Expected Uncertainty Reduction Research Articles

AK-SEUR: An adaptive Kriging-based learning function for structural reliability analysis through sample-based expected uncertainty reduction

Reliability Analysis (RA) is a critical aspect of structural design and performance evaluation aiming to determine the probability of structural failure under given random input parameters. With modern development of modeling techniques, computational models have achieved higher fidelity but at the increased cost of computational time, which poses a significant challenge for RA. Consequently, surrogate model-assisted RA has been explored as a means of improved efficiency and accuracy. This study proposes a novel learning function, Sample-based Expected Uncertainty Reduction (SEUR), for surrogate model-assisted RA. The SEUR function uses statistical information from the metamodeling with fixed hyper-parameters to construct expected failure probability bounds to sequentially update the design of experiment (DoE). The joint probability densities of input variables are accounted for through simulation methods, including Monte Carlo (MC) and subset simulation (SS). Furthermore, the discrete simulated annealing algorithm is used to search for the optimal design point. The performance of proposed AK-SEUR function is systematically evaluated using six examples of different dimensions, failure probability levels and nonlinearities. The AK-SEUR function is demonstrated to be more effective and efficient than other popular active learning methods in dealing with nonlinear performance functions, small probabilities, and complex limit states. The proposed SEUR function has the potential to improve the efficiency and accuracy of RA, particularly in situations where computational models are time-consuming and the search for the optimal solution is challenging.

A SUR version of the Bichon criterion for excursion set estimation

Many model inversion problems occur in industry. These problems consist in finding the set of parameter values such that a certain quantity of interest respects a constraint, for example remains below a threshold. In general, the quantity of interest is the output of a simulator, costly in computation time. An effective way to solve this problem is to replace the simulator by a Gaussian process regression, with an experimental design enriched sequentially by a well chosen acquisition criterion. Different inversion-adapted criteria exist such as the Bichon criterion (also known as expected feasibility function) and deviation number . There also exist a class of enrichment strategies (stepwise uncertainty reduction—SUR) which select the next point by measuring the expected uncertainty reduction induced by its selection. In this paper we propose a SUR version of the Bichon criterion. An explicit formulation of the criterion is given and test comparisons show good performances on classical test functions.

An expected uncertainty reduction of reliability: adaptive sampling convergence criterion for Kriging-based reliability analysis

An expected uncertainty reduction of reliability: adaptive sampling convergence criterion for Kriging-based reliability analysis

Kriging-based reliability analysis considering predictive uncertainty reduction

Over the past decade, several acquisition functions have been proposed for kriging-based reliability analysis. Each of these acquisition functions can be used to identify an optimal sequence of samples to be included in the kriging model. However, no single acquisition function provides better performance over the others in all cases. Further, the best-performing acquisition function can change at different iterations over the sequential sampling process. To address this problem, this paper proposes a new acquisition function, namely expected uncertainty reduction (EUR), that serves as a meta-criterion to select the best sample from a set of optimal samples, each identified from a large number of candidate samples according to the criterion of an acquisition function. EUR does not rely on the local utility measure derived based on the kriging posterior of a performance function as most existing acquisition functions do. Instead, EUR directly quantifies the expected reduction of the uncertainty in the prediction of limit-state function by adding an optimal sample. The uncertainty reduction is quantified by sampling over the kriging posterior. In the proposed EUR-based sequential sampling process, a portfolio that consists of four acquisition functions is first employed to suggest four optimal samples at each iteration of sequential sampling. Each of these samples is optimal with respect to the selection criterion of the corresponding acquisition function. Then, EUR is employed as the meta-criterion to identify the best sample among those optimal samples. The results from two mathematical and one practical case studies show that (1) EUR-based sequential sampling can perform as well as or outperform the single use of any acquisition function in the portfolio, and (2) the best-performing acquisition function may change from one problem to another or even from one iteration to the next within a problem.

Improving Risk Analysis Precision for Geologic CO2 Sequestration by Quantifying the Uncertainty Reduction Before and after Acquiring Monitoring Data

Monitoring is an essential component of risk management for geologic carbon sequestration. The high cost of conducting monitoring operations often requires evaluating the potential value of data before the actual measurement are collected. The value of information (VOI) of the data is defined here as the uncertainty reduction in the objective of interest (e.g., cumulative CO2 leakage in this study) that will be obtained once the data are assimilated into model(s). In a previous study, we introduced a novel approach to quantify the expected uncertainty reduction or VOI before the monitoring data are acquired, such that the optimal monitoring operation can be determined. After the installation of an optimized monitoring strategy, collected monitoring data can be incorporated into the models to reduce the uncertainty of CO2 and brine leakage through wellbores. This study introduces an integrated workflow to improve the precision of risk assessments by quantifying the uncertainty reduction in CO2 sequestration before and after acquiring monitoring data. This paper mainly focuses on the application of an Affine Invariant Markov chain Monte Carlo (MCMC) algorithm to quantify the uncertainty reduction after acquiring monitoring data. The proposed approach for uncertainty quantification after acquiring monitoring data is demonstrated with a simple example. The uncertainty in CO2 and brine leakage rate through wellbores can be significantly reduced by applying the MCMC algorithm to assimilate monitoring data. This allows for a more precise estimate of the leakage risk for a sequestration operation.

