Comparative study on response surfaces for reliability analysis of spatially variable soil slope

Extension of Hassan and Wolff method for system reliability analysis of soil slopes

Finding the critical slip surface and estimating the landslide volume are of primary importance for slope seismic design. However, this may be difficult due to the uncertainty of ground motions. To address this problem, a new method for calculating uncertainties is recommended in this paper, especially for the critical slip surface and landslide volume under random earthquake ground motions. Firstly, a series of intensity–frequency nonstationary random earthquake ground motions were generated based on an improved orthogonal expansion method. A given number of potential slip surfaces were set in a soil slope. Subsequently, the factor of safety (FOS) of each slip surface for all ground motions was calculated and the minimum FOS curves were obtained. It was found that the critical slip surfaces and failure times are uncertain under different earthquakes. The Monte Carlo method was used to verify the accuracy of probability density evolution method (PDEM), and the results of the PDEM and the Monte Carlo method are consistent, meaning that the PEDM has higher computational efficiency. Moreover, the distributions of earthquake-triggered landslide volume and landslide depth were analyzed by considering equivalent extreme events. Both landslide volume and depth exhibit a normal distribution for a homogeneous soil slope. The framework of this study is meaningful for slope seismic design in engineering, for example, the location of critical slip surface can be used for slope reinforcement, and the distribution of sliding volume can be used for disaster assessment.

본 연구에서는 다중 파괴모드를 고려한 사면의 신뢰도해석에 대하여 연구한다. 해석은 크게 두 부분으로 나뉜다. 첫 번째, Der Kiureghian과 Dakessian이 제안한 barrier method를 사용하여 시스템 신뢰도에 크게 영향을 미치는 중요 파괴모드를 연속적으로 탐색하여 찾아낸다. 둘째로, 찾아낸 중요 파괴모드들과 이에 해당하는 설계점들을 바탕으로 사면의 파괴확률을 계산한다. 다중 파괴모드를 갖는 사면의 신뢰도해석에서 파괴확률은 다중점 일차신뢰도법, Ditlevsen의 구간해법 및 몬테카를로 시뮬레이션 등을 이용하여 평가할 수 있다. 본 연구에서는 예제 해석을 통하여 이들 방법들의 비교연구를 수행하였다. 해석결과는 토사사면에 많은 수의 잠재적인 파괴면이 존재할 수 있지만, 사면의 시스템 파괴확률은 소수의 중요 파괴면에 의해 지배된다는 것을 보여준다. 따라서 토사사면의 시스템 신뢰도해석을 위해서 가장 중요한 단계는 모든 중요 파괴모드를 효율적인 방법에 의해서 탐색하여 결정하는 것이다. This work studies the reliability analysis of a slope that considers multiple failure modes. The analysis consists of two parts. First, significant failure modes that contribute most to system reliability are determined. The so-called barrier method proposed by Der Kiureghian and Dakessian to identify significant failure modes successively is employed. Second, the failure probability for the slope is estimated on the basis of the identified significant failure modes and corresponding design points. For reliability problems entailing multiple design points, failure probability can be estimated by the multi-point first-order reliability method (FORM), Ditlevsen's bounds method, and Monte Carlo simulation. In this paper, a comparative study between these methods has been made through example problems. Analysis results showed that while a soil slope may have a large number of potential slip surfaces, its system failure probability is usually governed by a few significant slip surfaces. Therefore, the most important step in the system reliability analysis for a soil slope is to identify all the significant failure modes in an efficient way.

Monte Carlo simulation (MCS) provides a conceptually simple and robust method to evaluate the system reliability of slope stability, particularly in spatially variable soils. However, it suffers from a lack of efficiency at small probability levels, which are of great interest in geotechnical design practice. To address this problem, this paper develops a MCS-based approach for efficient evaluation of the system failure probability Pf,s of slope stability in spatially variable soils. The proposed approach allows explicit modeling of the inherent spatial variability of soil properties in a system reliability analysis of slope stability. It facilitates the slope system reliability analysis using representative slip surfaces (i.e., dominating slope failure modes) and multiple stochastic response surfaces. Based on the stochastic response surfaces, the values of Pf,s are efficiently calculated using MCS with negligible computational effort. For illustration, the proposed MCS-based system reliability analysis is applied to two slope examples. Results show that the proposed approach estimates Pf,s properly considering the spatial variability of soils and improves the computational efficiency significantly at small probability levels. With the aid of the improved computational efficiency offered by the approach, a series of sensitivity studies are carried out to explore the effects of spatial variability in both the horizontal and vertical directions and the cross-correlation between uncertain soil parameters. It is found that both the spatial variability and cross-correlation affect Pf,s significantly. The proposed approach allows more insights into such effects from a system analysis point of view.

