基于Bayesian分析的垂穗披碱草根系力学特性估计方法

    Distributional parameter inferences on the mechanical properties of roots for E. nutans based on Bayesian analysis

    • 摘要: 植物根系力学特性是度量植物根系对土体抗剪强度贡献,评价植物根系提高土壤抗侵蚀性和边坡稳定性的重要指标之一。该研究基于Bayesian分析,选取生长于青海天峻县江仓矿区排土场人工种植的垂穗披碱草(Elymus nutans Griseb.)为研究对象,在对其根系力学特性进行测定基础上,以测得的28组根系力学特性的期望值和方差为先验信息,以第29组根系力学特性测定值为样本信息,建立了用于计算该区域垂穗披碱草根系力学特性的正态-逆伽马后验分布,并分别计算了先验分布的超参数以及后验分布中的分布参数。研究结果表明,先验信息中,除极限拉伸应变外,其余指标均值的期望值变异性均较小且各指标的均值均服从正态分布,方差的倒数则满足伽马分布,而各指标的样本分布满足正态分布,故可通过正态-逆伽马分布对区内垂穗披碱草根系力学特性的后验分布进行描述;后验信息概率密度曲线与样本信息概率密度曲线几何形状较为相似,该结果说明后验信息更倾向于样本信息,且得到的结果亦可由柯尔莫哥洛夫-斯米洛夫检验予以佐证。此外,样本数量与先验信息离散度决定了先验均值和样本均值在决定后验均值时所占的权重。在其他条件不变的情况下,样本数量越大则样本所占权重越大。该研究可为准确计算植物根系力学特性提供思路和研究方法。

       

      Abstract: Mechanical properties are the essential parameters to assess the contribution rates of roots in the soil strength, the slope stability, and the prevention of soil erosion. Therefore, an accurate and rapid measurement is required to determine the role of vegetation roots in the soil cohesion, and the slope stability. However, the commonly-used uniaxial tension tests cannot fully meet the large-scale measurement at present, due to the labor-consuming and time-costing. It is very necessary for the high precision on the biomechanical properties of roots. In this study, the distribution parameters were assessed on the biomechanical properties of roots using Bayesian analysis. The research object was selected as Elymus nutans from the landfill dumps in the Jiangcang coal mining, Tianjun County, Qinghai Province, China. The reason was the excellent adaptability and performance of the plant in the long cold climate condition of soil and water preservation. Subsequently, the uniaxial tension test was carried out to measure the biomechanical properties (such as the root diameter, tensile resistance, tensile strength, and tensile strain at crack and Young’s modulus). 28 datasets of roots were randomly collected with the mean values and variance as the prior information. The control group was treated as the sampling information for this herb. The prior mean of properties and sampling information were followed the Normal distribution, while the variance was the Inverse Gamma distribution. The posterior distribution (named Normal-Inverse Gamma distribution) was then established to calculate the hyper- and distributional parameters using the maximum likelihood method or moment estimation. The results show that the more comprehensive information was achieved in the Bayesian estimation, considering both prior and sampling information. Among the prior information, there was the small variable coefficient of the mean values in the biomechanical properties, except for tensile strain at crack. The geometric shape of posterior information was similar to that of the sampling one after the Kolmogorov-Smirov test. The size of sampling and the discreteness of prior information were determined as the mean value of the posterior that weighted by the mean between the prior and sampling information. The sizes of sampling and prior information were 28 and 63, respectively, indicating the relatively high sampling information. Therefore, the mean values of posterior information were adjusted, where the diameter from 0.331 3 to 0.330 4 mm, the tensile resistance from 2.639 to 2.575 5 N, tensile strength from 32.098 to 31.280 MPa, tensile strain at crack from 8.413% to 9.520 6%, and Young’s modulus from 107.24 to 98.634 6 MPa. Similarly, the variances of posterior information were adjusted, where the diameter from 0.010 8 to 0.018 6, tensile resistance from 3.019 to 5.412 4 N, tensile strength from 308.214 to 566.004 MPa, tensile strain at crack from 14.106 to 188.655 9, and Young’s modulus from 3 392.55 to 6 805.60. Both the size and discreteness should be considered in both prior and sampling information in the future. The biomechanical properties of vegetation roots can be expected to accurately estimate for the shear strength of rooted soil.

       

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