Sobol Sequence Research Articles

The Impact of the Yeoh Model’s Variability in Contact on Knee Joint Mechanics

The aim of this study was to assess the impact of the variability of the Yeoh model when modeling the contact of bones through cartilage in the knee in compression and flexion–extension within a hybrid knee model. Firstly, a Sobol sequence of 64 samples and four variables representing the Yeoh parameters of the cartilage of the femur and tibia was generated. Based on these samples, 2 × 64 finite element contact models of the geometry of the sphere plane were generated and solved for healthy tissue affected by osteoarthritis. The resulting indentation curves were incorporated into a multibody knee joint model. The obtained results suggested that cartilage variability severely affected the knee in compression by up to 32%. However, the same variability also affected the flexion–extension motion, although to a lesser extent, with a relative change to the range of angular displacements of almost 7%. Osteoarthritic tissue was consistently more affected by this variability, suggesting that when modeling degenerated tissue, complex joint models are necessary.

INVESTIGATION OF GEOMETRIC PARAMETERS ON FLAP AND SLAT AERODYNAMICS IN A THREE-ELEMENT AIRFOIL

Three-element airfoils are commonly employed in airplanes to provide additional lift, reduce runway length requirements, and improve cargo capacity. Due to the small distances between its components and flow interactions, the three-element airfoil has complex flow dynamics. The aerodynamic characteristics of an airfoil system comprising of three elements are greatly influenced by the geometric positioning of the flap and slat. The present study uses the computational techniques to examine how the geometric characteristics affect the aerodynamics of specific pieces, particularly the flap and slat. In this work, computational techniques are used to examine how geometric characteristics, particularly those affecting the flap and slat, affect the aerodynamics of individual components of the multielement airfoil. The chosen design space is generated through the sampling based on the Sobol sequence. The flow physics around each element due to the change in position of individual elements of the three-element airfoil is investigated in detail. Furthermore, it was shown that the leading-edge components greatly influence the flow behavior of the trailing edge components, while the opposite is not significant. Finally, the study reveals that the most significant effect on the aerodynamics characteristics of the three-element airfoil is governed by the gap in the flap.

Research on cross-provincial power trading strategy considering the medium and long-term trading plan

To accommodate China’s electricity market reforms integrating medium and long-term (MLT) transactions and spot transactions, and to boost renewable energy consumption through the spot market, this paper proposes an optimized cross-provincial electricity trading strategy model based on a two-layer game framework. The proposed model incorporates an MLT green certificate contract decomposition method, enabling nested optimization of green certificate contracts and scheduling plans for cross-provincial power transactions. To encourage broader participation, a bilateral green certificate trading framework is established, which globally optimizes green certificate allocation to increase benefits for market participants. A Nash-Stackelberg game model is introduced to address complex game interactions among multiple participants under the green certificate mechanism and the limitation of assuming complete rationality. The game model combines supply and demand sides with an embedded demand-side evolutionary game. Additionally, an improved Aquila optimization algorithm (IAOA) is developed to accurately calculate electricity supply and demand. The algorithm integrates a Circle chaotic map, Sobol sequence, random walk strategy, and filtering technology to enhance optimization capabilities and manage complex constraints. The algorithm is then embedded with a distributed iterative approach to achieve equilibrium strategies. A real-world case study was conducted to validate the feasibility and effectiveness of the proposed model. The results demonstrate that the proposed approach effectively achieves equilibrium, optimizes trading strategies, and fosters win-win, coordinated development among participants in the cross-provincial electricity market.

Data-driven optimization of nose profiles for water entry impact load reduction

The prediction and reduction of impact loads during water entry are critical in various engineering applications, such as ship slamming and seaplane landings. Traditional methods, including theoretical models, computational fluid dynamics (CFD), and experimental approaches, often suffer from limited applicability, lengthy processing times, and high costs. To address these challenges, this study explores the use of Deep Neural Networks (DNNs) for predicting peak impact loads during the oblique water entry of cylinders with different nose profiles. Optimized Latin Hypercube Sampling (OLHS) and Sobol sequences are employed to generate dataset inputs from a 7-dimensional parameter space that governs impact dynamics. These inputs are then fed into OpenFOAM solvers to compute the peak impact accelerations, serving as dataset outputs for training and testing the DNN. Experiments are conducted to validate the numerical method, confirming that the resulting dataset outputs can be considered as ground truth. With Bayesian hyperparameter optimization, the well-trained DNN model demonstrates reliable accuracy in predicting peak axial and normal accelerations. Further, this study integrates the DNN model with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to optimize the nose profiles, resulting in a maximum weighted reduction of 48% in the combined axial and normal accelerations.

