Modeling of Part Surface Topography Based on Adaptive Composite Kernel Functions

Part surface topography is characterized by complex multi-scale and multi-feature coupling, and accurate topography modeling is essential for predicting assembly precision in high-performance mechanical systems. Gaussian Process Regression (GPR) offers a principled, probabilistic framework for surface modeling from sparse measurements, but its performance depends critically on kernel function selection. A fixed single kernel lacks the flexibility to represent surfaces that simultaneously exhibit smooth trends, periodic textures, and linear drift. To address this limitation, an adaptive composite kernel method is proposed. Initial GPR residuals are analyzed through statistical hypothesis tests and spectral decomposition to identify which geometric features are present; matching base kernels—Squared Exponential (SE), Periodic (PER), and Linear (LIN)—are then selected and combined additively or multiplicatively. Experiments on three representative synthetic surfaces show that the composite kernels reduce RMSE by up to 95.09% relative to the single SE kernel. Validation on a machined part confirms that the method successfully transfers to real measured data, achieving a 30.65% RMSE reduction and raising R² from 0.9536 to 0.9777. The results demonstrate that residual-analysis-driven kernel selection yields physically interpretable models with substantially improved reconstruction accuracy.