Relative Root Mean Square Error Research Articles

A novel Bayesian updating finite element model using enhanced unscented Kalman filter for time-dependent estimation of rockfill dam structure deformation

Due to the time-dependent effect of rockfill dams, the conventional time-invariant finite element method (FEM) can hardly meet practical engineering requirements. This paper proposes an updating Bayesian FEM method for accurate long-term deformation analysis. A combined FEM model is introduced accounting for both instantaneous and creep behaviors. The FEM model is then updated using a Bayesian algorithm, unscented Kalman filter (UKF). The UKF calibrates the prior FEM predictions by incorporating real-time measurement data, thus iteratively reducing discrepancies between model predictions and actual observations. To further enhance the algorithm accuracy, a power-law-based fading memory factor is proposed to mitigate measurement noise in standard UKF. For parameter identification, a slice approach of the high-dimensional covariance confidence ellipsoid is developed. The methodology is validated in Qingyuan rockfill dam, in Guangdong province, China. Results show that the updated FEM is more consistent with the actual monitoring data. The fading memory improves standard UKF performance with a lower relative root-mean-square error (RRMSE). Additionally, the slice method reveals that a specific three-parameter configuration behaves better than the others. The proposed approach can also be extended to other fields including slope and tunneling.

Hybrid modeling approaches for agricultural commodity prices using CEEMDAN and time delay neural networks

Improving the forecasting accuracy of agricultural commodity prices is critical for many stakeholders namely, farmers, traders, exporters, governments, and all other partners in the price channel, to evade risks and enable appropriate policy interventions. However, the traditional mono-scale smoothing techniques often fail to capture the non-stationary and non-linear features due to their multifarious structure. This study has proposed a CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise)-TDNN (Time Delay Neural Network) model for forecasting non-linear, non-stationary agricultural price series. This study has evaluated its suitability in comparison with the other three major EMD (Empirical Mode Decomposition) variants (EMD, Ensemble EMD and Complementary Ensemble EMD) and the benchmark (Autoregressive Integrated Moving Average, Non-linear Support Vector Regression, Gradient Boosting Machine, Random Forest and TDNN) models using monthly wholesale prices of major oilseed crops in India. Outcomes from this investigation reflect that the CEEMDAN-TDNN hybrid models have outperformed all other forecasting models on the basis of evaluation metrics under consideration. For the proposed model, an average improvement of RMSE (Root Mean Square Error), Relative RMSE and MAPE (Mean Absolute Percentage Error) values has been observed to be 20.04%, 19.94% and 27.80%, respectively over the other EMD variant-based counterparts and 57.66%, 48.37% and 62.37%, respectively over the other benchmark stochastic and machine learning models. The CEEMD-TDNN and CEEMDAN-TDNN models have demonstrated superior performance in predicting the directional changes of monthly price series compared to other models. Additionally, the accuracy of forecasts generated by all models has been assessed using the Diebold-Mariano test, the Friedman test, and the Taylor diagram. The results confirm that the proposed hybrid model has outperformed the alternative models, providing a distinct advantage.

Accuracy and robustness of a plant-level cabbage yield prediction system generated by assimilating UAV-based remote sensing data into a crop simulation model

AbstractIn-season crop growth and yield prediction at high spatial resolution are essential for informing decision-making for precise crop management, logistics and market planning in horticultural crop production. This research aimed to establish a plant-level cabbage yield prediction system by assimilating the leaf area index (LAI) estimated from UAV imagery and a segmentation model into a crop simulation model, the WOrld FOod STudies (WOFOST). The data assimilation approach was applied for one cultivar in five fields and for another cultivar in three fields to assess the yield prediction accuracy and robustness. The results showed that the root mean square error (RMSE) in the prediction of cabbage yield ranged from 1,314 to 2,532 kg ha–1 (15.8–30.9% of the relative RMSE). Parameter optimisation via data assimilation revealed that the reduction factor in the gross assimilation rate was consistently attributed to a primary yield-limiting factor. This research further explored the effect of reducing the number of LAI observations on the data assimilation performance. The RMSE of yield was only 107 kg ha–1 higher in the four LAI observations obtained from the early to mid-growing season than for the nine LAI observations over the entire growing season for cultivar ‘TCA 422’. These results highlighted the great possibility of assimilating UAV-derived LAI data into crop simulation models for plant-level cabbage yield prediction even with LAI observations only in the early and mid-growing seasons.

