Displacement Prediction Research Articles

Large deformation simulation of uprooting of trees with complex root system architectures using material point method with embedded truss elements

Abstract Background and aims Urban trees in coastal cities like Hong Kong may suffer from an uprooting failure when subjected to extreme winds. A proper numerical model for tree uprooting simulation can help to select tree species or soil types that better resist uprooting failure. However, modeling tree uprooting is challenging as it is a cross-disciplinary problem involving complex root system architectures (RSAs) and large deformation of both roots and soils. This study aims to develop a hybrid numerical model that combines truss elements and material point method (MPM) to simulate the entire large-deformation uprooting process of trees with complex RSAs. Methods The tree uprooting model is developed by coupling truss elements in finite element method (FEM) with MPM. Laboratory pull-out tests using artificial roots and real root cuttings are adopted to validate the developed model. A comparative study is performed to investigate the difference between using complex and simplified RSAs in tree uprooting simulations. Results The developed model provides consistent predictions of peak load, critical displacement and failure mode when compared with results from laboratory tests. Moreover, the comparative study shows that the uprooting resistance obtained with a complex RSA is higher than that with a simplified RSA. The difference varies with the soil and root mechanical properties. Conclusion The developed hybrid model offers a novel way for simulating an entire tree uprooting process involving large deformations and complex RSAs. The study shows that using a simplified RSA to approximate the complex RSA might result in misleading failure modes.

Landslide Displacement Prediction Stacking Deep Learning Algorithms: A Case Study of Shengjibao Landslide in the Three Gorges Reservoir Area of China

Computational models enable accurate, timely prediction of landslides based on the monitoring data on-site as the development of artificial intelligence technology. The most existing prediction methods focus on finding a single prediction algorithm with excellent performance or an integrated and efficient hyperparameter optimization algorithm with a highly accurate regression prediction algorithm. In order to break through the limitation of generalization of prediction models, this paper proposes an ensemble model that combines deep learning algorithms, with a stacking framework optimized with the sliding window method. Multiple deep learning algorithms are set as the first layer of the stacking framework, which is optimized with the sliding window method to avoid confusion in the time order of datasets based on time series analysis. The Shengjibao landslide in the Three Gorges Reservoir is used as a case study. First, the cumulative displacement is decomposed into a trend and a periodic term using a moving average method. A single-factor and a multi-factor superposition model based on multiple deep learning algorithms are used to predict the trend and periodic term of the displacement, respectively. Finally, the predicted values of the trend and periodic terms are added to obtain the total predicted landslide displacement. For monitoring point ZK2-3, the values of RMSE and MAPE of the total displacement prediction with the stacking model are 15.93 mm and 0.54%, and the values of RMSE and MAPE of the best-performing individual deep learning model are 20.00 mm and 0.64%. The results show that the stacking model outperforms other models by combining the advantages of each individual deep learning algorithm. This study provides a framework for integrating landslide displacement prediction models. It can serve as a reference for the geological disaster prediction and the establishment of an early warning system in the Three Gorges Reservoir Area.

Multi-relation spatiotemporal graph residual network model with multi-level feature attention: A novel approach for landslide displacement prediction

Accurate prediction of landslide displacement is crucial for effective early warning of landslide disasters. While most existing prediction methods focus on time-series forecasting for individual monitoring points, there is limited research on the spatiotemporal characteristics of landslide deformation. This paper proposes a novel Multi-Relation Spatiotemporal Graph Residual Network with Multi-Level Feature Attention (MFA-MRSTGRN) that effectively improves the prediction performance of landslide displacement through spatiotemporal fusion. This model integrates internal seepage factors as data feature enhancements with external triggering factors, allowing for accurate capture of the complex spatiotemporal characteristics of landslide displacement and the construction of a multi-source heterogeneous dataset. The MFA-MRSTGRN model incorporates dynamic graph theory and four key modules: multi-level feature attention, temporal-residual decomposition, spatial multi-relational graph convolution, and spatiotemporal fusion prediction. This comprehensive approach enables the efficient analyses of multi-source heterogeneous datasets, facilitating adaptive exploration of the evolving multi-relational, multi-dimensional spatiotemporal complexities in landslides. When applying this model to predict the displacement of the Liangshuijing landslide, we demonstrate that the MFA-MRSTGRN model surpasses traditional models, such as random forest (RF), long short-term memory (LSTM), and spatial temporal graph convolutional networks (ST-GCN) models in terms of various evaluation metrics including mean absolute error (MAE = 1.27 mm), root mean square error (RMSE = 1.49 mm), mean absolute percentage error (MAPE = 0.026), and R-squared (R2 = 0.88). Furthermore, feature ablation experiments indicate that incorporating internal seepage factors improves the predictive performance of landslide displacement models. This research provides an advanced and reliable method for landslide displacement prediction.

