Accurate Estimation Method Research Articles

An RNN-CNN-Based Parallel Hybrid Approach for Battery State of Charge (SoC) Estimation Under Various Temperatures and Discharging Cycle Considering Noisy Conditions

With the increasing use of lithium-ion (Li-ion) batteries in electric vehicles (EVs), accurately measuring the state of charge (SoC) has become crucial for ensuring battery reliability, performance, and safety. In addition, EVs operate in different environmental conditions with different driving styles, which also cause inaccurate SoC estimation resulting in reduced reliability and performance of battery management systems (BMSs). To address this issue, this work proposes a new hybrid method that integrates a gated recurrent unit (GRU), temporal convolution network (TCN), and attention mechanism. The TCN and GRU capture both long-term and short-term dependencies and the attention mechanism focuses on important features within input sequences, improving model efficiency. With inputs of voltage, current, and temperature, along with their moving average, the hybrid GRU-TCN-Attention (GTA) model is trained and tested in a range of operating cycles and temperatures. Performance metrics, including average RMSE (root mean squared error), MAE (mean absolute error), MaxE (maximum error), and R2 score indicates the model is performing well, with average values of 0.512%, 0.354%, 1.98%, and 99.94%, respectively. The proposed model performs well under both high and low noise conditions, with an RMSE of less than 2.18%. The proposed hybrid approach is consistently found to be superior when compared against traditional baseline models. This work offers a potential method for accurate SoC estimation in Li-ion batteries, which has an important impact on clean energy integration and battery management systems in EVs.

Driving range estimation for electric bus based on atomic orbital search and back propagation neural network

AbstractAs urbanization and transportation demands continue to increase, electric buses play an important role in sustainable urban development thanks to their advantages of emission reduction, noise and pollution reduction. However, electric buses still face some challenges, in which, range anxiety is one of the main factors limiting its popularization. To solve this problem, an accurate estimation method for the driving range of electric buses based on atomic orbital search (AOS) algorithm and back propagation neural network (BPNN) was used, in which a long‐term bus operation dataset under different driving conditions is utilized to train BPNN, and then weight and bias are taken as the first generation provided for AOS approach to find a more appropriate parameter combination. Simulation and experimental analysis show that the algorithm introduced in this paper has higher prediction accuracy and efficiency compared to the traditional machine learning algorithms, that compared with BPNN, AOSBP reduced MAE, RMSE and MAPE by 85.6%, 50.9% and 64.6%, respectively, which effectively relieves range anxiety, and ensures the normal operation of the electric bus fleet.

Correlation of weight and volume of modified radical mastectomy specimen with ptosis of breast in patients of breast cancer

BackgroundPreoperative assessment of breast features is indispensable for both cosmetic and reconstructive breast surgical procedures. In this study we aim to investigate the effect of breast ptosis on breast volume estimation by various methods. MethodsFifty patients of breast cancer planned for modified radical mastectomy were taken up. Preoperatively breast anthropometric measurement taken, grade of ptosis was noted and breast volume was calculated by anthropometry and mammography and intraopratively mastectomy specimen weight and volume was recorded. Breast volume calculated by mammography and anthropometry compared with mastectomy specimen volume and weight and correlation with ptosis was statistically analyzed. ResultsMastectomy specimen volume showed best agreement with mastectomy specimen weight (r ​= ​.993, <.001), followed by mammographic method (r ​= ​.985, P ​< ​.001), anthropometry by breast circumference in supine method (r ​= ​.982, P ​< ​.001), anthropometry by breast circumference in upright method (r ​= ​.979, P ​< ​.001) and anthropometry by breast radius and mammary projection method (r ​= ​.969, P ​< ​.001). ConclusionMammography is simple, cost effective and most accurate method for breast volume estimation followed by anthropometric breast volume calculation. As size of breast and grade of breast ptosis increases the accuracy of all methods of breast volume estimation decreases.

