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. To address this issue, this study proposes a multivariate and multidimensional quality gain-loss function model based on a nonseparable Gaussian process (NSGP). A spatiotemporal interaction term is constructed using the Matérn kernel function, while the Kalman filtering and smoothing algorithms are introduced to improve computational efficiency. In addition, the signal-to-noise ratio is employed to determine the joint gain-loss weights, thereby establishing the multivariate and multidimensional quality gain-loss function model. Taking hydraulic concrete construction as the research background, simulation experiments and a practical engineering case are used to examine the performance and applicability of the proposed model. The results indicate that, compared with conventional machine learning methods, the NSGP model achieves superior predictive accuracy and can effectively characterize the spatiotemporal evolution patterns of concrete slump and segregation resistance. However, the interval coverage probability in the dam concrete case study remains lower than the nominal level, indicating that uncertainty quantification requires further improvement. The proposed model does not require prior determination of covariance separability during computation. Under the given dataset and assumptions, it provides an exploratory quantitative tool for point prediction, multivariate quality evaluation, and parameter optimization of selected fresh concrete indicators.