Weibull distribution

Weibull 分布
  • 文章类型: Journal Article
    沥青混凝土面板的开裂问题是水工沥青混凝土防渗体设计中的重要考虑因素。蓄水期间水位不均匀上升或下降的面板可能会产生加载率影响。研究沥青混凝土在不同加载速率下的断裂韧性值至关重要。本研究采用统计学方法计算断裂指数KIC,使用半圆形弯曲试验(SCB)来检查加载速率对水工沥青混凝土I型断裂模式的影响。采用双参数威布尔分布曲线对数据进行分析,提供对KIC试样的最小数量的见解。结果表明KIC随加载速率而增加,以更快的速度获得更大的数据分散。Weibull分布曲线成功地拟合了不同加载速率下的断裂行为,提供有价值的预测。这项研究估计SCB测试样本的最小数量为9,基于0.95的置信水平和不超过5%的相对偏差。
    The cracking problem of asphalt concrete panels is a crucial consideration in the design of hydraulic asphalt concrete seepage control bodies. Panels experiencing uneven rises or falls of water levels during impoundment may exhibit loading rate effects. Investigating the fracture toughness value of asphalt concrete under varying loading rates is essential. This study employs a statistical method to calculate the fracture index KIC, using the semi-circular bending test (SCB) to examine the effect of loading rates on the Type I fracture mode of hydraulic asphalt concrete. The data are analyzed using the two-parameter Weibull distribution curve, offering insights into the minimum number of KIC test specimens. The results indicate an increase in KIC with loading rate, with greater data dispersion at faster rates. The Weibull distribution curve successfully fits the fracture behavior under different loading rates, providing valuable predictions. This study estimates the minimum number of SCB test specimens to be nine, based on a confidence level of 0.95 and a relative deviation not exceeding 5%.
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  • 文章类型: Journal Article
    对新能源汽车(NEV)的需求不断增长,导致对钴作为关键材料的需求相应增加。对我国新能源汽车产业的钴资源回收潜力进行估算,以确保钴金属矿产的供需平衡至关重要。本文基于2013年至2022年新能源乘用车(NEPV)销量的历史数据,估算了2023年至2035年的NEPV销量。在此基础上,Weibull分布用于分析NEPV在中国的不同销售场景(低销售和高销售),从2023年到2035年,在三种电池寿命情景(8年、10年和12年)下评估了钴金属在NEPV中的回收潜力。根据上述情况,2035年,钴的最大回收潜力预计为166.9千吨,经济价值49.01-946亿元。此外,分析了钴的回收潜力可以满足NEPV市场需求的程度。我们的分析得出结论,回收钴作为二次供应已经成为补充一次供应的必要解决方案,可以为缓解供需压力做出重大贡献。
    The growing demand for new energy vehicles (NEVs) has resulted in a corresponding increase in demand for cobalt as a critical material. It is crucial to estimate the cobalt resource recycling potential of China\'s NEV industry to ensure a balance between the supply and demand for cobalt metal minerals. This article is based on using the historical data of the new energy passenger vehicle (NEPV) sales volume from 2013 to 2022 to estimate the NEPV sales volume from 2023 to 2035. On this basis, the Weibull distribution was used to analyse the different sales scenarios (low sales and high sales) of NEPVs in China, and the recycling potential of cobalt metal in NEPVs was evaluated under three battery life scenarios (8, 10 and 12 years) from 2023 to 2035. Based on the above scenarios, in 2035, the greatest recycling potential of cobalt is predicted to be 166.9 kilotonnes, with economic values of CNY 49.01-94.60 billion. Moreover, the extent to which the recycling potential of cobalt can cover the market demand for NEPVs was analysed. Our analysis concluded that recycling cobalt as a secondary supply has emerged as a necessary solution to supplement the primary supply, which can make a significant contribution to alleviating the pressure of the supply and demand.