Improving airborne laser scanning-based species-specific forest volume estimation using sentinel-2 time series

ABSTRACT Species-specific timber volume estimates are required to support forest planning and conservation. We evaluated whether additional predictors from a Sentinel-2 time series can improve airborne laser scanning (ALS)-based estimation of species-specific timber volumes. Furthermore, we determined the satellite image dates that provided the greatest improvement in accuracy. The Sentinel-2 time series was constructed to cover 1 March–30 November time-period, with a focus on late spring and early summer. The estimation was done using the k Most Similar Neighbor method and predictors extracted from the ALS data and Sentinel-2 images. Our best model included both ALS and Sentinel-2 time-series predictors, and the relative root mean square error (RMSE) values for pine, spruce and deciduous timber volumes were 40.8%, 57.0% and 51.3%, respectively (mean 49.7%). All deciduous trees were treated as one species. When bands from an individual image were used instead of the time series, the best result was obtained with an image from September where the respective relative RMSE values were 42.2% (deciduous), 58.4% (pine) and 60.6% (spruce) with a mean value of 53.7%. A fusion of a Sentinel-2 time-series and ALS data can improve species-specific estimation results compared to the use of individual Sentinel-2 images or ALS only.

Regional frequency analysis of extreme wind in Pakistan using robust estimation methods

The quantile estimates of extreme wind speed are needed for various areas of interest using regional frequency analysis (RFA) and extreme value theory. These calculations are crucial for the coding of wind speed. The data was taken from the NASA official website at a 10-meter distance and measured in meters per second (m/s). RFA of annual maximum wind speed (AMWS) using L-moments is performed utilizing annual maximum wind speed data from sixteen sites (16) in Pakistan’s Khyber Pakhtunkhwa province. There are no sites that are found to be discordant. The wards method is used to construct a homogenous region and make two homogenous regions from 16 sites. The heterogeneity test justifies that both clusters are homogeneous. The most appropriate probability distribution from the Generalized Normal (GNO), Generalized Logistic (GLO), Pearson Type-3 (P3), Generalized Pareto (GPA), and Generalized Extreme Value (GEV) distributions is chosen to calculate regional quantiles. According to the L-moments diagram and Z statistics, the GEV for Cluster- Ι and GLO for Cluster- ΙΙ are the best suggestions from the others. Both clusters’ robustness is measured utilizing relative bias (RB) and relative root mean square error (RRMSE). Overall, GEV distribution is fit for cluster-Ι, and the GLO distribution is fit for cluster-ΙΙ. Utilizing the site mean and median as index parameters, we can also find at-site quantiles from regional quantiles. The study’s quantile estimates can be employed in codified structural designs with policy consequences.

A novel hybrid model for predicting the bearing capacity of piles

Due to the uncertainty of soil condition and pile design characteristics, it is always a challenge for geotechnical engineers to accurately determine the bearing capacity of piles. The main objective of this study is to propose a hybrid model coupling least squares support vector machine (LSSVM) with an improved particle swarm optimization (IPSO) algorithm for the prediction of bearing capacity of piles. The improved PSO algorithm was used to optimize the LSSVM hyperparameters. The performance of the IPSO-LSSVM model was compared with seven artificial intelligence models, namely adaptive neuro-fuzzy inference system (ANFIS), M5 model tree (M5MT), multivariate adaptive regression splines (MARS), gene expression programming (GEP), random forest (RF), regression tree (RT) and a stacked ensemble model. Six statistical indices (e.g., coefficient of determination (R2), mean absolute error (MAE), root mean squared error (RMSE), relative root mean squared error (RRMSE), BIAS and discrepancy ratio (DR)) were used to evaluate the performance of the models. The R2, MAE, RMSE, RRMSE and BIAS values of the IPSO-LSSVM model were 1, 4.27 kN, 6.164 kN, 0.005 and 0, respectively, for the training datasets and 0.9977, 22 kN, 36.03 kN, 0.0275 and –11, respectively, for the testing datasets. Compared with the ANFIS, MARS, GEP, M5MT, RF, RT and the stacked ensemble models, the proposed IPSO-LSSVM model shows high accuracy and robustness on the test datasets. In addition, the sensitivity, uncertainty, reliability and resilience of the IPSO-LSSVM model were also analyzed in this study. First published online 22 October 2024