GMDIC: a digital image correlation measurement method based on global matching for large deformation displacement fields

The digital image correlation method is a non-contact optical measurement method, which has the advantages of full-field measurement, simple operation, and high measurement accuracy. The traditional DIC method can accurately measure displacement and strain fields, but there are still many limitations. (i) In the measurement of large displacement deformations, the calculation accuracy of the displacement field and strain field needs to be improved due to the unreasonable setting of parameters such as subset size and step size. (ii) It is difficult to avoid under-matching or over-matching when reconstructing smooth displacement or strain fields. (iii) When processing large-scale image data, the computational complexity will be very high, resulting in slow processing speeds. In recent years, deep-learning-based DIC has shown promising capabilities in addressing the aforementioned issues. We propose a new, to the best of our knowledge, DIC method based on deep learning, which is designed for measuring displacement fields of speckle images in complex large deformations. The network combines the multi-head attention Swin-Transformer and the high-efficient channel attention module ECA and adds positional information to the features to enhance feature representation capabilities. To train the model, we constructed a displacement field dataset that conformed to the real situation and contained various types of speckle images and complex deformations. The measurement results indicate that our model achieves consistent displacement prediction accuracy with traditional DIC methods in practical experiments. Moreover, our model outperforms traditional DIC methods in cases of large displacement scenarios.

Displacement prediction of tunnel entrance slope based on LSSVM and bacterial foraging optimization algorithm

In order to realize the effective prediction of landslide risk in the tunnel entrance area, an multivariate time series model is established on the basis of the traditional model, taking temperature and rainfall factors as additional input indicators. Bacterial foraging optimization algorithm (BFOA) is used to search the global optimal solution of the key parameters \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document} and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma^{2}$$\\end{document} of least squares support vector machine (LSSVM) to improve its regression accuracy, and the evolved LSSVM is used to describe the aforementioned multivariate time series model. At the same time, a remote real-time internet of things (IoT) monitoring system for the tunnel entrance section, including monitoring indicators such as surface subsidence, temperature, and rainfall, has also been designed and implemented, providing a stable and accurate data source for the realization of this prediction model. Based on the engineering measurement data, the accuracy of the established model is checked and analyzed, the optimal value of historical data amount is determined to be 5 days, and the optimal value of prediction step is 1 day. The research results are applied in the construction of Wendong tunnel of Molin expressway, Yunnan, China. Practice shows that the prediction results of the multivariate time series model established in this study is accurate. This method can realize the prediction and early warning of slope risk, which provides a effective technical means for risk control of tunnel portal section.

Uncertainty propagation of initial conditions in thermal models

The operation of machine tools often demands a highly accurate knowledge of the tool center point’s (TCP) position. The displacement of the TCP over time can be inferred from coupled thermal models, which comprise a set of geometrically coupled heat equations. Each of these equations represents the temperature in part of the machine, and they are often formulated on complicated geometries. The accuracy of the TCP prediction depends highly on the accuracy of the model parameters, such as heat exchange parameters, and the initial temperature. Thus it is of utmost interest to determine the influence of these parameters on the TCP displacement prediction. In turn, the accuracy of the parameter estimate is essentially determined by the measurement accuracy and the sensor placement. Determining the accuracy of a given sensor configuration is a key prerequisite of optimal sensor placement. In this paper, we develop a thermal model for the discretization of realistic machine tool. On top of this model we propose two numerical algorithms to evaluate any given thermal sensor configuration with respect to its accuracy. We compute the posterior variances from the posterior covariance matrix with respect to an uncertain initial temperature field. The full matrix is dense and potentially very large, depending on the size of the discretized model. We first present a way to compute this approximation, which relies on the computation of the model sensitivities with respect to the initial values. Additionally, we present a low-rank tensor method which exploits the underlying system structure. We compare the efficiency of both algorithms with respect to runtime and memory requirements and discuss their respective advantages with regard to optimal sensor placement problems.

