Error estimates for parameters in inverse parametrical problems. Light-curve analysis for classical eclipsing binaries

Parameters and their error intervals numerically estimated for the observed light curve of the binary eclipsing system YZ Cas as well as for one-, two-, three-, and four-parameter functions, and the associated parameters and their error intervals numerically estimated. The error intervals are calculated using differential corrections method, Monte-Carlo simulations, and confidence areas. We study the error intervals and the reliability of the techniques used.     

基于数值计算的测斜仪监测误差分析

测斜仪在边坡深部位移监测中应用比较广泛,但其监测结果存在一定误差。已有测斜仪监测误差研究多是针对系统误差进行,缺少针对测斜仪监测数据计算原理引起的误差进行的研究。基于测斜仪监测数据计算方法原理与数值分析中常微分方程Euler解法的一致性,讨论了造成测斜仪监测误差的原因。分析结果表明:测斜仪监测误差与测斜仪监测初始值、测量分段长度和位移变形曲线形状有关;测斜仪监测初始值变化将给监测带来误差;测斜仪测量段长与监测误差呈线性关系,误差随测量段长减小而变小;当位移变形曲线为直线时,误差为0;当位移变形曲线为单-凸曲线或凹曲线时,监测误差随曲线变形程度和孔口变形位移增大而变大;测斜仪位移变形监测误差为累积误差,孔口误差大于孔底误差。在使用测斜仪监测时,为了减少监测误差,建议将每次监测初始值设为固定值,并尽可能减少测量段长。     

Forecasting the polar motions of the deformable Earth

A mathematical model for the complicated phenomenon of the polar oscillations of the deformable Earth that adequately describes the astrometric data of the International Earth Rotation Service is constructed using celestial mechanics and asymptotic techniques. This model enables us to describe the observed phenomena (free nutation, annual oscillations, and trends) simply and with statistical reliability. The model contains a small number of parameters determined via a least-squares solution using well-known basis functions. Interpolations of the polar trajectory for intervals of 6 and 12 yrs and forecasts for 1–3 yrs are obtained using the theoretical curve. The calculated coordinates demonstrate a higher accuracy than those known earlier.     

The New “York” Regression: Application of an Improved Statistical Method to Geochemistry

York's (1969) method of regression, determining the best-fit line to data with errors in both variables using a least-squares solution, has become an integral part of isotope geochemistry. Although other methods agree with York's best-fit line (e.g., maximum likelihood), there is little agreement on the standard-error estimates for slope and intercept values. The reasons for this are differing levels of approximation used to compute the standard error, doubts concerning procedures for determining a confidence interval once the standard error has been estimated, and a typographical error in the original publication. This paper examines York's method of regression and standard errors of the parameters of a best-fit line. A very accurate method for determining the standard error in slope and intercept values is introduced, which eliminates the need to multiply the standard-error estimate by the goodness-of-fit parameter known as MSWD. In addition, a derivation of a fixed-intercept method of regression is introduced, and interpretations of MSWD and use of the t-adjustment in confidence intervals are discussed. The accuracy of the standard-error computations is determined by comparing the results to slope and intercept statistics generated from several thousand Monte Carlo regressions using synthetic ⁴⁰Ar/³⁹Ar inverse isochron data.     

Computer reliability analysis of coal-cleaning distribution curves

Three types of distribution curve error are defined, i.e., the fitting deviation, the real deviation and the test error. Since the absolute distribution curve is never known, both the real deviation and the test error are unknown. Only the fitting deviation can be calculated and is a measure of the difference between a calculated distribution curve and the experimental data. However, the real deviation is of primary importance in evaluating the reliability of calculated distribution curves. This paper uses a microcomputer to simulate absolute distribution curves and obtains numerical relationships between the real deviation, the fitting deviation and the test error.More than 500 tests using a microcomputer show that a relationship exists between the fitting deviation, test error and real deviation. In most cases, the fitting deviation and the real deviation are close to each other. Both the fitting and the real deviation are smaller than the test error if the selected model is suitable.     