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  • 文章类型: Journal Article
    三相异步电动机在机械工业中具有广泛的应用,并且故障诊断有助于电动机的健康运行。为了提高三相异步电动机故障诊断的准确性和通用性,提出了一种基于多尺度Weibull色散熵(WB-MDE)和粒子群优化-支持向量机(PSO-SVM)相结合的三相异步电机故障诊断方法。首先,Weibull分布(WB)用于线性化和平滑振动信号,以获得有关电机状态的更清晰的信息。其次,使用多尺度色散熵(MDE)提取给定序列的规则性和有序性的定量特征。然后,支持向量机(SVM)用于构造分类器,参数通过粒子群优化(PSO)算法进行优化,并将提取的特征向量送入优化的SVM模型进行分类识别。最后,通过添加具有不同信噪比的高斯白噪声的原始数据和CHIST-ERASOON公共数据集,测试了本文提出的模型的准确性和泛化性。本文搭建了三相异步电机振动信号实验平台,通过压电加速度传感器来辨别电机的四种状态数据,验证了所提方法的有效性。利用本文提出的WB-MDE方法对采集到的数据进行特征提取和利用优化的PSO-SVM方法对提取到的特征进行故障分类和识别的准确率为100%。此外,对所提出的模型进行了抗噪性和泛化性测试。最后,通过实验以及抗噪和泛化测试验证了该方法的优越性。
    Three-phase asynchronous motors have a wide range of applications in the machinery industry and fault diagnosis aids in the healthy operation of a motor. In order to improve the accuracy and generalization of fault diagnosis in three-phase asynchronous motors, this paper proposes a three-phase asynchronous motor fault diagnosis method based on the combination of multiscale Weibull dispersive entropy (WB-MDE) and particle swarm optimization-support vector machine (PSO-SVM). Firstly, the Weibull distribution (WB) is used to linearize and smooth the vibration signals to obtain sharper information about the motor state. Secondly, the quantitative features of the regularity and orderliness of a given sequence are extracted using multiscale dispersion entropy (MDE). Then, a support vector machine (SVM) is used to construct a classifier, the parameters are optimized via the particle swarm optimization (PSO) algorithm, and the extracted feature vectors are fed into the optimized SVM model for classification and recognition. Finally, the accuracy and generalization of the model proposed in this paper are tested by adding raw data with Gaussian white noise with different signal-to-noise ratios and the CHIST-ERA SOON public dataset. This paper builds a three-phase asynchronous motor vibration signal experimental platform, through a piezoelectric acceleration sensor to discern the four states of the motor data, to verify the effectiveness of the proposed method. The accuracy of the collected data using the WB-MDE method proposed in this paper for feature extraction and the extracted features using the optimization of the PSO-SVM method for fault classification and identification is 100%. Additionally, the proposed model is tested for noise resistance and generalization. Finally, the superiority of the present method is verified through experiments as well as noise immunity and generalization tests.
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  • 文章类型: Journal Article
    许多桥梁结构部件承受着重复的车辆载荷和温度梯度作用。结构内产生的循环拉伸应力可能导致混凝土过早疲劳破坏,显著损害结构部件的耐久性和可持续性。尽管已经获得了有关低强度路面混凝土和高强度结构混凝土的疲劳性能的大量知识,桥梁工程中使用最广泛的普通混凝土的研究仍在进行中。因此,在实验室进行了97个C50混凝土试件在恒定振幅正弦波下的四点弯曲疲劳试验,研究了普通混凝土和钢筋混凝土试件的弯曲疲劳行为,得到了混凝土在疲劳荷载作用下的循环变形演化规律。通过对试验结果的统计分析,推导了混凝土失效概率p为0.1~0.5的经验疲劳S-N方程。试样的疲劳寿命呈双参数威布尔分布。除了最大应力水平Smax之外,应力比R也是影响混凝土N的弯曲疲劳寿命的关键因素。在测试的应力水平下,半对数和对数方程几乎相同。后者预测Smax<0.70的疲劳寿命更长。钢筋的约束作用略微延长了混凝土的疲劳开裂起始寿命。从这项研究中对混凝土弯曲疲劳性能的了解不仅有助于更好地理解结构混凝土,同时也为混凝土或复合桥面的实际评估提供了依据。
    Many bridge structural components are subjected to repetitive vehicle load and temperature gradient action. The resulting cyclic tensile stresses within the structures could cause premature fatigue failure of concrete, dramatically impairing structural components\' durability and sustainability. Although substantial knowledge of fatigue properties on low-strength pavement concrete and high-strength structural concrete has been obtained, research on the most widely used normal-grade ordinary concrete in bridge engineering is still ongoing. Therefore, a four-point bending fatigue test of 97 C50 concrete specimens under a constant amplitude sinusoidal wave was conducted in the laboratory, the flexural fatigue behavior of plain and reinforced concrete specimens was studied, and the cyclic deformation evolution of concrete under fatigue loading was obtained. The empirical fatigue S-N equations of concrete with a failure probability p of 0.1~0.5 were derived through statistical analysis of the test results. The fatigue life of the tested specimens exhibited a two-parameter Weibull distribution. In addition to the maximum stress level Smax, the stress ratio R is also a key factor affecting the flexural fatigue life of concrete N. The semi-logarithmic and logarithmic equations were almost identical at the tested stress levels, the latter predicting longer fatigue life for Smax < 0.70. The restraining effect from steel reinforcement slightly lengthened the concrete\'s fatigue cracking initiation life. The insight into concrete flexural fatigue properties from this study not only contributes to a better understanding of structural concrete, but also provides a basis for the practical evaluation of concrete or composite bridge decks.