Landslide Displacement Prediction Using Kernel Extreme Learning Machine with Harris Hawk Optimization Based on Variational Mode Decomposition

Displacement deformation prediction is critical for landslide disaster monitoring, as a good landslide displacement prediction system helps reduce property losses and casualties. Landslides in the Three Gorges Reservoir Area (TGRA) are affected by precipitation and fluctuations in reservoir water level, and displacement deformation shows a step-like curve. Landslide displacement in TGRA is related to its geology and is affected by external factors. Hence, this study proposes a novel landslide displacement prediction model based on variational mode decomposition (VMD) and a Harris Hawk optimized kernel extreme learning machine (HHO-KELM). Specifically, VMD decomposes the measured displacement into trend, periodic, and random components. Then, the influencing factors are also decomposed into periodic and random components. The feature data, with periodic and random data, are input into the training set, and the trend, periodic, and random term components are predicted by HHO-KELM, respectively. Finally, the total predicted displacement is calculated by summing the predicted values of the three components. The accuracy and effectiveness of the prediction model are tested on the Shuizhuyuan landslide in the TGRA, with the results demonstrating that the new model provides satisfactory prediction accuracy without complex parameter settings. Therefore, under the premise of VMD effectively decomposing displacement data, combined with the global optimization ability of the HHO heuristic algorithm and the fast-learning ability of KELM, HHO-KELM can be used for displacement prediction of step-like landslides in the TGRA.

Landslide Deformation Analysis and Prediction with a VMD-SA-LSTM Combined Model

The evolution of landslides is influenced by the complex interplay of internal geological factors and external triggering factors, resulting in nonlinear dynamic changes. Although deep learning methods have demonstrated advantages in predicting multivariate landslide displacement, their performance is often constrained by the challenges of extracting intricate features from extended time-series data. To address this challenge, we propose a novel displacement prediction model that integrates Variational Mode Decomposition (VMD), Self-Attention (SA), and Long Short-Term Memory (LSTM) networks. The model first employs VMD to decompose cumulative landslide displacement into trend, periodic, and stochastic components, followed by an assessment of the correlation between these components and the triggering factors using grey relational analysis. Subsequently, the self-attention mechanism is incorporated into the LSTM model to enhance its ability to capture complex dependencies. Finally, each displacement component is fed into the SA-LSTM model for separate predictions, which are then reconstructed to obtain the cumulative displacement prediction. Using the Zhonghai Village tunnel entrance (ZVTE) landslide as a case study, we validated the model with displacement data from GPS point 105 and made predictions for GPS point 104 to evaluate the model’s generalization capability. The results indicated that the RMSE and MAPE for SA-LSTM, LSTM, and TCN-LSTM at GPS point 105 were 0.3251 and 1.6785, 0.6248 and 2.9130, and 1.1777 and 5.5131, respectively. These findings demonstrate that SA-LSTM outperformed the other models in terms of complex feature extraction and accuracy. Furthermore, the RMSE and MAPE at GPS point 104 were 0.4232 and 1.0387, further corroborating the model’s strong extrapolation capability and its effectiveness in landslide monitoring.

Advanced Predictive Structural Health Monitoring in High-Rise Buildings Using Recurrent Neural Networks

This study proposes a machine learning (ML) model to predict the displacement response of high-rise structures under various vertical and lateral loading conditions. The study combined finite element analysis (FEA), parametric modeling, and a multi-objective genetic algorithm to create a robust and diverse dataset of loading scenarios for developing a predictive ML model. The ML model was trained using a recurrent neural network (RNN) with Long Short-Term Memory (LSTM) layers. The developed model demonstrated high accuracy in predicting time series of vertical, lateral (X), and lateral (Y) displacements. The training and testing results showed Mean Squared Errors (MSE) of 0.1796 and 0.0033, respectively, with R2 values of 0.8416 and 0.9939. The model’s predictions differed by only 0.93% from the actual vertical displacement values and by 4.55% and 7.35% for lateral displacements in the Y and X directions, respectively. The results demonstrate the model’s high accuracy and generalization ability, making it a valuable tool for structural health monitoring (SHM) in high-rise buildings. This research highlights the potential of ML to provide real-time displacement predictions under various load conditions, offering practical applications for ensuring the structural integrity and safety of high-rise buildings, particularly in high-risk seismic areas.

