Differential Evolution Adaptive Metropolis Research Articles

A Comparison of Inversion Methods for Surrogate‐Based Groundwater Contamination Source Identification With Varying Degrees of Model Complexity

AbstractAccurate identification of groundwater contamination sources is important for designing efficacious site remediation strategies. Currently, the methods for identifying contamination sources mainly fall into three distinct categories: simulation optimization, Bayesian inference, and data assimilation. Each method has its own advantages and disadvantages under specific site conditions. To evaluate the applicability of these methods, we chose one representative inversion algorithm from each category, namely the Improved Butterfly Optimization Algorithm (IBOA) for simulation optimization, the Ensemble Smoother with Multiple Data Assimilation (ES‐MDA) for data assimilation, and the DiffeRential Evolution Adaptive Metropolis with a Snooker Update and Sampling from a Past Archive (DREAM(ZS)) for Bayesian inference. We conducted a comprehensive evaluation of these methods' performance under different model complexities, employing a surrogate model as a substitute for the complex forward model. By addressing two distinct problems involving conservative pollutant transport and Light Non‐Aqueous Phase Liquid (LNAPL) transport with biodegradation, we employed four criteria (elapsed time, result accuracy, posterior probability distribution, and noise resistance) for evaluation. The findings unequivocally indicate that DREAM(ZS) outperforms others in terms of result accuracy and posterior probability distribution. It also adeptly navigates the interrelations among disparate unknown variables. The strength of ES‐MDA lies in its efficiency. It achieves relatively satisfactory results with a reduced computational burden. In contrast, IBOA underperforms in both test problems. In terms of resistance to noise, both DREAM(ZS) and ES‐MDA perform better than IBOA does.

A DiffeRential Evolution Adaptive Metropolis (DREAM)-based inverse model for continuous release source identification in river pollution incidents: Quantitative evaluation and sensitivity analysis

The identification of continuous pollution sources for rivers is of great concern for emergency response. Most studies focused on instantaneous river pollution sources and associated incidents. There is a dire need to address continuous pollution sources, as pollutant discharge may impose a major impact on the water ecosystem. Therefore, in this study, a novel inverse model is proposed to identify the continuous point sources in river pollution incidents that would estimate the source strength, location, release time, and spill time. The proposed inverse model combines the advanced DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm and the forward transport advection-dispersion equation to infer the posterior probability distribution of source parameters for quantifying uncertainties. In addition, the performance of the DREAM-based model is compared with those of the Metropolis-Hastings (MH)-based and genetic algorithm (GA)-based models. The results show that the DREAM-based model performs accurately for both the hypothetical and the field tracer cases. The comparative analysis shows that the DREAM-based model performs better in saving computation time, improving the accuracy of results, and reconstructing pollutant concentrations. Observation errors significantly influence the accuracy of the identification results from the DREAM-based model. In addition, a comprehensive sensitivity analysis of the DREAM-based model is conducted. The identification results from the DREAM-based model are sensitive to the dispersion coefficient and river velocity. The accuracy of the inverse model could be improved by increasing the monitoring number and by monitoring locations closer to the spill site. The findings of this study can improve decision-making during emergency responses to sudden river pollution incidents.

A Computational Tool to Track Sewage Flow Discharge into Rivers Based on Coupled HEC-RAS and DREAM

Worldwide abatement of untreated sewage discharge into surface water is a challenging task. Sewage discharging into surface waters has a detrimental impact on water quality. This paper presents a MATLAB (R2018b) framework designed to identify sewage flow discharges into rivers from an inverse problem-solving perspective. The computational tool integrates a hydrodynamic model using the Hydrologic Engineering Center’s River Analysis System (HEC-RAS 5.0.0) and an open-source toolbox for Differential Evolution Adaptive Metropolis (DREAM) as the inverse problem method. The proposed framework can effectively infer discharge sources in scenarios of highly transient flow based on hydraulic data at pre-set monitoring sites. To validate its capabilities, one hypothetical case and two real cases of sewage flow discharges entering a river were used to test the developed modeling framework. The results based on three performance metrics showed that this mathematical tool can be extended to simulate complex hydrodynamic flow patterns. This accomplishment underscores its potential as a valuable asset for environmental monitoring and water quality restoration efforts.

