scholarly journals Topological analysis in Monte Carlo simulation for uncertainty propagation

Solid Earth ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 1663-1684 ◽  
Author(s):  
Evren Pakyuz-Charrier ◽  
Mark Jessell ◽  
Jérémie Giraud ◽  
Mark Lindsay ◽  
Vitaliy Ogarko
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Input Data ◽  
Topological Analysis ◽  
Uncertainty Propagation ◽  
Population Heterogeneity ◽  
Plausible Model ◽  
Uncertainty Index ◽  
Uncertainty Estimates ◽  
Geological Models

Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for uncertainty propagation (MCUP) method. MCUP is a type of Bayesian Monte Carlo method aimed at input data uncertainty propagation in implicit 3-D geological modeling. In the Monte Carlo process, a series of statistically plausible models is built from the input dataset of which uncertainty is to be propagated to a final probabilistic geological model or uncertainty index model. Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUP. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets' variability and plausible model's variability. Non-linearity is shown to mainly arise from the effect of the geometrical rule set on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces topological heterogeneity and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUP is introduced. Boolean topological signatures recording lithological unit adjacency are used as n-dimensional points to be considered individually or clustered using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the probabilistic geological models and uncertainty index models. Highlights. Monte Carlo uncertainty propagation (MCUP) methods often produce topologically distinct plausible models. Plausible models can be differentiated using topological signatures. Topologically similar probabilistic geological models may be obtained through topological signature clustering.

scholarly journals Topological Analysis in Monte Carlo Simulation for Uncertainty Estimation

2019 ◽  
Author(s):  
Evren Pakyuz-Charrier ◽  
Mark Jessell ◽  
Jérémie Giraud ◽  
Mark Lindsay ◽  
Vitaliy Ogarko
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Input Data ◽  
Topological Analysis ◽  
Uncertainty Estimation ◽  
Population Heterogeneity ◽  
Underlying Assumption ◽  
3D Geological Modeling ◽  
Plausible Model ◽  
Uncertainty Estimates

Abstract. This paper proposes and demonstrates improvements for the Monte Carlo simulation for Uncertainty Estimation (MCUE) method. MCUE is a type of Bayesian Monte Carlo aimed at input data uncertainty propagation in implicit 3D geological modeling. In the Monte Carlo process, a series of statistically plausible models are built from the input data set which uncertainty is to be propagated to a final probabilistic geological model (PGM) or uncertainty index model (UIM). Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUE. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets’ variability and plausible model’s variability. Non-linearity is shown to arise from the effect of the geometrical ruleset on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces geological incompatibility and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUE is introduced. Boolean topological signatures recording lithological units’ adjacency are used as n-dimensional points to be considered individually or clustered using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the PGMs and UIMs.

scholarly journals Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

Solid Earth ◽  
2018 ◽  
Vol 9 (2) ◽  
pp. 385-402 ◽  
Author(s):  
Evren Pakyuz-Charrier ◽  
Mark Lindsay ◽  
Vitaliy Ogarko ◽  
Jeremie Giraud ◽  
Mark Jessell
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Input Data ◽  
Structural Data ◽  
Uncertainty Estimation ◽  
Data Sets ◽  
Geological Modeling ◽  
Input Uncertainty ◽  
Wide Range ◽  
Geological Models