A rate of penetration (ROP) prediction method based on improved dung beetle optimization algorithm and BiLSTM-SA

In the field of oil drilling, accurately predicting the Rate of Penetration (ROP) is crucial for improving drilling efficiency and reducing costs. Traditional prediction methods and existing machine learning approaches often lack accuracy and generalization capabilities, leading to suboptimal results in practical applications. This study proposes an end-to-end ROP prediction model based on BiLSTM-SA-IDBO, which integrates Bidirectional Long Short-Term Memory (BiLSTM), a Self-Attention mechanism (SA), and an Improved Dung Beetle Optimization algorithm (IDBO), incorporating the Bingham physical equation.We enhanced the DBO algorithm by using Sobol sequences for population initialization and integrating the Golden Sine algorithm and dynamic subtraction factors to develop a more robust IDBO. This optimized the BiLSTM-SA model, resulting in a BiLSTM-SA-IDBO model with an RMSE of 0.065, an R² of 0.963, and an MAE of 0.05 on the test set. Compared to the original BiLSTM-SA model, these metrics improved by 78%, 21%, and 83%, respectively. Additionally, we compared this model with BP Neural Network, Random Forest, XGBoost, and LSTM models, and found that our proposed model significantly outperformed these traditional models. Finally, through practical testing, the model’s excellent predictive ability and generalization were verified, demonstrating its great potential for practical applications.

Adaptive PSO-SO algorithm with Sobol sequence for aerodynamic physical parameter identification of projectiles

In the domain of aerodynamic physical parameter identification, conventional optimization algorithms are often limited by falling into local optima. To overcome this limitation, a novel adaptive PSO-SO algorithm based on Sobol sequences (SAPSO-SO) algorithm is proposed in this study. The algorithm integrates particle swarm optimization algorithms and snake optimization algorithms, utilizing Sobol sequences for initialization, which enhances the global search and local development ability of the algorithm by adaptively adjusting the inertia weights and learning factors. In addition, this study introduced a local optimal discriminant mechanism and a local search function to further enhance the optimization performance of the algorithms. In this study, the small interval constant method was used to subdivide the trajectory, relying on the three-degree-of-freedom ballistic model to identify the starting ballistic parameters and aerodynamic physical parameters of each small interval. The performances of the snake optimization algorithm, particle swarm optimization algorithm, C-K method, and SAPSO-SO algorithm in the identification of ballistic physical parameters were compared using the full ballistic simulation data of a high-speed rotating projectile as measurement data. The results show that the SAPSO-SO algorithm demonstrates excellent accuracy and effectiveness, especially in noisy simulation data, where its recognition accuracy is improved by 7.79% over the C-K method, highlighting its superior anti-noise performance and global optimization capability. It is comprehensively analyzed that the SAPSO-SO algorithm has strong global optimization potential in theory and shows a high degree of accuracy and stability in practical applications, independent of the selection of initial parameters.

A hybrid method for fault diagnosis of rolling bearings

Abstract Traditional diagnostic methods often have insufficient accuracy and noise reduction, which leads to diagnostic errors. To address these issues, this paper proposes an advanced fault diagnosis model that combines the variational mode decomposition (VMD) improved by a Variable-Objective Search Whale Optimization Algorithm (VSWOA) with a Pelican Optimization (PO)-boosted Kernel Extreme Learning Machine (KELM) algorithm. The application of the method is shown here in the fault diagnosis of rolling bearings. The proposed VSWOA enhances the performance of VMD by incorporating a Sobol sequence, nonlinear time-varying factors, a multi-objective initial search strategy, and an elite Cauchy chaos mutation strategy, significantly improving noise reduction in vibration signals. Fault information is precisely extracted using waveform factors, sample entropy, and advanced composite multiscale fuzzy entropy, which enables effective feature screening and dimensionality reduction. The POA fine-tunes the KELM parameters, increasing the classification accuracy. The effectiveness of the model is verified through experimental evaluations using bearing data with injected Gaussian noise (from Case Western Reserve University) and the SpectraQuest datasets, where significant improvements in noise reduction and fault detection accuracy are achieved.