Economic valuation of hydrogeological information when managing groundwater drawdown

A procedure is presented for valuation of information analysis (VOIA) to determine the need for additional information when assessing the effect of several design alternatives to manage future disturbances in hydrogeological systems. When planning for groundwater extraction and drawdown in areas where risks—such as land subsidence, wells running dry and drainage of streams and wetlands—are present, the need for risk-reducing safety measures must be carefully evaluated and managed. The heterogeneity of the subsurface calls for an assessment of trade-offs between the benefits of additional information to reduce the risk of erroneous decisions and the cost of collecting this information. A method is suggested that combines existing procedures for inverse probabilistic groundwater modelling with a novel method for VOIA. The method results in (1) a prior analysis where uncertainties regarding the efficiency of safety measures are estimated, and (2) a pre-posterior analysis, where the benefits of expected uncertainty reduction deriving from additional information are compared with the costs for obtaining this information. In comparison with existing approaches for VOIA, the method can assess multiple design alternatives, use hydrogeological parameters as proxies for failure, and produce spatially distributed VOIA maps. The method is demonstrated for a case study of a planned tunnel in Stockholm, Sweden, where additional investigations produce a low number of benefits as a result of low failure rates for the studied alternatives and a cause-effect chain where the resulting failure probability is more dependent on interactions within the whole system rather than on specific features.

Quantifying Expected Uncertainty Reduction and Value of Information Using Ensemble-Variance Analysis

Summary Data-acquisition programs, such as surveillance and pilots, play an important role in minimizing subsurface risks and improving decision quality for reservoir management. For design optimization and investment justification of these programs, it is crucial to be able to quantify the expected uncertainty reduction and the value of information (VOI) attainable from a given design. This problem is challenging because the data from the acquisition program are uncertain at the time of the analysis. In this paper, a method called ensemble-variance analysis (EVA) is proposed. Derived from a multivariate Gaussian assumption between the observation data and the objective function, the EVA method quantifies the expected uncertainty reduction from covariance information that is estimated from an ensemble of simulations. The result of EVA can then be used with a decision tree to quantify the VOI of a given data-acquisition program. The proposed method has several novel features compared with existing methods. First, the EVA method directly considers the data/objective-function relationship. Therefore, it can handle nonlinear forward models and an arbitrary number of parameters. Second, for cases when the multivariate Gaussian assumption between the data and objective function does not hold, the EVA method still provides a lower bound on expected uncertainty reduction, which can be useful in providing a conservative estimate of the surveillance/pilot performance. Finally, EVA also provides an estimate of the shift in the mean of the objective-function distribution, which is crucial for VOI calculation. In this paper, the EVA work flow for expected-uncertainty-reduction quantification is described. The result from EVA is benchmarked with recently proposed rigorous sampling methods, and the capacity of the method for VOI quantification is demonstrated for a pilot-analysis problem using a field-scale reservoir model.

MERLIN: A French-German Space Lidar Mission Dedicated to Atmospheric Methane

The MEthane Remote sensing Lidar missioN (MERLIN) aims at demonstrating the spaceborne active measurement of atmospheric methane, a potent greenhouse gas, based on an Integrated Path Differential Absorption (IPDA) nadir-viewing LIght Detecting and Ranging (Lidar) instrument. MERLIN is a joint French and German space mission, with a launch currently scheduled for the timeframe 2021/22. The German Space Agency (DLR) is responsible for the payload, while the platform (MYRIADE Evolutions product line) is developed by the French Space Agency (CNES). The main scientific objective of MERLIN is the delivery of weighted atmospheric columns of methane dry-air mole fractions for all latitudes throughout the year with systematic errors small enough (<3.7 ppb) to significantly improve our knowledge of methane sources from global to regional scales, with emphasis on poorly accessible regions in the tropics and at high latitudes. This paper presents the MERLIN objectives, describes the methodology and the main characteristics of the payload and of the platform, and proposes a first assessment of the error budget and its translation into expected uncertainty reduction of methane surface emissions.

