Combination of Dependent Realizations Within the Gradual Deformation Method

Gradual deformation is a parameterization method that reduces considerably the unknown parameter space of stochastic models. This method can be used in an iterative optimization procedure for constraining stochastic simulations to data that are complex, nonanalytical functions of the simulated variables. This method is based on the fact that linear combinations of multi-Gaussian random functions remain multi-Gaussian random functions. During the past few years, we developed the gradual deformation method by combining independent realizations. This paper investigates another alternative: the combination of dependent realizations. One of our motivations for combining dependent realizations was to improve the numerical stability of the gradual deformation method. Because of limitations both in the size of simulation grids and in the precision of simulation algorithms, numerical realizations of a stochastic model are never perfectly independent. It was shown that the accumulation of very small dependence between realizations might result in significant structural drift from the initial stochastic model. From the combination of random functions whose covariance and cross-covariance are proportional to each other, we derived a new formulation of the gradual deformation method that can explicitly take into account the numerical dependence between realizations. This new formulation allows us to reduce the structural deterioration during the iterative optimization. The problem of combining dependent realizations also arises when deforming conditional realizations of a stochastic model. As opposed to the combination of independent realizations, combining conditional realizations avoids the additional conditioning step during the optimization process. However, this procedure is limited to global deformations with fixed structural parameters.     

Refinement Indicators for Optimal Selection of Geostatistical Realizations Using the Gradual Deformation Method

In the analysis of petroleum reservoirs, one of the most challenging problems is to use inverse theory in the search for an optimal parameterization of the reservoir. Generally, scientists approach this problem by computing a sensitivity matrix and then perform a singular value decomposition in order to determine the number of degrees of freedom i.e. the number of independent parameters necessary to specify the configuration of the system. Here we propose a complementary approach: it uses the concept of refinement indicators to select those degrees which have the greatest sensitivity to an objective function quantifying the mismatch between measured and simulated data. We apply this approach to the problem of data integration for petrophysical reservoir charaterization where geoscientists are currently working with multimillion cell geological models. Data integration may be performed by gradually deforming (by a linear combination) a set of these multimillion grid geostatistical realizations during the optimization process. The inversion parameters are then reduced to the number of coefficients of this linear combination. However, there is an infinity of geostatistical realizations to choose from which may not be efficient regarding operational constraints. Following our new approach, we are able through a single objective function evaluation to compute refinement indicators that indicate which realizations might improve the iterative geological model in a significant way. This computation is extremely fast as it implies a single gradient computation through the adjoint state approach and dot products. Using only the most sensitive realizations from a given set, we are able to resolve quicker the optimization problem case. We applied this methodology to the integration of interference test data into 3D geostatistical models.     

Experimental Assessment of Gradual Deformation Method

Uncertainty in future reservoir performance is usually evaluated from the simulated performance of a small number of reservoir realizations. Unfortunately, most of the practical methods for generating realizations conditional to production data are only approximately correct. It is not known whether or not the recently developed method of Gradual Deformation is an approximate method or if it actually generates realizations that are distributed correctly. In this paper, we evaluate the ability of the Gradual Deformation method to correctly assess the uncertainty in reservoir predictions by comparing the distribution of conditional realizations for a small test problem with the standard distribution from a Markov Chain Monte Carlo (MCMC) method, which is known to be correct, and with distributions from several approximate methods. Although the Gradual Deformation algorithm samples inefficiently for this test problem and is clearly not an exact method, it gives similar uncertainty estimates to those obtained by MCMC method based on a relatively small number of realizations.     