A General Method for Solving Differential Equations of Motion Using Physics-Informed Neural Networks

The physics-informed neural network (PINN) is an effective alternative method for solving differential equations that do not require grid partitioning, making it easy to implement. In this study, using automatic differentiation techniques, the PINN method is employed to solve differential equations by embedding prior physical information, such as boundary and initial conditions, into the loss function. The differential equation solution is obtained by minimizing the loss function. The PINN method is trained using the Adam algorithm, taking the differential equations of motion in structural dynamics as an example. The time sample set generated by the Sobol sequence is used as the input, while the displacement is considered the output. The initial conditions are incorporated into the loss function as penalty terms using automatic differentiation techniques. The effectiveness of the proposed method is validated through the numerical analysis of a two-degree-of-freedom system, a four-story frame structure, and a cantilever beam. The study also explores the impact of the input samples, the activation functions, the weight coefficients of the loss function, and the width and depth of the neural network on the PINN predictions. The results demonstrate that the PINN method effectively solves the differential equations of motion of damped systems. It is a general approach for solving differential equations of motion.

Energy efficient clustering and routing protocol based on quantum particle swarm optimization and fuzzy logic for wireless sensor networks

Clustering and routing protocols play a pivotal role in reducing energy consumption and extending the lifespan of wireless sensor networks. However, optimizing energy efficiency to maximize network longevity remains a primary challenge for these protocols. This paper introduces QPSOFL, a clustering and routing protocol that integrates quantum particle swarm optimization and a fuzzy logic system to enhance energy efficiency and prolong network lifespan. QPSOFL employs an enhanced quantum particle swarm optimization algorithm to select optimal cluster heads, utilizing Sobol sequences for population diversification during initialization. Additionally, it incorporates Lévy flight and Gaussian perturbation-based position updates to prevent trapping in local optima. Benchmark experiments validate QPSOFL's efficacy compared to Harris Hawks Optimization (HHO), Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and Quantum Particle Swarm Optimization (QPSO), focusing on accuracy, search capability, and convergence speed. Within QPSOFL, a fuzzy logic system determines the best next-hop cluster head based on descriptors such as residual energy, energy deviation, and relay distance. Extensive simulations compare QPSOFL's performance in terms of network lifetime, throughput, energy consumption, and scalability against existing protocols E-FUCA, IHHO-F, F-GWO, and FLPSOC, demonstrating its superior performance over these counterparts.

Prediction of Bonding Strength of Heat-Treated Wood Based on an Improved Harris Hawk Algorithm Optimized BP Neural Network Model (IHHO-BP)

In this study, we proposed an improved Harris Hawks Optimization (IHHO) algorithm based on the Sobol sequence, Whale Optimization Algorithm (WOA), and t-distribution perturbation. The improved IHHO algorithm was then used to optimize the BP neural network, resulting in the IHHO-BP model. This model was employed to predict the bonding strength of heat-treated wood under varying conditions of temperature, time, feed rate, cutting speed, and grit size. To validate the effectiveness and accuracy of the proposed model, it was compared with the original BP neural network model, WOA-BP, and HHO-BP benchmark models. The results showed that the IHHO-BP model reduced the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) by at least 51.16%, 40.38%, and 51.93%, respectively, while increasing the coefficient of determination (R2) by at least 10.85%. This indicates significant model optimization, enhanced generalization capability, and higher prediction accuracy, better meeting practical engineering needs. Predicting the bonding strength of heat-treated wood using this model can reduce production costs and consumption, thereby significantly improving production efficiency.