Bayesian model updating for bridge engineering applications based on DREAMKZS algorithm and Kriging model

The Differential Evolution Adaptive Metropolis (DREAM) based Bayesian model updating suffers from low convergence speed and high computational cost. This study proposes a Bayesian updating framework based on the DREAM and KZS strategies (DREAMKZS) assisted with the Kriging model to enhance the algorithm’s convergence speed and computational efficiency. The KZS strategies represent the Kalman-inspired proposal distribution, sampling from the past states, and snooker updates. The model updating of a numerical beam and a full-scale bridge were employed to test the DREAMKZS algorithm’s performance. The results demonstrated that DREAMKZS accelerates the chain exploration in high-dimensional target distributions and improves the convergence speed. The DREAMKZS outperforms the DREAM in achieving rapid convergence of the Markov chains while maintaining the precision of the posterior distribution. In the two case studies, the efficiency of model evaluation is improved by 3.66 times and 1.72 times, respectively. Compared with the traditional Bayesian approach without a surrogate model, the computational cost is reduced by 80.04% and 95.37%, respectively.

Predicting maize yield in Northeast China by a hybrid approach combining biophysical modelling and machine learning

ContextChina produces more than 20 % of maize grain in the world, and Northeast China (NEC) accounts for ∼30 % of the nation's total maize production. Previous studies have used either climate data, satellite data, or crop growth model (CGM) to predict or forecast maize yield. However, maize is highly susceptible to the effect of extreme climate events (such as drought, heat) in NEC, and there is a lack of studies to predict/forecast maize yield by integrating climate data, satellite data, extreme climate events, and CGM-simulated data. ObjectiveWe aim to develop a hybrid approach with machine learning to blend different sources of data (climate data, satellite data, extreme climate events) and process-based modelling results to improve predictive accuracy of maize yield in NEC. MethodsUsing maize data from 44 sites during the period of 2000–2013 in NEC, we firstly optimized Agricultural Production System sIMulator (APSIM) using Differential Evolution Adaptive Metropolis combined with Gaussian likelihood function and Bayesian multiplication method. Next, we divided the growing season into five phases, and selected variables of different phases using exploratory data analysis and Random Forest. Then, we developed a hybrid model using Random Forest by blending of multiple sources of data and APSIM simulations to predict maize yield from the start to the end of the growing season, and quantified the relative contribution of predictors. Results and conclusionsA hybrid model developed with random forest by combining climate data, NDVI, extreme climate events and APSIM simulations can achieve high performance for predicting yield toward the end of the growing season. The accuracy of in-season yield prediction showed a linear increase with MAPE/KGE changing from 19 %/0.05 to 13 %/0.53 from start to end of the growing season. Yield forecasts are acceptable with RMSE/MAE of 1.20/1.01 Mg ha−1 (16 %/13 % of the observed mean yield) approximately one-month prior to harvest. The most important predictor that affect yield forecast was APSIM-simulated biomass or yield, and the most important extreme climate event was drought during early grain-filling stage. SignificanceWith the increasing availability of crop-related data, we expect that the in-season forecasting capacity of the proposed methodology could be further improved, and the methodology can be extended to other crops and other regions for yield forecast.

A calibration method for SWMM to mitigate the impact of the structure defect without considering runoff on building walls

In this study, we propose a hypothesis that an automatic calibration framework can address modeling uncertainties in the Storm Water Management Model (SWMM) due to structural defects that result in the inability of the model to account for runoff generated on building walls from wind-driven rain. To test this hypothesis, we introduce a rainfall error model into the calibration framework to indirectly consider the effects of inclined wind-driven rain on building walls. We couple the optimization algorithm Differential Evolution Adaptive Metropolis (DREAM) with SWMM using newly developed API functions. To demonstrate the effectiveness of the framework, we conduct a case study in Guangzhou, China and assess the impacts of rainfall uncertainty on model parameter estimations and simulated runoff boundaries. The results show that the framework can improve the average Nash–Sutcliffe index of selected events by more than 5%. It also captures peak flow more accurately. This framework contributes to the theory of SWMM calibration by accounting for structural defects and considering rainfall uncertainty.