Convolutional neural network for colorimetric glucose detection using a smartphone and novel multilayer polyvinyl film microfluidic device

Detecting glucose levels is crucial for diabetes patients as it enables timely and effective management, preventing complications and promoting overall health. In this endeavor, we have designed a novel, affordable point-of-care diagnostic device utilizing microfluidic principles, a smartphone camera, and established laboratory colorimetric methods for accurate glucose estimation. Our proposed microfluidic device comprises layers of adhesive poly-vinyl films stacked on a poly methyl methacrylate (PMMA) base sheet, with micro-channel contours precision-cut using a cutting printer. Employing the gold standard glucose-oxidase/peroxidase reaction on this microfluidic platform, we achieve enzymatic glucose determination. The resulting colored complex, formed by phenol and 4-aminoantipyrine in the presence of hydrogen peroxide generated during glucose oxidation, is captured at various glucose concentrations using a smartphone camera. Raw images are processed and utilized as input data for a 2-D convolutional neural network (CNN) deep learning classifier, demonstrating an impressive 95% overall accuracy against new images. The glucose predictions done by CNN are compared with ISO 15197:2013/2015 gold standard norms. Furthermore, the classifier exhibits outstanding precision, recall, and F1 score of 94%, 93%, and 93%, respectively, as validated through our study, showcasing its exceptional predictive capability. Next, a user-friendly smartphone application named “GLUCOLENS AI” was developed to capture images, perform image processing, and communicate with cloud server containing the CNN classifier. The developed CNN model can be successfully used as a pre-trained model for future glucose concentration predictions.

Accurate Inference of the Polyploid Continuum using Forward-time Simulations.

Multiple rounds of whole-genome duplication (WGD) followed by diploidization have occurred throughout the evolutionary history of angiosperms. Much work has been done to model the genomic consequences and evolutionary significance of WGD. While researchers have historically modeled polyploids as either allopolyploids or autopolyploids, the variety of natural polyploids span a continuum of differentiation across multiple parameters, such as the extent of polysomic vs. disomic inheritance, and the degree of genetic differentiation between the ancestral lineages. Here we present a forward-time polyploid genome evolution simulator called SpecKS. SpecKS models polyploid speciation as originating from a 2D continuum, whose dimensions account for both the level of genetic differentiation between the ancestral parental genomes, as well the time lag between ancestral speciation and their subsequent reunion in the derived polyploid. Using extensive simulations, we demonstrate that changes in initial conditions along either dimension of the 2D continuum deterministically affect the shape of the Ks histogram. Our findings indicate that the error in the common method of estimating WGD time from the Ks histogram peak scales with the degree of allopolyploidy, and we present an alternative, accurate estimation method that is independent of the degree of allopolyploidy. Lastly, we use SpecKS to derive tests that infer both the lag time between parental divergence and WGD time, and the diversity of the ancestral species, from an input Ks histogram. We apply the latter test to transcriptomic data from over 200 species across the plant kingdom, the results of which are concordant with the prevailing theory that the majority of angiosperm lineages are derived from diverse parental genomes and may be of allopolyploid origin.

Developing a Method to Estimate Above-Ground Carbon Stock of Forest Tree Species Pinus densata Using Remote Sensing and Climatic Data

