用复形法反求水文地质参数

０．６１８法，单纯形法是反求水文地质参数常用的最优化方法，本文介绍了另一种最优化方法－复形法，复形法也为直接搜索法，同时亦具有约束最优化法，用复形法水文地质参数，结果表明复形法不失为一种较好的计算方法。     

使用双核计算机并行求解水文地质参数研究

在建立地下水流模型的过程中，模型验证一直是较为复杂的步骤之一，具体难点包括寻优方法的选用，为保持总体平衡所引起的参数峰值异常以及总体寻优需要大量的计算机时等问题。本文运用区域分解法中D-N交替法的基本思想，在计算目标函数值时，将整体求解水文地质模型的过程分解为计算各参数分区内的子模型的过程，并在双核计算机上实现了并行计算。理想算例的计算结果证明了该方法用于水文地质逆问题求解的可行性，它不仅减少了求解过程中所需要的计算机时，而且提高了参数的拟合度。最后将这种方法应用到山东鹏山水源地的水文地质参数求解问题中，由结果可以看出，运用该方法反求水文地质参数是可行的，具有很好的应用前景。     

反求水文地质参数方法——单纯形调优法

目前反求水文地质参数方法中用得较多的是间接法,即试算校正法,其主要缺点是太费机时,尤其当要识别的参数很多时,反复调试可能延续很久。为克服这个缺点,引进最优化计算。本文仅介绍我们使用过的单纯形调优法。用这种方法可以自动反复调整参数,能找到一组最优的参数。     

非均质性对反求水文地质参数精确性影响研究

地下水文地质参数是衡量含水层导水性质和贮水性质的重要指标,是地下水资源评价的重要基础资料。本文利用GMS软件中的高斯模拟随机场生成不同非均质强度的含水层,对抽水试验进行数值模拟。利用得到的抽水实验数据,分别用解析法和数值法进行反求水文地质参数的计算。分析对比两种方法反求参数的精度,确定两种方法的适用性。结果显示:在反求参数的情况下,解析法要优于数值法;对于推算地下水的水头值时数值法要优于解析法。     

应用改进并行遗传算法反求水文地质参数研究

利用单纯形法局部搜索速度快和遗传算法全局寻优的特点,同时为了克服两种方法各自的弊病,提出采用混合单纯形技术的并行遗传算法(Hybrid Simplex Parallel Genetic Algorithm,SPGA)进行水文地质逆问题的求解。详细阐述了SPGA算法的具体操作和实现,并将该方法应用于水源地的地下水模拟反演中。计算结果表明,SPGA算法在水文地质参数寻优计算中具有比较好的可靠性和计算效率。     

基于区域分解法的水文地质参数寻优研究

在建立地下水流模型的过程中，水文地质参数寻优一直是较为复杂的步骤之一，具体难点包括寻优方法的取用，为保持总体平衡所引起的参数峰值异常以及总体寻优需要大量的计算机时等问题。本文运用区域分解法（Domain Decomposition method，DDM）的基本思想，将整个区域的参数寻优问题分解为各参数分区内的子域问题求解，通过寻找整个区域上的Nash均衡最终获得各子域上的最优参数。实验算例及其结果证明应用该方法实现水文地质参数自动寻优，不但具有高度的可靠性，同时优化问题的规模减小。此举不但减少了求解过程所需要的CPU时间，而且提高了参数拟合度。     

水文地质参数识别的连续禁忌搜索改进算法

水文地质参数的正确与否是构建地下水数值模型的根本,而参数寻优结果很大程度上取决于优化算法的选择。禁忌搜索算法是一种广泛应用于组合优化问题的启发式全局寻优算法,但在连续函数优化领域应用比较少。基于上述考虑,本文首先引入求解连续函数优化问题的连续禁忌搜索算法并对其进行改进,进而提出一种连续禁忌搜索改进算法(ICTS),最后将其与地下水模型耦合进行水文地质参数识别。算例研究表明,ICTS算法较其他算法(CTS,SGA,Micro-GA,PSO)求解效率提高1.87～4.64倍,求解精度提高1.08～12.86倍。因此ICTS算法在参数反演计算中求解精度高、收敛速度快、寻优性能强,是一种值得推广的水文地质参数识别方法。     

单纯形一模拟退火混合算法反求水文地质参数及其并行求解

本文利用单纯形法局部搜索速度快和模拟退火算法全局寻优的特点，同时为了克服各自算法的弊病，提出采用单纯形一模拟退火混合算法（SMSA）进行水文地质逆问题的求解。论文详细描述了SMSA算法的具体操作算子的实现，并将该算法应用于一个大型水源地的地下水模拟反演。计算结果表明，SMSA算法在水文地质参数反演计算具有求解速度快，精度高的特点，而且易于实现并行运算。     

