Application of a 2 Parameter Weibull Distribution in Modeling of State Holding Time in HIV/AIDS Transition Dynamics

This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Failure Time (AFT) model, Cox Proportional Hazards model, and Survival model, we assess the effectiveness of these models in capturing survival rates across varying gender, age groups, and treatment categories. Simulated data was used to fit the models, with model identification criteria (AIC, BIC, and R2) applied for evaluation. Results indicate that the AFT model is particularly sensitive to interaction terms, showing significant effects for older age groups (50 - 60 years) and treatment interaction, while the Cox model provides a more stable fit across all age groups. The Survival model displayed variability, with its performance diminishing when interaction terms were introduced, particularly in older age groups. Overall, while the AFT model captures the complexities of interactions in the data, the Cox model’s stability suggests it may be better suited for general analyses without strong interaction effects. The findings highlight the importance of model selection in survival analysis, especially in complex disease progression scenarios like HIV/AIDS.

基于Weibull分布的煤矸石对混凝土断裂损伤特性的影响

为探索煤矸石质量取代率、粉煤灰质量取代率、水灰比对I型裂缝煤矸石混凝土荷载-裂缝张开位移、荷载-跨中挠度曲线、断裂韧性、断裂能的影响规律,对I型裂缝煤矸石混凝土进行三点弯曲试验,将所得结果结合损伤力学及Weibull分布函数建立煤矸石混凝土的断裂损伤本构模型。结果表明:煤矸石质量取代率对预制I型裂缝的煤矸石混凝土断裂性能影响最大,粉煤灰质量取代率对其断裂韧度影响较大,水灰比对其断裂能影响较大;提升煤矸石混凝土断裂时断裂韧度及断裂能的最佳组合的煤矸石质量取代率为25%、粉煤灰质量取代率为10%、水灰比为0.5;经对比可知,所得损伤本构模型对应的应力-应变曲线与试验曲线高度吻合。研究成果为煤矸石混凝土的制备及工程实际应用研究提供了参考。

基于Weibull混合分布的航空发动机零部件寿命建模

针对航空发动机在维修工作中存在重要零部件使用寿命及失效率难以估算的问题,搜集了发动机重要零部件燃油计量活门、整体驱动发电机、液压机械组件的使用寿命数据,并运用Weibull混合分布及单Weibull分布分别建立了上述重要零部件的寿命模型。在模型求解过程中采用了经典的三参数相关系数优化法,求出发动机重要零部件的可靠度、失效率及故障概率密度函数。通过计算得出Weibull混合分布模型的线性相关系数r_(g)比单Weibull分布模型的大;同时K-S假设检验结果显示,Weibull混合分布的统计量观测值D_(n)均小于临界值D_(30,0.1)。结果表明:相对于单Weibull分布,Weibull混合分布模型更精确地表征了发动机重要零部件的寿命数据,从而有效地提高寿命参数的估算精度;Weibull混合分布模型的可靠性有助于发动机管理工程师制定视情维修方案;并对航材备件的数量有指导意义,具有较高的推广应用价值。

基于Weibull分布的石砌体单轴受压损伤本构模型

石砌体的本构模型是石砌体力学计算和有限元数值模拟的重要基础和前提条件。为了深入研究石砌体单轴受压下的本构关系,基于损伤力学理论,应用双参数Weibull分布函数反映损伤变量,根据石砌体单轴受压应力-应变全过程曲线的特征条件确定其参数,推导并建立了石砌体单轴受压损伤本构模型,将已有试验数据验证本构模型的正确性,并将本构模型与典型的砌体本构模型进行对比分析,最后应用本构模型对已有石砌体拱桥试验进行有限元分析以验证本构模型的适用性。结果表明:所建模型与已有石砌体单轴受压试验结果吻合良好;所建模型验证了石砌体损伤演化的一般规律,符合典型的砌体本构模型的一般趋势;所建模型可应用于石砌体结构有限元分析计算,适用性良好。

基于Weibull分布的缺口件多轴疲劳寿命建模

针对多轴缺口件,引入Weibull分布建立考虑应力梯度效应的疲劳寿命预测方法.首先,将最大应变能密度定义为损伤参量,并结合坐标变换确定能反映裂纹萌生和扩展的临界面位置;其次,利用有限元方法提取临界面特定路径的应力分布,并对其进行归一化处理得到多轴等效应力梯度因子,进而基于GSP应变能密度模型得出应变能密度与实验寿命的线性关系;最后,结合等效应力梯度因子、应变能密度模型和Weibull分布,基于Von-Mises准则提出了新的疲劳寿命预测方法,并利用该方法分别求出失效概率10%、50%和90%对应的疲劳寿命.为验证该方法,将计算结果与SWT模型、FS模型和Manson-Coffin方程的计算结果进行对比,结果表明该方法的预测精度较高.