Landslide displacement prediction using time series InSAR with combined LSTM and TCN: application to the Xiao Andong landslide, Yunnan Province, China

AbstractResearch on landslide displacement prediction based on interferometric synthetic aperture radar (InSAR) deformation data involves two main issues. First, InSAR can provide only one-dimensional deformation data along the satellite’s line of sight (LOS), which cannot truly reflect the deformation of the landslide body in the downward direction along the slope. Second, the use of a single prediction model does not adequately account for both long-term and local changes in landslide displacement, affecting the accuracy of the predictions. To address this, in this study, Long Short-Term Memory networks (LSTM) and temporal convolutional network (TCN) models are combined to construct a method (LSTM-TCN) of landslide displacement prediction. This method can consider the long-term and localized changes in landslide displacement. The method is first based on InSAR technology to obtain surface deformation. The deformation of the landslide is subsequently computed in the downward direction along the slope to obtain the landslide displacement time series data. Next, the LSTM-TCN is used for landslide displacement prediction. Finally, the mean absolute error (MAE), root mean square error (RMSE) and coefficient of determination (R2) are used to evaluate the performance of the model. The experiment is conducted on the Xiao Andong landslide in Anshi village, Fengqing County, Lincang City, Yunnan Province, China. The LSTM-TCN model achieves an R2 of 0.75, an RMSE of 0.43 cm, and an MAE of 0.36 cm. Compared with the individual LSTM and TCN models, the LSTM-TCN model exhibits the highest prediction accuracy and the smallest prediction error, which is closer to the true result that in the other models. These results demonstrate that the combined LSTM-TCN model effectively captures the complex features and long-term trends in landslide displacement data, significantly enhancing the accuracy of predictions.

Artificial neural network-enhanced mathematical simulation based on Carrera unified formulation for dynamic analysis and structural integrity assessment of advanced nanocomposites reinforced tunnel structures

This article presents the application of the Carrera Unified Formulation (CUF) for dynamic analysis and structural integrity assessment of advanced nanocomposite-reinforced tunnel structures. CUF offers a generalized framework that simplifies the modeling of complex structures, providing an efficient approach to address the dynamic behavior of nanocomposites. Advanced nanocomposites, which enhance mechanical performance and durability, are increasingly used in critical infrastructure such as tunnel systems. Traditional methods often fall short in capturing the intricate interactions within these materials, particularly under dynamic loads. CUF overcomes these challenges by incorporating higher-order theories and multi-scale analysis, allowing for accurate prediction of displacements, stresses, and potential failure modes. To further validate the results, an Artificial Neural Network (ANN) model is trained using simulated data, ensuring robust predictions for various loading conditions. The ANN assists in approximating the dynamic response and integrity of the structure, enabling real-time assessments with minimal computational expense. The combined CUF-ANN approach demonstrates high accuracy and efficiency, making it a reliable tool for the structural integrity assessment of nanocomposite-reinforced tunnels. This study highlights the significant potential of integrating CUF and ANN for the analysis and design of advanced engineering structures subjected to dynamic environmental conditions.

Prediction of topside displacement of offshore platforms based on multi-source data fusion with multilayer perceptron neural network

Prediction of topside displacement of offshore platforms based on multi-source data fusion with multilayer perceptron neural network

Efficient prediction uncertainty quantification in dam behavior monitoring with attention-based sequence-to-sequence learning

Displacement is an intuitive monitoring indicator of dam structural behavior. Conventional deterministic modeling methods frequently disregard the inherent uncertainty associated with monitoring data. This study aims to quantify such uncertainties within dam displacement predictions by augmenting a sequence-to-sequence structure with the novel recurrent unit, termed as tiny gated unit (TGU), attention mechanism, as well as quantile regression, resulting in the Att-S2STQ model. Specifically, TGU adopts only one gate to identify nonlinearity in data sequences, while Bahdanau attention mechanism dynamically assigns weights to different parts of the input sequence. The inclusion of quantile regression allows Att-S2STQ to produce prediction intervals (PIs), from which the probability density functions (PDFs) and cumulative distribution functions (CDFs) are further derived via kernel density estimation. PIs, PDFs, and CDFs jointly serve to reveal the prediction uncertainty. The effectiveness of the model is illustrated through comparative experiments using real-world dam monitoring datasets. Results indicate that the proposed model outperforms traditional methods in point, interval, and probability predictions, while also having a simpler structure and faster training. The superiority of both accuracy and efficiency makes it a valuable tool for dam management, aiding in data-driven decision-making and enhancing operational safety.

