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介绍了一种线性模型参数回归分析方法-正交最小二乘法，并以电子探针微区分析技术分析环境样品的数据为例，对正交最小二乘法和经典最小二乘法的结果进行了详细比较。数据处理结果表明，当变自量和因变量都同时存在测量误差时（或自变量的测量误差与因变量的测量误差相比不能忽略时），正交最小二乘法获得的回归系数优于经典最小二乘法。对正交最小二乘法中的线性模型能解释的方差与经典最小二乘法中的相关系数的关系也进行了讨论。 相似文献
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将偏最小二乘回归（PLS）与神经网络（NN）耦合，建立了储层参数预报模型。利用偏最小二乘对影响储层参数的诸多因素进行分析，提取对因变量影响强的成分，从而克服了变量间的多重相关性问题，降低了神经网络的输入维数；同时，利用神经网络建模可以较好地解决非线性的储层参数预测问题。计算实例表明，本耦合模型的拟合和预报精度优于独立使用神经网络模型的精度。 相似文献
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最小二乘直线拟合方法及其在同位素地质年代学中的应用研究 总被引：2，自引：0，他引：2
最小二乘法(least squares method)是直线拟合常用的方法,在自然科学和社会科学内被广泛应用,尤其在同位素地质年代学领域更是必不可少。仅考虑x或y误差的普通最小二乘法(normal/ordinary least squares)广为人知,但事实上最小二乘法并非如此简单,尤其是在同时考虑x、y误差(乃至误差相关)并采用加权处理时,其数学处理方法会变得十分复杂,而此时普通最小二乘法显得极不合理。本文在前人研究的基础上,结合同位素地质年龄计算的需要,对直线拟合的最小二乘法进行了系统地总结研究,详细介绍了普通最小二乘法、加权普通最小二乘法(normal/ordinary weighting least squares)、标准加权最小二乘法(standard weighting model)、标准独立加权最小二乘法(standard independent weighting model)、独立加权最小二乘法(independent weighting model)及误差相关最小二乘法(error correlated independent weighting model)的数学原理及相关变量的计算过程。在此基础上,进一步阐述了MSWD(mean squared weighted deviation)这个同位素地质年代学中经常使用的参数的数学意义,以及MSWD对计算结果的评判意义。准确理解这些数学方法,对于我们合理选择同位素地质年龄相关参数的计算方法,科学评价直线拟合结果并探讨其地质意义至关重要。我们的研究同时有助于拓展和完善数学领域最小二乘法的基本理论,并可用于其他领域相似的研究之中。 相似文献
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在水分析计算中，经常涉及到变量之间的线性或非线性拟合，而在拟合各种特性曲线时，通常应用以实测资料与拟合曲线间的误差平方和最小作为目标函数的方法——最小二乘法，但这种方法忽视了所有实测点应与拟合曲线间的相对误差尽量不超过某一百分比的原则，为了达到上述要求，提出了非线性的加权最小二乘法及线性相关方程的最小距离平方和法，探讨改进了传统的最小二乘法达到优化的效果。最小距离平方和法与常用的图解法相比，本法所得成果较为客观；与传统的单方向(x或y方向)最小二乘回归法相比，所求线性方程不会因坐标系的选取而改变。最后应用算例进行了初步讨论。 相似文献
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基于响应面方法的围岩参数随机反分析 总被引：5，自引：4，他引：5
在有限元分析的基础上，应用响应面方法拟合岩体参数与岩体位移之间的非线性映射关系，以代替有限元的数值模拟，考虑变形量测的随机性，结合响应面方程、优化方法和Monte-Carlo技术，根据位移反分析的最小二乘原理，对围岩参数进行随机反分析，反演结果给出参数的特征值，为围岩稳定性和可靠度分析提供必要的数据，数值结果表明该方法具有较好的计算精度。 相似文献
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回归计算中，由于资料和计算上的误差，使结果也产生一定的误差，通常，采用最小二乘法或最小一乘法来估计回归模型中的参数，即是取目标函数为最小来实现的，如果使目标函数在允许的误差范围内变化，则参数会有相应的变幅，本文探讨了两变数回归时参数估计的灵敏度，在相关关系不甚密切时，误差对结果的影响是较大的。 相似文献
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基于LSSVM与MCS的路基沉降可靠度分析 总被引：1，自引：0，他引：1
提出了一种计算路基沉降可靠度的新方法。基于FLAC中的修正剑桥模型,以最小二乘支持向量机为核心技术,结合蒙特卡罗法构建计算模型。由于修正剑桥模型参数较多,对模型参数进行了敏感性分析,将对沉降影响较大的参数确定为随机变量。选取训练样本对支持向量机进行训练,按照随机变量的概率分布进行抽样,馈送到最小二乘支持向量机得到相应的响应值,用Matlab编制程序完成可靠度计算,并进行了算例分析。计算结果表明,蒙特卡罗法结合支持向量机的沉降可靠度计算方法应用于公路软基沉降可靠度计算是可行的。 相似文献
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利用最小二乘原理，研究了实测径流量资料平差处理问题，并推导了参数平差法的具体计算模型，通过计算实例说明了利用此方法可以合理地消除实测径流量计算结果中的偶然误差，解决了实测径流量不同年份各站之间的矛盾，给出了客观、实用、可靠的径流计算结果，并可对实测径流资料进行精度评定和分析。 相似文献
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非线性回归法求解爆破振动速度衰减公式参数 总被引：15，自引：1，他引：15
准确分析场地爆破振动衰减规律是爆破工程设计的基本依据。通过考察爆破振动速度衰减公式中参数的线性回归方法和非线性回归方法,提出了线性残差平方和与非线性（亦即标准残差平方和）的概念,给出了求解衰减公式参数的非线性回归法,并详述了该方法的实现过程。结合工程实例,以标准残差平方和作为爆破振动实测数据与衰减公式拟合值偏差大小的判断依据,分析了线性和非线性回归分析方法得到的萨道夫斯基公式和其修正公式的标准残差平方和。分析结果表明,非线性回归分析方法的准确度明显高于线性回归分析方法;分别采用线性回归和非线性回归方法得到的萨道夫斯基公式和其修正公式的标准残差平方和非常接近,因此,采用两种形式的公式拟合爆破振动衰减规律都是可行的。 相似文献