Bayesian model updating utilizing scaled likelihood ratio and BCT-PCA with frequency response function

Bayesian inference has now been widely practiced for model updating. In this study, the discussion is conducted about two issues facing the implementation of Bayesian model updating when the Gaussian distribution is assumed. To begin with, the problem of the normal likelihood function used in Markov chain Monte Carlo (MCMC) is demonstrated and presented with an alternative approach by defining the scaled likelihood ratio (SLR). Then, a data preprocessing technique is proposed by introducing the Box-Cox transformation and principal component analysis (BCT-PCA) to address the obstacles in the practice of frequency response function (FRF)-based Bayesian model updating. The differential evolution adaptive metropolis (DREAM) is applied to explore the posterior distribution of the parameters. In addition, a novel procedure for FRF-based Bayesian model updating is presented. The effectiveness of the proposed methodology is verified in both numerical and experimental cases of dynamical model updating. In the numerical case, the results of eigenfrequency-based model updating show that the SLR is advantageous over the normal likelihood ratio (NLR) in estimating the posterior distribution of parameters. The results of FRF-based model updating show that the consistency and robustness of model updating performance as achieved through the BCT-PCA method are improved when different schemes of frequency selection are implemented. The results of the experimental case also show the superiority of the proposed method.

Bayesian Model Updating for Structural Dynamic Applications Combing Differential Evolution Adaptive Metropolis and Kriging Model

The Bayesian model updating approach has attracted much attention by providing the most probable values (MPVs) of physical parameters and their uncertainties. However, the Bayesian approach has challenges in high-dimensional problems and requires high computational costs in large-scale engineering structures dealing with structural dynamics. This study proposes a new Bayesian updating framework using the Differential Evolution Adaptive Metropolis (DREAM) algorithm to enhance the Bayesian approach’s performance and computational efficiency. In addition, two time-saving strategies are proposed. Firstly, variance-based global sensitivity analysis is used to eliminate insignificant parameters to model responses and reduce model dimensionality. Secondly, a fast-running kriging model is employed as a surrogate of the time-consuming finite-element (FE) model to alleviate the computational burden. DREAM essentially is a multichain sampling method that runs different paths to seek all possible solutions and accurately approximate the posterior probability distribution function in the Bayesian approach. The proposed updating framework was demonstrated using one numerical example and a real-world cable-stayed pedestrian bridge. The results showed that the proposed method enables rationally identifying structural parameters and recovering dynamic responses. Compared with the traditional Bayesian approach without a surrogate model, the computational cost is orders of magnitude lower.

Application of Parameter Optimization Methods Based on Kalman Formula to the Soil—Crop System Model

Soil-crop system models are effective tools for optimizing water and nitrogen application schemes, saving resources and protecting the environment. To guarantee model prediction accuracy, we must apply parameter optimization methods for model calibration. The performance of two different parameter optimization methods based on the Kalman formula are evaluated for a parameter identification of the soil Water Heat Carbon Nitrogen Simulator (WHCNS) model using mean bias error (ME), root-mean-square error (RMSE) and an index of agreement (IA). One is the iterative local updating ensemble smoother (ILUES), and the other is the DiffeRential Evolution Adaptive Metropolis with Kalman-inspired proposal distribution (DREAMkzs). Our main results are as follows: (1) Both ILUES and DREAMkzs algorithms performed well in model parameter calibration with the RMSE_Maximum a posteriori (RMSE_MAP) values were 0.0255 and 0.0253, respectively; (2) ILUES significantly accelerated the process to the reference values in the artificial case, while outperforming in the calibration of multimodal parameter distribution in the practical case; and (3) the DREAMkzs algorithm considerably accelerated the burn-in process compared with the original algorithm without Kalman-formula-based sampling for parameter optimization of the WHCNS model. In conclusion, ILUES and DREAMkzs can be applied to a parameter identification of the WHCNS model for more accurate prediction results and faster simulation efficiency, contributing to the popularization of the model.

Concentration Profile Measurement of Liquid–Solid Two-Phase Horizontal Pipe Flow Using Ultrasound Doppler

Concentration measurement of multiphase flow is essential to flow assurance and monitoring in industrial processes. The concentration profile is a quantitative parameter to diagnose the multiphase flow states and has drawn wide attention from researchers. An ultrasound Doppler technique is adopted to measure the concentration profile of liquid-solid two-phase horizontal pipe flow. A Bayesian inference based on the Differential Evolution Adaptive Metropolis sampling algorithm is proposed to solve the statistical inversion of the concentration profile. The posterior probability distributions of the solid concentration are sampled, and the final concentration profile is chosen with the maximum a posteriori probability. An experimental platform is built for liquid-solid two-phase flow experiments and ultrasound concentration profile measurement. The measured concentration profiles are verified with a maximum mean absolute error of 8.14%.

