Statistical inverse analysis based on genetic algorithm and principal component analysis: Applications to excavation problems and pressuremeter tests

This study concerns the identification of constitutive models from geotechnical measurements by inverse analysis. Soil parameters are identified from measured horizontal displacements of sheet pile walls and from a measured pressuremeter curve. An optimization method based on a genetic algorithm (GA) and a principal component analysis (PCA), developed and tested on synthetic data in a previous paper, is applied. These applications show that the conclusions deduced from synthetic problems can be extrapolated to real problems. The GA is a robust optimization method that is able to deal with the non‐uniqueness of the solution in identifying a set of solutions for a given uncertainty on the measurements. This set is then characterized by a PCA that gives a first‐order approximation of the solution as an ellipsoid. When the solution set is not too curved in the research space, this ellipsoid characterizes the soil properties considering the measured data and the tolerate margins for the response of the numerical model. Besides, optimizations from different measurements provide solution sets with a common area in the research space. This intersection gives a more relevant and accurate identification of parameters. Finally, we show that these identified parameters permit to reproduce geotechnical measurements not used in the identification process. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Inverse analysis for geomaterial parameter identification using Pareto multiobjective optimization

An inverse analysis method that combines the back propagation neural network (BPNN) and vector evaluated genetic algorithm (VEGA) was proposed to identify mechanical geomaterial parameters for a more accurate prediction of deformation. The BPNN is used to replace the time‐consuming numerical calculations, thus enhancing the efficiency of the inverse analysis. The VEGA is used to find the Pareto‐optimal solutions to multiobjective functions. Unlike traditional back‐analysis methods which are based on only 1 type of field measurement and a single objective function, this proposed method can consider multiple field observations simultaneously. The proposed method was applied to the Shapingba foundation pit excavation located in Chongqing city, China. Two types of measurements are considered in the method simultaneously: the displacements in the x‐direction (north orientation) and those in the y‐direction (east orientation). Five deformation modulus parameters for artificial backfill soil, silty clay, siltstone, sandstone, and mudstone were selected as the inversion parameters. Compared with the weighted sum approach, the proposed method was demonstrated as an efficient multi‐objective optimization tool for back calculating undetermined parameters. After performing a forward‐calculation using the optimized parameters obtained by the inverse analysis, the predicted results were well consistent with the practical deformation in magnitude and trend.     

基于区域Delaunay自动剖分的含水层参数反演

针对地下水有限元数值模拟中区域三角网格剖分复杂难以处理的情况,提出适合其特点的Delaunay三角网格自动剖分方法,并对含有多个参数分区的含水层进行网格剖分,最后利用遗传算法和有限元程序相耦合来反演含水层水文地质参数。结果表明此方法可大大简化地下水数值模拟的前处理工作,并能提高有限元网格剖分的有效性和准确性,从而得到令人满意的数值模拟结果。     

Parameter identification of minifrac numerical tests using a gradient boosting-based proxy model and genetic algorithm

In recent years, the petroleum industry has devoted considerable attention to studying fluid flow inside fracture channels due to the discovery of naturally fractured reservoirs. The behavior prediction of these reservoirs is a well-known challenging task, in which the initial stage consists of identifying reservoir hydromechanical parameters. This work proposes an artificial intelligence-based approach to identify hydromechanical parameters from borehole injection pressure curves acquired through minifrac tests. This approach combines proxy modeling with a stochastic optimization algorithm to match observed and predicted borehole pressure curves. Therefore, a gradient boosting-based proxy model is built to predict borehole pressure curves, considering a proper strategy to develop time series modeling. Moreover, a Bayesian optimization algorithm is applied to compute the gradient boosting hyperparameters. In this optimization scenario, this paper proposes an appropriate objective function established from the assumed time series prediction strategy and the k-fold cross-validation. Finally, a genetic algorithm is adopted to identify unknown hydromechanical parameters, solving an inverse problem. Based on the proposed workflow, a study of the importance of the hydromechanical parameters is developed. To assess the methodology applicability, the approach is employed to identify parameters in synthetic and field minifrac tests. The results present how this approach can adequately identify hydromechanical parameters of hydraulic fracturing problems.     

Statistical inverse analysis based on genetic algorithm and principal component analysis: Method and developments using synthetic data

This study concerns the identification of parameters of soil constitutive models from geotechnical measurements by inverse analysis. To deal with the non‐uniqueness of the solution, the inverse analysis is based on a genetic algorithm (GA) optimization process. For a given uncertainty on the measurements, the GA identifies a set of solutions. A statistical method based on a principal component analysis (PCA) is, then, proposed to evaluate the representativeness of this set. It is shown that this representativeness is controlled by the GA population size for which an optimal value can be defined. The PCA also gives a first‐order approximation of the solution set of the inverse problem as an ellipsoid. These developments are first made on a synthetic excavation problem and on a pressuremeter test. Some experimental applications are, then, studied in a companion paper, to show the reliability of the method. Copyright © 2009 John Wiley & Sons, Ltd.     

