Khatti Jitendra, Khanmohammadi Mohammadreza, Fissha Yewuhalashet
Department of Civil Engineering, Rajasthan Technical University, Kota, Rajasthan, 324010, India.
Department of Civil Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran.
Sci Rep. 2024 Dec 30;14(1):32047. doi: 10.1038/s41598-024-83784-8.
The present investigation employs relevance vector machine (RVM) and long short-term memory (LSTM) models to predict the time-dependent bearing capacity of concrete piles. Each RVM model (SRVM) is configured by each linear, polynomial, gaussian, sigmoid, laplacian, and exponential kernel function. Each SRVM model has been optimized by each genetic (GA_SRVM) and particle swarm optimization (PSO_RVM) algorithm. Moreover, the double kernel-based RVM models (DRVM) have been employed and optimized by each GA (GA_DRVM) and PSO (PSO_DRVM) algorithm. Thus, an extensive comparison among 33 RVM (6SRVM + 6GA_RVM + 6PSO_RVM + 5DRVM + 5GA_DRVM + 5PSO_DRVM) has been carried out. Conversely, the Adam, root mean squared propagation and stochastic gradient descent with momentum algorithms have optimized the LSTM model. Each optimized RVM and LSTM model has been trained and tested by 100 and 26 datasets. In addition, the effect of structural and database multicollinearities has been analyzed on models' prediction capabilities. The performance index (PI), the variance accounted for (VAF), performance (R), mean absolute error (MAE), normalized mean bias error (NMBE), and root mean square error (RMSE) matrices have analyzed the prediction capabilities of each model. The comparison of 33 RVM and 3 LSTM models reveals that the genetic algorithm-optimized Gaussian kernel function-based SRVM model, i.e., UBC7, has been recognized as the optimal performance model with the RMSE = 146.3962 kPa, PI = 1.85, VAF = 94.60, NMBE = 30.1379 kPa, MAE = 105.7009 kPa, and R = 0.9727, close to the ideal values. Furthermore, the score (= 56), Wilcoxon (= 94.95% confidence), uncertainty (= 1 rank), generalizability (= close to ideal values), and Anderson Darling (= 9.435 ≈ 9.336) tests confirm the superiority of model UBC7. Still, structural and database multicollinearity has drastically impacted dual kernel-based RVM and stochastic gradient descent optimized LSTM models.
本研究采用相关向量机（RVM）和长短期记忆（LSTM）模型来预测混凝土桩随时间变化的承载能力。每个RVM模型（SRVM）由线性、多项式、高斯、Sigmoid、拉普拉斯和指数核函数配置而成。每个SRVM模型都通过遗传算法（GA_SRVM）和粒子群优化算法（PSO_RVM）进行了优化。此外，基于双核的RVM模型（DRVM）也已被采用，并通过遗传算法（GA_DRVM）和粒子群优化算法（PSO_DRVM）进行了优化。因此，对33个RVM模型（6个SRVM + 6个GA_RVM + 6个PSO_RVM + 5个DRVM + 5个GA_DRVM + 5个PSO_DRVM）进行了广泛比较。相反，Adam、均方根传播算法和带动量的随机梯度下降算法对LSTM模型进行了优化。每个优化后的RVM和LSTM模型都用100个和26个数据集进行了训练和测试。此外，还分析了结构和数据库多重共线性对模型预测能力的影响。性能指标（PI）、方差贡献率（VAF）、性能（R）、平均绝对误差（MAE）、归一化平均偏差误差（NMBE）和均方根误差（RMSE）矩阵分析了每个模型的预测能力。33个RVM模型和3个LSTM模型的比较表明，基于遗传算法优化的高斯核函数的SRVM模型，即UBC7，被认为是性能最优的模型，其RMSE = 146.3962 kPa，PI = 1.85，VAF = 94.60，NMBE = 30.1379 kPa，MAE = 105.7009 kPa，R = 0.9727，接近理想值。此外，得分（= 56）、威尔科克森检验（= 94.95%置信度）、不确定性（= 1级）、泛化能力（= 接近理想值）和安德森-达林检验（= 9.435 ≈ 9.336）证实了模型UBC7的优越性。不过，结构和数据库多重共线性对基于双核的RVM模型和随机梯度下降优化的LSTM模型产生了巨大影响。