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  • 文章类型: Journal Article
    作为复杂和异质的材料,岩石的力学性质仍需要进一步研究水的作用机理。在采空区地基处理、生态修复等工程项目中,描述非均匀含水砂岩介质的压裂过程尤为重要。该研究利用连续介质力学理论,采用弹塑性应变软化本构关系,并建立了数值模型,用于分析非均匀含水砂岩的单轴抗压强度和破坏特征。结果表明,与参考岩石样品相比,水进入岩样内部孔隙的毛细路径越短或与水的接触面积越大,岩石样品饱和所需的时间越短。水含量的增加会导致岩石样品的弹性模量迅速下降,并加剧其脆性。D2和D3组样品表现出平均峰强度下降到70.4%和62.1%,分别,随着弹性模量相应下降到90.78%和76.55%,表明显著的应变软化。虽然不同含水量的岩石样品的破坏模式保持一致,破坏的均匀性表现出显著的变化。体积含水量的增加增加了岩石样品之间互连裂缝的可能性,导致宏观机械性能如峰值强度逐渐下降,临界应变,和弹性模量。该研究对于推进采空区生态修复理论和施工技术具有重要意义。
    As complex and heterogeneous materials, the mechanical properties of rocks are still in need of further investigation regarding the mechanisms of the effects of water. In engineering projects such as goaf foundation treatment and ecological restoration, it is particularly important to describe the fracturing process of non-uniform water-containing sandstone media. The study utilized the theory of continuum mechanics to adopt an elastoplastic strain-softening constitutive relationship and develop a numerical model for analyzing the uniaxial compressive strength and failure characteristics of non-uniform water-containing sandstone. The results indicate that, compared with the reference rock sample, the shorter the capillary path of water entering the rock sample\'s internal pores or the larger the contact area with water, the shorter the time required for the rock sample to be saturated. Increasing the water content causes a rapid decline in the rock sample\'s elastic modulus and intensifies its brittleness. Group D2 and D3 samples exhibited a decrease in average peak strength to 70.4% and 62.1%, respectively, along with a corresponding decrease in the elastic modulus to 90.78% and 76.55%, indicating significant strain softening. While the failure mode of the rock sample remains consistent across different water contents, the homogeneity of failure shows significant variation. Increasing volumetric water content raises the likelihood of interconnecting cracks between rock samples, resulting in a progressive decline in macroscopic mechanical properties such as peak strength, critical strain, and elastic modulus. This research is significant in advancing the theory and construction technology for ecological restoration in goaf areas.
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  • 文章类型: Journal Article
    针对地下工程中岩石遇到的化学-力学-水力(C-M-H)作用问题,化学损伤变量,水损害变量,引入力损伤变量来定义岩石材料的退化程度。选择石材作为在pH3、4和7下进行酸腐蚀处理的样品,并定义了将pH值和暴露持续时间耦合的化学损伤因子。然后基于空间动员平面(SMP)准则和Lemaitre应变等效假设,本研究建立了考虑岩石化学腐蚀-水围压损伤的本构模型。提出的损伤本构模型采用极值方法通过理论推导确定了两个威布尔分布参数(m和F0),并在理论和实验曲线之间表现出令人满意的一致性。损伤本构模型可以在岩石三轴压缩过程的应力-应变特性中保持一致,验证了模型参数的合理性和可靠性。当受到水化学和约束的综合影响时,该模型有效地表示了岩石的力学性质和损伤特征。所提出的模型有助于更好地了解在水下环境中受化学腐蚀的有形岩石工程结构。
    Aiming at the problem of chemical-mechanics-hydro (C-M-H) action encountered by rocks in underground engineering, chemical damage variables, water damage variables, and force damage variables are introduced to define the degree of degradation of rock materials. Stone is selected as the sample for acid corrosion treatment at pH 3, 4, and 7, and a chemical damage factor is defined that coupled the pH value and duration of exposure. Then based on the spatial mobilized plane (SMP) criterion and the Lemaitre strain equivalence hypothesis, this research develops a constitutive model considering rock chemical corrosion-water-confining pressure damage. The proposed damage constitutive model employs the extremum method to ascertain the two Weibull distribution parameters (m and F0) by theoretical derivation and exhibits satisfactory conformity between the theoretical and experimental curves. The damage constitutive model can be consistent in the stress-strain characteristics of the rock triaxial compression process, which verifies the rationality and reliability of the model parameters. The model effectively represents the mechanical properties and damage characteristics of rocks when subjected to the combined influence of water chemistry and confinement. The presented model contributes to a better understanding of tangible rock-engineered structures subjected to chemical corrosion in underwater environments.