PARAMETER AND VARIANCE ESTIMATION IN GEOTECHNICAL BACKANALYSIS USING PRIOR INFORMATION

A probabilistic framework to perform inverse analysis of geotechnical problems is presented. The formulation allows the incorporation of existing prior information on the parameters in a consistent way. The method is based on the maximum likelihood approach that allows a straightforward introduction of the error structure of field measurements and prior information. The difficulty of ascribing definite values to the uncertainties associated with the various types of observations is overcome by including the corresponding variances in the set of parameters to be identified. The inverse analysis results in a minimization problem that is solved by coupling the optimization technique to the finite element method. Two examples are presented to illustrate the performance of the method. The first one corresponds to a synthetic case simulating the excavation of a tunnel. Young's modulus, K₀ value and measurements variances are identified. The second case concerns the excavation of a large underground cavern in which again Young's modulus and K₀ are identified. It is shown that introduction of prior information permits the estimation of parameters more consistent with all available informations that include not only monitored displacements but also results from in situ tests carried out during the site investigation stage.     

基于十进制遗传算法的含水层参数的反演

含水层参的反演是一个复杂的非线性优化问题,针对传统二进制遗传算法收敛性能差的缺陷,提出了反演含水层参数的十进制遗传算法。以直线隔水边界附近的井流模型为例,讨论了十进制遗传算法在含水层参数反演中的应用,并与二进制遗传算法的进行比较。结果表明,该方法在含水层参数的反演中不仅是可行的,而且具有较好的确定性和较高的精度;与二进制遗传算法相比,十进制遗传算法的收敛性较好,省时高效,且表示较为自然,容易引入相关领域知识。同时,结合实例的分析结果得出种群的规模对算法的收敛性没有明显的影响。     

用十进制遗传算法识别泰斯模型参数

提出了用十进制遗传算法识别泰斯模型参数的方法和步骤,并给出了计算实例。本方法和传统的配线法与高斯牛顿法相比,具有更好的确定性和更高的精度。十进制遗传算法的主要优点在于采用十进制编码表达实际问题比较简单,算法的平均效率高,特别是对于高维和复杂优化问题。     

Sensitivity analysis for parameter identification in quasi‐static poroelasticity

This paper is devoted to the formulation of the direct differentiation method and adjoint state method in quasi‐static linear poroelasticity. We derive the strong and weak formulation of both methods and discuss their solutions using the finite element method. The techniques are illustrated and tested on two numerical examples for the case of isotropic and homogeneous material. The presented formulations can be extended to more complex behaviour in poromechanics. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimization techniques for identifying soil parameters in geotechnical engineering: Comparative study and enhancement

A comparative study of optimization techniques for identifying soil parameters in geotechnical engineering was first presented. The identification methodology with its 3 main parts, error function, search strategy, and identification procedure, was introduced and summarized. Then, current optimization methods were reviewed and classified into 3 categories with an introduction to their basic principles and applications in geotechnical engineering. A comparative study on the identification of model parameters from a synthetic pressuremeter and an excavation tests was then performed by using 5 among the mostly common optimization methods, including genetic algorithms, particle swarm optimization, simulated annealing, the differential evolution algorithm and the artificial bee colony algorithm. The results demonstrated that the differential evolution had the strongest search ability but the slowest convergence speed. All the selected methods could reach approximate solutions with very small objective errors, but these solutions were different from the preset parameters. To improve the identification performance, an enhanced algorithm was developed by implementing the Nelder‐Mead simplex method in a differential algorithm to accelerate the convergence speed with strong reliable search ability. The performance of the enhanced optimization algorithm was finally highlighted by identifying the Mohr‐Coulomb parameters from the 2 same synthetic cases and from 2 real pressuremeter tests in sand, and ANICREEP parameters from 2 real pressuremeter tests in soft clay.     

A finite element algorithm for parameter identification of material models for fluid saturated porous media

In this contribution an algorithm for parameter identification of geometrically linear Terzaghi–Biot‐type fluid‐saturated porous media is proposed, in which non‐uniform distributions of the state variables such as stresses, strains and fluid pore pressure are taken into account. To this end a least‐squares functional consisting of experimental data and simulated data is minimized, whereby the latter are obtained with the finite element method. This strategy allows parameter identification based on in situ experiments. In order to improve the efficiency of the minimization process, a gradient‐based optimization algorithm is applied, and therefore the corresponding sensitivity analysis for the coupled two‐phase problem is described in a systematic manner. For illustrative purpose, the performance of the algorithm is demonstrated for a slope stability problem, in which a quadratic Drucker–Prager plasticity model for the solid and a linear Darcy law for the fluid are combined. Copyright © 2001 John Wiley & Sons, Ltd.     