Dynamical Embedding of Single-Channel Electroencephalogram for Artifact Subspace Reconstruction.

This study introduces a novel framework to apply the artifact subspace reconstruction (ASR) algorithm on single-channel electroencephalogram (EEG) data. ASR is known for its ability to remove artifacts like eye-blinks and movement but traditionally relies on multiple channels. Embedded ASR (E-ASR) addresses this by incorporating a dynamical embedding approach. In this method, an embedded matrix is created from single-channel EEG data using delay vectors, followed by ASR application and reconstruction of the cleaned signal. Data from four subjects with eyes open were collected using Fp1 and Fp2 electrodes via the CameraEEG android app. The E-ASR algorithm was evaluated using metrics like relative root mean square error (RRMSE), correlation coefficient (CC), and average power ratio. The number of eye-blinks with and without the E-ASR approach was also estimated. E-ASR achieved an RRMSE of 43.87% and had a CC of 0.91 on semi-simulated data and effectively reduced artifacts in real EEG data, with eye-blink counts validated against ground truth video data. This framework shows potential for smartphone-based EEG applications in natural environments with minimal electrodes.

A Virtual Reality Tool for Accuracy Assessment of 3D Models in an Immersive Virtual Environment

Abstract. Accurate validation and assessment techniques are essential for ensuring the reliability of spatial reconstructions derived from photogrammetry, enabling well-informed decision-making across diverse domains. This study presents a Virtual Reality (VR) based accuracy assessment tool tailored for evaluating the accuracy and quality of 3D models generated by Unmanned Aerial Vehicles (UAVs). Leveraging the Unity game engine platform, our workflow entails three key steps: aligning real-world coordinates with an arbitrary Unity coordinate system, transforming the positions of Ground Control Points (GCPs) from field survey to the arbitrary system using a reference GCP, and marking observed points on the 3D models. Absolute and Relative Root Mean Square Errors (RMSE), Mean Errors (ME), and Standard Deviation of errors (SD) are computed within the virtual environment via the game object transform properties. The error distributions around each GCP are visually depicted using Unity game engine components for enhanced interaction and comprehension. The efficacy of the tool is validated through experimentation on four 3D models generated from varying camera angles during UAV data capture. The tool provides the opportunity to directly interact with the 3D models and visualize the errors, which is quite distinct from traditional methods. Using the developed tool, results were obtained to indicate that configurations employing camera angles of 60° + 75º exhibit notable performance in terms of relative and absolute accuracy.

DMATCH: A novel integrated testing method for floating wind turbine dynamics – Potential error and its impact

With floating offshore wind turbines (FOWT) steadily advancing towards large-scale deployments in deep water, the traditional wave basin model testing method shows its shortage to fulfill the testing requirement. To enhance the effectiveness of model tests for FOWT, this paper introduces a distributed model testing method, dMATCH (distributed-Mooring-Aerodynamics-Testing-Control-Hydrodynamics). The dMATCH method separates the experiment into aerodynamic testing in the wind tunnel and hydrodynamic testing in the wave basin, achieving integrated coupling through real-time data transmission using a data exchange system. Errors in sensor acquisition and actuator actuation during data communication may impact the accuracy of experiments. To investigate the potential error and its impact within dMATCH, an integrated model testing system in the wave basin was constructed. Four load cases were established, introducing varying magnitudes of normally distributed random errors to simulate acquisition and actuation inaccuracies. The investigation revealed a positive correlation between errors in experimental results and those in acquisition and actuation. As error increased, result fluctuations became more pronounced. Within the current experimental framework, acquisition error had a greater influence on results compared to actuation error, with aerodynamic thrust being more sensitive to error than the pitch and surge motions of platform. When acquisition and actuation errors were controlled below 5%, the relative RMSE of the results remained below 5%. The dMATCH method proposed in this paper offers a new approach for integrated model testing of FOWT, and the study of potential error impact is crucial to ensuring the reliability of this innovative testing method.