基于粒子群优化神经网络算法的深基坑变形预测方法

深基坑变形预测是进行施工参数调整和确保深基坑施工安全的重要手段,而如何对其变形进行有效、准确的预测是一个有待解决的技术难题。采用粒子群优化算法对神经网络模型的初始权值和阈值进行优化,并将已有的变形监测数据作为神经网络的输入参数,建立了基于粒子群优化神经网络算法的深基坑变形预测方法。将形成的方法应用于长春市火车站北广场深基坑开挖监测工程中。结果表明：8号水平位移测点预测结果的均方根误差为3.78%,平均百分比误差为5.48%;9号地面沉降点预测结果的均方根误差为5.62%,平均百分比误差为3.23%。经验证,本文方法预测深基坑开挖过程中的变形具有较高的可信度。     

Gradual Deformation and Iterative Calibration of Sequential Stochastic Simulations

Based on the algorithm for gradual deformation of Gaussian stochastic models, we propose, in this paper, an extension of this method to gradually deforming realizations generated by sequential, not necessarily Gaussian, simulation. As in the Gaussian case, gradual deformation of a sequential simulation preserves spatial variability of the stochastic model and yields in general a regular objective function that can be minimized by an efficient optimization algorithm (e.g., a gradient-based algorithm). Furthermore, we discuss the local gradual deformation and the gradual deformation with respect to the structural parameters (mean, variance, and variogram range, etc.) of realizations generated by sequential simulation. Local gradual deformation may significantly improve calibration speed in the case where observations are scattered in different zones of a field. Gradual deformation with respect to structural parameters is necessary when these parameters cannot be inferred a priori and need to be determined using an inverse procedure. A synthetic example inspired from a real oil field is presented to illustrate different aspects of this approach. Results from this case study demonstrate the efficiency of the gradual deformation approach for constraining facies models generated by sequential indicator simulation. They also show the potential applicability of the proposed approach to complex real cases.     

Comparing the Gradual Deformation with the Probability Perturbation Method for Solving Inverse Problems

Inverse problems are ubiquitous in the Earth Sciences. Many such problems are ill-posed in the sense that multiple solutions can be found that match the data to be inverted. To impose restrictions on these solutions, a prior distribution of the model parameters is required. In a spatial context this prior model can be as simple as a Multi-Gaussian law with prior covariance matrix, or could come in the form of a complex training image describing the prior statistics of the model parameters. In this paper, two methods for generating inverse solutions constrained to such prior model are compared. The gradual deformation method treats the problem of finding inverse solution as an optimization problem. Using a perturbation mechanism, the gradual deformation method searches (optimizes) in the prior model space for those solutions that match the data to be inverted. The perturbation mechanism guarantees that the prior model statistics are honored. However, it is shown with a simple example that this perturbation method does not necessarily draw accurately samples from a given posterior distribution when the inverse problem is framed within a Bayesian context. On the other hand, the probability perturbation method approaches the inverse problem as a data integration problem. This method explicitly deals with the problem of combining prior probabilities with pre-posterior probabilities derived from the data. It is shown that the sampling properties of the probability perturbation method approach the accuracy of well-known Markov chain Monte Carlo samplers such as the rejection sampler. The paper uses simple examples to illustrate the clear differences between these two methods     

Gradual Deformation and Iterative Calibration of Gaussian-Related Stochastic Models

This paper describes a new method for gradually deforming realizations of Gaussian-related stochastic models while preserving their spatial variability. This method consists in building a stochastic process whose state space is the ensemble of the realizations of a spatial stochastic model. In particular, a stochastic process, built by combining independent Gaussian random functions, is proposed to perform the gradual deformation of realizations. Then, the gradual deformation algorithm is coupled with an optimization algorithm to calibrate realizations of stochastic models to nonlinear data. The method is applied to calibrate a continuous and a discrete synthetic permeability fields to well-test pressure data. The examples illustrate the efficiency of the proposed method. Furthermore, we present some extensions of this method (multidimensional gradual deformation, gradual deformation with respect to structural parameters, and local gradual deformation) that are useful in practice. Although the method described in this paper is operational only in the Gaussian framework (e.g., lognormal model, truncated Gaussian model, etc.), the idea of gradually deforming realizations through a stochastic process remains general and therefore promising even for calibrating non-Gaussian models.     