Abstract. Three-dimensional (3-D) geological structural modeling aims to determine geological information in a 3-D space using structural data (foliations and interfaces) and topological rules as inputs. This is necessary in any project in which the properties of the subsurface matters; they express our understanding of geometries in depth. For that reason, 3-D geological models have a wide range of practical applications including but not restricted to civil engineering, the oil and gas industry, the mining industry, and water management. These models, however, are fraught with uncertainties originating from the inherent flaws of the modeling engines (working hypotheses, interpolator's parameterization) and the inherent lack of knowledge in areas where there are no observations combined with input uncertainty (observational, conceptual and technical errors). Because 3-D geological models are often used for impactful decision-making it is critical that all 3-D geological models provide accurate estimates of uncertainty. This paper's focus is set on the effect of structural input data measurement uncertainty propagation in implicit 3-D geological modeling. This aim is achieved using Monte Carlo simulation for uncertainty estimation (MCUE), a stochastic method which samples from predefined disturbance probability distributions that represent the uncertainty of the original input data set. MCUE is used to produce hundreds to thousands of altered unique data sets. The altered data sets are used as inputs to produce a range of plausible 3-D models. The plausible models are then combined into a single probabilistic model as a means to propagate uncertainty from the input data to the final model. In this paper, several improved methods for MCUE are proposed. The methods pertain to distribution selection for input uncertainty, sample analysis and statistical consistency of the sampled distribution. Pole vector sampling is proposed as a more rigorous alternative than dip vector sampling for planar features and the use of a Bayesian approach to disturbance distribution parameterization is suggested. The influence of incorrect disturbance distributions is discussed and propositions are made and evaluated on synthetic and realistic cases to address the sighted issues. The distribution of the errors of the observed data (i.e., scedasticity) is shown to affect the quality of prior distributions for MCUE. Results demonstrate that the proposed workflows improve the reliability of uncertainty estimation and diminish the occurrence of artifacts.

Investigation Into the Effect of Uncertainty in Thermal Properties on Turbomachinery Disc Heat Transfer Using Both a Monte Carlo Simulation Technique and a Taylor Series Uncertainty Propagation Method

2007 ◽  
Author(s):  
Adam Cooke ◽  
Peter Childs ◽  
Christopher Long
Keyword(s):  
Heat Transfer ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Thermal Properties ◽  
Boundary Conditions ◽  
Taylor Series ◽  
Uncertainty Propagation ◽  
Outer Radius ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

The effect of uncertainties in the thermal properties of components and surrounding fluids is often ignored in the field of experimental turbomachinery heat transfer. The work reported here uses two different methods of uncertainty analysis to help quantify these effects: 1) a stochastic Monte Carlo simulation and 2) a Taylor series uncertainty propagation. These two methods were used on a steady state free disc test case having a turbulent flow regime. The disc modelled was made from IMI 318 titanium and had an inner and outer radius of 0.115 m and 0.22 m respectively, representative of engine and test rig geometry. The disc thickness was 0.016 m. Convective boundary conditions were derived from the relevant equation for local Nusselt number. The applied boundary conditions resulted in local heat transfer coefficients in the range of approximately 120 W/m2 K to 170 W/m2 K. Uncertainties for these heat transfer coefficients were a near identical match between the two different uncertainty methods and were found to be ± 0.66%. Calculated heat flux values fell within the range of approximately 1500 W/m2 and 5200 W/m2. The Monte Carlo uncertainty method returned uncertainty values varying from ± 1.17% to ± 0.47% from the inner and outer radii respectively. An extended Taylor series of uncertainty propagation returned uncertainties varying from ± 1.82% to ± 0.96%, from the inner and outer radius respectively and increased and decreased a number of times in between. These differences are due to assumptions and simplifications which need to be made when using the Taylor series method and shows that a Monte Carlo simulation analysis offers a better way of quantifying the uncertainties associated with disc to air heat transfer as it is more realistic. Studying the magnitudes of uncertainty allows the analyst to understand the impact that uncertainties in thermal properties can have on calculated values of disc to air heat fluxes and heat transfer coefficients.

scholarly journals Monte Carlo Simulations for Uncertainty Estimation in 3D Geological Modeling, A Guide for Disturbance Distribution Selection and Parameterization

2017 ◽  
Author(s):  
Evren Pakyuz-Charrier ◽  
Mark Lindsay ◽  
Vitaliy Ogarko ◽  
Jeremie Giraud ◽  
Mark Jessell
Keyword(s):  
Monte Carlo ◽  
Input Data ◽  
Uncertainty Estimation ◽  
Data Sets ◽  
Geological Modeling ◽  
Data Set ◽  
Input Uncertainty ◽  
3D Geological Modeling ◽  
Wide Range ◽  
Geological Models