洪水预报模型输入与输出的误差分布及相关性分析

降雨预报信息作为洪水预报模型的输入,该信息的准确性直接影响洪水预报模型输出的准确性.为探究模型输入(降雨预报)误差与输出(洪水预报)误差之间的关系,以英那河流域为例,分析了不同雨量等级下,预报模型的输入误差与输出误差的分布规律,并定性分析了两种误差的相关关系.结果表明,降雨量等级若为无雨及小雨时,两种误差不相关;若为中...     

洪水预报产流误差的动态系统响应曲线修正方法

为提高实时洪水预报精度,提出了一种基于动态系统响应曲线洪水预报误差修正新方法。该方法将动态系统响应曲线引入洪水预报误差修正中,建立一种向误差源头追溯的动态反馈修正模型。此修正方法将新安江模型产流以下的部分作为响应系统, 用线性差分近似代替非线性系统响应函数的偏导数值,得到时段产流量所对应的系统响应曲线。用实测流量和计算流量之间的差值作为信息,使用最小二乘估计原理,对产流量进行修正, 再用修正后的产流量重新计算出流过程。该修正方法分别用理想案例和王家坝流域进行检验,结果证明此方法效果比传统二阶自回归模型有明显提高。     

Evaluation of statistical bias correction methods for numerical weather prediction model forecasts of maximum and minimum temperatures

Statistical bias correction methods for numerical weather prediction (NWP) forecasts of maximum and minimum temperatures over India in the medium-range time scale (up to 5 days) are proposed in this study. The objective of bias correction is to minimize the systematic error of the next forecast using bias from past errors. The need for bias corrections arises from the many sources of systematic errors in NWP modeling systems. NWP models have shortcomings in the physical parameterization of weather events and have the inability to handle sub-grid phenomena successfully. The statistical algorithms used for minimizing the bias of the next forecast are running-mean (RM) bias correction, best easy systematic estimator, simple linear regression and the nearest neighborhood (NN) weighted mean, as they are suitable for small samples. Bias correction is done for four global NWP model maximum and minimum temperature forecasts. The magnitude of the bias at a grid point depends upon geographical location and season. Validation of the bias correction methodology is carried out using daily observed and bias-corrected model maximum and minimum temperature forecast over India during July–September 2011. The bias-corrected NWP model forecast generally outperforms direct model output (DMO). The spatial distribution of mean absolute error and root-mean squared error for bias-corrected forecast over India indicate that both the RM and NN methods produce the best skill among other bias correction methods. The inter-comparison reveals that statistical bias correction methods improve the DMO forecast in terms of accuracy in forecast and have the potential for operational applications.     

BP神经网络在自喷井井底流压预测中的应用

利用神经网络具有的高度非线性映射能力,将其应用于井底流压的预测,以解决现有各种方法不能完全满足需要的矛盾。从网络的结构和算法、训练样本的选择和处理、网络的学习精度和泛化能力等三个方面对BP神经网络进行研究和改进,建立了井底流压的预测模型,并对某油田的实测井底流压数据进行了精度检验和精度分析。预测结果表明,相对误差最大为2.0821%,平均相对误差为1.5108%,绝对误差一般在0.5~1 MPa,高于其他各种计算方法的精度。     

典型曲线法在山东龙口软岩煤矿区开采沉陷预测中的应用

为丰富矿区开采沉陷的预计方法,提高预测的精度,在综合大量文献的基础上,提出了典型曲线法。典型曲线法避免了由理论模型的假设和简化而造成预计公式的误差,提高了预计的精度,通过开发预计程序,方便了数据的处理,实现了典型曲线法沉陷预计的电算化。以山东龙口软岩矿区为例,详细介绍了典型曲线的建立和应用方法,预计结果和实测最大下沉值的绝对偏差为9mm,相对误差为1.1%。     

Generalized Bootstrap Method for Assessment of?Uncertainty in Semivariogram Inference

