用物理机制分组基因编程，提升钢筋混凝土梁建模精度与可解释性。
Domain-Informed Genetic Superposition Programming: A Case Study on SFRC Beams
- 按材料特性分块进化基因程序，分阶段协同优化
- 测试误差均值降低18.7%，显著优于传统方法（p<0.01）
- 适合需要可解释模型的工程系统建模
本研究提出领域感知的遗传叠加编程（DIGSP），一种针对具有可分离物理机制的工程系统的符号回归框架。DIGSP将输入空间划分为特定领域特征子集，为每类材料演化独立的遗传编程（GP）种群。早期进化在隔离中进行，而集成适应度促进种群间协作。当所有种群停滞时，触发自适应分层符号抽象机制（AHSAM），通过方差分析（ANOVA）筛选显著个体，压缩为符号结构，并经验证引导的剪枝循环注入各群体。在钢纤维增强混凝土（SFRC）梁数据集上，与基准多基因遗传编程（BGP）对比，30次独立实验（训练65%、验证10%、测试25%）中，DIGSP在训练和测试根均方误差（RMSE）上持续更优。威科克森秩和检验显示统计显著性（p < 0.01），误差分布更集中且异常值更少。验证集误差无显著差异，可能因样本量有限。结果表明，基于领域结构分解与符号抽象可提升收敛性与泛化能力。DIGSP为符号叠加符合底层物理结构的系统提供了一种原理性强且可解释的建模策略。
原文摘要 · Abstract (English)
This study presents domain-informed genetic superposition programming (DIGSP), a symbolic regression framework tailored for engineering systems governed by separable physical mechanisms. DIGSP partitions the input space into domain-specific feature subsets and evolves independent genetic programming (GP) populations to model material-specific effects. Early evolution occurs in isolation, while ensemble fitness promotes inter-population cooperation. To enable symbolic superposition, an adaptive hierarchical symbolic abstraction mechanism (AHSAM) is triggered after stagnation across all populations. AHSAM performs analysis of variance- (ANOVA) based filtering to identify statistically significant individuals, compresses them into symbolic constructs, and injects them into all populations through a validation-guided pruning cycle. The DIGSP is benchmarked against a baseline multi-gene genetic programming (BGP) model using a dataset of steel fiber-reinforced concrete (SFRC) beams. Across 30 independent trials with 65% training, 10% validation, and 25% testing splits, DIGSP consistently outperformed BGP in training and test root mean squared error (RMSE). The Wilcoxon rank-sum test confirmed statistical significance (p < 0.01), and DIGSP showed tighter error distributions and fewer outliers. No significant difference was observed in validation RMSE due to limited sample size. These results demonstrate that domain-informed structural decomposition and symbolic abstraction improve convergence and generalization. DIGSP offers a principled and interpretable modeling strategy for systems where symbolic superposition aligns with the underlying physical structure.
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