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  • 文章类型: Journal Article
    玻璃纤维增强聚合物(GFRP)具有优于传统钢的特性,比如轻量级,高强度,耐腐蚀性和高耐久性。GFRP钢筋可以是结构中钢筋的有用替代品,特别是那些在高腐蚀性环境中,以及承受高压缩压力的结构,如桥梁基础。采用数字图像相关(DIC)技术分析了GFRP筋在压缩条件下的应变演化规律。从DIC技术可以看出,GFRP筋的表面应变是均匀分布的,并且近似线性增加,GFRP筋的脆性劈裂破坏是由于在破坏阶段局部发生的高应变而发生的。此外,关于使用分布函数来描述GFRP的抗压强度和弹性模量的研究有限。在本文中,采用威布尔分布和伽马分布拟合GFRP筋的抗压强度和抗压弹性模量。平均抗压强度为667.05MPa,遵循威布尔分布。此外,平均压缩弹性模量为47.51GPa,遵循伽马分布。为了验证GFRP筋在受压条件下仍具有一定的强度,本文为其大规模应用提供了参数参考。
    Glass fiber-reinforced polymer (GFRP) has superior characteristics over traditional steel, such as lightweight, high strength, corrosion resistance and high durability. GFRP bars can be a useful alternative to steel bars in structures, specifically those in highly corrosive environments, as well as structures subjected to high compressive pressure such as bridge foundations. Digital image correlation (DIC) technology is used to analyze the strain evolution of GFRP bars under compression. It can be seen from using DIC technology that the surface strain of GFRP reinforcement is uniformly distributed and increases approximately linearly, and brittle splitting failure of GFRP bars happens due to locally occurring high strain at the failure stage. Moreover, there are limited studies on the use of distribution functions to describe the compressive strength and elastic modulus of GFRP. In this paper, Weibull distribution and gamma distribution are used to fit the compressive strength and compressive elastic modulus of GFRP bars. The average compressive strength is 667.05 MPa and follows Weibull distribution. Moreover, the average compressive elastic modulus is 47.51 GPa and follows gamma distribution. In order to verify that GFRP bars still have certain strength under compressive conditions, this paper provides a parameter reference for their large-scale application.
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  • 文章类型: Journal Article
    在珊瑚礁附近的基础设施建设方面,天然珊瑚骨料已被广泛用作制备“珊瑚混凝土”的替代有效建筑材料。这项研究的重点是在水泥基体系下珊瑚颗粒的力学性能和硬化机理。首先,珊瑚颗粒分为两类:珊瑚生物碎片颗粒(钙砂)和珊瑚母岩颗粒(石灰石)。随后,进行了一些基本的实验室测试,以比较样品的物理和化学性质。结果表明,珊瑚颗粒的比表面积和开孔大于石英砂。此外,岩屑和母岩颗粒的吸水率分别达到9.9%和22%,分别。为了进一步研究珊瑚颗粒的硬化机制,我们进行了颗粒压碎强度测试,抗压强度试验和纳米压痕试验。无论测试的组和粒子类别如何,结果表明,包裹的水泥浆普遍表现出成功的抗碎强度σ0,d的提高。特别是,在1.18-2.36毫米的尺寸范围内,碎片和母岩的包裹颗粒均达到异常高的σ0,d值:10.14MPa和8.74MPa,分别。然而,尺寸范围从9.5毫米到16毫米,包裹岩屑和母岩的σ0、d值分别达到4.75MPa和3.18MPa,分别。根据纳米压痕测试,ITZ的亚显微强度提高到1GPa以上,比常规混凝土高,就样品而言,为期28天的维护。总之,本研究为进一步研究珊瑚混凝土材料及其硬化机理提供了依据。
    In terms of the infrastructure construction near coral reefs, native coral aggregates have been widely implemented as alternative efficient building materials to prepare the \"coral concrete\". This study focused on the mechanical properties and hardening mechanism of coral particles under cement-based systems. Firstly, coral particles were divided into two categories: coral biological debris particles (calcium sand) and coral parent rock particles (limestone). Subsequently, several elementary laboratory tests were conducted to compare the physical and chemical properties of the samples. The results demonstrate that the specific surface area and open pores of coral particles are bigger than those of quartz sand. Moreover, the water absorption rate of debris and parent rock particles reach 9.9% and 22%, respectively. To further examine the hardening mechanism of coral particles, we carried out particle crushing strength tests, compressive strength tests and nanoindentation tests. Regardless of the tested groups and particle categories, the results show that the wrapped cement slurry universally demonstrated the successful enhancement of crushing strength σ0,d. Particularly, in the size range from 1.18-2.36 mm, wrapped particles of debris and parent rock both reached unusually high σ0,d values: 10.14 MPa and 8.74 MPa, respectively. However, in the size range from 9.5 mm to 16 mm, the σ0,d values of wrapped debris and parent rock reached 4.75 MPa and 3.18 MPa, respectively. According to the nanoindentation tests, the sub-microscopic strength of ITZs was enhanced to more than 1 GPa, which is higher than that of conventional concrete, in terms of the sample with 28-day maintenance. In conclusion, this study has provided a further basis for studying coral concrete material and its hardening mechanism.