Forest above-ground carbon stock (AGCS) is one of the primary ecological evaluation indicators, so it is crucial to estimate the AGCS accurately. In this research, we added the climatic and topographic factors to the estimation process by a remote sensing approach to explore their impact and to achieve more precise estimations. We hope to develop a more accurate estimation method for AGCS based on remote sensing data and climate data. The random forest (RF) method has good robustness and wide applicability. Therefore, we modeled and predicted the AGCS by RF based on sixty field sample plots of Pinus densata pure forests in southwest China and the factors extracted from Landsat 8 OLI images (source I), Sentinel-2A images (source II), and combined Landsat 8 OLI and Sentinel-2A images (source III). We added the topographic and climatic factors to establish the AGCS estimation model and compared the results. The topographic factors contain elevation, slope, and aspect. Climatic factors contain mean annual temperature, annual precipitation, annual potential evapotranspiration, and monthly mean potential evapotranspiration. It was found that the R2 and RMSE of the model based on source III were better than the R2 and RMSE of the models based on source I and source II. Compared to the models based on source I and source II, the model based on source III improved R2 by up to 0.08, reduced RMSE by up to 2.88 t/ha, and improved P by up to 4.29%. Among the models without adding factors, the model based on source III worked the best, with an R2 of 0.87, an RMSE of 10.81 t/ha, an rRMSE of 23.19%, and a P of 79.71%. Among the models that added topographic factors, the model based on source III worked best after adding elevation, with an R2 of 0.89, an RMSE of 10.01 t/ha, an rRMSE of 21.47%, and a P of 82.17%. Among the models that added climatic factors, the model that added the annual precipitation factor had the best modeling result, with an R2 of 0.90, an RMSE of 9.53 t/ha, an rRMSE of 20.59%, and a P of 83.00%. The prediction result exhibited that the AGCS of the Pinus densata forest in 2021 was 9,737,487.52 t. The combination of Landsat 8 OLI and Sentinel-2A could improve the prediction accuracy of the AGCS. The addition of annual precipitation can effectively improve the accuracy of AGCS estimation. Higher resolution of climate data is needed to enhance the modeling in future work.

Terrain parameter identification for wheeled mobile robots using deep neural networks

This paper introduces an innovative approach to soil parameter estimation using deep artificial neural networks (ANN) tailored to estimate a wide range of soil types. Previous research in this field has relied on limited datasets and oversimplified assumptions in semi-empirical models. In this work, the sensitivity of stress distribution is analyzed with respect to soil parameters, revealing significant errors resulting from the simplifications in semi-empirical models and emphasizing the need for more accurate estimation methods with minimal reliance on simplifying assumptions. Training an ANN requires a comprehensive dataset, which has been a challenge due to limited access to diverse soil samples. Addressing this issue, the paper conducts simulations of a single wheel’s movement across a wide range of soil parameter combinations to generate the required dataset. These simulations are done using a dynamic motion-compliant semi-empirical model detailed in the article. Subsequently, the network’s hyperparameters are fine-tuned through a grid search, followed by extensive training of the optimized ANN model. In the end, the ANN demonstrates promising performance in accurately estimating soil parameters, validated through simulation results of both single wheel and Mars rover motion.

Иглоподобные листовые органы хвойных. Часть II. Моделирование площади поверхности иглы

In ecological and physiological studies of plant cover, the predominant participation of leaves in the processes of photosynthesis, transpiration and respiration determines the key role of such a morphometric parameter as leaf surface area. The estimation of the area of needle-like leaf organs of conifers often requires an individual approach. The diversity of needle shapes is determined by species affiliation, morphological structure, ecological conditions and age, and, in turn, determines the diversity of methods for estimating the needle surface area. Therefore, the search for simple standard methods for determining the surface area of leaf organs of conifers is an urgent task for plant physiologists. The aim of this work has been to create a universal model for estimating the needle surface area, independent of species. To achieve it, the needle cross-section model proposed by the authors has been used, based on the transformation of the perimeter of the cross-section into an equivalent circle, the perimeter of which is associated with the parameters of the needle cross-section before the transformation. To estimate the surface area of the needle, it is possible to approximate the needle with a geometric body, which is a combination of an ellipsoid of revolution, a cone and a cylinder, with the radius of the cylinder being estimated using the needle cross-section model. The model allows to estimate the surface area of the needle by its 4 morphometric parameters: thickness, width, length of the middle part and total length. Full verification of the model proposed in the article has turned out to be impossible due to the lack of methods for accurate estimation of the needle surface area. The developed method has been compared to other methods for estimating the surface area of needle-like samples by the examples of the needles of Siberian fir (Abies sibirica L.) and common juniper (Juniperus communis L.), as well as banana fruits (Musa paradisiaca L.), and the good predictive ability of the model has been demonstrated. It can be characterized as universal with a theoretical relative error of no more than 5 %.