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The least squares Monte Carlo method is a decision evaluation method that can capture the effect of uncertainty and the value of flexibility of a process. The method is a stochastic approximate dynamic programming approach to decision making. It is based on a forward simulation coupled with a recursive algorithm which produces the near-optimal policy. It relies on the Monte Carlo simulation to produce convergent results. This incurs a significant computational requirement when using this method to evaluate decisions for reservoir engineering problems because this requires running many reservoir simulations. The objective of this study was to enhance the performance of the least squares Monte Carlo method by improving the sampling method used to generate the technical uncertainties used in obtaining the production profiles. The probabilistic collocation method has been proven to be a robust and efficient uncertainty quantification method. By using the sampling methods of the probabilistic collocation method to approximate the sampling of the technical uncertainties, it is possible to significantly reduce the computational requirement of running the decision evaluation method. Thus, we introduce the least squares probabilistic collocation method. The decision evaluation considered a number of technical and economic uncertainties. Three reservoir case studies were used: a simple homogeneous model, the PUNQ-S3 model, and a modified portion of the SPE10 model. The results show that using the sampling techniques of the probabilistic collocation method produced relatively accurate responses compared with the original method. Different possible enhancements were discussed in order to practically adapt the least squares probabilistic collocation method to more realistic and complex reservoir models. Furthermore, it is desired to perform the method to evaluate high-dimensional decision scenarios for different chemical enhanced oil recovery processes using real reservoir data. 相似文献
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线性矩法估计参数的保证修正值系数B的推求 总被引：3，自引：0，他引：3
在设计洪水的抽样误差估计中,采用保证修正值系数B方法估计均方差简单易用。应用线性矩法估计频率分布曲线的参数,有较好的无偏性和有效性,具有一定的应用前景。目前线性矩法的B值诺模图尚未确定,给用线性矩法确定参数时估计抽样误差带来了难度与不便。采用统计试验,分析了离差系数、偏态系数和样本长度对B值的影响,结果表明线性矩法估计参数时仍可采用保证修正值系数B值诺模图方法来估计抽样误差,并推求了不同偏态系数、设计频率情形下的B值,制成了线性矩法的B值诺模图备用。 相似文献
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In a probabilistic analysis of rock slope stability, the Monte Carlo simulation technique has been widely used to evaluate
the probability of slope failure. While the Monte Carlo simulation technique has many advantages, the technique requires complete
information of the random variables in stability analysis; however, in practice, it is difficult to obtain complete information
from a field investigation. The information on random variables is usually limited due to the restraints of sampling numbers.
