Federated Learning Model for Auto Insurance Rate Setting Based on Tweedie Distribution

In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry.To study the mechanical behavior of a typical ductile cast iron(GJS-450)with nodular graphite,uni-axial quasi-static and dynamic tensile tests at strain rates of 10^(-4),1,10,100,and 250 s^(-1)were carried out.In order to investigate the influence of stress state on the deformation and fracture parameters,specimens with various geometries were used in the experiments.Stress strain curves and fracture strains of the GJS-450 alloy in the strain rate range of 10^(-4)to 250 s^(-1)were obtained.A strain rate-dependent plastic flow model was proposed to describe the mechanical behavior in the corresponding strain-rate range.The available damage model was extended to take the strain rate into account and calibrated based on the analysis of local fracture strains.Simulations with the proposed plastic flow model and the damage model were conducted to observe the deformation and fracture process.The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys.The predictions with the proposed plastic flow and damage models at various strain rates agree well with the experimental results,which illustrates that the rate-dependent plastic flow and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.The proposed plastic flow and damage models can be used to describe the deformation and fracture analysis of materials with similar properties.

Evaluation of the Impact of Refined Quality Control Management Model on the Qualified Rate of Disinfection and Sterilization of Surgical Instruments in the Sterilization Supply Center

Objective:To evaluate the application value of a refined quality control management model for a sterilization supply center.Methods:A retrospective analysis was conducted on the work situation of the sterilization supply center from January 2021 to January 2023.The work situation before January 31,2022,was classified as the control group;a routine quality control management model was implemented,and the work situation after January 31,2022,was classified as the observation group.The quality of medical device management and department satisfaction between the two groups were compared.Results:The timely recovery and supply rate,classification and cleaning pass rate,disinfection pass rate,packaging pass rate,sterilization pass rate,and department satisfaction score in the observation group were all higher than those of the control group(P<0.05).Conclusion:Implementing a refined quality control management model in the sterilization supply center can improve the quality management level of medical devices and department satisfaction and is worthy of promotion.

Application of site-specific biomass models to quantify spatial distribution of stocks and historical emissions from deforestation in a tropical forest ecosystem

Allometric equations developed for the Lama forest, located in southern Benin, West Africa, were applied to estimate carbon stocks of three vegetation types：undisturbed forest, degraded forest, and fallow. Carbon stock of the undisturbed forest was 2.7 times higher than that in the degraded forest and 3.4 times higher than that in fallow. The structure of the forest suggests that the individual species were generally concentrated in lower diameter classes. Carbon stock was positively correlated to basal area and negatively related to tree density, suggesting that trees in higher diameter classes contributed significantly to the total carbon stock. The study demonstrated that large trees constitute an important component to include in the sampling approach to achieve accurate carbon quantification in forestry. Historical emissions from deforestation that converted more than 30% of the Lama forest into cropland between the years 1946 and 1987 amounted to 260,563.17 tons of carbon per year（t CO2/year） for the biomass pool only. The study explained the application of biomass models and ground truth data to estimate reference carbon stock of forests.

Country-based modelling of COVID-19 case fatality rate:A multiple regression analysis

BACKGROUND The spread of the severe acute respiratory syndrome coronavirus 2 outbreak worldwide has caused concern regarding the mortality rate caused by the infection.The determinants of mortality on a global scale cannot be fully understood due to lack of information.AIM To identify key factors that may explain the variability in case lethality across countries.METHODS We identified 21 Potential risk factors for coronavirus disease 2019(COVID-19)case fatality rate for all the countries with available data.We examined univariate relationships of each variable with case fatality rate(CFR),and all independent variables to identify candidate variables for our final multiple model.Multiple regression analysis technique was used to assess the strength of relationship.RESULTS The mean of COVID-19 mortality was 1.52±1.72%.There was a statistically significant inverse correlation between health expenditure,and number of computed tomography scanners per 1 million with CFR,and significant direct correlation was found between literacy,and air pollution with CFR.This final model can predict approximately 97%of the changes in CFR.CONCLUSION The current study recommends some new predictors explaining affect mortality rate.Thus,it could help decision-makers develop health policies to fight COVID-19.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates (da/dN) of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-ΔK relations, the confidence-based da/dN-ΔK relations, and the probabilistic- and confidence-based da/dN-ΔK relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

Quantitative Model for Estimating Soil Erosion Rates Using 137 Cs *1

A quantitative model was developed to relate the amount of 137 Cs loss from the soil profile to the rate of soil erosion. According to mass balance model, the depth distribution pattern of 137 Cs in the soil profile, the radioactive decay of 137 Cs, sampling year and the difference of 137 Cs fallout amount among years were taken into consideration. By introducing typical depth distribution functions of 137 Cs into the model, detailed equations for the model were got for different soils. The model shows that the rate of soil erosion is mainly controlled by the depth distribution pattern of 137 Cs, the year of sampling, and the percentage reduction in total 137 Cs. The relationship between the rate of soil loss and 137 Cs depletion is neither linear nor logarithmic. The depth distribution pattern of 137 Cs is a major factor for estimating the rate of soil loss. Soil erosion rate is directly related with the fraction of 137 Cs content near the soil surface. The influences of the radioactive decay of 137 Cs, sampling year and 137 Cs input fraction are not large compared with others.

