Published in the journal AI in Civil Engineering, the study introduces a Particle Swarm Optimization-Back Propagation Neural Network-Random Forest (PSO-BPNN-RF) inversion model. This approach addresses a persistent challenge in geotechnical engineering: determining reliable model parameters for explicit settlement calculations. By integrating intelligent optimization with an enhanced ensemble learning strategy, the team demonstrated superior accuracy in predicting soil deformation under cyclic dynamic loads, specifically applied to the taxiway of Xiaoshan International Airport in Hangzhou.
The central problem addressed by the study is the difficulty in forecasting long-term foundation settlement, which is critical for the safety and durability of urban transportation networks. While explicit models for settlement calculation have advanced to handle general three-dimensional stress states, a major practical hurdle remains the determination of reliable model parameters. Conventional inversion techniques often fall short in accuracy, and while ensemble learning methods can improve data precision by synthesizing predictions from multiple intelligent models, commonly used soft voting strategies tend to overlook systemic bias across base models and the distinct contribution of each predictor. The proposed PSO-BPNN-RF model incorporates a refined soft voting method to address these limitations, enabling high-precision parameter identification when coupled with a three-dimensional explicit settlement calculation framework.
The study builds upon existing research strands in long-term foundation settlement, which largely follow two parallel paths: constitutive models and empirical models. Constitutive models, grounded in soil mechanics principles, aim to characterize the stress–strain behavior of soils under dynamic loading but often become computationally prohibitive for long-term, cyclic loading scenarios. Conversely, empirical models offer simplified, data-driven formulations that balance accuracy and computational efficiency but frequently fail to fully capture the true three-dimensional stress states induced by real-world traffic patterns. The current work adopts and extends an explicit model-based finite element analysis framework, following the methodology introduced by Sun in 2023, to bridge these gaps by providing a mechanistic basis for settlement prediction while maintaining computational feasibility.
The explicit cyclic model used in the study formulates a functional relationship between the number of cyclic loads and strain, simplifying the computation of soil deformation under cyclic dynamic loads. This model defines accumulated axial plastic strain as a function of dynamic deviatoric stress, mean principal stress, and the number of loading cycles. To verify the validity of the method, the researchers performed a numerical validation using a soil element model with dimensions of 40 mm by 40 mm by 40 mm. The simulation captured the deformation behavior of soil under various confining pressures and dynamic stresses. The results showed that the long-term settlement calculation method yielded predictions in good agreement with the explicit model proposed by Huang and Yao in 2011, with differences within approximately 5% to 10%, indicating high numerical accuracy in capturing cyclic cumulative deformation characteristics.
To enhance the parameter inversion process, the study introduces an improved soft voting method for ensemble methods. Traditional soft voting aggregates predictions from multiple models through a weighted average, but it has recognizable limitations. If all base models share a systematic bias for certain inputs, the weighted average perpetuates this error regardless of weight assignment. Furthermore, traditional methods apply a single, static weight to each model’s entire output, lacking the granularity to adjust influence on a per-prediction basis. The proposed modification refines weighting at the level of individual prediction points and incorporates explicit bias correction terms. This dual adjustment allows the ensemble to be locally sensitive and globally calibrated, effectively mitigating the inherent biases of individual base learners and capturing localized data features more effectively.
The selection of base models for the ensemble was pivotal, with Back-Propagation Neural Networks (BPNN) and Random Forests (RF) chosen for their complementary strengths. BPNN excels at capturing complex nonlinear relationships and can adapt its parameters to learn intricate data patterns, though its performance is sensitive to data scaling and can be unstable. In contrast, RF offers remarkable stability, requiring no feature normalization and making no assumptions about data distribution, which makes it robust to noise and missing values. To optimize the parameters of the improved soft voting scheme, the researchers employed the Particle Swarm Optimization (PSO) algorithm. As a gradient-free, metaheuristic global optimizer, PSO is particularly suited for navigating complex, non-convex search spaces where derivative information is unavailable or unreliable, allowing for the optimal calibration of contribution weights within the ensemble.
The practical application of this framework was tested on the new taxiway project at Xiaoshan International Airport in Hangzhou, China. The taxiway has a length of 1,104.5 m and a width of 75 m, with its lower section crossing underneath Metro Lines 1, 7, and 19. The underlying foundation soil consists primarily of sandy silt, silty soil, and muddy silty clay. A three-dimensional finite element model was established in ABAQUS to simulate the settlement of the foundation under combined aircraft and metro loads. The Boeing 777-300ER was selected as the representative aircraft, and the finite element mesh was locally refined according to the wheelbase and axle spacing characteristics of the aircraft’s main landing gear. The model utilized C3D8 elements and comprised a total of 70,110 elements, with boundary conditions constraining horizontal displacements on all vertical sides.