基于点目标分析的InSAR技术检测地表微小形变的研究

近年来,由合成孔径雷达干涉测量技术(InSAR)技术发展而来的时间序列影像点目标分析技术已发展成为大范围地提取地表微小形变信息的关键技术。本研究针对地表形变检测中经常出现的时间、空间去相干问题和大气效应等问题,从常规的合成孔径雷达差分测量技术(D-InSAR)入手,深入探讨了以永久散射体(PSI)和相干目标分析(CTA)方法为代表的点目标分析技术原理和方法,阐述了它们的特点和优势。最后,介绍了CTA方法对提取长时间地表形变场的具体应用实例,说明其方法的有效性和可靠性。     

一种新的构造变形热年代学研究方法——显微构造变形热年代学

显微构造变形热年代学是一种新兴的研究构造变形热年代学方法,能够解决一些常用方法无法解决的或很困难的构造问题。显微构造变形热年代学利用因构造变形事件而产生的新生矿物结晶年龄来测定小至一般的构造变形,大至区域构造乃至造山带或碰撞带构造变形的年龄,建立构造演化时间序列,并可以计算其变形速率或隆升速率。     

Approximate Derivative Computations for the Gradient-Based Optimization Methods in the Local Gradual Deformation for History Matching

Reservoir characterization needs the integration of various data through history matching, especially dynamic information such as production or four-dimensional seismic data. To update geostatistical realizations, the local gradual deformation method can be used. However, history matching is a complex inverse problem, and the computational effort in terms of the number of reservoir simulations required in the optimization procedure increases with the number of matching parameters. History matching large fields with a large number of parameters has been an ongoing challenge in reservoir simulation. This paper presents a new technique to improve history matching with the local gradual deformation method using the gradient-based optimizations. The new approach is based on the approximate derivative calculations using the partial separability of the objective function. The objective function is first split into local components, and only the most influential parameters in each component are used for the derivative computation. A perturbation design is then proposed to simultaneously compute all the derivatives with only a few simulations. This new technique makes history matching using the local gradual deformation method with large numbers of parameters tractable.     

基坑变形影响因素与有限元数值模拟

基坑变形影响因素是其变形控制的重要内容之一，在自制深基坑工程变形控制优化设计及其有限元数值模拟系统(SDCDEFEM)的基础上，重点对影响基坑变形的各因素进行了有限元数值模拟分析，并对实测和计算的基坑周边最大沉降、支护结构最大水平位移和坑底最大隆起及其位置进行了统计分析，得出了简明估算基坑最大变形及其位置的统计关系式，提出了经济有效的变形控制对策。     

一种土体固结变形的数值计算方法

在给出反映土体团结流变性的本构方程基础上．捉出一种土体固结变形的数值计算方法。该方法依据有效应力增量方程式,利用西瓦伦公式计算有效应力值,采用逐步递推迭代方法,实现土体固结变形的计算。     

An Improved Gradual Deformation Method for Reconciling Random and Gradient Searches in Stochastic Optimizations

Constraining stochastic models of reservoir properties such as porosity and permeability can be formulated as an optimization problem. While an optimization based on random search methods preserves the spatial variability of the stochastic model, it is prohibitively computer intensive. In contrast, gradient search methods may be very efficient but it does not preserve the spatial variability of the stochastic model. The gradual deformation method allows for modifying a reservoir model (i.e., realization of the stochastic model) from a small number of parameters while preserving its spatial variability. It can be considered as a first step towards the merger of random and gradient search methods. The gradual deformation method yields chains of reservoir models that can be investigated successively to identify an optimal reservoir model. The investigation of each chain is based on gradient computations, but the building of chains of reservoir models is random. In this paper, we propose an algorithm that further improves the efficiency of the gradual deformation method. Contrary to the previous gradual deformation method, we also use gradient information to build chains of reservoir models. The idea is to combine the initial reservoir model or the previously optimized reservoir model with a compound reservoir model. This compound model is a linear combination of a set of independent reservoir models. The combination coefficients are calculated so that the search direction from the initial model is as close as possible to the gradient search direction. This new gradual deformation scheme allows us for reducing the number of optimization parameters while selecting an optimal search direction. The numerical example compares the performance of the new gradual deformation scheme with that of the traditional one.     