A hybrid deep learning-based short-term forecast model for ionospheric foF2 in East Asia region

The short-term forecast of the critical frequency of the ionospheric F2 layer (foF2) is particularly challenging due to its nonlinear and non-stationary characteristics. To improve the short-term forecast accuracy of foF2, we propose a short-term hybrid deep learning model that integrates the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and long short-term memory (LSTM) algorithms. The proposed model leverages the ICEEMDAN decomposition algorithm to expand foF2 time series data into multi-dimensional space and utilizes the LSTM algorithm to preserve long-term data information, capturing detailed changes in foF2 parameters and obtaining internal information about foF2. The 2014 and 2017 foF2 data from four observation stations located in Mohe, Beijing, Jeju, and Kokubunji in the mid-latitudes of East Asia were utilized for modeling and 1-hour forecast analysis. The forecast values of the proposed model align closely with the measured data, exhibiting minimal fluctuation in forecast error and effectively tracking the changing trend of foF2. The average root mean square error (RMSE) across the four stations in 2014 is 0.40 MHz, with a relative RMSE (RRMSE) of 7.11 % and a coefficient of determination (R2) of 0.98. The average RMSE in 2017 is 0.43 MHz, RRMSE is 7.68 %, and R2 is 0.92. The proposed model reveals significant improvements in the forecast accuracy of the comparison model compared with the CCIR, URSI, NN, and LSTM models. Especially compared with the CCIR and URSI models in the International Reference Ionosphere (IRI), demonstrating superior real-time tracking capability for foF2 and effectively addressing the challenge of poor short-term forecast accuracy observed in the IRI model.

Rapid patient-specific organ dose estimation in computed tomography scans via integration of radiomics features and neural networks.

Computed tomography (CT) offers detailed cross-sectional images of internal anatomy for disease detection but carries a risk of solid cancer or blood malignancies due to exposure to X-ray radiation. This study aimed to develop a new method to quickly predict patient-specific organ doses from CT examinations by training neural networks (NNs) based on radiomics features. CT Digital Imaging and Communications in Medicine (DICOM) image data were exported to DeepViewer, a clinical autosegmentation software, to segment the regions of interest (ROIs) for patient organs. Radiomics feature extraction was performed based on the selected CT data and ROIs. Reference organ doses were computed using Monte Carlo (MC) simulations. Patient-specific organ doses were predicted by training a NN model based on radiomics features and reference doses. For the dose prediction performance, the relative root mean squared error (RRMSE), mean absolute percentage error (MAPE), and coefficient of determination (R2) were evaluated on the test sets. The robustness of the NN model was evaluated via the random rearrangement of patient samples in the training and test sets. The maximal difference between the reference and predicted doses was less than 1 mGy for all investigated organs. The range of MAPE was 1.68% to 5.2% for head organs, 11.42% to 15.2% for chest organs, and 5.0% to 8.0% for abdominal organs; the maximal R2 values were 0.93, 0.86, and 0.89 for the head, chest, and abdominal organs, respectively. The radiomics feature-based NN model can achieve accurate prediction of patient-specific organ doses at a high speed of less than 1 second using a single central processing unit, which supports its use as a user-friendly online clinical application.

