Composition Analysis and Identification of Ancient Glass Artifacts

This project addressed Problem C, “Composition Analysis and Identification of Ancient Glass Artifacts,” in the 2022 China Undergraduate Mathematical Contest in Modeling sponsored by Higher Education Press. Surface weathering can develop during burial and preservation, while glass type, visible characteristics, and chemical composition interact in complex ways. Starting from the supplied artifact dataset, the team analyzed weathering and composition changes, derived subtypes for high-potassium and lead-barium glass, and identified unknown samples. The project won a Provincial First Prize.

The analysis faced three challenges. First, some samples had component totals outside the valid range and some records contained missing values, so data eligibility had to be established before modeling. Second, weathering status, glass type, decoration, color, and multiple chemical components all interacted, making a single statistic insufficient. Third, identifying unknown samples required not only a prediction but also comparison across classifiers and stability checks under composition perturbations.

The project addressed five tasks: test how surface weathering relates to glass type, decoration, and color; analyze chemical composition changes before and after weathering; develop interpretable subtypes for high-potassium and lead-barium glass; classify unknown samples and test result stability; and explain relationships among chemical components. The team had to complete data cleaning, model comparison, stability testing, and paper delivery within the competition timeline.

The modeling process began with a validity review of the supplied data. The paper treated records whose component totals fell outside 85% to 105% as anomalous and handled them together with missing-data checks. Descriptive review across weathering status, type, decoration, color, and chemical composition then established variable relationships and the order of later statistical and classification work. This section describes dataset investigation rather than separate user interviews or field research.

The solution used a layered model pipeline. The team first applied a chi-square test to examine whether surface weathering was associated with glass type, decoration, or color, followed by descriptive statistics and multivariate linear regression for composition changes. PCA reduced the chemical feature space before hierarchical clustering and K-means were compared. Decision trees and naive Bayes formed the main classification path presented in the paper, while my code experiments also included random forest. Sensitivity analysis perturbed key components, and grey relational analysis interpreted relationships among chemical components.

The paper first removed samples with invalid component totals and missing data, then built separate analyses for weathering relationships, composition changes, subtype discovery, and unknown-sample identification. My contribution focused on implementation and selected modeling tasks: I used R and SPSS for data processing and model validation, with primary responsibility for random forest, Bayes, multivariate regression, and sensitivity analysis code. The team compared clustering methods, cross-checked decision-tree and Bayes outputs, and varied key component ratios to observe whether predictions changed.

The paper reported a strong association between surface weathering and glass type, but no similarly clear association with color or decoration. High-potassium and lead-barium glass showed different composition shifts after weathering. PCA with two clustering approaches produced subtype schemes for both glass families, while decision trees and Bayes gave broadly consistent classifications for the unknown samples. Sensitivity analysis tested classification stability, and grey relational analysis added an explanation of component relationships. The team completed a 37-page submission and won a Provincial First Prize.

Comparing multiple models improved the interpretability of the classification process, but the conclusions remain sensitive to sample size, anomaly rules, and measurement error in chemical composition. The project also reinforced that implementation is not merely translating equations into code: assumptions, outputs, and written conclusions must remain aligned throughout the workflow. Future work could add cross-validation, class-imbalance evaluation, clearer error analysis, and a more complete reproducible pipeline for preprocessing, model selection, and parameter sensitivity.