Mixed estimation methods for Halphen distributions with applications in extreme hydrologic events

The Halphen family of distributions is a flexible and complete system to fit sets of observations independent and identically distributed. Recently, it is shown that this family of distributions represents a potential alternative to the generalized extreme value distributions to model extreme hydrological events. The existence of jointly sufficient statistics for parameter estimation leads to optimality of the method of maximum likelihood (ML). Nevertheless, the ML method requires numerical approximations leading to less accurate values. However, estimators by the method of moments (MM) are explicit and their computation is fast. Even though MM method leads to good results, it is not optimal. In order to combine the advantages of the ML (optimality) and MM (efficiency and fast computations), two new mixed methods were proposed in this paper. One of the two methods is direct and the other is iterative, denoted respectively direct mixed method (MMD) and iterative mixed method (MMI). An overall comparison of the four estimation methods (MM, ML, MMD and MMI) was performed using Monte Carlo simulations regarding the three Halphen distributions. Generally, the MMI method can be considered for the three Halphen distributions since it is recommended for a majority of cases encountered in hydrology. The principal idea of the mixed methods MMD and MMI could be generalized for other distributions with complicated density functions.     

Discrimination test between the Halphen (A and B) and the gamma distributions

Hydrological frequency analysis is the most widely used method to estimate risk for extreme values. The most used statistical distributions to fit extreme value data in hydrology can be regrouped in three classes: class C of regularly varying distributions, class D of sub exponential and class E, Exponential depending on their tail behavior. The Halphen distributions (Halphen type A (HA), Halphen type B (HB)) are separated by the Gamma distribution; these three distributions belong to class D and can be displayed in the (δ₁, δ₂) moment-ratio diagram. In this study, a statistical test for discriminating between HA, HB and the Gamma distribution is developed. The methodology is based on: (1) the generation of N samples of different sizes n around the Gamma curve; (2) the determination of the confidence zones around the Gamma curve for each fixed couple (δ₁, δ₂) moment-ratios and finally; (3) the study of the power of the test developed and the calculation of the type 2 error β and the power of the test which is 1-β for a fixed significance level α. Results showed that the test is powerful especially for high coefficients of skewness. This test will be included in Decision Support System of the HYFRAN-PLUS software.     

太湖叶绿素a同化系统敏感性分析

太湖叶绿素a同化系统对于不同参数的敏感性将直接影响到该系统能否精确的估算太湖叶绿素a的浓度分布.利用2009年4月21日环境一号卫星(HJ-1B CCD2)影像数据反演太湖叶绿素a浓度场信息.以此作为背景场信息,结合基于集合均方根滤波的太湖叶绿素a同化系统,分析和评价了样本数目、同化时长、背景场误差、观测误差和模型误差对于同化系统性能的影响.结果表明:从计算成本、系统运行时间和同化效果等方面分析,当集合样本数目达到30~40左右时同化系统取得了较好的结果;同化系统对于背景场误差的估计变化不是很敏感,即初始场的估计是否准确对于同化系统的性能影响不是很大;同化系统对于模型误差和观测误差的变化较为敏感,不同的测试点位由于水体动力学性质不一,其敏感性的表现形式有所差异;利用数据同化方法可以有效地估算太湖叶绿素a浓度.     

Stochastic modelling and risk analysis of groundwater pollution using FORM coupled with automatic differentiation

The first order reliability method (FORM) has been widely used in probabilistic modelling of groundwater problems. The FORM approach requires an iterative optimization procedure to find out the system failure point (the most probable point).The advantages of this approach are that it does not require many computations in comparison with other methods when applied to simple problems, and it produces reasonably accurate results. However, it has been found that the computations of FORM can equal or exceed that of other methods in case of large number of variables.In this paper, a new implementation of FORM was proposed with more efficiency and accuracy than the traditional FORM method. In the proposed approach, automatic differentiation is used to obtain the gradient vector of the limit state function, which is required by FORM, instead of using finite difference estimation. This way, the first order derivative was obtained with a very good accuracy, and with less computational effort. Based on the obtained results, it is found that the proposed implementation of FORM is a very good tool for probabilistic risk assessment and uncertainty analysis in groundwater problems.     

地震预警震级计算方法研究综述

地震预警系统是减轻地震灾害的有效手段之一,世界上多个国家和地区都已经建立了地震预警系统,并在实际应用中取得了显著的减灾实效.由于地震预警系统应用中的高度时效性要求,预警震级计算是整个地震预警系统中最重要也是最困难的一部分.本文回顾总结了地震预警研究中采用的一些震级计算方法,并将其归纳为三大类算法:与初始周期相关的算法、与初始幅值相关的算法和与初始强度相关的算法.对每种算法都做了详尽介绍和仔细分析,同时列举出与该算法相关的研究成果.通过对这些算法的分析总结并结合我国地震观测台网的实际情况,作者推荐τc、Pd两种方法作为我国地震预警系统建设中优先采用的两种预警震级算法.     