Abstract. Three-dimensional (3D) geological modeling aims to determine geological information in a 3D space using structural data (foliations and interfaces) and topological rules as inputs. They are necessary in any project where the properties of the subsurface matters, they express our understanding of geometries in depth. For that reason, 3D geological models have a wide range of practical applications including but not restrained to civil engineering, oil and gas industry, mining industry and water management. These models, however, are fraught with uncertainties originating from the inherent flaws of the modeling engines (working hypotheses, interpolator’s parameterization) combined with input uncertainty (observational-, conceptual- and technical errors). Because 3D geological models are often used for impactful decision making it is critical that all 3D geological models provide accurate estimates of uncertainty. This paper’s focus is set on the effect of structural input data uncertainty propagation in implicit 3D geological modeling using GeoModeller API. This aim is achieved using Monte Carlo simulation uncertainty estimation (MCUE), a heuristic stochastic method which samples from predefined disturbance probability distributions that represent the uncertainty of the original input data set. MCUE is used to produce hundreds to thousands of altered unique data sets. The altered data sets are used as inputs to produce a range of plausible 3D models. The plausible models are then combined into a single probabilistic model as a means to propagate uncertainty from the input data to the final model. In this paper, several improved methods for MCUE are proposed. The methods pertain to distribution selection for input uncertainty, sample analysis and statistical consistency of the sampled distribution. Pole vector sampling is proposed as a more rigorous alternative than dip vector sampling for planar features and the use of a Bayesian approach to disturbance distribution parameterization is suggested. The influence of inappropriate disturbance distributions is discussed and propositions are made and evaluated on synthetic and realistic cases to address the sighted issues. The distribution of the errors of the observed data (i.e. scedasticity) is shown to affect the quality of prior distributions for MCUE. Results demonstrate that the proposed workflows improve the reliability of uncertainty estimation and diminishes the occurrence of artefacts.

scholarly journals Computationally effient geostatistical simulation for uncertainty propagation in models with spatially distributed parameters

2017 ◽  
Author(s):  
Στυλιανός Λιοδάκης
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Sampling Methods ◽  
Uncertainty Propagation ◽  
Stratified Sampling ◽  
Spatial Context ◽  
Flow And Transport ◽  
Model Predictions ◽  
Spatially Distributed

Uncertainty is endemic in geospatial data due to the imperfect means of recording, processing, and representing spatial information. Propagating geospatial model inputs inherent uncertainty to uncertainty in model predictions is a critical requirement in each model's impact assessment and risk-conscious policy decision-making. It is still extremely difficult, however, to perform in practice uncertainty analysis of model outputs, particularly in complex spatially distributed environmental models, partially due to computational constraints.In the field of groundwater hydrology, the "stochastic revolution" has produced an enormous number of theoretical publications and greatly influenced our perspective on uncertainty and heterogeneity; it has had relatively little impact, however, on practical modeling. Monte Carlo simulation using simple random (SR) sampling from a multivariate distribution is one of the most widely used family of methods for uncertainty propagation in hydrogeological flow and transport model predictions, the other being analytical propagation.Real-life hydrogeological problems however, consist of complex and non-linear three dimensional groundwater models with millions of nodes and irregular boundary conditions. The number of Monte-Carlo runs required in these cases, depends on the number of uncertain parameters and on the relative accuracy required for the distribution of model predictions. In the context of sensitivity studies, inverse modelling or Monte-Carlo analyses, the ensuing computational burden is usually overwhelming and computationally impractical. These tough computational constrains have to be relaxed and removed before meaningful stochastic groundwater modeling applications are possible.A computationally efficient alternative to classical Monte Carlo simulation based on SR sampling is Latin hypercube (LH) sampling, a form of stratified random sampling. The latter yields a more representative distribution of model outputs (in terms of smaller sampling variability of their statistics) for the same number of input simulated realizations. The ability to generate unbiased LH realizations becomes critical in a spatial context, where random variables are geo-referenced and exhibit spatial correlation, to ensure unbiased outputs of complex models. On this regard, this dissertation offers a detailed analysis of LH sampling and compares it with SR sampling in a hydrogeological context. Additionally, two alternative stratified sampling methods, here named stratified likelihood (SL) sampling and minimum energy (ME) sampling, are examined (proposed in a spatial context) and their efficiency is further compared to SR and LH in a hydrogeological context; also accounting for the uncertainty related to the particular model at hand via a two step sampling method. All three stratified sampling methods (accounting for model sensitivity in the second case study) were found in this work to be more efficient than simple random sampling.Additionally, this thesis proposes a novel method for the expansion of the application domain of LH sampling to very large regular grids which is the common case in environmental (hydrogeological or not) models. More specifically, a novel combination of Stein's Latin Hypercube sampling with a Monte Carlo simulation method applicable over high discretization domains is proposed, and its performance is further validated in 2D and 3D hydrogeological problems of flow and transport in a mid-heterogeneous porous media, both consisting of about $1$ million nodes. Last, an additional novel extension of the proposed LH sampling on large grids is adopted for conditional high discretized problems. In this case too, the performance of the proposed approach is evaluated in a 3D hydrogeological model of flow and transport. Results indicate that both extensions (conditional and not) of LH sampling on large grids facilitate efficient uncertainty propagation with fewer model runs due to more representative model inputs. Overall, it could be argued that all the proposed methodological approaches could reduce the time and computer resources required to perform uncertainty analysis in hydrogeological flow and transport problems. Additionally, since it is the first time that stratified sampling is performed over high discretization domains, it could be argued that the proposed extensions of LH sampling on large grids could be considered a milestone for future uncertainty analysis efforts. Moreover, all the proposed stratified methods could contribute to a wider application of uncertainty analysis endeavors in a Monte Carlo framework for any spatially distributed impact assessment study.

