Physics-Prior and Multi-Scale Attention-Based Three-Dimensional Quality Field Reconstruction for Sparse Industrial Manufacturing Inspection

INTRODUCTION: Three-dimensional quality field reconstruction from sparse industrial measurements is critical for intelligent manufacturing yet remains challenging due to sensor accessibility limitations, high inspection costs, and component occlusion.

Objectives

This study develops a reconstruction framework that recovers full-domain three-dimensional fields from sparse observations by integrating physics-based constraints with data-driven deep learning, and validates it on simulated three-dimensional optical scattering fields that serve as a controlled, physically rigorous proxy for industrial quality fields.

Methods

A physics-guided loss function embedding Helmholtz equation residuals and boundary conditions is constructed, combined with a multi-scale three-dimensional convolutional network incorporating serial channel-spatial attention to capture both global structural and local high-frequency defect features. The benchmark fields are solved on a 128 × 128 × 128 grid, and 5% of voxels are retained as labeled samples.

Results

Under 5% sparse sampling of the simulated optical scattering fields, the proposed framework achieved the best reconstruction performance among all compared methods. On 40 independent test samples, it reached a PSNR of 34.6 ± 1.3 dB, an SSIM of 0.932 ± 0.011, and a phase RMSE of 0.183 ± 0.025 rad, outperforming MS-CNN by 4.5 dB, 0.049, and 33.2%, respectively. Visual comparisons showed improved recovery of strong scattering regions, boundary variations, diffraction-focus positions, and high-frequency defect-related structures, with an average peak-intensity error of about 4.2% and centroid deviation of about 0.3 μm. Under noisy inputs, the method retained PSNR above 29 dB and SSIM above 0.88 at SNR = 10 dB, indicating stronger robustness than 3D U-Net and standard PINN. Ablation experiments (reported as mean ± standard deviation over the 40 test fields) further confirmed that physical constraints, multi-scale convolution, channel attention, and spatial attention each contributed to the overall performance gain, with paired statistical tests confirming significant improvements across the main comparisons.

Conclusion

The framework offers a robust, physically consistent route for sparse quality-field reconstruction in intelligent manufacturing. Validation currently relies on high-fidelity numerical simulation; extension to real industrial measurements is identified as the primary direction of future work.