Using query semantic and feature transfer fusion to enhance cardinality estimating of property graph queries

With the increasing complexity and diversity of query tasks, cardinality estimation has become one of the most challenging problems in query optimization. In this study, we propose an efficient and accurate cardinality estimation method to address the cardinality estimation problem in property graph queries, particularly in response to the current research gap regarding the neglect of contextual semantic features. We first propose formal representations of the property graph query and define its cardinality estimation problem. Then, through the query featurization, we transform the query into a vector representation that can be learned by the estimation model, and enrich the feature vector representation by the context semantic information of the query. We finally propose an estimation model for property graph queries, specifically introducing a feature information transfer module to dynamically control the information flow meanwhile achieving the model’s feature fusion and inference. Experimental results on three datasets show that the estimation model can accurately and efficiently estimate the cardinality of property graph queries, the mean Q_error and RMSE are reduced by about 30% and 25% than the state-of-art estimation models. The context semantics features of queries can improve the model’s estimation accuracy, the mean Q_error result is reduced by about 20% and the RMSE result is about 5%.

A new adaptive approach for bridging the gap in insurance premium estimation

This paper proposes a new adaptive approach called adaptive mean (ADM) that combines the strengths of trimming and winsorization to minimize the mean square error (MSE). ADM will contribute significantly to insurers by enabling them to mitigate risk exposure caused by inaccurate premium estimation and establish more precise premiums for their clients. Furthermore, the proposed mean offers several pros compared to the conventional mean. It facilitates the natural and intuitive calculation of risk loading, identifies and measures the impact of large claims, and analyzes premium susceptibility to skewed risk by capturing the tails of the relevant loss models. In addition, this paper reviews two established, robust credibility methods (trimming and winsorization). It compares them with our proposed method, resulting in a more reliable and robustly accurate method for credibility premium estimation. We presented and analyzed two real data sets from engineering insurance companies and the Wisconsin Office of the Insurance Commissioner to highlight the advances of ADM in minimizing the MSE and building more robust credibility models that are less vulnerable to outlier events and model uncertainty.

Estimation of SOC for Li-ion battery-powered three-wheeled electric vehicle using machine learning methods

Abstract The Battery Management System (BMS) serves as the heart of the electric vehicle system, in which estimating the state of charge (SOC) is the crucial part of the BMS to ensure the durability, reliability, and sustainability of the battery pack. Due to its nonlinear characteristics, accurately estimating the SOC for a slow degradation of the charge is highly cumbersome. The literature provides a series of machine learning algorithms (MLA) to estimate and predict the SOC of lithium-ion (Li-ion) battery systems for electric vehicle (EV) applications. The literature has proposed various MLA, coulomb counting, and different Kalman filter methods to address this challenge and estimate the SOC of Li-ion battery systems for EV applications. This research looks at the differences and similarities between the coulomb counting method, the unscented Kalman filter method, and a number of machine learning algorithms. These include linear regression, polynomial linear regression, support vector regression, decision trees, random forests, artificial neural networks (ANN), and long short-term memory (LSTM). The goal is to assess the MLAs' accuracy in estimating battery SOC. Analyzing model errors optimizes the battery's performance parameter. We identify ANN and LSTM as the two most efficient methods for accurate SOC estimation in an EV-operated BMS system by evaluating the performance indices of the aforementioned machine learning methodologies. Once again, the LSTM model for SOC estimation has proven to be highly accurate in analyzing the discrepancy between the actual and predicted traveling ranges of the designed prototype. We design a MATLAB/SIMULINK EV powertrain by collecting realtime data from the Li-ion battery pack, analyzing the SOC variation data, and using the previously mentioned MLA in the Python platform to estimate the SOC and its accuracy. It highlights the effectiveness of advanced MLAs in improving SOC estimation, thereby enhancing the performance and reliability of EV battery systems.