Efficient Bayesian updating for deformation prediction of high rock slopes induced by excavation with monitoring data

This study develops an efficient Bayesian updating method with monitoring data for predicting the deformation of high rock slopes induced by excavation. The importance ranking based on random forest is introduced to identify the key rock parameters as random variables in the Bayesian updating. The surrogate models using support vector machine are constructed to approximate the physical numerical models using FLAC3D for evaluating slope deformation. A practical example involving deformation prediction of the excavated left-bank rock slope for the well-known Baihetan hydropower station in southwest China is presented. The results indicate that the developed Bayesian updating method can efficiently and accurately update the posterior distributions of rock parameters and predict the deformation of high rock slopes induced by excavation. Incorporating the monitoring data of displacement into the Bayesian updating can effectively reduce the uncertainty of rock parameters and displacement prediction. As a result, the displacement predictions made by the Bayesian updating are closer to the monitoring data than the prior displacement predictions. In addition, incorporating more monitoring data of displacement from the previous excavation stages produces more accurate displacement predictions for subsequent excavation stages.

Analyzing failure mechanisms and predicting step-like displacement: Rainfall and RWL dynamics in lock-unlock landslides

Lock-unlock landslides have thick sliding zones that store a lot of energy. This makes them start quickly, happen suddenly, and have serious consequences. Therefore, it becomes urgent to study the deformation and failure mechanisms of such landslides and develop rational predictive models. Taking the Jiuxianping landslide as an example, this study investigates the regularity of landslide displacement changes using multi-source data, focusing on the abrupt displacement patterns in the unlock phase. Furthermore, employing Transient Release and Inhalation Method tests combined with Geo-Studio’s SEEP/W and SIGMA/W modules for fluid–solid coupled simulation calculations, the evolution process of landslide failure mechanisms and deformation characteristics is analyzed and discussed. Lastly, utilizing data mining analysis of multi-source data, a hybrid optimized machine learning predictive model is established for model prediction comparison. The study reveals that: (1) The rise in infiltration line elevates pore water pressure, affecting the stability of the sliding zone, leading to “unlock effects” and step-like displacement deformation; (2) Simulation shows that YY208 is closer to the actual situation, located at the far bank position, while YY210 is greatly influenced by the “buoyancy effect”, resulting in a slowdown in deformation velocity; (3) After data preprocessing, overall actual displacement prediction performs better than simulation displacement prediction in terms of Mean Absolute Error, Mean Squared Error and Correlation Coefficient, but noise reduction processing can improve the periodic prediction effect of simulation displacement.

A similarity-aware ensemble method for displacement prediction of concrete dams based on temporal division and fully Bayesian learning

Precisely predicting concrete dam displacements is crucial for assessing their structural behavior during operation. Many studies have testified that ensemble methods are more accurate and applicable in practice than individual predictive models. Nevertheless, the common way handling massive monitoring data is still conventional, that is, training and testing them as a whole, neglecting the internal law and pattern difference within data, which probably limits advancements in predictive effect. To this end, the patterns of monitoring data are identified and classified before model establishment, and a similarity-aware ensemble method (SAEM) using temporal division and fully Bayesian learning is presented for dam displacement prediction. Specifically, the unsupervised fuzzy C-means approach and sparrow search algorithm are fused for similar pattern clustering of environmental factors, thus achieving temporal division in displacement responses. Fully considering the adaptability of model structure and parameters to various data patterns, a non-parametric fully Bayesian Gaussian process regression (FBGPR) model is proposed by augmenting the standard GPR with Markov chain Monte Carlo simulation and Bayesian evidence evaluation theory. Different data clusters are then fed into FBGPR in chronological order, and the final results are derived through a grouping ensemble scheme. Multiple sets of monitoring data collected from a real-world dam project are employed for method verification. The results show that our proposed SAEM has better prediction accuracy compared to homogeneous clustering-based ensemble methods and commonly used individual models. The superior performance in two additional cases also verifies the adaptability and generalization ability of our method, which provides a new modeling tool for structural health monitoring of concrete dams.