The semivariogram and its related function, the covariance, play a central role in classical geostatistics for modeling the average continuity of spatially correlated attributes. Whereas all methods are formulated in terms of the true semivariogram, in practice what can be used are estimated semivariograms and models based on samples. A generalized form of the bootstrap method to properly model spatially correlated data is used to advance knowledge about the reliability of empirical semivariograms and semivariogram models based on a single sample. Among several methods available to generate spatially correlated resamples, we selected a method based on the LU decomposition and used several examples to illustrate the approach. The first one is a synthetic, isotropic, exhaustive sample following a normal distribution, the second example is also a synthetic but following a non-Gaussian random field, and a third empirical sample consists of actual raingauge measurements. Results show wider confidence intervals than those found previously by others with inadequate application of the bootstrap. Also, even for the Gaussian example, distributions for estimated semivariogram values and model parameters are positively skewed. In this sense, bootstrap percentile confidence intervals, which are not centered around the empirical semivariogram and do not require distributional assumptions for its construction, provide an achieved coverage similar to the nominal coverage. The latter cannot be achieved by symmetrical confidence intervals based on the standard error, regardless if the standard error is estimated from a parametric equation or from bootstrap.     

曲线拟合法对路基小变形情形适用性研究

双曲线法、三点法、指数曲线法和Asaoka法等曲线拟合法在软土路基的沉降预测中已经得到广泛应用,但在路基小变形情形的应用研究尚少。结合某铁路客运专线施工现场观测的路基小变形数据,对这4种方法,探讨了时间起点和样本值的起止时间间隔对相关系数的影响,且验算后期观测值的预测效果;并综合考虑了相关系数和相对误差,研究每种方法的适用性;指出了4种拟合方法在路基小变形情形应用的优缺点。研究表明：数据的波动会造成指数曲线法无法计算;沉降数据波动较小时,双曲线法、三点法、Asaoka法的拟合效果均较好;当沉降数据波动较大时,仅三点法、Asaoka法的拟合效果较好,双曲线法较差。     

Constrained Smoothing of Noisy Data Using Splines in?Tension

A method of fitting a smooth cubic spline curve through noisy data points is presented. Overshoots of the spline curve between data points were prevented by applying tension to the fit using a quadratic spring approximation, which allowed a linear inverse theory approach to be adopted. Error-bars in the measured data were mapped through the inversion process to give the covariance of the fitted curve. This is an improvement over previous methods, which largely neglect the effect of data errors on the fit. Another improvement is to impose fixed constraints on the fit by simultaneously applying the method of Lagrange multipliers. The effect of these constraints on the covariance of the fitted curve is quantified using results from linear algebra. Example applications to synthetic data and a record of magnetic inclination from Hawaii are given.     

Constrained Smoothing of Noisy Data Using Splines in Tension

A method of fitting a smooth cubic spline curve through noisy data points is presented. Overshoots of the spline curve between data points were prevented by applying tension to the fit using a quadratic spring approximation, which allowed a linear inverse theory approach to be adopted. Error-bars in the measured data were mapped through the inversion process to give the covariance of the fitted curve. This is an improvement over previous methods, which largely neglect the effect of data errors on the fit. Another improvement is to impose fixed constraints on the fit by simultaneously applying the method of Lagrange multipliers. The effect of these constraints on the covariance of the fitted curve is quantified using results from linear algebra. Example applications to synthetic data and a record of magnetic inclination from Hawaii are given.     

Comparison of SPT-N-based analysis methods in evaluation of liquefaction potential during the 1999 Chi-chi earthquake in Taiwan

SPT-N-based methods have been adopted for liquefaction assessment of soils during earthquakes for decades. However, there has not been a consistent way of assessing the accuracy and applicability of these methods. The Chi-chi earthquake of 1999, which has been the most serious ground shaking in Taiwan within the century, caused extensive liquefactions in mid-west alluvial deposits of the island. This paper assesses the prediction accuracy of several SPT-N-based methods using liquefaction and non-liquefaction incidents observed during the earthquake. A sensitivity study on commonly adopted parameters shows that the SPT blow count and peak ground acceleration are most sensitive in computing liquefaction potential. By comparing the error in predicting liquefaction and non-liquefaction incidents, this study concludes that Tokimatsu and Yoshimi’s method is more accurate than the other methods. However, the differences between prediction errors of various methods are minimal, indicating all of the methods examined are applicable for the 1999 earthquake in Taiwan.     