ANN uncertainty estimates in assessing fatty liver content from ultrasound data

Background and objectiveThis article uses three different probabilistic convolutional architectures applied to ultrasound image analysis for grading Fatty Liver Content (FLC) in Metabolic Dysfunction Associated Steatotic Liver Disease (MASLD) patients. Steatosis is a new silent epidemic and its accurate measurement is an impelling clinical need, not only for hepatologists, but also for experts in metabolic and cardiovascular diseases. This paper aims to provide a robust comparison between different uncertainty quantification strategies to identify advantages and drawbacks in a real clinical setting. MethodsWe used a classical Convolutional Neural Network, a Monte Carlo Dropout, and a Bayesian Convolutional Neural Network with the goal of not only comparing the goodness of the predictions, but also to have access to an evaluation of the uncertainty associated with the outputs. ResultsWe found that even if the prediction based on a single ultrasound view is reliable (relative RMSE [5.93%-12.04%]), networks based on two ultrasound views outperform them (relative RMSE [5.35%-5.87%]). In addition, the results show that the introduction of a “not confident” category contributes to increase the percentage of correctly predicted cases and to decrease the percentage of mispredicted cases, especially for semi-intrusive methods. ConclusionsThe possibility of having access to information about the confidence with which the network produces its outputs is a great advantage, both from the point of view of physicians who want to use neural networks as computer-aided diagnosis, and for developers who want to limit overfitting and obtain information about dataset problems in terms of out-of-distribution detection.

Multi-sensor fusion for biomechanical analysis: evaluation of dynamic interactions between self-contained breathing apparatus and firefighter using computational methods

Understanding the complex three-dimensional (3D) dynamic interactions between self-contained breathing apparatus (SCBA) and the human torso is critical to assessing potential impacts on firefighter health and informing equipment design. This study employed a multi-inertial sensor fusion technology to quantify these interactions. Six volunteer firefighters performed walking and running experiments on a treadmill while wearing the SCBA. Calculations of interaction forces and moments from the multi-inertial sensor technology were validated against a 3D motion capture system. The predicted interaction forces and moments showed good agreement with the measured data, especially for the forces (normal and lateral) and moments (x- and z-direction components) with relative root mean square errors (RMSEs) below 9.4%, 7.7%, 7.7%, and 7.8%, respectively. Peak pack force reached up to 150 N, significantly exceeding the SCBA’s intrinsic weight during SCBA carriage. The proposed multi-inertial sensor fusion technique can effectively evaluate the 3D dynamic interactions and provide a scientific basis for health monitoring and ergonomic optimization of SCBA systems for firefighters.

Data Monetization Service Development Using Iterative Lifecycle Framework, Quality Assurance, and Open Web Application Security Project: A Case Study of a Utility Company in Indonesia

The research aims to provide Data Monetization (DM) services for an Indonesian utility company as a pilot to generate additional revenue beyond the primary operation. The service is built using an iterative development lifecycle framework and evaluated based on five Quality Goals (QGs), including application and security testing activities. The framework includes methods for processing and modeling electricity usage data, testing application quality, checking infrastructure quality, and ensuring access security for front-end and back-end applications using the Open Web Application Security Project (OWASP). For data modeling, Support Vector Regression (SVR) is used, and it outperforms Polynomial Regression (PR) and Multi-Layer Perception (MLP) Neural Networks. Furthermore, QG shows strong performance with an Relative Root Mean Squared Error (RRMSE) value < 10%, high forecasting ability with Mean Average Probability Error (MAPE) < 10%, and a near-zero average error rate (Mean Squared Error (MSE)) square using minimal data from four months. The services go through functional and integration test to ensure product quality and application performance, which results in a minimum of 95% service response in throughput, 0.128 seconds for processing 2,000 requests, stability at 300–500 in one second per hour, and 7–21 seconds during peak hours. Additionally, the service passes nine penetration tests and ten vulnerability assessments using the OWASP top 10:2021 category. Based on the comprehensive testing and evaluation results, both the application and the service are considered ready and secured for deployment.

Machine learning and multiple linear regression models can predict ascorbic acid and polyphenol contents, and antioxidant activity in strawberries.

