Construction and application of connection number and projection pursuit models for groundwater quality evaluation: A case study of the main urban area of Bozhou City

To address the limitations of existing groundwater quality evaluation methods, such as subjective weighting, ambiguous classification boundaries, and the lack of multi-perspective robustness verification, this study constructed two quantitative groundwater evaluation frameworks by coupling the Projection Pursuit (PP) model with the Set Pair Analysis (SPA) model. First, a PP-based evaluation model was established. An Accelerated Genetic Algorithm (AGA) was employed to optimize both the projection direction and the parameters of the Logistic curve, thereby fully exploiting the intrinsic structural features of high-dimensional water quality data to achieve objective dimensionality reduction and continuous grade quantification driven by multi-index data. Second, to overcome the ambiguity at the classification boundaries of water quality grades and to validate the evaluation results, the SPA model was further introduced for fuzzy evaluation. Innovatively, the optimal projection direction derived from the PP model was utilized as the objective weight in the SPA model to quantify the degree of membership of the samples to different water quality grades. Taking the groundwater in the main urban area of Bozhou City, Anhui Province, as the study subject, the results indicated that the overall groundwater quality in this area belongs to Grade II (Class II water). The characteristic values of the water quality grades calculated by the PP model ranged from 1.89 to 2.00, while those calculated by the SPA model ranged from 1.95 to 2.03. The evaluation results of these two models, which are based on different mathematical mechanisms, exhibited high consistency. Furthermore, index perturbation sensitivity analysis and independent weight control experiments systematically verified the robustness of the evaluation results and the scientific validity of the weighting method. This study provides a rigorous theoretical basis and technical support for the precise evaluation and sustainable management of regional groundwater.