This is why approximation methods have been proposed for reliability analyses. Approximation methods, such as the first-order
second-moment method and the point estimate method, require only the mean and standard deviation of the random variable; therefore,
it is easy to utilize when the information is limited. Usually, a single closed form of the formula for the evaluation of
the factor of safety is needed for an approximation method. However, the commonly used stability analysis method of wedge
failure is complicated and cumbersome and does not provide a simple equation for the evaluation of the factor of safety. Consequently,
the approximation method is not appropriate for wedge failure. In order to overcome this limitation, a simple equation, which
is obtained from the maximum likelihood estimation method for wedge failure, is utilized to calculate the probability of failure.
A simple equation for the direct estimation of the safety factors for wedge failure has been empirically derived from failed
and stable cases of slope, using the maximum likelihood estimation method. The developed technique has been applied to a practical
example, and the results from the developed technique were compared to the results from the Monte Carlo simulation technique. 相似文献
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Method of Data Reduction and Uncertainty Estimation for Platinum-Group Element Data Using Inductively Coupled Plasma-Mass Spectrometry 总被引：1，自引：0，他引：1
A data reduction method is described for determining platinum-group element (PGE) abundances by inductively coupled plasma-mass spectrometry (ICP-MS) using external calibration or the method of standard addition. Gravimetric measurement of volumes, the analysis of reference materials and the use of procedural blanks were all used to minimise systematic errors. Internal standards were used to correct for instrument drift. A linear least squares regression model was used to calculate concentrations from drift-corrected counts per second (cps). Furthermore, mathematical manipulations also contribute to the uncertainty estimates of a procedure. Typical uncertainty estimate calculations for ICP-MS data manipulations involve: (1) Carrying standard deviations from the raw cps through the data reduction or (2) calculating a standard deviation from multiple final concentration calculations. It is demonstrated that method 2 may underestimate the uncertainty estimate of the calculated data. Methods 1 and 2 do not typically include an uncertainty estimate component from a regression model. As such models contribute to the uncertainty estimates affecting the calculated data, an uncertainty estimate component from the regression must be included in any final error calculations. Confidence intervals are used to account for uncertainty estimates from the regression model. These confidence intervals are simpler to calculate than uncertainty estimates from method 1, for example. The data reduction and uncertainty estimation method described here addresses problems of reporting PGE data from an article in the literature and addresses both precision and accuracy. The method can be applied to any analytical technique where drift corrections or regression models are used. 相似文献