Development and Validation of Novel RP-HPLC Method for the Simultaneous Estimation of Itraconazole and Secnidazole in Bulk and Pharmaceutical Formulations

Simple, accurate and precise RP-HPLC method for the simultaneous estimation of Itraconazole (ITZ) and Secnidazole (SEC) in bulk and pharmaceutical formulations has been developed and validated. The chromatographic analysis was performed on Shimadzu model equipped with SPD-20 AD UV detector, isocratic pump LC- 20 AD and loop injector. The chromatographic separation was performed using C18 column (250mm x 4.6mm i.d. and 5µm particle size). The analytes were monitored at 257nm using methanol: potassium dihydrogen phosphate buffer (PDP) pH 5.5 in the ratio of 90:10v/v with a flow rate of 1.5ml/min. The retention time was found to be 6.037 min for ITZ and 3.788 min for SEC. The linearity was found to be in the range of 10-50µg/ml for both ITZ and SEC with a regression coefficient of 0.999 and 0.998 for ITZ and SEC respectively. The method was validated in accordance with ICH guidelines for its linearity, precision, accuracy, robustness, ruggedness, LOD and LOQ. The recovery studies were carried out which confirmed the accuracy of the proposed method. LOD values for ITZ &amp; SEC was found to be 0.583µg/ml and 0.241µg/ml, respectively. LOQ values for ITZ and SEC was found to be 1.749µg/ml and 0.732µg/ml, respectively. The developed method was also found to be precise and robust for the simultaneous determination of ITZ and SEC in bulk and pharmaceutical formulations.

A Real-Time Beam Steering and Accurate Vital Sign Estimation Method in an Indoor Environment

A Real-Time Beam Steering and Accurate Vital Sign Estimation Method in an Indoor Environment

Design Optimization of a Run-Of-River Small Hydropower Plant: A Case Study of Mabula Kapi Site

Prior to construction, small or large hydropower plants undergo feasibility studies, which involve technical, economic, financial, social, and environmental aspects. Technical studies, particularly, include various engineering disciplines. This study sought to conduct a component of technical feasibility studies, focused on design optimization of the turbine-plant capacity size for a run-of-river case study called Mabula Kapi, on Kaombe River, Serenje, Zambia. The study method used computational modelling, simulation, and optimization techniques, and used secondary data from previous site. A prefeasibility study conducted earlier had underestimated the turbine-plant capacity owing to underestimated discharge data, owing to lack of site gauging station. A less accurate discharge estimation method involving transposition from a gauged similar catchment had been used. A later feasibility-level site hydrological study found improved discharge data. Riding on the improved discharge data, this study found the following optimised plant design parameters based on plant design discharge of 6.20 m3/s: Installed capacity of 10.20 MW; Annual energy production of 42 GWh; Capacity factor of 47.1%; 3 x Pelton wheel of 272 rpm speed, 2.1 m diameter, 2-nozzles of diameter 0.16 m each, 21 buckets of 0.58m width each; and 3 x 4 MVA generators of 50Hz, 22-poles, and 11kV.

Masked contrastive graph representation learning for age estimation

Age estimation of face images is a crucial task with various practical applications in areas such as video surveillance and Internet access control. While deep learning-based age estimation methods like Convolutional Neural Networks (CNN), Multilayer Perceptrons (MLP), and Transformers have shown remarkable performance, they have limitations when modeling complex or irregular objects, and often contain redundant information. Although existing graph neural networks (GNNs) can alleviate this issue, they only considers the structural information of the image and ignores the semantic features, thus the feature representation capability of graph nodes is limited. To address these issues, this paper proposes a novel Masked Contrastive Graph Representation Learning (MCGRL) method for accurate age estimation of face images. Our approach leverages CNN to extract semantic features of the image, which are then partitioned into patches that serve as nodes in the graph. We use a masked graph convolutional network (GCN) to derive image-based node representations that capture rich structural information. Finally, we incorporate multiple losses to explore the complementary relationship between structural information and semantic features, which improves the feature representation capability of GCN. Experimental results on real-world face image datasets demonstrate the superiority of our proposed method over other state-of-the-art age estimation approaches. Our code is available at https://github.com/yuntaoshou/MCGRL

Kidney function assessment for eligibility in clinical cancer trials – Data from the European Organisation for Research and Treatment of Cancer

