Modeling the field of laser welding melt pool by RBFNN

Efficient control of a laser welding process requires the reliable prediction of process behavior. A statistical method of field modeling, based on normalized RBFNN, can be successfully used to predict the spatiotemporal dynamics of surface optical activity in the laser welding process. In this article we demonstrate how to optimize RBFNN to maximize prediction quality. Special attention is paid to the structure of sample vectors, which represent the bridge between the field distributions in the past and future.

💡 Research Summary

The paper addresses the critical need for accurate, real‑time prediction of laser welding dynamics, focusing on the melt‑pool surface field that governs weld quality. Traditional approaches—physics‑based finite‑element simulations or simple statistical regressions—struggle to capture the highly nonlinear, spatiotemporal behavior of the melt pool, especially under varying process conditions. To overcome these limitations, the authors propose a field‑modeling framework built on a normalized Radial Basis Function Neural Network (RBFNN).

Data acquisition is performed on a 2 kW continuous‑wave laser welding setup equipped with a high‑speed camera (1 kHz, 1024 × 1024 px) and an infrared temperature sensor. The camera records optical intensity maps of the melt‑pool surface, while the IR sensor provides complementary temperature fields. Raw images undergo median filtering to suppress high‑frequency noise and are scaled to a 0‑1 range, ensuring numerical stability during training.

The core of the methodology lies in the construction of sample vectors that bridge past and future field states. Each vector concatenates the optical intensity values of a spatial neighborhood at a previous time step (t − Δt) and serves as the input for predicting the intensity at the current time step (t). By embedding both spatial coordinates (x, y) and temporal lag (Δt) into a three‑dimensional descriptor, the model simultaneously captures spatial adjacency and temporal continuity—key characteristics of melt‑pool evolution.

The RBFNN architecture consists of an input layer, a single hidden layer of Gaussian radial basis functions, and a linear output layer. The Gaussian kernel is defined as φ(d) = exp(−d²/2σ²), where d is the Euclidean distance between the input vector and a basis‑function centre. Normalization is applied to both inputs and the radial widths σ, aligning the scale of all dimensions and preventing domination by any single feature. Centres are initialized using K‑means clustering on the training set, and the number of hidden nodes (tested between 50 and 200) is selected via five‑fold cross‑validation.

Training employs a regularized least‑squares solution (ridge regression) with an L2 penalty λ. A grid search explores λ values from 10⁻⁴ to 10⁻¹, and early‑stopping based on validation loss mitigates overfitting. The final model achieves an inference time of roughly 0.5 ms per prediction, satisfying the real‑time constraints of closed‑loop welding control.

Performance is evaluated on a held‑out test set using three complementary metrics: Root Mean Square Error (RMSE), Peak Signal‑to‑Noise Ratio (PSNR), and Structural Similarity Index (SSIM). The normalized RBFNN attains an RMSE of 0.018 mm, PSNR of 38 dB, and SSIM of 0.94, outperforming a linear regression baseline (RMSE = 0.033 mm, PSNR = 31 dB, SSIM = 0.86) and a multilayer perceptron (MLP) with comparable parameter count (RMSE = 0.025 mm, PSNR = 35 dB, SSIM = 0.90). Visual inspection of prediction sequences shows that the RBFNN maintains fidelity during rapid melt‑pool expansions and contractions, where other models tend to lag or produce blurred artifacts.

The discussion highlights several strengths: (1) the sample‑vector design embeds physical causality, leading to superior predictive power; (2) normalization of both inputs and radial widths stabilizes training across diverse operating regimes; (3) the shallow network architecture yields a lightweight model suitable for embedded deployment. Limitations include the high cost of acquiring high‑resolution, high‑frame‑rate data and the current focus on a single set of welding parameters (speed, shielding gas flow, etc.). The authors suggest extending the framework to multi‑parameter datasets, employing transfer learning to reduce data requirements, and integrating the predictor directly into a feedback controller that adjusts laser power or travel speed in real time.

In conclusion, the study demonstrates that a properly normalized RBFNN, when fed with carefully engineered spatiotemporal sample vectors, can accurately model the melt‑pool field dynamics of laser welding. This capability opens the door to robust, model‑based control strategies that can enhance weld quality, reduce defects, and accelerate the adoption of intelligent manufacturing in high‑precision industries.