A global sensitivity analysis method based on IBWO-SVR-SS

PurposeAiming at the inefficiency of solving the Sobol index using the traditional mathematical analytical method, a Sobol global sensitivity analysis method is proposed.Design/methodology/approachIn this paper, a support vector regression (SVR) surrogate model is constructed to solve the Sobol index. The optimal combination of SVR hyperparameters is obtained by using the improved beluga whale optimization (IBWO). Meanwhile, in order to solve the problem that Sobol sequences will form correlation regions in high-dimensional space leading to the uneven distribution of sampling points, a scrambled strategy is introduced in the Sobol sensitivity analysis using IBWO-SVR. Thus, the IBWO-SVR-SS sensitivity analysis model is established.FindingsThe results of two test functions show that the method further improves the accuracy of the sensitivity analysis. Finally, the first-order Sobol index and second-order Sobol index are solved by the IBWO-SVR-SS method using the metro bogie frame as an engineering example. Through the analysis results, the key design parameters of the frame and the design parameter combinations with more obvious coupling relationships are identified, providing a strong reference for the subsequent analysis and structural optimization.Originality/valueSobol sensitivity analysis using the surrogate model method can effectively improve the efficiency of the solution. In addition, IBWO is used for the optimization of the SVR hyperparameters to improve the accuracy and efficiency of the optimization, and finally, the correction of the Sobol sequence through the introduction of the disruption strategy also further improves the accuracy of the sensitivity analysis of Sobol.

Probabilistic optimal power flow computation for power grid including correlated wind sources

AbstractThis paper sets out to develop an efficient probabilistic optimal power flow (POPF) algorithm to assess the influence of wind power on power grid. Given a set of wind data at multiple sites, their marginal distributions are fitted by a newly developed generalized Johnson system, whose parameters are specified by a percentile matching method. The correlation of wind speeds is characterized by a flexible Liouville copula, which allows to model the asymmetric dependence structure. In order to improve the efficiency for solving POPF problem, a lattice sampling method is developed to generate wind samples at multiple sites, and a logistic mixture model is proposed to fit distributions of POPF outputs. Finally, case studies are performed, the generalized Johnson system is compared with Weibull distribution and the original Johnson system for fitting wind samples, Liouville copula is compared against Archimedean copula for modelling correlated wind samples, and lattice sampling method is compared with Sobol sequence and Latin hypercube sampling for solving POPF problem on IEEE 118‐bus system, the results indicate the higher accuracy of the proposed methods for recovering the joint cumulative distribution function of correlated wind samples, as well as the higher efficiency for calculating statistical information of POPF outputs.

Research on Quantification of Structural Natural Frequency Uncertainty and Finite Element Model Updating Based on Gaussian Processes

During bridge service, material degradation and aging occur, affecting bridge functionality. Bridge health monitoring, crucial for detecting structural damage, includes finite element model modification as a key aspect. Current finite element-based model updating techniques are computationally intensive and lack practicality. Additionally, changes in loading and material property deterioration lead to parameter uncertainty in engineering structures. To enhance computational efficiency and accommodate parameter uncertainty, this study proposes a Gaussian process model-based approach for predicting structural natural frequencies and correcting finite element models. Taking a simply supported beam structure as an example, the elastic modulus and mass density of the structure are sampled by the Sobol sequence. Then, we map the collected samples to the corresponding physical space, substitute them into the finite element model, and calculate the first three natural frequencies of the model. A Gaussian surrogate model was established for the natural frequency of the structure. By analyzing the first three natural frequencies of the simply supported beam, the elastic modulus and mass density of the structure are corrected. The error between the corrected values of elastic modulus and mass density and the calculated values of the finite element model is very small. This study demonstrates that Gaussian process models can improve calculation efficiency, fulfilling the dual objectives of predicting structural natural frequencies and adjusting model parameters.

Optimization Design of PSS and SVC Coordination Controller Based on the Neighborhood Rough Set and Improved Whale Optimization Algorithm

Aimed at reducing the redundancy of parameters for the power system stabilizer (PSS) and static var compensator (SVC), this paper proposes a method for coordinated control and optimization based on the neighborhood rough set and improved whale optimization algorithm (NRS-IWOA). The neighborhood rough set (NRS) is first utilized to simplify the redundant parameters of the controller to improve efficiency. Then, the methods of the Sobol sequence initialization population, nonlinear convergence factor, adaptive weight strategy, and random differential mutation strategy are introduced to improve the traditional whale optimization algorithm (WOA) algorithm. Finally, the improved whale optimization algorithm (IWOA) is utilized to optimize the remaining controller parameters. The simulation results show that the optimization parameters were reduced from 12 and 18 to 3 and 4 in the single-machine infinity bus system and dual-machine power system, and the optimization time was reduced by 74.5% and 42.8%, respectively. In addition, the proposed NRS-IWOA method exhibits more significant advantages in optimizing parameters and improving stability than other algorithms.

