A collinearity-aware spatiotemporal graph attention fusion network for spindle thermal-error prediction and digital-twin compensation

Thermal error is a dominant dynamic and nonlinear error source in precision computer numerical control machining and directly affects part geometric accuracy. Accurate prediction and real-time compensation are therefore essential. Existing data-driven models often emphasize temporal patterns, discard auxiliary sensors to reduce collinearity, or construct spatial graphs only from fixed sensor distances, which may limit their ability to describe changing thermal regimes. In addition, digital-twin-based compensation systems are often reported without explicit analysis of worst-case latency, jitter, deadline misses, and fallback behavior. To address these issues, this study proposes a dual-stream collinearity-aware spatiotemporal graph attention fusion network embedded in a digital-twin-based compensation framework. As an artificial intelligence implementation for spindle thermal-error prediction, the proposed model is embedded into a digital-twin compensation loop to support both prediction and compensation decision-making. Temperature-sensitive points are routed as primary features, while non-temperature-sensitive points are retained as secondary features to preserve auxiliary thermal-field information. A multiscale attention-gated temporal unit, a large selective-kernel spatial extractor, dynamic spatiotemporal convolution, and bidirectional stream interaction are integrated with a fused adjacency matrix that combines Euclidean sensor proximity and derivative dynamic time-warping-based thermal similarity. Experiments were conducted on spindle thermal-error datasets collected from two machine-tool platforms. The data for Conditions 1 and 2 were obtained from the same machine tool, while the data for Condition 3 were obtained from another machine tool platform and were used for preliminary cross-machine prediction validation. All prediction experiments were repeated five times with different random seeds. In two same-machine scenarios and one preliminary cross-machine scenario, the proposed model achieved a prediction accuracy index η of 98.12-98.64%, a mean absolute error of 0.3048-0.3766 μm (μm), and a root mean square error of 0.4121-0.6176 μm, with detailed standard deviations and 95% confidence intervals reported in the experimental section. Compared with temporal and representative spatiotemporal baselines, the proposed model achieved lower prediction errors under the same evaluation protocol. Ablation results further show that removing the main temporal, spatial, or interactive-fusion components reduces η to 96.35-97.88%, confirming the contribution of the proposed modules. When deployed in the tested digital-twin compensation loop, the proposed system reduced the residual thermal-error root mean square error by approximately 89.8% relative to the static-map baseline. For the tested workpiece geometry, the closed-loop compensation achieved average geometric-error reductions of 64.95% and 64.92% relative to the no-compensation group under the two Machine A compensation trials, denoted as compensation Conditions C1 and C2, respectively, over three repeated machining trials. Real-time profiling on an industrial personal computer equipped with an Intel Core i7 processor, 16 gigabytes memory, a real-time Linux runtime, and a Siemens 840Dsl controller showed bounded end-to-end latency, with 99.9th-percentile latency of 1.42-1.79 ms (ms), worst-case latency below the 2 ms interpolation period, no observed deadline misses after fallback activation, and any-time fallback activation below 0.62%. These results demonstrate the feasibility of cycle-level spindle thermal-error prediction and compensation on the main tested platform, and provide preliminary evidence of prediction transferability to one additional machine-tool platform. However, the real-time closed-loop compensation and part-level machining validation were still conducted on the main tested platform, while cross-machine evaluation was limited to prediction validation on one additional machine-tool platform. More extensive validation on different machine tools, spindle configurations and machining operations will be carried out in the future.