W-87% coating, a deep neural network and simulation indicate that both the uniform layer and the bond layer reach the melting point, with simulation and prediction errors within 10%.
5.2. Prediction of coating ablation behavior based on Pix2pixHD deep learning model
##Fig. 17 shows the predicted temperature field distribution for the test set and randomly generated parameters using the Pix2PixHD deep learning model. Different colored bands represent different laser parameters: blue represents laser time, green represents laser power and red represents laser reflectivity. The laser parameters for the test set and randomly generated values are listed in Table 5. By comparing with the finite element simulation results, it is found that the Pix2PixHD neural network model can accurately predict the ablation results for the test set. However, for randomly generated parameters, such as the 2250 W-87% laser parameters, some frame loss occurs in the prediction results. This is due to the limited ability of generation networks to extract local features of the temperature field under high power conditions. Nevertheless, the model still provides a reasonably good prediction of the overall temperature field distribution.
To improve the structural transparency of the Pix2PixHD model, feature maps from the intermediate hidden layers were extracted, as shown in Fig. 18. As the training epoch increases from Epoch 10 to Epoch 550, the random noise in the feature responses gradually decreases, and the local high-response regions become clearer. This indicates that the model progressively learn the local gradient and spatial diffusion features of the temperature field, thereby improving the interpretability of the temperature-field reconstruction process.
By constructing a hybrid error evaluation metric, a quantitative comparative analysis of the performance of the Pix2PixHD neural network model on the test set samples and randomly generated samples was conducted, as shown in Fig.19. The experimental results indicate that the error curve exhibits a significant stepped distribution. On the constructed test set, the hybrid error values show very high stability, remaining within a low range of 0.05-0.07. This indicates that the model accurately capture the feature distribution of the input data, achieving high structural and textural alignment while maintaining pixel-level color fidelity. In contrast, the error values for the randomly generated samples increase significantly, ranging from 0.12 to 0.15, with considerable fluctuation across samples. However, the errors in both cases remain below 20%, demonstrating that the model can reliably predict the temperature field distribution under laser irradiation, providing data support for the design and optimization of laser protective coatings.
6. Conclusion
To address the complex evolution of temperature fields and the difficulty of quickly predicting the failure behavior of laser protective coatings under high-power laser irradiation, a method for predicting temperature fields and ablation behavior was proposed in this paper by combining finite element simulations with deep learning. This method enables efficient prediction of the coating's temperature distribution, failure process and ablation behavior, providing a theoretical basis and methodological support for the structural optimization, performance evaluation and lifetime prediction of laser protective coatings. The following conclusions can be drawn:
(1) The finite element simulation results show that the surface temperature of the coating is positively correlated with laser power and negatively correlated with reflectivity. For the coating with 87% reflectivity, the peak surface temperature rises sharply from 553°C at 500 W to 2765°C at 3000 W. When the reflectivity is increased to 97%, the surface temperature under 3000 W high-power irradiation is only 744°C, with a relative temperature reduction of 73.1%. The high-reflectivity surface layer combined with the 8YSZ insulating layer can significantly reduce energy deposition and suppress heat diffusion. The parameter sensitivity analysis based on the SHAP method indicates that material reflectivity is the most significant dominant factor affecting the coating temperature (average SHAP value of about 435), followed by laser power (average SHAP value of about 380). A strong coupling effect exists between the two, where high laser power and low reflectivity lead to peak sensitivity of temperature to parameter changes, which easily induces coating failure.
(2)The experimental results reveal the damage evolution patterns of the Y₂O3/8YSZ/NiCrAlY multilayer coating under different laser power levels. After 10 s of 500 W laser irradiation, the coating microstructure remains in its original as-prepared state and no significant surface damage is observed. After 5 s of 2500 W laser irradiation, obvious ablation rings appear on the surface and when the exposure time is further extended to 10 s, the surface shows molten features. After 5 seconds of 3000 W laser irradiation, the laser energy exceeds the damage threshold of the coating, causing the coating structure to be destroyed. The NiCrAlY layer is exposed and rapidly oxidized under high-energy laser exposure, leading to the accumulation of elements such as Al, Ni and Cr on the coating surface. The experimental phenomena are generally consistent with the simulation results.
(3)Based on finite element simulations, a deep learning-based multi-dimensional prediction framework for coating thermal damage is established, enabling high-precision inversion of transient temperature curves and spatial physical fields. The results indicate that, in the time domain, the deep neural network achieves a temperature prediction R² greater than 0.95 across the entire time domain, with a melt failure time prediction error controlled within 10%. Additionally, the Pix2pixHD network model accurately reconstructs the temperature field distribution maps, with results highly consistent with finite element simulation outcomes.
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