Initial static stress fields were established using the pre-embedding method, which is generally preferred in problems involving tunnels as it exerts a smaller influence on subsequent settlement calculations. Regarding the initial dynamic stress field, the study adopted the pseudo-static approach recommended by Ma in 2014 for estimating additional dynamic stresses induced by traffic loads. For metro-induced stress response, an empirical formulation was used with a speed of 80 km/h and an axle load of 20 t. For aircraft loads, the load exerted by the main landing gear was simplified as a uniformly distributed strip load, resulting in a uniformly distributed load of 334.4 kPa. Cyclic load repetitions were set at 80,000 cycles per year for metro operations and 17,000 cycles per year for aircraft loads, based on airport takeoff/landing frequencies and taxiway design data.
Multiple surface settlement sensors were installed on-site to monitor settlement variations during the operation of the airport. In the area where the taxiway intersects with Metro Line 1, three intelligent settlement sensors, designated as C1-1, C1-2, and C1-3, were installed to measure the taxiway surface settlement. The one-year monitoring data from these points were processed using the Savitzky-Golay method for noise reduction. A comparison between the one-year finite element method-simulated settlement curves and the observed settlement curves revealed significant discrepancies in settlement values, highlighting the necessity of performing parameter inversion for the explicit model to obtain results that align more closely with actual measurements. Based on this comparison, point C1-2 was selected as the critical location for parameter inversion due to its consistently largest settlement value.
A sensitivity analysis was conducted to streamline the inversion process and enhance computational efficiency. The parameters a, m, and b for sandy silt and silty soil exhibited markedly higher sensitivity compared to other parameters, suggesting that the cumulative axial strain parameters dominate the response. Within the considered variation range, parameter m displayed a negative correlation with calculated settlement, while parameters a and b were positively correlated. Given that the initially computed settlement at monitoring point C1-2 was underestimated, the inversion parameter ranges were adjusted accordingly. Using Latin Hypercube Sampling, a total of 220 sample sets were generated within the defined 6-dimensional parameter space, comprising 200 for training and 20 for independent testing. The PSO-BPNN-RF inversion framework was then applied to train on the 200 sample training sets, with a tenfold cross-validation strategy adopted to enhance generalization and avoid overfitting.
The comparative analysis of inversion prediction results on the test sets showed that the PSO-BPNN-RF model achieved an average relative error of 3.96%, compared to 6.98% for the single BPNN model and 5.46% for the single RF model. This indicates the superior generalization capability of the PSO-BPNN-RF ensemble. The training time for each model was under 30 minutes, and the time required to output predictions for single test samples was on the order of milliseconds, indicating that once trained, the corresponding inversion parameters can be obtained immediately from on-site monitoring data. The inverted parameters obtained from the PSO-BPNN-RF model were substituted into the explicit model, and the calculated settlement curves were compared with the monitoring curves for points C1-1, C1-2, and C1-3. The results demonstrated that the computed values of the PSO-BPNN-RF inversion model align more closely with the monitoring data than the other models.
The study concludes that the proposed integrated framework successfully inverted key soil parameters using settlement time-series data, validating the practical applicability of the explicit model for analyzing settlement under cyclic dynamic loads in three-dimensional space. The refinement of the soft voting method to account for the individual contributions of predictions while mitigating biases in base model outputs significantly improved parameter inversion accuracy. However, limitations remain in the research, and future studies could incorporate a broader range of base models, such as gradient boosting machines, support vector machines, or deep neural networks.
Subject of Research: Development of an intelligent optimization framework for geotechnical settlement prediction
Article Title: Evaluating long-term settlements under complex traffic loads via explicit cyclic model augmented by intelligent optimization
Article References: Guo, S., Zhang, J., Shi, Z., Li, Y., Li, J., & Qian, J. (2026). Evaluating long-term settlements under complex traffic loads via explicit cyclic model augmented by intelligent optimization. AI in Civil Engineering, 5(1), Article 1. https://doi.org/10.1007/s43503-025-00083-5
Image Credits: AI Generated
DOI: 10.1007/s43503-025-00083-5
Keywords: geotechnical engineering, settlement prediction, ensemble learning, particle swarm optimization, civil infrastructure, finite element analysis, traffic loads, parameter inversion, Evaluating, long-term, settlements, under
News Source: Denise Maddox. (November 8, 2026). AI Ensemble Model Refines Airport Settlement Predictions. Scienmag.