PurposeThere is no consensus on how to estimate kidney function for the assessment of eligibility in clinical cancer trials. Patients and methodsWe recalculated the creatinine clearance (CrCl)/glomerular filtration rate (GFR) at baseline in a total of 1768 patients enrolled in twelve clinical trials using the Cockcroft-Gault (CG), Modification of Diet in Renal Disease (MDRD), 2021 Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI 2021) and European Kidney Function Consortium (EKFC) formulas. Patients were classified as having renal impairment (RI; CrCl/GFR <60 mL/min) or no renal impairment (NRI; CrCl/GFR ≥60 mL/min) with each of the four formulas, respectively. Furthermore, we analyzed the number of adverse events (AE) per month under study treatment using measures of central tendency, variability and regression models. ResultsUsing CG, EKFC, MDRD and CKD-EPI 2021, 152 (8 %), 140 (8 %), 110 (6 %), and 61 (4 %) patients had RI respectively. Indeed, 47 (3 %) patients had RI using all 4 formulas, while 158 (9 %) had RI by at least one but not all four methods. CG showed the broadest variability and inconsistencies with other methods. All calculation methods performed similarly for excluding patients at risk of severe AE. EKFC demonstrated superior predictive ability for excluding patients at risk of renal and urinary tract AE. ConclusionThis post hoc analysis highlights the importance of choosing accurate and representative methods for kidney function estimation in clinical cancer trials. CG should be replaced by newer methods. While CKD-EPI 2021 may maximize trial accrual, EKFC should be considered for treatment affecting kidney function.

Enhancing capacity estimation of retired electric vehicle lithium-ion batteries through transfer learning from electrochemical impedance spectroscopy

The low economic feasibility caused by inefficient testing and inaccurate performance estimation is one of the main bottlenecks in the echelon utilization of large-scale retired batteries. This study proposes a fast and accurate capacity estimation method for retired batteries based on electrochemical impedance spectroscopy (EIS). Firstly, the EIS of the batteries that experience multi-condition aging in the laboratory are collected. EIS characteristic parameter sequences highly related to battery performance, including real part and magnitude, are directly extracted to establish a base bi-directional long short-term memory model. Secondly, a transfer learning method based on feature matching is designed, which applies a linear transformation layer to map the features between the source and target domains. The proposed transfer learning method has been effectively validated on laboratory battery data measured at different temperatures and retired battery datasets of different material types. The improvements are especially notable for retired batteries. The detection time has been reduced, with each cell requiring only 1.67 min. And using only a small amount of data as input for transfer learning can achieve an accuracy improvement of over 90 %, indicating an effective transfer channel from the base model established on laboratory small-capacity battery aging data to large-capacity retired battery data is successfully established for the first time. For retired nickel-cobalt-manganese batteries, the mean absolute percentage error (MAPE) and the root mean square percentage error (RMSPE) are 2.33 % and 2.75 %, respectively, while for retired lithium-iron-phosphate batteries, the MAPE and RMSPE reached 4.12 % and 5.04 %, respectively. The results demonstrate the proposed method reduces the cost of repeated testing, modeling, and training for specific retired batteries while maintaining the accuracy of capacity estimation. This advancement helps to improve the efficiency of large-scale retired battery grading, and injects new momentum into facilitating more effective decision-making processes.

Recognizing the Most Accurate Herschel-Bulkley Fluid Pressure Estimation Method for Annulus: An Update to API RP 13D, 7th Edition