Pitfalls and a feasible solution for using KGE as an informal likelihood function in MCMC methods: DREAM(ZS) as an example

Abstract. The Kling–Gupta efficiency (KGE) is a widely used performance measure because of its advantages in orthogonally considering bias, correlation and variability. However, in most Markov chain Monte Carlo (MCMC) algorithms, error-based formal likelihood functions are commonly applied. Due to its statistically informal characteristics, using the original KGE in MCMC methods leads to problems in posterior density ratios due to negative KGE values and high proposal acceptance rates resulting in less identifiable parameters. In this study we propose adapting the original KGE using a gamma distribution to solve these problems and to apply KGE as an informal likelihood function in the DiffeRential Evolution Adaptive Metropolis DREAM(ZS), which is an advanced MCMC algorithm. We compare our results with the formal likelihood function to show whether our approach is robust and plausible to explore posterior distributions of model parameters and to reproduce the system behaviors. For that we use three case studies that contain different uncertainties and different types of observational data. Our results show that model parameters cannot be identified and the uncertainty of discharge simulations is large when directly using the original KGE. The adapted KGE finds similar posterior distributions of model parameters derived from the formal likelihood function. Even though the acceptance rate of the adapted KGE is lower than the formal likelihood function for some systems, the convergence rate (efficiency) is similar between the formal and the adapted KGE approaches for the calibration of real hydrological systems showing generally acceptable performances. We also show that both the adapted KGE and the formal likelihood function provide low performances for low flows, while the adapted KGE has a balanced performance for both low and high flows. Furthermore, the adapted KGE shows a generally better performance for calibrations of solute concentrations. Thus, our study provides a feasible way to use KGE as an informal likelihood in the MCMC algorithm and provides possibilities to combine multiple data for better and more realistic model calibrations.

Development of a DREAM-based inverse model for multi-point source identification in river pollution incidents: Model testing and uncertainty analysis

Source identification plays a vital role in implementing control measures for sudden river pollution incidents. In contrast to single-point source identification problems, there have been no investigations into inverse identification of multi-point emissions. In this study, an inverse model is developed based on the observed time series of pollutant concentrations and the DiffeRential Evolution Adaptive Metropolis (DREAM) method to identify multi-point sources with uncertainty quantification. We aim to simultaneously determine source mass, release location and time of multi-point sources. The newly developed DREAM-based model has been tested and verified through both numerical and field data case studies in terms of accuracy, reliability, and computational time. Adapted cases with single-point, two-point and three-point sources in the Songhua River are conducted to test the applicability of the modeling approach, respectively. The developed model can correctly quantify source parameters with a relative error that does not exceed ±0.63%, although it shows that an increase of emission sources may slightly increase the identification error. Among the three source parameters, the identification error of the release time tends to rise more obviously in response to the increase in the number of pollution sources. It is also found that the identification accuracy is primarily sensitive to the river velocity, followed by the dispersion coefficient and the river cross-sectional area. Furthermore, good monitoring strategies, including reducing observation errors, shortening monitoring interval time and selecting the proper monitoring distance between the monitoring and the source sites, help to achieve a better application of the developed model in river pollution incidents.

Probabilistic Predictions of Ecologically Relevant Hydrologic Indices Using a Hydrological Model

AbstractThis study evaluated the effects of prior knowledge obtained from multi‐objective optimization on the uncertainty quantification of simulated ecologically relevant hydrologic indices (ERHIs) using a hydrological model. Two experiments were formulated considering contrasting conditions in prior knowledge when implementing Bayesian parameter estimation. In the first experiment, we reproduced a common modeling practice in the absence of previous information where uniform priors are considered when calibrating hydrological and error model parameters. In the second experiment, near‐optimal Pareto solutions from multi‐objective calibration were used to build a multivariate prior distribution for estimating hydrological and error model parameters using Bayesian calibration. In both experiments, a likelihood function considering heteroscedasticity and autocorrelation effects was employed. The Unified Non‐dominated Sorting Algorithm III was used for multi‐objective calibration, whereas the multiple‐try differential evolution adaptive metropolis algorithm was used for Markov Chain Monte Carlo sampling. The experiments were tested using a hydrologic model. We selected a subset of ERHIs comprised of 32 central tendency Indicators of Hydrologic Alteration and seven additional indices describing basic streamflow statistical properties. In general, using near‐optimal Pareto parameter distributions as prior knowledge in Bayesian calibration reduced both the bias and variability ranges in ERHIs prediction. Furthermore, there was no significant loss in the reliability of streamflow predictions (from 2% to 6%, p = 0.07) when targeting the selected ERHIs, while improving precision (from 66% to 58%, p < 0.05) and reducing the bias (from 6% to 4%, p < 0.05). Moreover, parametric uncertainty substantially shrank by 72% when linking multi‐objective calibration and Bayesian parameter estimation.