Most of the studies in Response Surface Methodology commonly involve one response or quality characteristics, whereas in most industrial applications considering all responses simultaneously is required. Multiple Response Surface (MRS) Optimization Problems often deal with responses that are conflicting. In dealing with incommensurate responses, incorporating a decision maker’s preference information into the problem has lots of advantages although a few researches in MRS literature have taken this into attention. The purpose of this paper is to take a detailed look at the most prominent approaches that has been suggested so far in MRS, and also to review and discuss the classifications with a special focus on the decision maker’s preference information. In today’s competitive market satisfying the customer is of high importance. The DM can be a customer and reaching a compromise with an interactive method would help the firm to succeed in having loyal customers. A case study is applied to show that interactive method with existing MRS approach leads to better results.

Complex engineering problems are represented by surrogate models in order to find the optimum design points with greater computational efficiency. The least-squares response surface methodology is one of the most commonly used approximation models and has been widely applied to optimization problems in the field of aerospace. In this paper, we propose a new surrogate modeling technique called the sorted -fold approach with which the entire sample points are sorted based on the residuals and then grouped into data sets. Multiple response surfaces are constructed while one data set used for cross-validating the representative response surface is omitted. Each response surface is weighted based on how well it can predict the cross-validating data response. Our investigations reveal that this approach has a higher ability of obtaining accurate predictions than the least-squares response surface methodology when tested at a large number of validation points. When the method is applied to benchmark problems and the numerical simulation of residual stress prediction (done by laser peening in order to improve the fatigue life of aircraft structures), the results maintain validity.

Multi-slip surfaces searching method for earth slope with weak interlayer based on local maximum shear strain increment

Spatial regression models are developed as a complementary alternative to second-order polynomial response surfaces in the context of process optimization. These models provide estimates of design variable effects and smooth, data-faithful approximations to the unknown response function over the design space. The predicted response surfaces are driven by the covariance structures of the models. Several structures, isotropic and anisotropic, are considered and connections with thin plate splines are reviewed. Estimation of covariance parameters is achieved via maximum likelihood and residual maximum likelihood. A feature of the spatial regression approach is the visually appealing graphical summaries that are produced. These allow rapid and intuitive identification of process windows on the design space for which the response achieves target performance. Relevant design issues are briefly discussed and spatial designs, such as the packing designs available in Gosset, are suggested as a suitable design complement. The spatial regression models also perform well with no global design, for example with data obtained from series of designs on the same space of design variables. The approach is illustrated with an example involving the optimization of components in a DNA amplification assay. A Monte Carlo comparison of the spatial models with both thin plate splines and second-order polynomial response surfaces for a scenario motivated by the example is also given. This shows superior performance of the spatial models to the second-order polynomials with respect to both prediction over the complete design space and for cross-validation prediction error in the region of the optimum. An anisotropic spatial regression model performs best for a high noise case and both this model and the thin plate spline for a low noise case. Spatial regression is recommended for construction of response surfaces in all process optimization applications.

Dominant failure mode analysis using representative samples obtained by multiple response surfaces method

The purpose of this study was to come up with a method to screen ultrasonication parameters that mainly predict ultrasound extraction process efficiency, using multiple regression analysis and response surface method (RSM). The relevance of this study is the fact that combining RSM with multiple regression modeling gives a conclusive report on the actual effects of individual treatment parameters. Although all predictors [time (A), frequency (B), power (C) and ratio (D)] showed significance in RSM models, multiple regression models further indicated that only D significantly influenced the variability observed in total phenol content and antioxidant activity of buckwheat extracts.

