Modeling and Validation of Diamagnetic Rotor Levitated by Permanent Magnetics

As an innovative,low-power consuming,and low-stiffness suspension approach,the diamagnetic levitation technique has attracted considerable interest because of its potential applicability in miniaturized mechanical systems.The foundation of a diamagnetic levitation system is mathematical modeling,which is essential for operating performance optimization and stability prediction.However,few studies on systematic mathematical modeling have been reported.In this study,a systematic mathematical model for a disc-shaped diamagnetically levitated rotor on a permanent magnet array is proposed.Based on the proposed model,the magnetic field distribution characteristics,diamagnetic levitation force characteristics(i.e.,levitation height and stiffness),and optimized theoretical conditions for realizing stable levitation are determined.Experiments are conducted to verify the feasibility of the proposed mathematical model.Theoretical predictions and experimental results indicate that increasing the levitation height enlarges the stable region.Moreover,with a further increase in the rotor radius,the stable regions of the rotor gradually diminish and even vanish.Thus,when the levitation height is fixed,a moderate rotor radius permits stable levitation.This study proposes a mathematical modeling method for a diamagnetic levitation system that has potential applications in miniaturized mechanical systems.

An internal ballistic model of electromagnetic railgun based on PFN coupled with multi-physical field and experimental validation

To accelerate the practicality of electromagnetic railguns,it is necessary to use a combination of threedimensional numerical simulation and experiments to study the mechanism of bore damage.In this paper,a three-dimensional numerical model of the augmented railgun with four parallel unconventional rails is introduced to simulate the internal ballistic process and realize the multi-physics field coupling calculation of the rail gun,and a test experiment of a medium-caliber electromagnetic launcher powered by pulse formation network(PFN)is carried out.Various test methods such as spectrometer,fiber grating and high-speed camera are used to test several parameters such as muzzle initial velocity,transient magnetic field strength and stress-strain of rail.Combining the simulation results and experimental data,the damage condition of the contact surface is analyzed.

Development and validation of a circulating tumor DNA-based optimization-prediction model for short-term postoperative recurrence of endometrial cancer

BACKGROUND Endometrial cancer(EC)is a common gynecological malignancy that typically requires prompt surgical intervention;however,the advantage of surgical management is limited by the high postoperative recurrence rates and adverse outcomes.Previous studies have highlighted the prognostic potential of circulating tumor DNA(ctDNA)monitoring for minimal residual disease in patients with EC.AIM To develop and validate an optimized ctDNA-based model for predicting shortterm postoperative EC recurrence.METHODS We retrospectively analyzed 294 EC patients treated surgically from 2015-2019 to devise a short-term recurrence prediction model,which was validated on 143 EC patients operated between 2020 and 2021.Prognostic factors were identified using univariate Cox,Lasso,and multivariate Cox regressions.A nomogram was created to predict the 1,1.5,and 2-year recurrence-free survival(RFS).Model performance was assessed via receiver operating characteristic(ROC),calibration,and decision curve analyses(DCA),leading to a recurrence risk stratification system.RESULTS Based on the regression analysis and the nomogram created,patients with postoperative ctDNA-negativity,postoperative carcinoembryonic antigen 125(CA125)levels of<19 U/mL,and grade G1 tumors had improved RFS after surgery.The nomogram’s efficacy for recurrence prediction was confirmed through ROC analysis,calibration curves,and DCA methods,highlighting its high accuracy and clinical utility.Furthermore,using the nomogram,the patients were successfully classified into three risk subgroups.CONCLUSION The nomogram accurately predicted RFS after EC surgery at 1,1.5,and 2 years.This model will help clinicians personalize treatments,stratify risks,and enhance clinical outcomes for patients with EC.

Practical Use of the Subjective Mathematical Model of Bayes and Its External Validation in Dental Medicine & Dentistry

Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of assisting diagnosis and treatment planning in Dentistry. Existing systems used few symptoms for dental diagnosis. In Dentistry, few symptoms are not enough for diagnosis. In this research, a conditional probability model (Bayes rule) was developed with increased number of symptoms associated with a disease for diagnosis. A test set of recurrent cases was then used to test the diagnostic capacity of the system. The generated diagnosis matched that of the human experts. The system was also tested for its capacity to handle uncommon dental diseases and the system portrayed useful potential. Method: The study used the Subjective Mathematical Bayes Model (SBM) approach and employed Logistic Regression Mathematical Model (LMR) techniques. The external validation of the subjective mathematical Bayes model (MSB) concerns the real cases of 625 patients who developed alveolar osteitis (OA). We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis Logistic Regression Mathematical Model (LMR) techniques and on artificial intelligence, a major goal in the next decade. Results: The internal validation had identified seven (7) etiological factors of OA, which will be compared to the cases of MRL, for the external validation which retained six (6) etiological factors of OA. The experts in the internal validation of the MSB had generated 40 cases of OA and a COP of (0.5), which will be compared to the MRL that collected 625 real cases of OA to produce a Cop of (0.6) in the external validation, which discriminates between healthy patients (Se) and sick patients (Sp). Compared to real cases and the logistic regression model, the Bayesian model is efficient and its validity is established.

THE MODEL VALIDATION OF DYNAMIC NEURAL NETWORKS

This paper investigates the problem of the model validation in identifying discrete-time-nonlinear dynamic systems by using neural networks with a single hidden layer.Based on the estimation theory,a synthetic error-index(SEI)criterion for the neural network models has been developed.By using the powerful training algorithm of recursive prediction error (RPE),two simulated non-linear systems are studied,and the results show that the synthetic error-index criterion can be used to verify the dynamic neural network models.Furthermore,the proposed technique is much simple in calculation than that of the effective correlation tests.Finally,some problems required by further study are discussed.

Establishing and clinically validating a machine learning model for predicting unplanned reoperation risk in colorectal cancer

BACKGROUND Colorectal cancer significantly impacts global health,with unplanned reoperations post-surgery being key determinants of patient outcomes.Existing predictive models for these reoperations lack precision in integrating complex clinical data.AIM To develop and validate a machine learning model for predicting unplanned reoperation risk in colorectal cancer patients.METHODS Data of patients treated for colorectal cancer(n=2044)at the First Affiliated Hospital of Wenzhou Medical University and Wenzhou Central Hospital from March 2020 to March 2022 were retrospectively collected.Patients were divided into an experimental group(n=60)and a control group(n=1984)according to unplanned reoperation occurrence.Patients were also divided into a training group and a validation group(7:3 ratio).We used three different machine learning methods to screen characteristic variables.A nomogram was created based on multifactor logistic regression,and the model performance was assessed using receiver operating characteristic curve,calibration curve,Hosmer-Lemeshow test,and decision curve analysis.The risk scores of the two groups were calculated and compared to validate the model.RESULTS More patients in the experimental group were≥60 years old,male,and had a history of hypertension,laparotomy,and hypoproteinemia,compared to the control group.Multiple logistic regression analysis confirmed the following as independent risk factors for unplanned reoperation(P<0.05):Prognostic Nutritional Index value,history of laparotomy,hypertension,or stroke,hypoproteinemia,age,tumor-node-metastasis staging,surgical time,gender,and American Society of Anesthesiologists classification.Receiver operating characteristic curve analysis showed that the model had good discrimination and clinical utility.CONCLUSION This study used a machine learning approach to build a model that accurately predicts the risk of postoperative unplanned reoperation in patients with colorectal cancer,which can improve treatment decisions and prognosis.

Direct Pointwise Comparison of FE Predictions to StereoDIC Measurements:Developments and Validation Using Double Edge-Notched Tensile Specimen

To compare finite element analysis(FEA)predictions and stereovision digital image correlation(StereoDIC)strain measurements at the same spatial positions throughout a region of interest,a field comparison procedure is developed.The procedure includes(a)conversion of the finite element data into a triangular mesh,(b)selection of a common coordinate system,(c)determination of the rigid body transformation to place both measurements and FEA data in the same system and(d)interpolation of the FEA nodal information to the same spatial locations as the StereoDIC measurements using barycentric coordinates.For an aluminum Al-6061 double edge notched tensile specimen,FEA results are obtained using both the von Mises isotropic yield criterion and Hill’s quadratic anisotropic yield criterion,with the unknown Hill model parameters determined using full-field specimen strain measurements for the nominally plane stress specimen.Using Hill’s quadratic anisotropic yield criterion,the point-by-point comparison of experimentally based full-field strains and stresses to finite element predictions are shown to be in excellent agreement,confirming the effectiveness of the field comparison process.