Uncertainty quantification and value of information assessment using proxies and Markov chain Monte Carlo method for a pilot project

A pilot project is a crucial step of reservoir management that enables the minimization of subsurface risks and improves the quality of decisions on full-field development. Selecting a pilot project involves evaluating the expected uncertainty reduction and the value of information (VOI) attainable from a set of plausible pilot projects. Proxy-based pilot analysis (PBPA) represents a promising approach for characterizing the uncertainty reduction and VOI from each of a set of feasible pilot projects. In the PBPA method, multiple plausible realizations of observed data from a pilot are generated and probabilistic history matching (based on filtering) is performed for each realization of the vector of observed data in order to obtain the corresponding posterior distribution. The multiple history-matching runs are accomplished with a manageable number of simulations with the help of proxies. Previously, PBPA was successfully applied to quantify the expected value of uncertainty reduction in cases where the history-matching tolerance is high, but as shown here, the filtering-based history-matching procedure can fail when the tolerance is low. Moreover, it has not been demonstrated previously that the PBPA method can quantify VOI. In this paper, enhancements to PBPA that eliminate these two PBPA shortcomings are introduced. First, a Markov chain Monte Carlo (MCMC) method is used in place of the filtering procedure to calculate the posterior distribution. The combined MCMC-PBPA procedure is shown to outperform the filtering-based PBPA when the history-matching tolerance is low. Secondly, we define a framework that combines the MCMC-PBPA method with decision tree analysis in order to calculate the VOI. The proposed framework is demonstrated for a synthetic waterflooding pilot in the Brugge reservoir where it successfully quantifies the VOI for different pilot designs.

Proxy-Based Work Flow for a Priori Evaluation of Data-Acquisition Programs

Summary Data-acquisition programs, such as surveillance and pilot, play an important role in reservoir management, and are crucial for minimizing subsurface risks and improving decision quality. Optimal design of the data-acquisition plan requires predicting the performance (e.g., in terms of the expected amount of uncertainty reduction in an objective function) of a given design before it is implemented. Because the data from the acquisition program are uncertain at the time of the analysis, multiple history-matching runs are required for different plausible realizations of the observed data to evaluate the expected effectiveness of the program in reducing uncertainty. As such, the computational cost may be prohibitive because the number of reservoir simulations needed for the multiple history-matching runs would be substantial. This paper proposes a framework on the basis of proxies and rejection sampling (filtering) to perform the multiple history-matching runs with a manageable number of reservoir simulations. The work flow proposed does not depend on the linear Gaussian assumption that is a common, yet questionable, assumption in existing methods. The work flow also enables both qualitative and quantitative analysis of a surveillance plan. Qualitatively, heavy-hitter alignment analysis for the objective function and the observed data provides actionable measures for screening different surveillance designs. Quantitatively, the evaluation of expected uncertainty reduction from different surveillance plans allows for optimal design and selection of surveillance plans.

Active Clustering with Model-Based Uncertainty Reduction.

Semi-supervised clustering seeks to augment traditional clustering methods by incorporating side information provided via human expertise in order to increase the semantic meaningfulness of the resulting clusters. However, most current methods are passive in the sense that the side information is provided beforehand and selected randomly. This may require a large number of constraints, some of which could be redundant, unnecessary, or even detrimental to the clustering results. Thus in order to scale such semi-supervised algorithms to larger problems it is desirable to pursue an active clustering method-i.e., an algorithm that maximizes the effectiveness of the available human labor by only requesting human input where it will have the greatest impact. Here, we propose a novel online framework for active semi-supervised spectral clustering that selects pairwise constraints as clustering proceeds, based on the principle of uncertainty reduction. Using a first-order Taylor expansion, we decompose the expected uncertainty reduction problem into a gradient and a step-scale, computed via an application of matrix perturbation theory and cluster-assignment entropy, respectively. The resulting model is used to estimate the uncertainty reduction potential of each sample in the dataset. We then present the human user with pairwise queries with respect to only the best candidate sample. We evaluate our method using three different image datasets (faces, leaves and dogs), a set of common UCI machine learning datasets and a gene dataset. The results validate our decomposition formulation and show that our method is consistently superior to existing state-of-the-art techniques, as well as being robust to noise and to unknown numbers of clusters.