基于Weibull分布的非均质隧洞围岩破裂碎胀FDEM数值模拟研究

岩石材料具有非均质特征,矿物颗粒和胶结材料强度在统计学上服从Weibull分布。基于有限元-离散元耦合数值模拟方法(FDEM)提出了三角形单元弹性模量和四边形节理单元强度服从Weibull分布的参数赋值流程,随后研究了非均质岩样在单轴压缩、三轴压缩和巴西劈裂下的力学特征和破坏行为,最后对非均质隧洞围岩在高应力下的破裂碎胀大变形机制进行了模拟研究。结果表明:提出的随机参数赋值方法可建立不同弹性模量三角形单元数目服从Weibull分布、且空间分布具有随机性的FDEM数值模型;非均质岩样单轴抗压强度、三轴抗压强度、巴西劈裂抗拉强度、等效粘聚力和等效内摩擦角随着非均质度m的增大,均呈指数增大,并向均质材料逼近;高应力非均质隧洞围岩随着m的增大,裂隙网络形态变化不大,均以共轭剪切破裂为主,并伴随少量拉伸裂隙,但围岩破坏程度和裂隙扩展范围呈指数降低。

基于混合双参数Weibull分布的冬夏两季香港地区某地的行人风环境舒适度分析

城市的密集建筑会影响周边区域风环境,甚至产生行人风环境问题。研究了香港地区气象条件,对比了双参数Weibull分布和混合双参数Weibull分布,结果表明混合双参数Weibull分布更加适合香港地区的气象数据;根据夏季以及冬季不同的情况,分析了夏季与冬季的行人风环境。在夏季,一号和二号建筑之间的空地有不舒适的区域,在冬季,行人风环境舒适度整体较好。

由Chvátal定理引出的关于Weibull分布和Pareto分布的研究

受Chvátal定理的启发,本文研究了随机变量不超过其期望的概率的下确界问题.利用分析的方法,我们得到了当随机变量的分布为Weibull分布或Pareto分布时该随机变量不超过其期望的概率的下确界.

A Novel Modified Alpha Power Transformed Weibull Distribution and Its Engineering Applications

This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.

A New Three-Parameter Inverse Weibull Distribution with Medical and Engineering Applications

The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.

结合改进Weibull时间函数的开采沉陷动态预测模型

煤炭开采引起的地表沉陷是一个多维动态变化过程,动态预测可以获取采空区上方任意位置、时刻的形变大小,对保护地面基础设施和人民生命安全具有重要意义。为实现地表沉陷的动态预测,针对Weibull时间函数模型结构复杂、参数较多等不足,基于开采沉陷相关理论,建立了仅含一个模型参数,且可以准确描述地表点下沉量、下沉速度、下沉加速度的改进Weibull时间函数模型。在此基础上,结合已有的地表沉陷盆地模型,建立了一种新的开采沉陷动态预测模型,详细阐述了模型参数的确定方法及其对沉陷盆地形态的影响,并结合某矿313工作面和3214工作面实测数据验证了模型的预测精度和适用性。结果表明:改进的Weibull时间函数模型最大均方根误差为52 mm,最大相对误差为2.1%,较改进前分别提高了60.3%和64.4%;开采沉陷动态预测模型预测的下沉曲线形态和实测下沉曲线形态一致,最大均方根误差为17 mm,最大相对误差为1.76%,表明该模型可以预测地表沉陷过程,具有较好的适用性和可靠性。该研究结果可为矿区地表沉陷动态预测提供参考。