Research on the influences of confining pressure and strain rate on NEPE propellant:Experimental assessment and constitutive model

In order to study the influences of confining pressure and strain rate on the mechanical properties of the Nitrate Ester Plasticized Polyether(NEPE)propellant,uniaxial tensile tests were conducted using the selfmade confining pressure system and material testing machine.The stress-strain responses of the NEPE propellant under different confining pressure conditions and strain rates were obtained and analyzed.The results show that confining pressure and strain rate have a remarkably influence on the mechanical responses of the NEPE propellant.As confining pressure increases(from 0 to 5.4 MPa),the maximum tensile stress and ultimate strain increase gradually.With the coupled effects of confining pressure and strain rate,the value of the maximum tensile stress and ultimate strain at 5.4 MPa and 0.0667 s^(-1)is 2.03 times and 2.19 times of their values under 0 MPa and 0.00333 s^(-1),respectively.Afterwards,the influence mechanism of confining pressure on the NEPE propellant was analyzed.Finally,based on the viscoelastic theory and continuous damage theory,a nonlinear constitutive model considering confining pressure and strain rate was developed.The damage was considered to be rate-dependent and pressuredependent.The constitutive model was validated by comparing experimental data with predictions of the constitutive model.The whole maximum stress errors of the model predictions are lower than 4%and the corresponding strain errors are lower than 7%.The results show that confining pressure can suppress the damage initiation and evolution of the NEPE propellant and the nonlinear constitutive model can describe the mechanical responses of the NEPE propellant under various confining pressure conditions and strain rates.This research can lay a theoretical foundation for analyzing the structural integrity of propellant grain accurately under working pressure loading.

GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.

PROBABILISTIC MODELS FOR LONG FATIGUE CRACK GROWTH RATES OF LZ50 AXLE STEEL

Experimental study is performed on the probabilistic models for the long fatigue crack growth rates （da/dN） of LZ50 axle steel. An equation for crack growth rate was derived to consider the trend of stress intensity factor range going down to the threshold and the average stress effect. The probabilistic models were presented on the equation. They consist of the probabilistic da/dN-△K relations, the confidence-based da/dN-△K relations, and the probabilistic- and confidence-based da/dN-△K relations. Efforts were made respectively to characterize the effects of probabilistic assessments due to the scattering regularity of test data, the number of sampling, and both of them. These relations can provide wide selections for practice. Analysis on the test data of LZ50 steel indicates that the present models are available and feasible.

A Dynamic Knowledge Model for Design of Suitable Sowing Date and Sowing Rate in Winter Wheat

Based on research concerning dynamic relationships of winter wheat growth to environments and production conditions, a winter wheat model for selecting suitable sowing date, population density and sowing rate under different varieties, spatial and temporal environments was developed. Case studies on sowing date with the data sets of five different eco-sites, three climatic years and soil fertility levels, and on population density and sowing rate with the data sets of two different variety types, three different soil types, soil fertility levels, sowing dates and grain yield levels indicate a good model performance for decision-making.

A Strain Rate Dependent Constitutive Model for the Lower Silurian Longmaxi Formation Shale in the Fuling Gas Field of the Sichuan Basin,China

Shale,as a kind of brittle rock,often exhibits different nonlinear stress-strain behavior,failure and timedependent behavior under different strain rates.To capture these features,this work conducted triaxial compression tests under axial strain rates ranging from 5×10-6 s-1 to 1×10-3 s-1.The results show that both elastic modulus and peak strength have a positive correlation relationship with strain rates.These strain rate-dependent mechanical behaviors of shale are originated from damage growth,which is described by a damage parameter.When axial strain is the same,the damage parameter is positively correlated with strain rate.When strain rate is the same,with an increase of axial strain,the damage parameter decreases firstly from an initial value(about 0.1 to 0.2),soon reaches its minimum(about 0.1),and then increases to an asymptotic value of 0.8.Based on the experimental results,taking yield stress as the cut-off point and considering damage variable evolution,a new measure of micro-mechanical strength is proposed.Based on the Lemaitre’s equivalent strain assumption and the new measure of micro-mechanical strength,a statistical strain-rate dependent damage constitutive model for shale that couples physically meaningful model parameters was established.Numerical back-calculations of these triaxial compression tests results demonstrate the ability of the model to reproduce the primary features of the strain rate dependent mechanical behavior of shale.