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大气颗粒物样品波长色散X射线荧光光谱法无机元素测量结果不确定度评估 总被引：4，自引：0，他引：4
分析了用X射线荧光光谱法（XRF）测定大气颗粒物样品（TSP）中Al、Na、Cl、Mg、Cu、zn、Ca、S、Fe、Mn、K、Pb、Cd、Ba等无机元素结果的不确定度来源，对石英滤膜颗粒物样品无机元素含量测量不确定度进行了评估。计算结果表明，XRF测定中无机元素薄膜标样示值误差和工作曲线拟合误差是测量结果不确定度的主要来源。对计算测量不确定度的公式合成法和蒙特卡洛（Monte Carlo）模拟法的结果进行了比较，两种计算方法所得的结果一致。 相似文献
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Uncertainty in surfactant–polymer flooding is an important challenge to the wide-scale implementation of this process. Any successful design of this enhanced oil recovery process will necessitate a good understanding of uncertainty. Thus, it is essential to have the ability to quantify this uncertainty in an efficient manner. Monte Carlo simulation is the traditional uncertainty quantification approach that is used for quantifying parametric uncertainty. However, the convergence of Monte Carlo simulation is relatively low, requiring a large number of realizations to converge. This study proposes the use of the probabilistic collocation method in parametric uncertainty quantification for surfactant–polymer flooding using four synthetic reservoir models. Four sources of uncertainty were considered: the chemical flood residual oil saturation, surfactant and polymer adsorption, and the polymer viscosity multiplier. The output parameter approximated is the recovery factor. The output metrics were the input–output model response relationship, the probability density function, and the first two moments. These were compared with the results obtained from Monte Carlo simulation over a large number of realizations. Two methods for solving for the coefficients of the output parameter polynomial chaos expansion are compared: Gaussian quadrature and linear regression. The linear regression approach used two types of sampling: full-tensor product nodes and Chebyshev-derived nodes. In general, the probabilistic collocation method was applied successfully to quantify the uncertainty in the recovery factor. Applying the method using the Gaussian quadrature produced more accurate results compared with using the linear regression with full-tensor product nodes. Applying the method using the linear regression with Chebyshev derived sampling also performed relatively well. Possible enhancements to improve the performance of the probabilistic collocation method were discussed. These enhancements include improved sparse sampling, approximation order-independent sampling, and using arbitrary random input distribution that could be more representative of reality. 相似文献
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爆破震动测试得到的数据常常具有较大的离散性,采用剔除错误数据和小波降噪对爆破震动检测数据进行预处理,以标准残差平方和作为爆破振动实测数据与萨道夫斯基公式拟合值偏差大小的判断依据,应用小波降噪对实测数据进行处理的方法,优化了粒子群算法对萨道夫斯基公式中的k和 的回归分析。研究结果表明,小波降噪和粒子群优化算法结合使用,能够较真实地反映爆破震动测试的真实情况,从而提高了对爆破震动测试模拟的精度。研究结果对爆破振动测试理论和工程实践具有一定的参考价值。 相似文献
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基于TRMM 3B42V7数据,综合采用多元线性回归、偏最小二乘回归和地理加权回归3种方法,建立了太行山区卫星降水产品的降尺度校正模型,将遥感降水信息从0.25°×0.25°降尺度到0.05°×0.05°。在结果评估和优选的基础上,分析了"像元-集水区-全区"年、月降水的多时空尺度干湿季节分布和垂向分布特征,并从机理方面论证了研究的合理性。结果表明:①地理加权回归校正效果最优,可明显降低校正降水与实测降水系列的均方根误差和平均相对偏差且提高决定系数;偏最小二乘回归可降低两项误差,但对决定系数无提升;多元线性回归最差,各项指标均无改善。②处于夏季风迎风侧的东坡和南坡降水量普遍高于500 mm,背风侧的西坡和北坡降水量较低,最大年降水量位于东南坡海拔1 300~1 500 m的地带。③研究区7-9月降水量占全年的58.7%,干湿季节降水量之比为1:18,各集水区的变化范围为1:13~1:25。④季风风向影响降水中心的移动路径,各月降水量沿高程变化梯度区间为-5.2~6.7 mm/hm,且迎风坡降水的垂向分布更复杂。 相似文献