A Land Surface Model(IAP94) for Climate Studies PartI:Formulation and Validation in Off-line Experiments

The IAP (Institute of Atmospheric Physics) land-surface model (IAP94) is described. This model is a comprehensive one with detailed description for the processes of vegetation, snow and soil. Particular attention has been paid to the cases with three water phases in the surface media. On the basis of the mixture theory and the theory of fluid dynamics of porous media, the system of universal conservational equations for water and heat of soil, snow and vegetation canopy has been constructed. On this background, all important factors that may affect the water and heat balance in media can be considered naturally, and each factor and term possess distinct physical meaning. In the computation of water content and temperature, the water phase change and the heat transportation by water flow are taken into account. Moreover, particular attention has been given to the water vapor diffusion in soil for arid or semi-arid cases, and snow compaction. In the treatment of surface turbulent fluxes, the difference between aerodynamic and thermal roughness is taken into account. The aerodynamic roughness of vegetation is calculated as a function of canopy density, height and zero-plane displacement. An extrapolation of log linear and exponential relationship is used when calculating the wind profile within canopy. The model has been validated against field measurements in off-line simulations. The desirable model′s performance leads to the conclusion that the IAP94 is able to reproduce the main physical mechanisms governing the energy and water balances in the global land surface. Part II of the present study will concern the validation in a 3-D experiment coupled with the IAP Two-Level AGCM.

A New Method with High Confidence for Validation of Computer Simulation Models of Flight Systems

Computer simulation models may by used to gain further information about missile performance variability. Model validation is an important aspect of the test program for a missile system. Validation provides a basis for confidence in the model's results and is a necessary step if the model is to be used to draw inference about the behavior of the real missile. This paper is a review of methods useful for validation of computer simulation models of missile systems and provides a new method with high degree of confidence for validation of computer simulation models of missile systems. Some examples of the use of the new method in validating computer simulation models are given.

Mathematical Model and Experiment Validation of Fluid Torque by Shear Stress under Influence of Fluid Temperature in Hydro-viscous Clutch

The current design of hydro-viscous clutch（HVC） in tracked vehicle fan transmission mainly focuses on high-speed and high power. However, the fluid torque under the influence of fluid temperature can not be predicted accurately by conventional mathematical model or experimental research. In order to validate the fluid torque of HVC by taking the viscosity-temperature characteristic of fluid into account, the test rig is designed. The outlet oil temperature is measured and fitted with different rotation speed, oil film thickness, oil flow rate, and inlet oil temperature. Meanwhile, the film torque can be obtained. Based on Navier-Stokes equations and the continuity equation, the mathematical model of fluid torque is proposed in cylindrical coordinate. Iterative method is employed to solve the equations. The radial and tangential speed distribution, radial pressure distribution and theoretical flow rate are determined and analyzed. The models of equivalent radius and fluid torque of friction pairs are introduced. The experimental and theoretical results indicate that tangential speed distribution is mainly determined by the relative rotating speed between the friction plate and the separator disc. However, the radial speed distribution and pressure distribution are dominated by pressure difference at the lower rotating speed. The oil film fills the clearance and the film torque increases with increasing rotating speed. However, when the speed reaches a certain value, the centrifugal force will play an important role on the fluid distribution. The pressure is negative at the outer radius when inlet flow rate is less than theoretical flow, so the film starts to shrink which decreases the film torque sharply. The theoretical fluid torque has good agreement with the experimental data. This research proposes a new fluid torque mathematical model which may predict the film torque under the influence of temperature more accurately.

A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models

We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.

Comparison of Crop Model Validation Methods

In this paper, the many indices used in validation of crop models, such as RMSE （root mean square errors）, Sd （standard error of absolute difference）, da （mean absolute difference）, dap （ratio of da to the mean observation）, r （correlation）, and R2 （determination coefficient）, are compared for the same rice architectural parameter model, and their advantages and disadvantages are analyzed. A new index for validation of crop models, dap between the observed and the simulated values, is proposed, with dap〈5% as the suggested standard for precision of crop models. The different kinds of validation methods in crop models should be combined in the following aspects：（1） calculating da and dap; （2） calculating the RMSE or Sd; （3） calculating r and R2, at the same time, plotting 1：1 diagram.