An Integrated Bayesian and Machine Learning Approach Application to Identification of Groundwater Contamination Source Parameters

The identification of groundwater contamination source parameters is an important prerequisite for the control and risk assessment of groundwater contamination. This study developed an innovative approach for the optimal design of observation well locations and the high-precision identification of groundwater contamination source parameters. The approach involves Bayesian theory and integrates Markov Chain Monte Carlo, Bayesian design, information entropy, machine learning, and surrogate modeling. The optimal observation well locations are determined by information entropy, which is adopted to mine valuable information about unknown groundwater contamination source parameters from measurements of contaminant concentration according to Bayesian design. After determining the optimal observation well locations, the identification of groundwater contamination source parameters is implemented through a Bayesian-based Differential Evolution Adaptive Metropolis with Discrete Sampling–Markov Chain Monte Carlo approach. However, the processes of both determination and identification are time-consuming because the original simulation model (that is, the contaminant transport model) needs to be invoked multiple times. To overcome this challenge, a machine learning approach, that is, Multi-layer Perceptron, is used to build a surrogate model for the original simulation model, which can greatly accelerate the determination and identification processes. Finally, two hypothetical numerical case studies involving homogeneous and heterogeneous cases are used to verify the performance of the proposed approach. The results show that the optimal design of observation well locations and high-precision identification of groundwater contamination source parameters can be implemented accurately and effectively by using the proposed approach. In summary, this study highlights that the integrated Bayesian and machine learning approach provides a promising solution for high-precision identification of groundwater contamination source parameters.

A Bayesian framework to assess and create risk maps of groundwater flooding

Groundwater flooding can cause severe damages to homes, utilities, and infrastructure and yield significant economic and social costs. Numerical models are used to understand these events and are the basis to produce imagery products for risk management and communication. However, such maps are generally produced using forward model simulations, and most of the mapping products are still deterministic. In contrast to pluvial and fluvial floods, an open issue in the analysis of susceptibility to groundwater flooding is the lack of probabilistic assessment and mapping products recognizing parametric uncertainty. Hence, we propose a Bayesian-based framework to create probabilistic risk maps and to identify the susceptibility to groundwater flood events. We aim to assess the spatial distribution and temporal variability of groundwater flooding by decomposing the uncertainty and the sensitivity of distributed groundwater numerical models. The scheme involves the use of the elementary effects method, the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm, and the exploration of the predictive posterior distributions of the groundwater heads to evaluate the susceptibility according to exceedance levels. We use the proposed Bayesian framework with a numerical model that simulates the groundwater flood event that occurred in the valley of the Alz River in 2013. This study developed two types of susceptibility maps based on the exceedance probability of certain groundwater levels and specific cellar depths. The Bayesian inference supports the parameter estimation and thereby increases the spatial confidence of the areas susceptible to inundation. This study shows that maps of susceptibility to groundwater flooding can be built over one single event models and acknowledge the inherent spatial and temporal uncertainty of such events.

Model Updating of a Prestressed Concrete Rigid Frame Bridge Using Multiple Markov Chain Monte Carlo Method and Differential Evolution

Model updating is a widely adopted method to minimize the error between test results from the real structure and outcomes from the finite element (FE) model for obtaining an accurate and reliable FE model of the target structure. However, uncertainties from the environment, excitation and measurement variability can reduce the accuracy of predictions of the updated FE model. The Bayesian model updating method using multiple Markov chains based on differential evolution adaptive metropolis (DREAM) algorithm is explored, which runs multiple chains simultaneously for a global exploration, and it automatically tunes the scale and orientation of the proposal distribution during the evolution of the posterior distribution. The performance of the proposed method is illustrated numerically with a beam model and a three-span rigid frame bridge. Results show that the DREAM algorithm is capable for updating the FE model in civil engineering. It extends the Bayesian model updating method to multiple Markov chains scenario, which provides higher accuracy than single chain algorithm such as the delayed rejection adaptive metropolis-hastings (DRAM) method. Moreover, results from both examples indicate that the proposed method is insensitive to values of initial parameters, which avoid errors resulting from inappropriate prior knowledge of parameters in the FE model updating.