This paper proposes a partial ensemble Pareto front estimation method for robustly estimating Pareto fronts with complex shapes, including both concave and convex regions. The conventional Pareto front estimation method faces difficulties in estimating complex-shaped Pareto fronts because it attempts to estimate the entire Pareto front at once. In contrast, the proposed method iteratively estimates each simpler segment of the complex-shaped Pareto front. The conventional method relies on a single response surface. However, multiple response surface methodologies exist, and their accuracy depends on the specific problem characteristics. To address this issue, the proposed method ensembles multiple response surfaces, each tailored to a specific segment of the Pareto front. To evaluate Pareto front estimation accuracy, this study compares the conventional and proposed methods using two- and three-objective WFG1 test problems with complex-shaped Pareto fronts. The comparison is conducted by varying both the number of known solutions used for Pareto front estimation and the number of concave and convex regions in the Pareto front. The results demonstrate that the proposed ensemble Pareto front estimation method achieves lower estimation errors than the conventional method in the majority of cases.

The purpose of this study is to statistically analyze the anodic current density and peak potential of methanol oxidation at Pt nanoparticles supported on functionalized reduced graphene oxide (RGO), using design of experiments methodology. RGO is functionalized with methyl viologen (MV) and chitosan (CH). The novel Pt/MV-RGO-CH catalyst is successfully prepared and characterized with transmission electron microscopy (TEM) image. The electrocatalytic activity of Pt/MV-RGOCH catalyst is experimentally evaluated for methanol oxidation. The effects of methanol concentration and scan rate factors are also investigated experimentally and statistically. The effects of these two main factors and their interactions are investigated, using analysis of variance test, Duncan’s multiple range test and response surface method. The results of the analysis of variance show that all the main factors and their interactions have a significant effect on anodic current density and peak potential of methanol oxidation at α = 0.05. The suggested models which encompass significant factors can predict the variation of the anodic current density and peak potential of methanol oxidation. The results of Duncan’s multiple range test confirmed that there is a significant difference between the studied levels of the main factors.

Multiple response surface methodology (MRSM) most often involves the analysis of small sample size datasets which have associated inherent statistical modeling problems. Firstly, classical model selection criteria in use are very inefficient with small sample size datasets. Secondly, classical model selection criteria have an acknowledged selection uncertainty problem. Finally, there is a credibility problem associated with modeling small sample sizes of the order of most MRSM datasets. This work focuses on determination of a solution to these identified problems. The small sample model selection uncertainty problem is analysed using sixteen model selection criteria and a typical two-input MRSM dataset. Selection of candidate models, for the responses in consideration, is done based on response surface conformity to expectation to deliberately avoid selection of models using the problematic classical model selection criteria. A set of permutations of combinations of response models with conforming response surfaces is determined. Each combination is optimised and results are obtained using overlaying of data matrices. The permutation of results is then averaged to obtain credible results. Thus, a transparent multiple model approach is used to obtain the solution which gives some credibility to the small sample size results of the typical MRSM dataset. The conclusion is that, for a two-input process MRSM problem, conformity of response surfaces can be effectively used to select candidate models and thus the use of the problematic model selection criteria is avoidable.

This paper develops an efficient methodology for conducting seismic reliability analysis of pile-reinforced slopes by combining a proposed bracketing-based pseudodynamic method with Hassan and Wolff-based multiple response surfaces. The proposed methodology is illustrated against two typical soil slopes emphasizing on the variation of critical sliding surfaces owing to the installation of piles and soil uncertainties and the variation of optimal pile locations from the aspect of failure probability and failure risk. The comparisons have demonstrated that the proposed method leads to identical predictions as compared to the traditional search method but with only 0.1% computational cost.

Response surface methods have been used for a variety of applications in aerospace engineering, particularly in multidisciplinary design optimization. We investigate the use of kriging models as alternatives to traditional second-order polynomial response surfaces for constructing global approximations for use in a real aerospace engineering application, namely, the design of an aerospike nozzle. Our objective is to examine the difeculties in building and using kriging models to create accurate global approximations to facilitate multidisciplinary design optimization. Error analysis of the response surface and kriging models is performed, along with a graphical comparison of the approximations. Four optimization problems are also formulated and solved using both sets of approximation models to gain insight into their use for multidisciplinary design optimization. We end that the kriging models, which use only a constant “global” model and a Gaussian correlation function, yield global approximations that are slightly more accurate than the response surface models.