Improved Snake Optimizer Using Sobol Sequential Nonlinear Factors and Different Learning Strategies and Its Applications

The Snake Optimizer (SO) is an advanced metaheuristic algorithm for solving complicated real-world optimization problems. However, despite its advantages, the SO faces certain challenges, such as susceptibility to local optima and suboptimal convergence performance in cases involving discretized, high-dimensional, and multi-constraint problems. To address these problems, this paper presents an improved version of the SO, known as the Snake Optimizer using Sobol sequential nonlinear factors and different learning strategies (SNDSO). Firstly, using Sobol sequences to generate better distributed initial populations helps to locate the global optimum solution faster. Secondly, the use of nonlinear factors based on the inverse tangent function to control the exploration and exploitation phases effectively improves the exploitation capability of the algorithm. Finally, introducing learning strategies improves the population diversity and reduces the probability of the algorithm falling into the local optimum trap. The effectiveness of the proposed SNDSO in solving discretized, high-dimensional, and multi-constraint problems is validated through a series of experiments. The performance of the SNDSO in tackling high-dimensional numerical optimization problems is first confirmed by using the Congress on Evolutionary Computation (CEC) 2015 and CEC2017 test sets. Then, twelve feature selection problems are used to evaluate the effectiveness of the SNDSO in discretized scenarios. Finally, five real-world technical multi-constraint optimization problems are employed to evaluate the performance of the SNDSO in high-dimensional and multi-constraint domains. The experiments show that the SNDSO effectively overcomes the challenges of discretization, high dimensionality, and multi-constraint problems and outperforms superior algorithms.

Study on driving safety of vehicle-bridge interaction system based on ultra-high-dimensional point-selected extremum methods

ABSTRACT The driving safety indexes involve the geometric nonlinear contact relationship of the wheel and rail and the high-frequency vibration of the wheel-set. The calculation of their probability characteristic parameters requires very precise selection of random excitation samples. Track irregularity is an essential external excitation force in the vehicle-bridge interaction system (VBIS). Besides, many random phase angles must be considered when using the harmonic superposition method to simulate VBIS, leading to the ultra-high-dimensional random variables problem. Thus, this paper proposes a square power point method and a pseudo-random sequence (Sobol sequence) based on a number theoretic approach to model ultra-high dimensional random variables accurately. This strategy reduces the deviation between the representative track irregularity samples (TIS) and can be applied to fields of strongly nonlinear and high-frequency vibration. Then, by increasing the number of representative TIS, the deviation between response samples caused by non-linear factors can be significantly reduced. Finally, this paper proposes a threshold method for driving safety indexes that determines the service life of bridges, which can quickly obtain the threshold of its extreme value distribution through the cumulative distribution function, and establish the relationship between the threshold and the number of trains travelled. The above theories are verified by calculation examples, and some engineering suggestions are obtained.

Enhanced Wild Horse Optimizer with Cauchy Mutation and Dynamic Random Search for Hyperspectral Image Band Selection

The high dimensionality of hyperspectral images (HSIs) brings significant redundancy to data processing. Band selection (BS) is one of the most commonly used dimensionality reduction (DR) techniques, which eliminates redundant information between bands while retaining a subset of bands with a high information content and low noise. The wild horse optimizer (WHO) is a novel metaheuristic algorithm widely used for its efficient search performance, yet it tends to become trapped in local optima during later iterations. To address these issues, an enhanced wild horse optimizer (IBSWHO) is proposed for HSI band selection in this paper. IBSWHO utilizes Sobol sequences to initialize the population, thereby increasing population diversity. It incorporates Cauchy mutation to perturb the population with a certain probability, enhancing the global search capability and avoiding local optima. Additionally, dynamic random search techniques are introduced to improve the algorithm search efficiency and expand the search space. The convergence of IBSWHO is verified on commonly used nonlinear test functions and compared with state-of-the-art optimization algorithms. Finally, experiments on three classic HSI datasets are conducted for HSI classification. The experimental results demonstrate that the band subset selected by IBSWHO achieves the best classification accuracy compared to conventional and state-of-the-art band selection methods, confirming the superiority of the proposed BS method.