scholarly journals Application of Monte Carlo Simulation to Find Travel Time of Groundwater in the Iraqi Western Desert

2017 ◽  
Vol 8 (1) ◽  
pp. 17
Author(s):  
Dawood Eisa Sachit ◽  
Hayat Kareem Shukur Azawi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Distribution Function ◽  
Hydraulic Conductivity ◽  
Groundwater Flow ◽  
Travel Time ◽  
Input Data ◽  
Western Desert ◽  
Triangular Distribution ◽  
Entire Area

In this study, a computerized mathematical method represented by Monte Carlo simulation was used to predict the travel time of the groundwater flow in the Iraqi western desert. During the run of the simulations, all the hydraulic parameters of Darcy’s Law were fixed but the hydraulic conductivity. The input data of the hydraulic conductivity is compared to the triangular distribution function to find the best number of iteration to run the simulations. The results showed that an iteration number of 5000 was enough to achieve best match between the input data of the hydraulic conductivity and the fitted distribution function. In addition, the estimated travel time of the groundwater flow is broadly varied through the entire area and ranges from 1983 years to 113 741 years based on 10 000 m of travel distance. Furthermore, hydraulic conductivity of the aquifer has high impact on the estimated travel time of the groundwater flow. However, head difference of groundwater elevation among the selected wells considerably influences the expected travel time of the groundwater flow.

scholarly journals Probabilistic Modelling for Incorporating Uncertainty in Least Cost Path Results: a Postdictive Roman Road Case Study

2021 ◽  
Author(s):  
Joseph Lewis
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Input Data ◽  
Study Finding ◽  
R Package ◽  
Least Cost Path ◽  
Vertical Error ◽  
The Impact ◽  
Modelling Process

AbstractThe movement of past peoples in the landscape has been studied extensively through the use of least cost path (LCP) analysis. Although methodological issues of applying LCP analysis in archaeology have frequently been discussed, the effect of DEM error on LCP results has not been fully assessed. Due to this, the reliability of the LCP result is undermined, jeopardising how well the method can confidently be used to model past movement. To strengthen the reliability of LCP results, this research proposes the use of Monte Carlo simulation as a method for incorporating and propagating the effects of error on LCP results. Focusing on vertical error, random error fields are calculated and incorporated into the documented and reproducible LCP modelling process using the R package leastcostpath. By graphically communicating the impact of vertical error using probabilistic LCPs, uncertainty in the results can be taken into account when interpreting LCPs. The method is applied to a Roman road case study, finding that the incorporation of vertical error results in the identification of multiple ‘least cost’ routes within the landscape. Furthermore, the deviation between the roman road and the probabilistic LCP suggests that the location of the roman road was influenced by additional factors other than minimising energy expenditure. This research finds that the probabilistic LCP derived using Monte Carlo simulation is a viable method for the graphical communication of the uncertainty caused by error within the input data used within the LCP modelling process. Therefore, it is recommended that probabilistic LCPs become the default approach when modelling movement using input data that contains errors.

Sign in / Sign up

Export Citation Format

Share Document