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  • 文章类型: Journal Article
    通过预测在役电表的故障数量来制定更换策略是有帮助的。提出了一种基于现场故障数据的智能电表故障数预测方法。将Weibull分布与赔率比相结合构建预测模型,然后是分布参数,故障预测数,并计算预测数的置信区间。根据预测结果,制定了电表更换和储备的策略。为避免因现场数据信息量小带来预测结果的不确定性,提出了一种贝叶斯故障数量预测方法。研究结果对制定电表运行计划和储备策略具有一定的参考价值。
    It is helpful to have a replacement strategy by predicting the number of failures of in-service electricity meters. This paper presents a failure number prediction method for smart electricity meters based on on-site fault data. The prediction model was constructed by combining Weibull distribution with odds ratios, then the distribution parameters, failure prediction number, and confidence intervals of prediction number were calculated. A strategy of meter replacement and reserve were developed according to the prediction results. To avoid the uncertainty of prediction results due to the small amount of field data information, a Bayesian failure number prediction method was developed. The research results have value for making operation plans and reserve strategies for electricity meters.
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  • 文章类型: Journal Article
    迄今为止,固化盐渍土的本构方程模型研究较少。本文提出了考虑冻融循环(FTC)和盐度的固化盐渍冻土损伤本构模型的建立。为了模拟固化的冻土,无侧限抗压强度试验(UCST)和固结不排水(CU)三轴剪切试验在三个环境温度(20、-10和-20°C)下进行,5岁(3、7、14、28和90d),六种盐度(0、1、2、3、4和5%),和本研究中的四个FTC(0、5、10和14次)。UCST结果表明,固化盐渍土在14日龄时的无侧限抗压强度(UCS)可以达到最大UCS的75%,基本满足工程建设要求。受盐度影响的强度损失率范围为16.2%~75.65%,而盐和冷冻条件的耦合作用放大了强度损失率。受盐度增加的影响,与解冻土壤相比,冻土的强度损失率放大了1.2到3.7倍。同样,CU三轴剪切试验表明,FTC和盐侵蚀的耦合作用放大了剪切强度的强度损失率。随着FTC的增加,杨氏模量的应变阈值逐渐向后推,这与盐度的影响相似。值得注意的是,对于盐冻耦合作用下的固化盐渍土,损伤本构模型的性能优于常规本构模型。
    To date, the modelling of constitutive equations of solidified frozen saline soil have seldom been studied. This paper presented the formulation of a damage constitutive model for solidified saline frozen soil considering both freeze thaw cycles (FTCs) and salinities. To model the solidified frozen saline soil, the unconfined compression strength test (UCST) and consolidated undrained (CU) triaxial shear test were conducted under three ambient temperatures (20, -10, and -20 °C), five ages (3, 7, 14, 28, and 90 d), six salinities (0, 1, 2, 3, 4, and 5%), and four FTCs (0, 5, 10, and 14 times) in this research. The UCST results showed that the unconfined compressive strength (UCS) of the solidified saline soils at an age of 14 days can reach 75% of the maximum UCS, which basically meets the engineering construction requirements. The range of the rate of strength loss as affected by salinity was 16.2% to 75.65%, while the coupling effect of salt and frozen conditions amplified the rate of strength loss. Affected by increasing salinity, the rate of strength loss of frozen soils was magnified by a factor of 1.2 to 3.7 compared to thawing soils. Likewise, the CU triaxial shear test showed that the rate of strength loss of shear strength was amplified by the coupling effect of FTCs and salt erosion. With increased FTCs, the strain threshold of Young\'s modulus was gradually pushed backward, which was similar to the effect of salinity. Remarkably, the damage constitutive model performed better than conventional constitutive models for the solidified saline soil under the salt-freezing coupling effect.
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