Development of an aftershock occurrence model calibrated for Turkey and the resulting likelihoods

This paper presents the calibration of Omori’s aftershock occurrence rate model for Turkey and the resulting likelihoods. Aftershock occurrence rate models are used for estimating the probability of an aftershock that exceeds a specific magnitude threshold within a time interval after the mainshock. Critical decisions on the post-earthquake safety of structures directly depend on the aftershock hazard estimated using the occurrence model. It is customary to calibrate models in a region-specific manner. These models depend on rate parameters(a, b, c and p) related to the seismicity characteristics of the investigated region. In this study, the available well-recorded aftershock sequences for a set of Mw ≥ 5.9 mainshock events that were observed in Turkey until 2012 are considered to develop the aftershock occurrence model. Mean estimates of the model parameters identified for Turkey are a =-1.90, b = 1.11, c = 0.05 and p = 1.20. Based on the developed model, aftershock likelihoods are computed for a range of different time intervals and mainshock magnitudes. Also, the sensitivity of aftershock probabilities to the model parameters is investigated. Aftershock occurrence probabilities estimated using the model are expected to be useful for post-earthquake safety evaluations in Turkey.

STUDY ON GREY FORECASTING MODEL OF COPPER EXTRACTION RATE WITH BIOLEACHING OF PRIMARY SULFIDE ORE

A model GM （grey model） （1,1） for forecasting the rate of copper extraction during the bioleaching of primary sulphide ore was established on the basis of the mathematical theory and the modeling process of grey system theory. It was used for forecasting the rate of copper extraction from the primary sulfide ore during a laboratory microbial column leaching experiment. The precision of the forecasted results were examined and modified via ＂posterior variance examination＂. The results show that the forecasted values coincide with the experimental values. GM （1,1） model has high forecast accuracy; and it is suitable for simulation control and prediction analysis of the original data series of the processes that have grey characteristics, such as mining, metallurgical and mineral processing, etc. The leaching rate of such copper sulphide ore is low. The grey forecasting result indicates that the rate of copper extraction is approximately 20% even after leaching for six months.

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

Predictive Model for Corrosion Rate of Oil Tubes in CO_2/H_2S Coexistent Environment Part Ⅰ: Building of Model

Based on an analysis of the existing models of CO 2 corrosion in literatures and the autoclave simulative experiments, a predictive model of corrosion rate (r corr) in CO 2/H 2S corrosion for oil tubes has been established, in which r corr is expressed as a function of pH, temperature (T), pressure of CO 2 (P CO 2) and pressure of H 2S (P H 2S). The model has been verified by experimental data obtained on N80 steel. The improved features of the predictive model include the following aspects: (1) The influence of temperature on the protectiveness of corrosion film is taken into consideration for establishment of predictive model of the r corr in CO 2/H 2S corrosion. The Equations of scale temperature and scale factor are put forward, and they fit the experimental result very well. (2) The linear relationship still exists between ln r corr and ln P CO 2 in CO 2/H 2S corrosion (as same as that in CO 2 corrosion). Therefore, a correction factor as a function of P H 2S has been introduced into the predictive model in CO 2/H 2S corrosion. (3) The model is compatible with the main existing models.

A model for estimating the rate constant between CO_2-CO gas and molten slag containing iron oxides using optical basicity

A simple model for estimating the rate constant between CO2-CO gas and molten slag containing iron oxides was developed using optical basicity only. In this model, the temperature dependence of the rate constant can be described by the Arrhenius law, and the activation energy can be expressed with a linear function of the slag＇s optical basicity. The model was applied to some molten slag systems, such as FeO, FeO-CaO, FeO-SiO2, FeO-Na2O, FeO-CaO-SiO2, FeO-SiO2-P2O5, FeO-SiOE-Na2O, and FeO-CaO-SiOE-P2O5. A comparison between the predicted results and measured data showed that the model worked well.

Prediction of leaching rate in heap leaching process by grey dynamic model GDM(1,1)

The method of developing GM（1,1） model is extended on the basis of grey system theory. Conditions for the transfer function that improve smoothness of original data sequence and decrease the revert error are given. The grey dynamic model is first combined with the transfer function to predict the leaching rate in heap leaching process. The results show that high prediction accuracy can be expected by using the proposed method. This provides a new approach to realize prediction and control of the future behavior of leaching kinetics.

DISSIPATION-BASED CONSISTENT RATE-DEPENDENT MODEL FOR CONCRETE

An energy-dissipation based viscoplastic consistency model is presented to describe the performance of concrete under dynamic loading. The development of plasticity is started with the thermodynamic hypotheses in order that the model may have a sound theoretical background. Independent hardening and softening and the rate dependence of concrete are described separately for tension and compression. A modified implicit backward Euler integration scheme is adopted for the numerical computation. Static and dynamic behavior of the material is illustrated with certain numerical examples at material point level and structural level, and compared with existing experimental data. Results validate the effectiveness of the model.