基于改进Weibull模型的高强缝合锚钉缝线强度预测

为消除缝合锚钉缝线在使用过程中存在断裂的风险,以8.3 tex超高分子量聚乙烯纤维为原材料,采用编织工艺制备了单层编织缝线和轴向衬纱双层编织缝线。为了研究其力学性能,选择8、16、24、32、40、48 mm隔距对单纤维的断裂强力进行测试,选择50、200 mm隔距对8.3 tex复丝的断裂强力进行测试,选择200 mm隔距对单层编织缝线和轴向衬纱双层编织缝线的断裂强力进行测试。对纤维的直径和缝线中纤维与轴向夹角的角度进行测量。采用两参数Weibull模型和改进Weibull模型对单纤维、8.3 tex复丝和单层编织缝线的断裂强度进行预测。结果表明:单层编织缝线的断裂强力为299.8 N,轴向衬纱双层编织缝线的断裂强力高达393.0 N。对8.3 tex复丝和单层编织缝线的断裂强度进行预测,改进Weibull模型的预测值准确度高。高强骨锚钉缝线的强力比同类型医用缝线更高,改进Weibull模型可对高强缝合锚钉缝线的强力进行精准预测,实现了从单纤维到复丝再到纱线的断裂强度预测,可为医用缝线结构设计和力学性能分析提供理论依据。

Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province,China

Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.

基于响应面法和Weibull分布的不锈钢纤维再生混凝土抗冻性能研究

【目的】在我国严寒地区,冻融损伤会使再生混凝土(RAC)结构提前达到耐久性极限甚至导致构件失效,为了延长再生混凝土(RAC)结构在严寒地区的使用寿命,【方法】对再生混凝土(RAC)、天然混凝土(NC)、普通钢纤维再生混凝土(PFRAC)和不锈钢纤维再生混凝土(SFRAC)进行冻融循环试验。经过冻融循环后,测得RAC、NC、PFRAC、SFRAC的质量损失及相对动弹性模量,分析冻融循环过程中混凝土内部的损伤机理及劣化规律。以相对动弹性模量为损伤变量,基于响应面模型(RSM)和Weibull分布建立了钢纤维再生混凝土冻融损伤模型,研究冻融循环次数、PF和SF的掺量对再生混凝土抗冻性的影响。【结果】结果表明,SF的掺入能有效延缓RAC质量的损失和相对动弹性模量的降低。冻融循环150次时,掺量为2%的SFRAC质量损失和相对动弹性模量分别下降3.01%和19.57%。SFRAC与RAC相比,质量损失率降低了0.4%,相对动弹性模量提高了14.17%。【结论】Weibull分布和响应面模型(RSM)的预测结果 基本一致,但RSM预测值的相对误差要低于Weibull分布的预测值。两种模型的相关系数R2均在0.94以上,预测结果较为准确,可为钢纤维再生混凝土在寒冷地区的使用提供理论参考。

Spatial distribution of shallow landslides caused by Typhoon Lekima in 2019 in Zhejiang Province, China

In recent years, the coastal region of Southeast China has witnessed a significant increase in the frequency and intensity of extreme rainfall events associated with landfalling typhoons. The hilly and mountainous terrain of this area, combined with rapid rainfall accumulation, has led to a surge in flash floods and severe geological hazards. On August 10, 2019, Typhoon Lekima made landfall in Zhejiang Province, China, and its torrential rainfall triggered extensive landslides, resulting in substantial damage and economic losses. Utilizing high-resolution satellite images, we compiled a landslide inventory of the affected area, which comprises a total of 2,774 rainfallinduced landslides over an area of 2965 km2. The majority of these landslides were small to mediumsized and exhibited elongated, clustered patterns. Some landslides displayed characteristics of high-level initiation, obstructing or partially blocking rivers, leading to the formation of debris dams. We used the inventory to analyze the distribution pattern of the landslides and their relationship with topographical, geological, and hydrological factors. The results showed that landslide abundance was closely related to elevation, slope angle, faults, and road density. The landslides were predominantly located in hilly and low mountainous areas, with elevations ranging from 150 to 300 m, slopes of 20 to 30 degrees, and a NE-SE aspect. Notably, we observed the highest Landslide Number Density(LND) and Landslide Area Percentage(LAP) in the rhyolite region. Landslides were concentrated within approximately 4 km on either side of fault zones, with their size and frequency negatively correlated with distances to faults, roads, and river systems. Furthermore, under the influence of typhoons, regions with denser vegetation cover exhibited higher landslide density, reaching maximum values in shrubland areas. In areas experiencing significantly increased concentrated rainfall, landslide density also showed a corresponding rise. In terms of spatial distribution, the rainfall-triggered landslides primarily occurred in the northeastern part of the study area, particularly in regions characterized by complex topography such as Shanzao Village in Yantan Town, Xixia Township, and Shangzhang Township. The research findings offer crucial data on the rainfallinduced landslides triggered by Typhoon Lekima, shedding light on their spatial distribution patterns. These findings provide valuable references for mitigating risks and planning reconstruction in typhoon-affected area.