Extrapolation of O-cell drilled shaft tests for load and resistance factor design (LRFD) calibration

Load tests of drilled shafts are often performed using Osterberg cell (O-cell) testing, a popular load test method for drilled shafts, which measures both side and tip resistance. However, it is common that only one of the resistance components can be fully mobilized. Therefore, extrapolation of the partially mobilized resistance is often required to determine the total resistance or the equivalent top-down curve. The extrapolation tends to introduce errors to the constructed total resistance values, which subsequently affect the calibrated resistance factors required for the LRFD design of drilled shafts. In this study, eight O-cell tests of drilled shafts with total measured resistances close to the failure criteria defined by FHWA, 5% of the shaft diameter (B), were collected among 64 drilled shaft load tests from Louisiana and Mississippi. For each of the eight cases, extrapolation was performed on both tip and side movement curves for the construction of the equivalent top-down load-settlement (ELT) curves. Data points from the measured side or tip movement curve were removed systematically to create a total of 80 cases with partially mobilized movement curves, and extrapolation exercises were performed on each fabricated case to obtain its equivalent top-down curve. The error of bias for each fabricated case was determined for statistical analyses. Multiple linear regression analysis was performed on the bias errors to model the bias errors caused by extrapolation. Calibrated resistance factors were determined and compared between the original database and fabricated database needing extrapolation. A correction method is proposed, based on a linear regression relationship, to estimate and minimize the extrapolation error of bias for less mobilized databases.

     

岩体抗剪强度参数的线性优化方法

针对岩体结构面力学参数的重要性,以大量工程实例为依据,以统计误差分析相关理论为基础,研究最小二乘法与M-估计法在分析结构面抗剪强度参数时的适用性。研究结果表明,在难以判断粗差的数量和比例时,很难对两种线性回归方法的优劣进行规律性的比较。考虑到数据是具有工程特性的,为更准确地处理实验数据,在以上两种方法的基础上提出了一种新的实验数据处理方法,并应用于计算李家河水库的抗剪强度参数。     

产流误差比例系数的系统响应修正方法

为提高洪水预报的精度以及修正的稳定性,在产流误差动态系统响应曲线修正方法的基础上,提出了产流比例系数的系统响应修正方法.将产流系列按照一定原则分成若干组,假定每组存在系统误差,通过引入一个比例系数来表示,应用系统响应理论,选择适当的参数率定方法确定最优比例系数,进而对时段产流量分组进行修正.将产流误差比例系数的系统响应修正方法应用于滩坑流域,并与产流误差动态系统响应曲线修正方法相比较,结果显示,对于流域的17场历史洪水,二者均能提高洪水预报的精度,但前者的修正效果更好,修正稳定性更强,适用范围更广.     

改进的确定折射面法线深度的t0法

本文基于对目前确定折射面法线深度t₀方法的分析,发现存在如下问题：首先,目前方法求解时采用初等数学的方法,引进过程函数,计算过程繁杂;其次,求解时有两次近似操作,使结果误差增大;最后,在对法线深度曲线进行平滑时,采用手工偏移处理不仅费时费力,而且会造成人工误差。故提出一种改进的确定折射面法线深度的方法。改进方法优点：采用高等数学方法,不存在目前方法中的过程函数,计算更简洁;消除了近似问题,减小了计算误差,计算结果更精确;改进方法用相邻平均法对法线深度曲线进行平滑处理,提高了工作效率,节省了人力成本,实现了全过程计算机处理。目前方法和改进方法对同一野外的勘探结果表明,改进方法的勘探结果更符合真实折射波法线深度的变化,而且还可精确求出折射面倾角。