A comparison of non-linear least square and GLUE for model calibration and uncertainty estimation for pesticide transport in soils

The problems of calibrating soil hydraulic and transport parameters are well documented, particularly when data are limited. Programs such as CXTFIT, UUCODE and PEST, based on well established principles of statistical inference, will often provide good fits to limited observations giving the impression that a useful model of a particular soil system has been obtained. This may be the case, but such an approach may grossly underestimate the uncertainties associated with future predictions of the system and resulting dependent variables. In this paper, this is illustrated by an application of CXTFIT within the generalised likelihood uncertainty estimation (GLUE) approach to model calibration which is based on a quite different philosophy. CXTFIT gives very good fits to the observed breakthrough curves for several different model formulations, resulting in very small parameter uncertainty estimates. The application of GLUE, however, shows that much wider ranges of parameter values can provide acceptable fits to the data. The wider range of potential outcomes should be more robust in model prediction, especially when used to constrain field scale models.     

二维叠后地震数据的平稳随机介质参数估计

随机介质参数估计是随机介质理论应用于地震勘探的关键.本文提出了一种从二维叠后地震数据中估计平稳随机介质参数的方法.文中阐述了二维叠后地震数据与随机介质波阻抗模型的关系,以及随机介质自相关函数参数的估计原理和方法,并结合实例详细介绍了应用功率谱法进行随机介质参数估计的具体步骤;通过多个二维理论模型的估计试验,验证了方法的可行性和正确性;还对实际地震数据进行了随机介质参数的估计试验,结果表明,随机介质参数可以为三角洲沉积相的进一步划分提供参考,反映了该方法有较好的应用前景.相比前人的研究,本文所提出的随机介质参数估计方法是一种真正的二维算法,特别是能给出自相关角度θ的估计,这种基于功率谱的估计方法具有直观且高效率的优点,但也存在着误差较大的问题,需要进一步的改进和完善.     

基于强震动台阵记录的震源破裂长度实时估测方法

本文提出一种通过小孔径台阵波束形成技术快速估测震源破裂长度的方法,同时提出了调整各台站相位的方法,即在每个台站的延时无法确定的情况下,近似地得到每个台站之间相位差的方法。在此基础上,利用自贡强震动观测台阵在汶川地震中得到的主震地震动记录进行了破裂长度的离线快速估测。结果表明,该方法的时效性较好,在地震动加速度峰值到来前约10 s时,便得到了断层破裂长度（约120 km）和相应破裂走向的估测结果,虽然此时的估测结果与最终估测结果（约230 km）有较大的偏差,但从实现快速地震预警的角度来看,还是有较好的实际意义。通过与前人的研究结果进行对比,结果显示该方法低估了东北方向的破裂长度,于是探讨了该现象产生的原因及可能的解决方案。最后对这种算法的计算速度进行了测试分析,结果表明通过并行计算该方法能够满足实时断层破裂长度估测的要求。      

广义Stein无偏风险估计与地球物理反问题正则化参数求取

地球物理反演是获取地球信息的重要手段,其求解具有严重的不适定性.为获得稳定的反问题结果,通常需要在目标泛函中加入正则化约束项.正确地估计正则化参数一直是地球物理反问题中的难点.目前存在的选取方法需要根据大量的试验来确定正则化参数,工作量十分巨大,并且存在很大的经验性,很难得到最优的正则化参数.针对这个问题,本文提出了一种基于广义Stein无偏风险估计的正则化参数求取方法.该方法的具体思路是通过求解模型参数均方误差的广义Stein无偏风险估计函数,在反问题求解过程中自动求取正则化参数.本文模型测试结果表明,相比于目前常用的方法,通过该方法得到的正则化参数是最优的.

     

