Prediction of Mechanical Properties of Bolted Connections in CFST Column–Steel Beam Assemblies Based on Improved Particle Swarm Optimization and Deep Neural Networks

Predicting the mechanical properties of bolted connection nodes in prefabricated Concrete-Filled Steel Tube (CFST) column–steel beam assemblies remains challenging due to complex nonlinear relationships, high degrees of parameter coupling, and limited generalization capabilities of traditional empirical formulas. This study proposes a data-driven prediction model integrating an Improved Particle Swarm Optimization (IPSO) algorithm with a Deep Neural Network (DNN). Drawing upon 196 sets of experimental data on CFST column–steel beam nodes with Extended Hollo-Bolt (EHB) connections from the published literature, the model employs bolt diameter, steel tube wall thickness, concrete compressive strength, beam–column cross-sectional parameters, and connection configuration parameters as input variables, while designating ultimate moment capacity, initial stiffness, and joint ductility coefficient as prediction targets. A multi-layer DNN is constructed to capture the highly nonlinear mapping between structural parameters and mechanical responses. The IPSO algorithm, enhanced with adaptive inertia weight and Lévy flight perturbation, performs global optimization of the network weights and hyperparameters to improve convergence speed and prediction stability. Five-fold cross-validation is embedded within the IPSO fitness evaluation loop to guide hyperparameter selection, while dropout regularization and early stopping are applied during final training to mitigate overfitting; prediction performance is ultimately verified on an independent hold-out test set. Experimental results demonstrate that the proposed IPSO-DNN model outperforms a tuned shallow neural network (SNN), Support Vector Regression (SVR), and Random Forest (RF) models across the coefficient of determination (R2), root mean square error (RMSE), and mean absolute error (MAE), effectively capturing the nonlinear mechanical characteristics of CFST nodes under complex loading conditions.

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Publication Details

Journal
Mathematics
Published
2026-08-03
DOI
https://doi.org/10.3390/math14152764
Primary Topic
Structural Load-Bearing Analysis
Type
article
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article

Prediction of Mechanical Properties of Bolted Connections in CFST Column–Steel Beam Assemblies Based on Improved Particle Swarm Optimization and Deep Neural Networks

Yurong Yao, Liang Zhang
Mathematics
Structural Load-Bearing Analysis
article

Prediction of Mechanical Properties of Bolted Connections in CFST Column–Steel Beam Assemblies Based on Improved Particle Swarm Optimization and Deep Neural Networks

Yurong Yao, Liang Zhang
article en

Abstract

Predicting the mechanical properties of bolted connection nodes in prefabricated Concrete-Filled Steel Tube (CFST) column–steel beam assemblies remains challenging due to complex nonlinear relationships, high degrees of parameter coupling, and limited generalization capabilities of traditional empirical formulas. This study proposes a data-driven prediction model integrating an Improved Particle Swarm Optimization (IPSO) algorithm with a Deep Neural Network (DNN). Drawing upon 196 sets of experimental data on CFST column–steel beam nodes with Extended Hollo-Bolt (EHB) connections from the published literature, the model employs bolt diameter, steel tube wall thickness, concrete compressive strength, beam–column cross-sectional parameters, and connection configuration parameters as input variables, while designating ultimate moment capacity, initial stiffness, and joint ductility coefficient as prediction targets. A multi-layer DNN is constructed to capture the highly nonlinear mapping between structural parameters and mechanical responses. The IPSO algorithm, enhanced with adaptive inertia weight and Lévy flight perturbation, performs global optimization of the network weights and hyperparameters to improve convergence speed and prediction stability. Five-fold cross-validation is embedded within the IPSO fitness evaluation loop to guide hyperparameter selection, while dropout regularization and early stopping are applied during final training to mitigate overfitting; prediction performance is ultimately verified on an independent hold-out test set. Experimental results demonstrate that the proposed IPSO-DNN model outperforms a tuned shallow neural network (SNN), Support Vector Regression (SVR), and Random Forest (RF) models across the coefficient of determination (R2), root mean square error (RMSE), and mean absolute error (MAE), effectively capturing the nonlinear mechanical characteristics of CFST nodes under complex loading conditions.

MathematicsVol. 14(15)
Soochow University (CN)
Openalex Percentile: Top 15%
Structural Load-Bearing Analysis
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