Model-Based Evaluation of Surveillance-Program Effectiveness With Proxies

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 173229, “Model-Based A Priori Evaluation of Surveillance-Program Effectiveness With Proxies,” by Jincong He, Jiang Xie, Pallav Sarma, Xian-Huan Wen, Wen H. Chen, and Jairam Kamath, Chevron, prepared for the 2015 SPE Reservoir Simulation Symposium, Houston, 23–25 February. The paper has not been peer reviewed. This paper proposes a framework based on proxies and rejection sampling (filtering) to perform multiple history-matching runs with a manageable number of reservoir simulations. The proposed work flow enables qualitative and quantitative analysis of a surveillance plan. Qualitatively, heavy-hitter-alignment analysis for the objective function and the observed data provides actionable measures for screening different surveillance designs. Quantitatively, the evaluation of expected uncertainty reduction from different surveillance plans allows for optimal design and selection of surveillance plans. Introduction In this work flow, the authors perform a set of training simulations (determined by experimental design) and use the result to build proxies for the objective function and each of the surveillance data points. Proxies are then used to generate a number of plausible realizations of the surveillance data. Then, in turn, one of the plausible data realizations is assumed to be the true data to be observed, and a history-matching run is performed to assimilate these ”true” data using proxy-based rejection sampling to establish the corresponding posterior distribution. The process is repeated for all plausible surveillance-data realizations, to obtain a set of plausible posterior distributions (one for each data realization). The amount of expected uncertainty reduction is obtained by comparing the amount of uncertainty in the prior distribution and the average amount of uncertainty in the posterior distribution. To the best of the authors’ knowledge, this is the first attempt for a priori surveillance analysis by multiple history matching under data uncertainty by use of rejection sampling and proxies. The proposed method has several benefits. First, the linear Gaussian assumption between surveillance data and objective function can have a major impact on the accuracy of the quantification of the uncertainty reduction. The method proposed in this work does not make the linear Gaussian assumption. Therefore, it can better capture the distributions of, and the relation between, the surveillance data and the objective function. Second, it is a black-box method that does not require gradient information, and therefore the work flow can be used with most simulators as long as it can predict the value of the surveillance data from the surveillance program and the value of the objective function. In addition, the number of training simulations needed is independent of the number of plausible data realizations and is thus independent of the number of history-matching runs. The computational cost is also insensitive to the number of data points to be collected in the surveillance program. Furthermore, besides the quantification of expected uncertainty reduction, the work flow also enables qualitative screening of surveillance concepts by analyzing the ranking and the magnitude of the sensitivities of the objective function and the surveillance data to different parameters. The complete paper provides a discussion of the formulation of the problem of quantifying the uncertainty reduction for surveillance programs and details the new work flow.

Potential Uncertainty Reduction in Model‐Averaged Benchmark Dose Estimates Informed by an Additional Dose Study

A methodology is presented for assessing the information value of an additional dosage experiment in existing bioassay studies. The analysis demonstrates the potential reduction in the uncertainty of toxicity metrics derived from expanded studies, providing insights for future studies. Bayesian methods are used to fit alternative dose-response models using Markov chain Monte Carlo (MCMC) simulation for parameter estimation and Bayesian model averaging (BMA) is used to compare and combine the alternative models. BMA predictions for benchmark dose (BMD) are developed, with uncertainty in these predictions used to derive the lower bound BMDL. The MCMC and BMA results provide a basis for a subsequent Monte Carlo analysis that backcasts the dosage where an additional test group would have been most beneficial in reducing the uncertainty in the BMD prediction, along with the magnitude of the expected uncertainty reduction. Uncertainty reductions are measured in terms of reduced interval widths of predicted BMD values and increases in BMDL values that occur as a result of this reduced uncertainty. The methodology is illustrated using two existing data sets for TCDD carcinogenicity, fitted with two alternative dose-response models (logistic and quantal-linear). The example shows that an additional dose at a relatively high value would have been most effective for reducing the uncertainty in BMA BMD estimates, with predicted reductions in the widths of uncertainty intervals of approximately 30%, and expected increases in BMDL values of 5-10%. The results demonstrate that dose selection for studies that subsequently inform dose-response models can benefit from consideration of how these models will be fit, combined, and interpreted.

Self-assessment and task performance

The present study tested the idea that the amount of effort expended in task performance is a function of the amount of uncertainty in one's ability level the resulting outcomes are expected to reduce. Two determinants of expected uncertainty reduction were manipulated: prior uncertainty about one's ability level and the diagnosticity of the task. Subjects first performed an initial task and then received fictitious feedback to manipulate their prior uncertainty. To induce low uncertainty, the feedback implied that the subjects are highly likely to have either low, intermediate, or a high level of ability. To induce high uncertainty, the feedback implied that the various ability levels were equally probable. Subjects then performed a task whose perceived diagnosticity regarding the ability under consideration was varied. As expected, subjects who were highly uncertain about their ability level performed better than subjects who were relatively certain they possessed either low, intermediate, or a high level of ability. Performance also improved with task diagnosticity, and the effect of task diagnosticity on performance was more pronounced when prior uncertainty was high than when it was low. Past research on the relationship between prior feedback and subsequent performance was discussed in light of the present results and a self-assessment model of achievement behavior.