SDG-based Model Validation in Chemical Process Simulation

Signed direct graph (SDG) theory provides algorithms and methods that can be applied directly to chemical process modeling and analysis to validate simulation models, and is a basis for the development of a software environment that can automate the validation activity. This paper is concentrated on the pretreatment of the model validation. We use the validation scenarios and standard sequences generated by well-established SDG model to validate the trends fitted from the simulation model. The results are helpful to find potential problems, assess possible bugs in the simulation model and solve the problem effectively. A case study on a simulation model of boiler is presented to demonstrate the effectiveness of this method.

Modeling Methane Emission from Rice Paddy Soils:Ⅱ.Model Validation and Application

A simulation model developed by the authors (Huang et al., 1999) was validated against independent field measurements of methane emission from rice paddy soils in Texas of USA, Tuzu Of China and Vercelli of Italy.A simplified version of the simulation model was further validated against methane emission measurements from various regions of the world, including italy, China, Indonesia, Philippines and the United States. Model validation suggested that the seasonal variation of methane emission was mainly regulated by rice growth and development and that methane emission could be predicted from rice net productivity, cultivar character, soil texture and temperature, and organic matter amendments. Model simulations in general agreed with the observations. The comparison between computed and measured methane emission resulted in correlation coefficients r2 values from 0.450 to 0.952, significant at 0.01-0.001 probability level.On the basis of available information on rice cultivated area, growth duration, grain yield, soil texture and temperature, methane emission from rice paddy soils of China's Mainland was estimated for 28 rice cultivated provinces/municipal cities by employing the validated model. The calculated daily methane emission rates, on a provincial scale, ranged from 0.12 to 0.71 g m-2 with an average of 0.26 g m-2. A total amount of 7.92 Tg CH4 per year, ranging from 5.89 to 11.17 Tg year-1, was estimated to be released from Chinese rice paddy soils. Of the total, 45% was emitted from the single-rice growing season, and 19% and 36% were from the early-rice and the late-rice growing seasons, respectively. Approximately 70% of the total was emitted in the region located at latitude between 25°and 32°N. The emissions from rice fields in Sichuan and Hunan provinces were calculated to be 2.34 Tg year-1, accounting for approximately 30% of the total.

Snow and sea ice thermodynamics in the Arctic:Model validation and sensitivity study against SHEBA data

Evolution of the Arctic sea ice and its snow cover during the SHEBA year were simulated by applying a high-resolution thermodynamic snow/ice model （HIGHTSI）. Attention was paid to the impact of albedo on snow and sea ice mass balance, effect of snow on total ice mass balance, and the model vertical resolution. The SHEBA annual simulation was made applying the best possible external forcing data set created by the Sea Ice Model Intercomparison Project. The HIGHTSI control run reasonably reproduced the observed snow and ice thickness. A number of albedo schemes were incorporated into HIGHTSI to study the feedback processes between the albedo and snow and ice thickness. The snow thickness turned out to be an essential variable in the albedo parameterization. Albedo schemes dependent on the surface temperature were liable to excessive positive feedback effects generated by errors in the modelled surface temperature. The superimposed ice formation should be taken into account for the annual Arctic sea ice mass balance.

Modeling of Arctic Sea Ice Variability During 1948–2009: Validation of Two Versions of the Los Alamos Sea Ice Model(CICE)

The Los Alamos sea ice model(CICE) is used to simulate the Arctic sea ice variability from 1948 to 2009. Two versions of CICE are validated through comparison with Hadley Centre Global Sea Ice and Sea Surface Temperature(Had ISST) observations. Version 5.0 of CICE with elastic-viscous-plastic(EVP) dynamics simulates a September Arctic sea ice concentration(SASIC) trend of –0.619 × 1012 m2 per decade from 1969 to 2009, which is very close to the observed trend(-0.585 × 1012 m2 per decade). Version 4.0 of CICE with EVP dynamics underestimates the SASIC trend(-0.470 × 1012 m2 per decade). Version 5.0 has a higher correlation(0.742) with observation than version 4.0(0.653). Both versions of CICE simulate the seasonal cycle of the Arctic sea ice, but version 5.0 outperforms version 4.0 in both phase and amplitude. The timing of the minimum and maximum sea ice coverage occurs a little earlier(phase advancing) in both versions. Simulations also show that the September Arctic sea ice volume(SASIV) has a faster decreasing trend than SASIC.