快速模拟退火算法在含水层参数识别中的应用

针对一般模拟退火算法收敛速度慢的缺陷,本文提出了含水层参数识别的快速模拟退火算法。它以广义Boltzmann-Gibbs统计理论为基础,采用依赖于温度的似Cauchy分布产生新的扰动模型,通过改变模型扰动、接收概率和降温方式来加快模拟退火算法的收敛速度。实例的计算结果表明,快速模拟退火算法不仅可行,而且求解精度高,收敛速度比其他算法快得多,是一种值得在实际中推广应用的高效的含水层参数识别方法。     

遗传算法在反演三维地下水流模型参数中的应用

本文以非均质各向同性承压三维非稳定流为理想模型,结合有限元法讨论了用遗传算法反演水文地质参数问题.计算结果表明,本文在简单遗传算法(SGA)的基础上提出的优体克隆+子体优生遗传算法(BCC-YGCD-GA)具有收敛速度快、解的精度高和避免出现早熟等优点.在水资源评价和矿床疏干计算中有广阔的应用前景.     

Comparative study of the effects of three data-interpretation methodologies on the performance of geotechnical back analysis

Back analysis can provide engineers with important information for better decision-making. Over the years, research on back analysis has focused mainly on optimisation techniques, while comparative studies of data-interpretation methodologies have seldom been reported. This paper examines the use of three data-interpretation methodologies on the performance of geotechnical back analysis. In general, there are two types of approaches for interpreting model predictions using field measurements, deterministic versus population-based, both of which are considered in this study. The methodologies that are compared are (a) error-domain model falsification (EDMF), (b) Bayesian model updating and (c) residual minimisation. Back analyses of an excavation case history in Singapore using the three methodologies indicate that each has strengths and limitations. Residual minimisation, though easy to implement, shows limited capabilities of interpreting measurement data with large uncertainty errors. EDMF provides robustness against incomplete information of the correlation structure. This is achieved at the expense of precision, as EDMF yields wider confidence intervals of the identified parameter values and predicted quantities compared with Bayesian model updating. In this regard, a modified EDMF implementation is proposed, which can improve upon the limitations of the traditional EDMF method, thus enhancing the quality of the identification outcomes.     

岩体初始应力场的遗传算法与有限元联合反演法

岩土工程问题的有限元分析一般需要考虑初始应力场。实际工程中,岩体往往为非线性。本文采用遗传算法与有限元联合反演法求解非线性岩体初始应力场,通过算例说明文中所提方法是合理的,可在工程应用中推广。     

Selection of sand models and identification of parameters using an enhanced genetic algorithm

Numerous constitutive models of granular soils have been developed during the last few decades. As a consequence, how to select an appropriate model with the necessary features based on conventional tests and with an easy way of identifying parameters for geotechnical applications has become a major issue. This paper aims to discuss the selection of sand models and parameters identification by using genetic algorithm. A real‐coded genetic algorithm is enhanced for the optimization with high efficiency. Models with gradually varying features (elastic‐perfectly plastic modelling, nonlinear stress–strain hardening, critical state concept and two‐surface concept) are selected from numerous sand models as examples for optimization. Conventional triaxial tests on Hostun sand are selected as the objectives in the optimization. Four key points are then discussed in turn: (i) which features are necessary to be accounted for in constitutive modelling of sand; (ii) which type of tests (drained and/or undrained) should be selected for an optimal identification of parameters; (iii) what is the minimum number of tests that should be selected for parameter identification; and (iv) what is the suitable and least strain level of objective tests to obtain reliable and reasonable parameters. Finally, a useful guide, based on all comparisons, is provided at the end of the discussion. Copyright © 2015 John Wiley & Sons, Ltd.     

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。     

挡土墙库仑土压力的遗传算法求解分析

在对破裂面上滑动土体静力极限平衡分析的基础上,建立了基于优化方法求解无黏性土、黏性土库仑土压力的自变量取值区间和目标函数模型,并采用遗传进化方法进行了实例求解分析。研究结果表明,遗传算法在计算挡土墙库仑主动土压力的过程中,收敛速度快、用时短,并具有较高的计算精度。算例1中5组无黏性土挡土墙的主动土压力的计算结果与经典库仑解析解非常接近,平均误差为1.748 %,平均进化代数为15代。算例2中8组黏性土挡土墙的主动土压力计算结果与文献的解答非常吻合,平均误差仅为0.017 %,平均进化代数为17.125代。遗传算法具有良好的适应性和强大的搜索性能,非常适合求解岩土工程优化问题。     

深部岩石考虑残余强度时三轴试验离散元定量模拟及参数分析

深部岩石在工程中具有高应力、大变形等典型特点,因此,高围压下考虑岩石残余强度的三轴试验对于分析深部岩石力学特性具有重要意义。离散单元法是分析岩石力学特性的重要数值方法,但是长期以来采用离散单元法定量模拟岩石的三轴试验一直存在诸多挑战,即数值模拟与室内试验得到的应力-应变全过程曲线难以定量匹配。采用改进的三维胶结抗弯-扭模型对深部砂岩考虑残余强度时的三轴试验进行了定量模拟,实现了数值模拟与室内试验应力-应变全过程曲线的定量匹配,获得了岩石较大的峰值/残余内摩擦角及非线性强度包线,克服了经典BPM模型存在的3个突出问题。通过参数分析,研究了峰值/残余内摩擦角及黏聚力与离散元微观参数之间的关系,同时这些大量的算例也证明了该模型具有较高的计算效率,可以满足模拟三维室内常规试验的要求。