高频GNSS实时地震学与地震预警研究现状

为实现从注重灾后救助向注重灾前预防转变,如何提高地震灾害监测预警和风险防范能力成为我们关注的重点.本文给出了国际上GNSS位移记录、强震动加速度记录、测震速度记录在地震预警中的应用现状,并总结了各自的特点,归纳出围绕高频GNSS地震学在震级与破裂过程实时反演中的几个需要进一步研究的关键问题：（1）引入北斗系统,基于高频GNSS（GPS/BDS）双系统的实时位移解算方法来提高实时单站位移解算精度,使实时解算精度达到厘米级;（2）开展强震仪加速度记录基线偏移校正研究,弥补地震近场GNSS站密度不足问题;（3）强震仪加速度记录与GNSS位移记录特点不同,开展强震仪加速度数据与GNSS位移数据实时融合处理研究,快速获得包含丰富地震形变和速率的波形数据;（4）测震学方法可快速估算震级,但是在强震发生时会出现震级饱和现象,造成震级估算偏低.需要开展基于GNSS位移时间序列的多种方法相结合的实时震级估算方法研究,通过与地震学方法比较和结合,来得到精度高、计算快的震级估值算法;（5）基于高频GNSS、断层初始模型快速选取、断层尺度、参数自适应调整是快速判断断层破裂方向的基础,在断层破裂过程自适应准实时反演算法方面需要进一步加强.通过国内外研究现状调研、分析,表明基于高频GNSS地震学的震级快速确定、震源破裂过程准实时反演算法的发展将对我国地震预警系统从"二网融合"到"三网融合"提供坚实的技术支撑.     

逆子波域消除多次波方法研究

SRMA（与表面相关多次波的衰减）算法包含预测和相减两步.相减算法中,当多次波与反射波同相轴相交时,如何有效减去多次波、保留反射波,是面临的主要问题.通过分析非正交性对滤波器（逆子波）的影响,可以证明：逆子波因非正交性产生的误差呈近似的高斯分布.在此基础上,本文提出了在逆子波域（单道自适应相减滤波的滤波算子的集合）,利用其误差的概率分布特征,对逆子波进行估计,用逆子波的估计对逆子波进行校正来消除多次波的方法.其步骤为：首先用SRMA方法预测出表面多次波,并对每一单炮进行单道自适应相减,得到逆子波,形成逆子波域;其次,在逆子波域采用中值滤波,提取接近真实逆子波的逆子波估计;第三,在逆子波域用逆子波估计对畸变的逆子波进行校正;最后采用校正后的逆子波来衰减多次波.通过简单模型和SMARRT模型的测试,该方法不仅能够有效减去多次波,而且在相交的区域,能够保持反射波同相轴的连续性并恢复其正确的振幅.     

A new method for aquifer system identification and parameter estimation

The standard practice for assessing aquifer parameters is to match groundwater drawdown data obtained during pumping tests against theoretical well function curves specific to the aquifer system being tested. The shape of the curve derived from the logarithmic time derivative of the drawdown data is also very frequently used as a diagnostic tool to identify the aquifer system in which the pumping test is being conducted. The present study investigates the incremental area method (IAM) to serve as an alternative diagnostic tool for the aquifer system identification as well as a supplement to the aquifer parameter estimation procedure. The IAM based diagnostic curves for ideal confined, leaky, bounded and unconfined aquifers have been derived as part of this study, and individual features of the plots have been identified. These features were noted to be unique to each aquifer setting, which could be used for rapid evaluation of the aquifer system. The effectiveness of the IAM methodology was investigated by analyzing field data for various aquifer settings including leaky, unconfined, bounded and heterogeneous conditions. The results showed that the proposed approach is a viable method for use as a diagnostic tool to identify the aquifer system characteristics as well as to support the estimation of the hydraulic parameters obtained from standard curve matching procedures. Copyright © 2012 John Wiley & Sons, Ltd.     

地球物理抗差估计和广义逆方法

为进行观测数据误差较大的地球物理资料的反演,引人抗差估计,称作地球物理抗差估计;为使病态方程组的反演解更可靠,又结合广义逆方法进行了算法改进．首先介绍抗差最小二乘（ＲＬＳ）的基本原理,然后推寻出适于广义逆反演方法的改进算式,最后举例加以讨论．分析表明,抗差估计可以有效地抑制地球物理观测异常的影响,得出正常模式下的较好估计值;而用改进后的算式和广义逆反演可以使反演解更加改善,不仅如此,改进后的方法还能直接给出解估计的可靠性评价．     

Conditional bias-penalized Kalman filter for improved estimation and prediction of extremes

Kalman filter (KF) and its variants are widely used for real-time state updating and prediction in environmental science and engineering. Whereas in many applications the most important performance criterion may be the fraction of the times when the filter performs satisfactorily under different conditions, in many other applications estimation and prediction specifically of extremes, such as floods, droughts, algal blooms, etc., may be of primary importance. Because KF is essentially a least squares solution, it is subject to conditional biases (CB) which arise from the error-in-variable, or attenuation, effects when the model dynamics are highly uncertain, the observations have large errors and/or the system being modeled is not very predictable. In this work, we describe conditional bias-penalized KF, or CBPKF, based on CB-penalized linear estimation which minimizes a weighted sum of error variance and expectation of Type-II CB squared and comparatively evaluate with KF through a set of synthetic experiments for one-dimensional state estimation under the idealized conditions of normality and linearity. The results show that CBPKF reduces root mean square error (RMSE) over KF by 10–20% or more over the tails of the distribution of the true state. In the unconditional sense CBPKF performs comparably to KF for nonstationary cases in that CBPKF increases RMSE over all ranges of the true state only up to 3%. With the ability to reduce CB explicitly, CBPKF provides a significant new addition to the existing suite of filtering techniques for improved analysis and prediction of extreme states of uncertain environmental systems.     