Quantification of Precipitation and Evapotranspiration Uncertainty in Rainfall-Runoff Modeling

Mountainous watersheds have always been a challenge for modelers due to large variability and insufficient ground observations, which cause forcing data, model structure, and parameter uncertainty. This study employed Differential Evolution Adaptive Metropolis (DREAM) algorithm which utilizes Markov Chain Monte Carlo (MCMC) approach to account for forcing data uncertainty. A conceptual degree day snowmelt model, MIKE 11 NAM (Nedbor Afstromnings Model), was used to simulate snowmelt runoff from Ilgaz basin, with an area of 28.4 km2 area, located in the northern part of Turkey. The mean elevation is around 1700 m and the basin is covered with broadleaf forest and has mainly brown soil with a high water holding capacity. Precipitation and evapotranspiration (ET) values were optimized in combination with model parameters conditioned on observed discharges and corrected values of input data were utilized for calibration and validation. Results showed that the observed precipitation was over-estimated by almost 10%, while evapotranspiration calculated by Penman–Monteith method was underestimated. The mean values of storm and ET multipliers were obtained as 1.14 and 0.84, respectively. When only parameter uncertainty was considered, calibration did not yield Nash–Sutcliffe Efficiency (NSE) greater than 0.64. However, when forcing data uncertainty was incorporated in the DREAM approach, an improved value of NSE (0.84) was obtained. After calibration and treatment of forcing data errors, the model yielded reasonable prediction uncertainty bounds and well-defined posterior distributions of NAM model parameters. Main objectives of the study are to assess the applicability of MIKE 11 NAM model to the selected catchment. In addition, the importance of errors in the input forcing variables to the model is demonstrated.

Parasite inversion for determining the coefficients and time‐validity of Philip's two‐term infiltration equation

AbstractMany different equations have been proposed to describe quantitatively one‐dimensional soil water infiltration. The unknown coefficients of these equations characterize soil hydraulic properties and may be estimated from a n record, , of cumulative infiltration measurements using curve fitting techniques. The two‐term infiltration equation, , of Philip has been widely used to describe measured infiltration data. This function enjoys a solid mathematical–physical underpinning and admits a closed‐form solution for the soil sorptivity, S [L T−1/2], and multiple, c [−], of the saturated hydraulic conductivity, Ks [L T−1]. However, Philip's two‐term equation has a limited time validity, tvalid [T], and thus cumulative infiltration data, , beyond will corrupt the estimates of S and Ks. This paper introduces a novel method for estimating S, c, Ks, and tvalid of Philip's two‐term infiltration equation. This method, coined parasite inversion, use as vehicle Parlange's three‐parameter infiltration equation. As prerequisite to our method, we present as secondary contribution an exact, robust and efficient numerical solution of Parlange's infiltration equation. This solution admits Bayesian parameter estimation with the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm and yields as byproduct the marginal distribution of Parlange's β parameter. We evaluate our method for 12 USDA soil types using synthetic infiltration data simulated with HYDRUS‐1D. An excellent match is observed between the inferred values of S and Ks and their “true” values known beforehand. Furthermore, our estimates of c and tvalid correlate well with soil texture, corroborate linearity of the relationship for , and fall within reported ranges. A cumulative vertical infiltration of about 2.5 cm may serve as guideline for the time‐validity of Philip's two‐term infiltration equation.

A comparative study of Bayesian inverse analyses of spatially varying soil parameters for slope reliability updating

ABSTRACT Bayesian estimation of spatially varying soil parameters is a challenging task in geotechnical engineering because a large number of random variables need to be learned. To address this challenge, three Bayesian methods are revisited, including Differential Evolution Adaptive Metropolis with sampling from past states [DREAM(zs)] method, Bayesian Updating with Structural reliability methods using Subset Simulation (BUS + SS), and modified BUS with Subset Simulation (mBUS + SS). The differences between the performances (i.e. convergences, computational accuracies, and efficiencies) of these three methods are not well understood. This study systematically investigates the differences of these three methods in the generation of random samples, convergence criterion, model evidence, and estimation of posterior probability of failure in slope reliability updating. Two slope examples are used for the comparative study. It is found that the BUS + SS method performs well not only in the low-dimensional Bayesian inverse problems but also in the high-dimensional Bayesian inverse problems of spatially varying soil parameters. The DREAM(zs) method is preferentially recommended to deal with the low-dimensional Bayesian inverse problems whereas the mBUS + SS method can well tackle the high-dimensional problems.

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system's radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. The DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.