单纯形—模拟退火混合算法反求水文地质参数及其并行求解

本文利用单纯形法局部搜索速度快和模拟退火算法全局寻优的特点,同时为了克服各自算法的弊病,提出采用单纯形—模拟退火混合算法(SMSA)进行水文地质逆问题的求解。论文详细描述了SMSA算法的具体操作算子的实现,并将该算法应用于一个大型水源地的地下水模拟反演。计算结果表明,SMSA算法在水文地质参数反演计算具有求解速度快,精度高的特点,而且易于实现并行运算。     

非稳定流的有限单元法中承压水析奇与潜水逐步析奇的一个方法(Ⅰ、Ⅱ)

本文研究的是地下水的水位予报及反求水文地质参数的有限单元法。由二部分组成:第一部分,用有限单元法预报承压水的水位。我们构造了一个函数,它可将井口的奇点析出,把井点附近水头变化极快的情形转变为缓慢,把有开采井的问题转化成没有开采井的等价问题,然后用通常的有限单元法求解,这对于提高水位预报的精度及消除反求水文地质参数的不适定性是有重要意义的。我们以“泰斯解”和“鸠布衣解”为例说明了这种析奇点方法的有效性;第二部分,研究了潜水不稳定流的有限单元法。我们提出了逐步线性化析奇点的方法,把潜水问题转化为类似承压水问题来处理因而可用有限单元法求得比较精确的解答。第三部分,在奇点析出的基础上,用有限元技术讨论了反求水文地质参数问题。     

A simplex analysis of slope stability

The downhill simplex algorithm is applied to systematically locate the critical failure mechanism in slopes and to compute the minimum factor of safety. The proposed method is illustrated with three examples of circular and noncircular slope stability and its results are compared to previously published solutions. Although it is not the most efficient optimization procedure, the simplex method is versatile, robust, and simple. It is recommended to enhance slope stability programs by providing for an automatic search of the critical failure mechanisms.     

水环境模型参数识别的一种新方法

通过在格雷码遗传算法进化过程中加入单纯形搜索算子,并利用格雷码遗传算法和单纯形法所得到的优秀个体群,作为变量新的变化范围,逐步缩小搜索空间,自动向最优解收缩,提出了水环境模型参数识别的一种新方法——格雷码混合加速遗传算法(GCHAGA),给出了实施该算法的详细步骤。对GCHAGA的收敛性和全局优化性进行了理论和实例分析,并在确定河流横向扩散系数等参数识别问题中,GCHAGA得到了精度较高的全局最优解。与格雷码遗传算法(GCGA)和常规优化方法相比,GCHAGA具有精度高、速度快和适用性强等特点,是一种既可以较大概率搜索全局最优解,又能进行局部细致搜索的较好的非线性优化方法,可广泛应用于各种水环境优化问题中。     

确定多重现期暴雨公式参数的二次优化算法

四参数非线性多重现期暴雨公式在城市排水规划设计中有着广泛的应用。搜索算法与最小二乘法是优化计算的两个简单有效的方法,不过单独直接用于求解四参数非线性多重现期暴雨公式的参数比较困难。提出耦合最小二乘法及搜索算法确定多重现期暴雨公式参数的二次优化算法,该方法可以一次得到多重现期暴雨强度公式的参数,参数优化过程不需要图解。研究表明,计算结果比较客观;成果精度高,例题的平均绝对均方差为0.035mm/min。与遗传算法、蚁群算法等比较,该方法计算原理容易理解,计算简便,可以用Excel进行参数优化计算。     

Wu-Bauer亚塑性模型参数确定方法的改进及其验证

研究了Wu-Bauer亚塑性模型参数试验确定方法及其存在的问题。根据单形调优法,对模型参数确定方法进行了改进,并通过三轴固结排水试验、侧限压缩试验和加卸载试验进行了验证。分析表明,该方法可有效地确定模型参数。最后分析了Wu-Bauer亚塑性模型的优点和不足之处。     

Optimization routine for identification of model parameters in soil plasticity

The paper presents an optimization routine especially developed for the identification of model parameters in soil plasticity on the basis of different soil tests. Main focus is put on the mathematical aspects and the experience from application of this optimization routine. Mathematically, for the optimization, an objective function and a search strategy are needed. Some alternative expressions for the objective function are formulated. They capture the overall soil behaviour and can be used in a simultaneous optimization against several laboratory tests. Two different search strategies, Rosenbrock's method and the Simplex method, both belonging to the category of direct search methods, are utilized in the routine. Direct search methods have generally proved to be reliable and their relative simplicity make them quite easy to program into workable codes. The Rosenbrock and simplex methods are modified to make the search strategies as efficient and user‐friendly as possible for the type of optimization problem addressed here. Since these search strategies are of a heuristic nature, which makes it difficult (or even impossible) to analyse their performance in a theoretical way, representative optimization examples against both simulated experimental results as well as performed triaxial tests are presented to show the efficiency of the optimization routine. From these examples, it has been concluded that the optimization routine is able to locate a minimum with a good accuracy, fast enough to be a very useful tool for identification of model parameters in soil plasticity. Copyright © 2001 John Wiley & Sons, Ltd.     