Strawberry is a rich source of antioxidants, including ascorbic acid (ASA) and polyphenols, which have numerous health benefits. Antioxidant content and activity are often determined manually using laboratory equipment, which is destructive and time-consuming. This study constructs a prediction model for antioxidant compounds utilizing machine learning (ML) and multiple linear regression based on environmental, plant growth and agronomic fruit quality-related parameters as well as antioxidant levels. These were studied in three farms at two-week intervals during two years of cultivation. During the ML model screening, artificial neural network (ANN)-boosted models displayed a moderate coefficient of determination (R2) at 0.68-0.78 and relative root mean square error (RRMSE) at 3.8-4.8% in polyphenols and total ASA levels, as well as a high R2 of 0.96 and low RRMSE at <3.0% in antioxidant activity. Additionally, we developed variable selection models regarding the antioxidant activity, and variables two and five (environmental parameters and leaf length, respectively) with high accuracy were selected. The linear regression analysis between the actual and predicted data of antioxidants in the ANN-boosted models revealed high fitness with all parameters in almost all training, validation and test sets. Furthermore, environmental parameters are essential in developing such reliable models. We conclude that ANN-boosted, stepwise and double-Lasso regression models can predict antioxidant compounds with enhanced accuracy, and the relevant parameters can be easily acquired on-site without the need for any specific equipment. © 2024 Society of Chemical Industry.

Crop yield estimation uncertainties at the regional scale for Saxony, Germany

AbstractIn times of climate change and global population growth, agricultural yield forecasts play an increasingly important role. For example, predicting yields as early as possible in the event of a drought is crucial for decision‐makers in politics, government, and business. The aim of this study was to provide precise yield predictions at agricultural regions as early as possible with a minimum amount of weather data. Random forest models were used for this purpose. Although more than 290,000 datasets were available for analysis, all models tended to be heavily overfitting, which can be explained by the strong fragmentation of the input data by crop, region, and prediction time. The models reacted very differently to unknown datasets. It was found that the regionally trained models achieved lower (≥10%) relative root mean square errors (RRMSEs) than the supra‐regionally trained models. Rapeseed and barley achieved good predictions. Wheat had good potential, too. Corn, potatoes, and sugar beet achieved often too high RRMSEs. The results showed that targeted model selection for each region and an extension of the training time series could enable very good regional yield forecasts for rapeseed and cereals in the future.

Analysis of WRF-solar in the estimation of global horizontal irradiation in Amapá, northern Brazil

Global horizontal irradiance (GHI) was simulated using version 4.3.1 of the WRF-Solar model over the state of Amapá in the northern region of Brazil. The performance of the Fast All-sky Model for Solar Applications (FARMS) algorithm, called WsolarAPf, was evaluated. The algorithm proposed by the Baseline Surface Radiation Network was used to treat hourly data from the automatic meteorological station of the National Institute of Meteorology in the city of Macapá-AP. Two cumulus parameterizations were needed to represent the rainy and less rainy periods. The modeling used input data from ERA5 reanalysis. Using cluster analysis, it was possible to estimate the typical meteorological year representative for a large area. The use of the FARMS algorithm reduced the relative RMSE of the GHI during winter (JJA) and austral spring (SON), from 26 % to 16 % in austral winter and from 17 % to 12 % in austral spring. The average daily maximum of GHI occurs at 13:00 local time during all seasons, and WRF-Solar showed it at 13:00 and 14:00 in the rainy season and 12:00 and 13:00 in the less rainy season. The suggestion to explore the development of an optimal combination of the two model predictions can be implemented using FARMS.

Study on the Factors Affecting the Humus Horizon Thickness in the Black Soil Region of Liaoning Province, China

Understanding the spatial variability and driving mechanisms of humus horizon thickness (HHT) degradation is crucial for effective soil degradation prevention in black soil regions. The study compared ordinary kriging interpolation (OK), inverse distance weighted interpolation (IDW), and regression kriging interpolation (RK) using mean error (ME), mean absolute error (MAE), root mean square error (RMSE), and relative RMSE to select the most accurate model. Environmental variables were then integrated to predict HHT characteristics. Results indicate that: (1) RK was superior to OK and IDW in characterizing HHT with the smallest ME (11.45), RMSE (14.98), MAE (11.45), and RRMSE (0.44). (2) The average annual temperature (0.29), precipitation (0.27), and digital elevation model (DEM) (0.21) were the primary factors influencing the spatial variability of HHT. (3) The HHT exhibited notable variability, with an increasing trend from the southeast towards the central and northern directions, being the thinnest in the southeast. It was thicker in the northeast and southwest regions, thicker but less dense along the southern Bohai coast, thicker yet sporadically distributed in the northwest (especially Chaoyang and Fuxin), and thick with aggregated distribution over a smaller area in the northeastern direction (e.g., Tieling). These findings provide a scientific basis for accurate soil management in Liaoning Province.