FPGA-based position reconstruction method for neutron beam flux spatial distribution measurement in BNCT

A new measurement method for the spatial distribution of neutron beam flux in boron neutron capture therapy(BNCT)is being developed based on the two-dimensional Micromegas detector.To address the issue of long processing times in traditional offline position reconstruction methods,this paper proposes a field programmable gate array based online position reconstruction method utilizing the micro-time projection chamber principle.This method encapsulates key technical aspects:a self-adaptive serial link technique built upon the dynamical adjustment of the delay chain length,fast sorting,a coordinate-matching technique based on the mapping between signal timestamps and random access memory(RAM)addresses,and a precise start point-merging technique utilizing a circular combined RAM.The performance test of the selfadaptive serial link shows that the bit error rate of the link is better than 10-12 at a confidence level of 99%,ensuring reliable data transmission.The experiment utilizing the readout electronics and Micromegas detector shows a spatial resolution of approximately 1.4 mm,surpassing the current method’s resolution level of 5 mm.The beam experiment confirms that the readout electronics system can obtain the flux spatial distribution of neutron beams online,thus validating the feasibility of the position reconstruction method.The online position reconstruction method avoids traditional methods,such as bubble sorting and traversal searching,simplifies the design of the logic firmware,and reduces the time complexity from O(n2)to O(n).This study contributes to the advancement in measuring neutron beam flux for BNCT.

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.

Predicting the probability distribution of Martian rocks mechanical property based on microscale rock mechanical experiments and accurate grain-based modeling

The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribution of Martian rocks mechanical property for the success of Mars exploration.In this paper,a fast and accurate probability distribution method for predicting the macroscale elastic modulus of Martian rocks was proposed by integrating the microscale rock mechanical experiments(micro-RME),accurate grain-based modeling(AGBM)and upscaling methods based on reliability principles.Firstly,the microstructure of NWA12564 Martian sample and elastic modulus of each mineral were obtained by micro-RME with TESCAN integrated mineral analyzer(TIMA)and nanoindentation.The best probability distribution function of the minerals was determined by Kolmogorov-Smirnov(K-S)test.Secondly,based on best distribution function of each mineral,the Monte Carlo simulations(MCS)and upscaling methods were implemented to obtain the probability distribution of upscaled elastic modulus.Thirdly,the correlation between the upscaled elastic modulus and macroscale elastic modulus obtained by AGBM was established.The accurate probability distribution of the macroscale elastic modulus was obtained by this correlation relationship.The proposed method can predict the probability distribution of Martian rocks mechanical property with any size and shape samples.

基于新扩展Weibull分布的参数估计及应用

Weibull分布是Arccosine-X分布族的一个特例,本文提出一种新的具有两参数的Arccosine-Weibull(AC-W)分布。研究了AC-W分布的基本统计性质,使用频率学派的最大似然估计(MLE)方法讨论了AC-W分布的参数估计,并通过蒙特卡罗模拟分析来评估所获得估计量的效率,最后选取一组真实的洪峰数据集,将AC-W与其他竞争分布进行比较。采用AIC、BIC、CAIC和HQIC等信息准则评估AC-W分布在拟合数据方面相较于竞争分布的优越性,证明了AC-W分布的有效性和灵活性。

基于Weibull分布和MOV脉冲电流特性的智能SPD脉冲电流寿命评估方法

浪涌保护器(SPD)是低压电力线路中用于限制过电压,泄放电涌电流的重要电气装置。随着物联网的发展,传统的SPD逐步发展成为具有在线监测工作状态、故障诊断、寿命预测等功能的智能SPD。由于SPD的寿命与其核心元件金属氧化物压敏电阻(MOV)的寿命密切相关,文中基于Weibull分布并结合MOV的脉冲电流寿命特性,通过试验得到了MOV在不同冲击下的特性方程。根据建立的脉冲电流寿命特性方程和运行中SPD的脉冲电流监测数据,提出了一种SPD剩余寿命评估方法,为智能SPD的不断发展提供了理论支持。