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     

Single‐and multi‐objective genetic algorithm optimization for identifying soil parameters

This paper discusses the quality of the procedure employed in identifying soil parameters by inverse analysis. This procedure includes a FEM‐simulation for which two constitutive models—a linear elastic perfectly plastic Mohr–Coulomb model and a strain‐hardening elasto‐plastic model—are successively considered. Two kinds of optimization algorithms have been used: a deterministic simplex method and a stochastic genetic method. The soil data come from the results of two pressuremeter tests, complemented by triaxial and resonant column testing. First, the inverse analysis has been performed separately on each pressuremeter test. The genetic method presents the advantage of providing a collection of satisfactory solutions, among which a geotechnical engineer has to choose the optimal one based on his scientific background and/or additional analyses based on further experimental test results. This advantage is enhanced when all the constitutive parameters sensitive to the considered problem have to be identified without restrictions in the search space. Second, the experimental values of the two pressuremeter tests have been processed simultaneously, so that the inverse analysis becomes a multi‐objective optimization problem. The genetic method allows the user to choose the most suitable parameter set according to the Pareto frontier and to guarantee the coherence between the tests. The sets of optimized parameters obtained from inverse analyses are then used to calculate the response of a spread footing, which is part of a predictive benchmark. The numerical results with respect to both the constitutive models and the inverse analysis procedure are discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

基于混合遗传算法估计van Genuchten方程参数

van Genuchten(VG)方程是最常用的土壤水分特征曲线方程,其参数取值的精度直接影响到土壤水分运动方程计算的精度.该文建立了VG方程参数的优化模型,构建遗传算法与Levenberg-Marquardt算法相结合的混合遗传算法对其进行求解,并进行了数值试验.结果表明采用混合遗传算法比普通遗传算法不但提高了收敛效率,而且收敛迭代次数也大大减少;采用混合遗传算法估计参数的精度比非线性单纯形法和阻尼最小二乘法要高一些,而且不需要给参数初值.因此,混合遗传算法可以作为估计VG方程参数的一种新方法.     

隧洞围岩损失位移估计的智能优化反分析

隧洞开挖过程中围岩监测断面的布置一般滞后于掌子面开挖,监测断面布置前围岩已发生的位移称为损失位移。采用优化反分析思路求取损失位移,该思路将损失位移的求解转化为以实测位移与计算位移的误差作为目标函数、岩体力学参数作为决策变量的全局优化反分析问题。针对该全局优化反分析问题是一类高度非线性多峰值且计算代价较高的优化问题,将性能优异的粒子群优化算法与高斯过程机器学习方法相融合,结合FLAC3D数值计算程序,提出隧洞围岩损失位移优化反分析的粒子群-高斯过程-FLAC3D智能协同优化方法。算例研究表明,该方法是可行的,不仅能获得可靠的损失位移预测结果,而且可获取合理的围岩计算模型力学参数,具有全局性好、计算效率高的特点,克服了传统优化反分析方法容易陷入局部最优或过于依赖初始学习样本的局限性。将该方法应用到锦屏二级水电站辅助洞BK14+599断面的损失位移反分析,获得了该断面围岩的损失位移和力学参数,其中,损失位移较大,原因在于岩体开挖后在短时间内弹性变形大。因此,对于地下工程,特别是深部地下岩体工程,在围岩稳定性评价与围岩参数反分析中,损失位移不可忽视,应给予足够重视。     

基于MPSO的RBF耦合算法的桩基动测参数辨识

变异粒子群优化算法（MPSO）是一种基于群体智能的改进全局优化技术,其优势在于减小陷入局部极值的机率,增加全局搜索能力。将变异粒子群算法与径向基函数（RBF）神经网络结构进行结合,建立了变异粒子群神经网络（MPSO-RBF）耦合算法,充分发挥了MPSO算法的全局寻优能力和RBF算法的局部搜索优势。数值计算结果表明,所建立的方法能够对桩基动测进行多参数的识别和非线性优化问题的求解,具有良好全局收敛能力,是一种行之有效的智能算法。