基于三分向台站波形的重复地下爆炸相关检测

在将相关检测方法应用于三分向台站记录数据时不能采用台阵数据检测时所使用的基于相关系数束慢度估计的虚假触发筛查方法来控制误检测.为此,本文根据重复事件的震中位置本身固定,各台站记录到的重复事件信号之间的到时差与相应参考事件的信号到时差基本相同的特性,根据两个以上三分向台站的相关检测触发到时差筛查相关检测虚假触发,从而解决了相关检测方法在应用于三分向台站数据时虚假触发过多的问题.利用新疆的三个三分向台站一个月的连续数据对该方法进行测试的结果表明,该方法能在接近零误检率的情况下对重复地下爆炸进行检测.     

Intelligent fuzzy weighted input estimation method for the multi-story buildings with unknown ground motion acceleration

This paper presents a novel intelligent fuzzy weighted input estimation method which effiviently and robustly estimates the unknown ground motion accelerations. The new input estimation method includes the Kalman Filter (KF) and the recursive least square estimator (RLSE), which is weighted by the fuzzy weighting factor proposed based on the fuzzy logic inference system. By directly synthesizing the Kalman filter with the estimator, this work presents an efficient robust forgetting zone, which is capable of providing a reasonable compromise between the tracking capability and the flexibility against noises. The excellent performace of this inverse method is demonstrated by solving the earthquake-excitation estimation problem, and the proposed algorithm is compared by alternating between the constant and adaptive weighting factors. The results reveal that this method has the properties of better target tracking capability and more effective noise reduction.     

Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions

Recently, Clauset, Shalizi, and Newman have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implementation is provided. The performance of our method is put to test on several empirical data which were previously analyzed with less systematic approaches. We find the functioning of the method very satisfactory.     

Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation

In order to evaluate the nonlinear performance and the possible damage to rubber-bearings (RBs) during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB (GZN110) under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least-square estimation (SNLSE), is introduced to identify the model parameters. It is shown that the proposed simplified Bouc-Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.     

The variable projection method for waveform inversion with an unknown source function

This paper compares three alternative algorithms for simultaneously estimating a source wavelet at the same time as an earth model in full‐waveform inversion: (i) simultaneous descent, (ii) alternating descent and (iii) descent with the variable projection method. The latter is a technique for solving separable least‐squares problems that is well‐known in the applied mathematics literature. When applied to full‐waveform inversion, it involves making the source wavelet an implicit function of the earth model via a least‐squares filter‐estimation process. Since the source wavelet becomes purely a function of medium parameters, it no longer needs to be treated as a separate unknown in the inversion. Essentially, the predicted data are projected onto the measured data in a least‐squares sense at every function evaluation, making use of the fact that the filter estimation problem is trivial when compared to the full‐waveform inversion problem. Numerical tests on a simple 1D model indicate that the variable projection method gives the best result; actually producing results in quality that are very similar to control experiments with a known, correct wavelet.     

Tensor Hydraulic Conductivity Estimation for Heterogeneous Aquifers under Unknown Boundary Conditions

A physically based inverse method is developed using hybrid formulation and coordinate transform to simultaneously estimate hydraulic conductivity tensors, steady‐state flow field, and boundary conditions for a confined aquifer under ambient flow or pumping condition. Unlike existing indirect inversion techniques, the physically based method does not require forward simulations to assess model‐data misfits. It imposes continuity of hydraulic head and Darcy fluxes in the model domain while incorporating observations (hydraulic heads, Darcy fluxes, or well rates) at measurement locations. Given sufficient measurements, it yields a well‐posed inverse system of equations that can be solved efficiently with coarse grids and nonlinear optimization. When pumping and injection are active, well rates are used as measurements and flux sampling is not needed. The method is successfully tested on synthetic aquifer problems with regular and irregular geometries, different hydrofacies and flow patterns, and increasing conductivity anisotropy ratios. All problems yield stable inverse solutions under increasing head measurement errors. For a given set of observations, inversion accuracy is strongly affected by the conductivity anisotropy ratio. Conductivity estimation is also affected by flow pattern: within a hydrofacies, when Darcy flux component is very small, the corresponding directional conductivity perpendicular to streamlines becomes less identifiable. Finally, inversion is successful even if the location of aquifer boundaries is unknown. In this case, the inversion domain is defined by the location of the measurements.