全站仪用于隧道三维变形测量的实施方法

叙述了全站仪用于隧道开挖施工中对围岩进行三维收敛变形测量的实施方法，其中包括：测量坐标系和基准点的建立；测点的布设要求；观测方法；观测精度以及空间边角网平差方法的介绍。结合北京地铁复线某车站地下施工现场所作的初步试验，进行了实际应用分析。     

非饱和土增湿变形的实用计算方法

非饱和土力学研究目前还未进入实用阶段,主要原因在于吸力量测困难。本文提出了用等效吸力代替真实吸力的试验方法。首先以常规静三轴试验得到的原状饱和土以及非饱和土的应力-应变曲线为基础,根据变形等效的原则确定与某一饱和度相当的围压即为等效吸力;然后建立饱和度与等效吸力之间的非线性关系,并验证了该数学公式的正确性;再根据试验结果分析含水量对非饱和土强度的影响,建立了非饱和土的实用抗剪强度公式;最后按照邓肯-张模型的参数整理方法得到了不同饱和度非饱和土的模型参数,探索这些参数随饱和度的变化规律,建立了引入饱和度的非饱和黄土实用非线性模型,并进行了降雨入渗情况下非饱和土增湿变形的计算。结果表明,饱和度最大值为95%,等效吸力最大值为160 kPa,最大水平位移与竖向位移分别为0.6 cm和20.0 cm,均出现在浸水位置。计算结果合理地反映了非饱和土变形的分布趋势,验证了方法的合理性。     

某地铁停车场出入线基坑支护方案优化设计及变形模拟

研究基于某地铁停车场出入段线基坑支护方案的优化设计,利用比选排除法得出适合该研究区基坑支护方案并对每个方案进行支护设计,进而利用数学模糊评判方法对所有适用方案进行综合评分,选出最优方案。对基坑设计进行验算,ADINA软件进行模拟,验证了最终方案的可行性,对基坑支护方案选型及设计有一定的参考意义。     

考虑变形影响的基坑土压力计算方法

土压力的分布和大小与变形密切相关。分析了目前考虑变形的土压力设计计算方法,并提出了考虑变形的土压力计算模型,对两个工程实例进行了计算分析,计算所得的主动土压力和被动土压力都在合理的范围内,显示出了该方法的合理性。     

地下巷道弹性位移反分析各种优化方法的探讨

探讨了６种最优化方法（鲍威尔法、单纯形加速法、阻尼最小二乘法、变尺度法、模式搜索法和变量轮换法）在巷道弹性位移反分析中的应用情况。从参数初始点的选择、收敛速度、收敛精度和可靠性方面评价了这６种无约束最优化方法的优劣。     

Deformation Control of Deep Excavation Pit and Numerical Simulation with Finite Element Method

The authors firstly introduce deformation control of deep excavation pit in detail, and then put forward new conceptions such as: effective coefficient of excavation pit, effective area, ineffective area and critical line, and also put forward the referential criteria of deformation control. The System of Optimization Design with Deformation Control of Deep Excavation Pit and Numerical Simulation with Finite Element Method (SDCDEFEM) is also briefly introduced. Factors influencing deformation of excavation pit are analyzed by the system. The measured and simulated data of maximum deformations (settlement, displacement and upheaval) and their positions are analyzed and discussed. The statistic formula estimating maximum deformations and their positions was gained, and economical-effective measures of deformation control were brought forward.     

真空预压方法在沿海软基处理中的应用及效果分析

为对软基施工实施有效控制 ,结合我国南方某度假村场地处理工程实例 ,对真空预压处理软基的效果进行了长达近两年的现场试验段实际测试 ,通过对沉降数据以及测斜数据的分析 ,得出了结论 :真空压力的实施和传递主要由两部分组成 ,间距为 1 2m的竖向塑料排水板和水平向铺设的Φ10 0mm的波纹管 ,塑料排水板起到增加土体中竖向排水通道的作用 ,而波纹管可同时起到传递真空压力和集水的作用 ,运用真空预压法处理本地区软土地基是成功的