Development of a Novel Beam-Based Finite-Element Approach for the Computationally Efficient Prediction of Residual Stresses and Displacements in Large 3D-Printed Polymer Parts

Recently, 3D printing of large, structural polymer parts has received increasing interest, especially for the creation of recyclable structural parts and tooling. However, the complexity of large-scale 3D polymeric printing often dictates resource-intensive trial and error processes to achieve acceptable parts. Existing computational models used to assess the impact of fabrication conditions typically treat the 3D-printed part as a continuum, incorporate oversimplified boundary conditions and take hours to days to run, making design space exploration infeasible. The purpose of this study is to create a structural model that is computationally efficient compared with traditional continuum models yet retains sufficient accuracy to enable exploration of the design space and prediction of part residual stresses and deformations. To this end, a beam-based finite element methodology was created where beads are represented as beams, vertical springs represent inter-bead transverse force transfer and multi-point, linear constraints enforce strain compatibility between adjacent beads. To test this framework, the fabrication of a large Polyethylene terephthalate glycol (PETG) wall was simulated. The PETG was modeled as linearly elastic with an experimentally derived temperature-dependent coefficient of thermal expansion and elastic modulus using temperature history imported from an ABAQUS thermal model. The results of the simulation were compared to those from a continuum model with an identical material definition, showing reasonable agreement of stresses and displacements. Further, the beam-based model required an order of magnitude less run time. Subsequently, the beam-based model was extended to allow separation of the part from the printing bed and the inclusion of part self-weight during fabrication to assess the significance of these effects that pose challenges for existing continuum models.

Machine learning based prediction for maximum base shear, top displacement, and vibration period for SCBF under nonlinear response history analysis

Machine learning based prediction for maximum base shear, top displacement, and vibration period for SCBF under nonlinear response history analysis

Automatic Modeling and Optimization Design Platform for Highway Tunnels with Application to Stress and Displacement Prediction of Surrounding Rocks during Tunnel Excavation

Automatic Modeling and Optimization Design Platform for Highway Tunnels with Application to Stress and Displacement Prediction of Surrounding Rocks during Tunnel Excavation

Back analysis of geomechanical parameters based on a data augmentation algorithm and machine learning technique

Accurate geomechanical parameters are key factors for stability evaluation, disaster forecasting, structural design, and supporting optimization. The intelligent back analysis method based on the monitored information is widely recognized as the most efficient and cost-effective technique for inverting parameters. To address the low accuracy of measured data, and the scarcity of comprehensive datasets, this study proposes an innovative back analysis framework tailored for small sample sizes. We introduce a multi-faceted back analysis approach that combines data augmentation with advanced optimization and machine learning techniques. The auxiliary classifier generative adversarial network (ACGAN)-based data augmentation algorithm is first employed to generate synthetic yet realistic samples that adhere to the underlying probability distribution of the original data, thereby expanding the dataset and mitigating the impact of small sample sizes. Subsequently, we harness the power of optimized particle swarm optimization (OPSO) integrated with support vector machine (SVM) to mine the intricate nonlinear relationships between input and output variables. Then, relying on a case study, the validity of the augmented data and the performance of the developed OPSO-SVM algorithms based on two different sample sizes are studied. Results show that the new datasets generated by ACGAN almost coincide with the actual monitored convergences, exhibiting a correlation coefficient exceeding 0.86. Furthermore, the superiority of the OPSO-SVM algorithm is also demonstrated by comparing the displacement prediction capability of various algorithms through four indices. It is also indicated that the relative error of the predicted displacement values reduces from almost 20% to 5% for the OPSO-SVM model trained with 25 samples and that trained with 625 samples. Finally, the inversed parameters and corresponding convergences predicted by the two OPSO-SVM models trained with different samples are discussed, indicating the feasibility of the combination application of ACGAN and OPSO-SVM in back analysis of geomechanical parameters. This endeavor not only facilitates the progression of underground engineering analysis in scenarios with limited data, but also serves as a pivotal reference for both researchers and practitioners alike.