Cross and local optimal avoidance of RIME algorithm: A segmentation study for COVID-19 X-ray images

Image segmentation is a crucial technique in analyzing X-ray medical images as it aids in uncovering relevant information concealed within a patient's body, a pivotal aspect of the diagnostic process. The effectiveness of computer-aided diagnosis systems largely depends on the accuracy of the image processing methods. In recent years, multi-threshold image segmentation methods have found widespread application in medical image analysis. Despite the effectiveness of some renowned methods for binary threshold segmentation, the field still faces challenges due to the high cost of threshold computation. Metaheuristic algorithms hold the potential to address this issue as they can produce sufficiently reasonable solutions with manageable computational overheads. While some similar methods have been proposed, the imbalance between exploration and exploitation results in instability as the number of thresholds increases. Consequently, these solutions suffer from reduced efficiency in computing thresholds. In this study, a variant of the latest RIME algorithm, termed SLCRIME, is proposed. This paper replaces the pseudo-random method with low-discrepancy Sobol sequences for solution initialization. Additionally, two methods aimed at avoiding local optima and promoting information exchange within the solution set are introduced, further enhancing its capability to search for optimal threshold sets for IS systems. Subsequently, a multi-threshold image segmentation model based on SLCRIME is proposed and applied to segment 6 COVID-19 X-ray images. In the experiments, SLCRIME is compared with 6 peer algorithms, and the results are evaluated using image segmentation accuracy, feature similarity index metrics (FSIM), peak signal-to-noise ratio (PSNR), and structural similarity index metrics (SSIM). The analysis indicates that SLCRIME achieves optimal thresholds at reasonable computational costs and outperforms other algorithms in terms of performance.

Enhancing population diversity based gaining-sharing knowledge based algorithm for global optimization and engineering design problems

Gaining-sharing knowledge based algorithm (GSK) is a recently emerged meta-heuristic algorithm based on human behavior and has been successfully applied to solve various optimization problems. However, GSK tends to get trapped in local optimum due to the rapid loss of population diversity during the optimization process, resulting in an imbalance between exploration and exploitation. To overcome this deficiency, this paper proposes an enhancing population diversity based GSK (EPD-GSK) framework. The proposed EPD-GSK framework incorporates three components: (1) The utilization of Sobol sequence with low divergence to initialize the population, enhancing the diversity of initial solutions. (2) The integration of the Cauchy mutation strategy in the junior phase to perturb individuals and expand the search space. (3) The application of the reverse learning update mechanism in the senior phase, increasing the likelihood of escaping local optimum. These techniques promote population diversity throughout the exploration and exploitation stages. The proposed EPD-GSK framework was evaluated on CEC2017, CEC2020, and the latest CEC2022 test suites as well as on four constrained real-world engineering design problems. The experimental results demonstrate that EPD-GSK can effectively improve the performance of various existing GSK algorithms. Furthermore, EPD-GSK also exhibits better performance compared with other state-of-the-art algorithms.

A Novel Inversion Method for Permeability Coefficients of Concrete Face Rockfill Dam Based on Sobol-IDBO-SVR Fusion Surrogate Model

The accurate and efficient inversion of permeability coefficients is significant for the scientific assessment of seepage safety in concrete face rockfill dams. In addressing the optimization challenge of permeability coefficients with few samples, multiple parameters, and strong nonlinearity, this paper proposes a novel intelligent inversion method based on the Sobol-IDBO-SVR fusion surrogate model. Firstly, the Sobol sequence sampling method is introduced to extract high-quality combined samples of permeability coefficients, and the equivalent continuum seepage model is utilized for the forward simulation to obtain the theoretical hydraulic heads at the seepage monitoring points. Subsequently, the support vector regression surrogate model is used to establish the complex mapping relationship between the permeability coefficients and hydraulic heads, and the convergence performance of the dung beetle optimization algorithm is effectively enhanced by fusing multiple strategies. On this basis, we successfully achieve the precise inversion of permeability coefficients driven by multi-intelligence technologies. The engineering application results show that the permeability coefficients determined based on the inversion of the Sobol-IDBO-SVR model can reasonably reflect the seepage characteristics of the concrete face rockfill dam. The maximum relative error between the measured and the inversion values of the hydraulic heads at each monitoring point is only 0.63%, indicating that the inversion accuracy meets the engineering requirements. The method proposed in this study may also provide a beneficial reference for similar parameter inversion problems in engineering projects such as bridges, embankments, and pumping stations.