Multivariate And Multidimensional Quality Gain-Loss Function and Its Applications Based on Nonseparable Gaussian Processes

Existing research on quality gain-loss functions predominantly focuses on single variables or separable quality characteristics, overlooking the correlations among multiple quality attributes and the complexity of spatiotemporal factors. This paper employs the Matérn kernel to construct spatiotemporal interaction terms, incorporates Kalman filtering and smoothing algorithms to enhance computational efficiency, and establishes joint gain-loss weights using the signal-to-noise ratio method. Consequently, a multivariate multidimensional quality gain-loss function model based on the Non-Separable Gaussian Process (NSGP) is developed. The NSGP model is applied to simulation cases and dam concrete production scenarios. Comparative optimization with machine learning methods such as Gaussian processes and linear regression validates the robustness of the NSGP model. Crucially, it eliminates the computational requirement for determining covariance separability, thereby reducing computational costs. This provides robust case support for quality management in hydraulic concrete construction.