EMMD-Prony approach for dynamic validation of simulation models

Model validation and updating is critical to model credibility growth. In order to assess model credibility quantitatively and locate model error precisely, a new dynamic validation method based on extremum field mean mode decomposition（EMMD） and the Prony method is proposed in this paper. Firstly, complex dynamic responses from models and real systems are processed into stationary components by EMMD. These components always have definite physical meanings which can be the evidence about rough model error location. Secondly, the Prony method is applied to identify the features of each EMMD component. Amplitude similarity, frequency similarity, damping similarity and phase similarity are defined to describe the similarity of dynamic responses.Then quantitative validation metrics are obtained based on the improved entropy weight and energy proportion. Precise model error location is realized based on the physical meanings of these features. The application of this method in aircraft controller design provides evidence about its feasibility and usability.

Validation and Scenario Analysis of a Soil Organic Carbon Model

A model developed by the authors was validated against independent data sets. The data sets were obtained from field experiments of crop residue decomposition and a 7-year soil improvement in Yixing City, Jiangsu Province. Model validation indicated that soil organic carbon dynamics can be simulated from the weather variables of temperature, sunlight and precipitation, soil clay content and bulk density, grain yield of previous crops, qualities and quantities of the added organic matter. Model simulation in general a-greed with the measurements. The comparison between computed and measured resulted in correlation coefficient γ2 values of 0.9291* * * (n= 48) and 0.6431* * (n = 65) for the two experiments, respectively. Model prediction under three scenarios of no additional organic matter input, with an annual incorporation of rice and wheat straw at rates of 6.75t/ha and 9.0t/ha suggested that the soil organic carbon in Wanshi Township of Yixing City would be from an initial value of 7.85g/kg in 1983 to 6.30g/kg, 11.42g/kg and 13g/kg in 2014, respectively. Consequently, total nitrogen content of the soil was predicted to be respectively 0.49g/kg, 0.89g/kg and 1.01g/kg under the three scenarios.

Validation of SSiB Model over Grassland with CHeRES Field Experiment Data in 2001

The Simplified Simple Biosphere model (SSiB) is validated in off-line simulations against field measurements in the summer of 2001 from the China Heavy Rainfall Experiment and Study (CHeRES) over a grassland site located in the lower reaches of the Yangtze River. When initialized and driven by the observed atmospheric forcing, the model reproduced the observed surface heat fluxes and surface skin temperature realistically. The model was also able to well simulate the variation of soil water content. The sensitivity experiments found that the leaf reflectance was the most significant parameter in improving the estimation of surface albedo during both wet and dry periods. This study suggests that the model is capable of simulating the physical processes and of assessing the impact of biophysical parameters that relate to land-atmosphere interactions over the eastern Asian monsoon regions, which is crucial for mesoscale atmospheric models.

Application of SWAT Model to the Olifants Basin: Calibration, Validation and Uncertainty Analysis

The application of the Soil and Water Assessment Tool (SWAT) to the Olifants Basin in South Africa was the focus of our study with emphasis on calibration, validation and uncertainty analysis. The Basin was discretized into 23 sub-basins and 226 Hydrologic Response Units (HRUs) using 3 arc second (90 m × 90 m) pixel resolution SRTM DEM with stream gauge B7H015 as the Basin outlet. Observed stream flow data at B7H015 were used for model calibration (1988-2001) and validation (2002-2013) using the split sample approach. Relative global sensitivity analysis using SUFI-2 algorithm was used to determine sensitive parameters to stream flow for calibration of the model. Performance efficiency of the Olifants SWAT model was assessed using Nash-Sutcliffe (NSE), coefficient of determination (R2), Percent Bias (PBIAS) and Root Mean Square Error-Observation Standard deviation Ratio (RSR). Sensitivity analysis revealed in decreasing order of significance, runoff curve number (CN2), alpha bank factor (ALPHA_BNK), soil evaporation compensation factor (ESCO), soil available water capacity (SOIL_AWC, mm H2O/mm soil), groundwater delay (GW_ DELAY, days) and groundwater “revap” coefficient (GW_REVAP) to be the most sensitive parameters to stream flow. Analysis of the model during the calibration period gave the following statistics;NSE = 0.88;R2 = 0.89;PBIAS = -11.49%;RSR = 0.34. On the other hand, statistics during the validation period were NSE = 0.67;R2 = 0.79;PBIAS = -20.69%;RSR = 0.57. The observed statistics indicate the applicability of the SWAT model in simulating the hydrology of the Olifants Basin and therefore can be used as a Decision Support Tool (DST) by water managers and other relevant decisions making bodies to influence policy directions on the management of watershed processes especially water resources.