Summary The Herschel-Bulkley (HB) model is widely regarded as highly accurate for modeling non-Newtonian fluid flow, applicable across diverse fields such as chemical, mechanical, and petroleum engineering. The American Petroleum Institute and other references recognize the HB model as the most accurate and recommend the industry use it for drilling hydraulics. Pressure estimation models are beneficial for applying the HB model in field settings, as numerical solutions may not be feasible due to the computational demands and time constraints, especially challenging for high-frequency real-time pressure loss estimation (at least 1 Hz). Past literature has presented four estimation methods for the HB fluid, consisting of Zamora and Lord (1974), Merlo et al. (1995), Gjerstad and Time (2015), and the generalized method. However, the recommended practice API RP 13D (2023), “Rheology and Hydraulics of Oilwell Drilling Fluids,” has considered the most traditional Zamora and Lord (1974) as their chosen estimation method for industry use while neglecting to identify the most accurate model. Therefore, to update API RP 13D (2023), this work addresses this shortcoming by investigating the performance of different methods in estimating pressure losses while providing user-friendly, straightforward procedures applicable for field use. To recognize the most accurate estimation method for industry use, different methods’ pressure losses were estimated and compared with the numerical solution as well as experimental data to find the errors. The results showed that the Merlo et al. (1995) method provides the most accurate estimates, with the least average absolute percent error (APE) of maximum 4% underestimating the numerical solution, followed by Zamora and Lord’s error overestimating the numerical solution. The errors may slightly vary depending on the input parameters used, including diameters, mud properties, and circulation rate. The effect of the circulation rate on the accuracy of different methods was also investigated; except for the generalized method, the accuracy of the other methods increases with increasing the circulation rate. This work is a very innovative practical work for finding annular pressure losses accurately without using complex numerical solutions.

Optimal Mapping of Soil Erodibility in a Plateau Lake Watershed: Empirical Models Empowered by Machine Learning

Soil erodibility (K) refers to the inherent ability of soil to withstand erosion. Accurate estimation and spatial prediction of K values are vital for assessing soil erosion and managing land resources. However, as most K-value estimation models are empirical, they suffer from significant extrapolation uncertainty, and traditional studies on spatial prediction focusing on individual empirical K values have neglected to explore the spatial pattern differences between various empirical models. This work proposed a universal framework for selecting an optimal soil-erodibility map using empirical models enhanced by machine learning. Specifically, three empirical models, namely, the erosion-productivity impact calculator model (K_EPIC), the Shirazi model (K_Shirazi), and the Torri model (K_Torri) were used to estimate K values. Random Forest (RF) and Gradient-Boosting Decision Tree (GBDT) algorithms were employed to develop prediction models, which led to the creation of three K-value maps. The spatial distribution of K values and associated environmental covariates were also investigated across varying empirical models. Results showed that RF achieved the highest accuracy, with R2 of K_EPIC, K_Shirazi, and K_Torri increasing by 46%, 34%, and 22%, respectively, compared to GBDT. And distinctions among environmental variables that shape the spatial patterns of empirical models have been identified. The K_EPIC and K_Shirazi are influenced by soil porosity and soil moisture. The K_Torri is more sensitive to soil moisture conditions and terrain location. More importantly, our study has highlighted disparities in the spatial patterns across the three K-value maps. Considering the data distribution, spatial distribution, and measured K values, the K_Torri model outperformed others in estimating soil erodibility in the plateau lake watershed. This study proposed a framework that aimed to create optimal soil-erodibility maps and offered a scientific and accurate K-value estimation method for the assessment of soil erosion.

STATISTICAL INFERENCE ON SINE-EXPONENTIAL DISTRIBUTION PARAMETER

The Sine-Exponential (Sine-E) distribution is a probability distribution that combines the periodic behavior of the sine function with the decay characteristic of the exponential function. This study addresses the problem of identifying the most accurate and reliable estimation method for the parameter of the Sine-E distribution. The objective is to evaluate various parameter estimation techniques, including Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE), Weighted Least Squares Estimation (WLSE), Maximum Product of Spacing Estimation (MPSE), Cramer-von-Mises Estimation (CVME), and Anderson-Darling Estimation (ADE), using Mean Square Error (MSE) as the criterion for determining the technique with the minimum error. The study’s findings reveal that as sample size increases, the parameter estimates for all techniques converge to the true parameter value, with decreases in bias, MSE, and mean relative estimates. Among the techniques evaluated, the MPSE method consistently provides estimates closest to the true parameter value and exhibits the least bias and lowest MSE across small, moderate, and large sample sizes, making it the best estimator for the Sine-E distribution.