Evaluating Model-assisted Estimators: A Comparative Study in High-dimensional Survey Data

Model-assisted estimators have gained significant attention due to their ability to efficiently utilize auxiliary information during the estimation process. These estimators rely on a working model that links the survey variable to the auxiliary variables, which is then fitted to the sample data to generate predictions. These predictions are subsequently integrated into the estimation procedures. In this study, were explores various model-assisted estimators including Generalized Regression (GREG), Ridge regression, Lasso regression, CART (Classification and Regression Tree), Random Forest, Cubist and Principal Components Regression (PCR) estimator. The analysis involved 2,000 samples of size 50 (n/N ≈ 10%) and employed a stepwise variable selection method to determine the most significant auxiliary variables, incrementally adding them to the model. The performance of these estimators was assessed using relative bias (RB), relative root mean square error (RRMSE) and relative efficiency (RE). Our findings reveal that tree-based models like CART and Random Forest and penalized regression estimators such as Ridge and Lasso display robustness with increased number of auxiliary variables. Among all the estimators, Random Forest consistently yielded the lowest RRMSE, particularly with five auxiliary variables, demonstrating superior efficiency. Conversely, the GREG estimator exhibited poor performance as the number of auxiliary variables increased. This study underscores the importance of selecting suitable model-assisted estimation procedures tailored to the data characteristics and the relationship between survey and auxiliary variables within this high-dimensional dataset.

A Spatial Reconstruction Method of Ionospheric foF2 Based on High Accuracy Surface Modeling Theory

The ionospheric F2 critical frequency (foF2) is one of the most crucial application parameters in high-frequency communication, detection, and electronic warfare. To improve the accuracy of spatial reconstruction of the ionospheric foF2, we propose a high-accuracy surface (HAS) modeling method. This method converts difficult-to-solve differential equations into more manageable algebraic equations using direct difference approximation, significantly reducing algorithm complexity and computational load while exhibiting excellent convergence properties. We used seven stations in Brisbane, Canberra, Darwin, Hobart, Learmonth, Perth, and Townsville, with one station as a validation station and six as training stations (e.g., Brisbane as a validation station and the other stations—Canberra, Darwin, Hobart, Learmonth, Perth, and Townsville—as training stations). The training stations and the HAS method were used to train and reconstruct the validation stations at different solar activity periods, seasons, and local times. The predicted values of the validation stations were compared with the measured values, and the proposed method was analyzed and validated. The reconstruction results show the following. (1) The relative root mean square errors (RRMSEs) of HAS method prediction in different solar activity epochs were 13.67%, 7.74%, and 9.19%, respectively, which are 13.57%, 7.41%, and 6.41% higher than the prediction accuracy of the Kriging method, respectively. (2) In the four seasons, the RRMSEs of the HAS method prediction are 9.27%, 13.1%, 8.81%, and 8.09%, respectively, which are 10.83%, 11.73%, 4.25%, and 12.00% higher than the prediction accuracy of the Kriging method. (c) During the daytime and nighttime, the RRMSEs of HAS method prediction were 9.23% and 11.17%, which were 5.92% and 11.99% higher than the prediction accuracy of the Kriging method, respectively. (d) Under the validation dataset, the average predictive RRMSE of the HAS method was 10.29%, and the average predictive RRMSE of the IRI prediction model was 12.35%, with a 2.06% improvement in the predictive accuracy of the HAS method. In general, the prediction effect of the HAS method was better than that of the Kriging method, thus verifying the effectiveness and reliability of the proposed method. In summary, the proposed reconstruction method is of great significance for improving usable frequency prediction and enhancing communication performance.