Data assimilation of subsurface flow via iterative ensemble smoother and physics-informed neural network

2020 ◽  
Author(s):  
Nanzhe Wang ◽  
Haibin Chang
Keyword(s):  
Neural Network ◽  
Data Assimilation ◽  
Surrogate Model ◽  
Flow Problem ◽  
Subsurface Flow ◽  
High Accuracy ◽  
Training Data ◽  
Model Parameters ◽  
Ensemble Smoother ◽  
Iterative Ensemble Smoother

<p>Subsurface flow problems usually involve some degree of uncertainty. For reducing the uncertainty of subsurface flow prediction, data assimilation is usually necessary. Data assimilation is time consuming. In order to improve the efficiency of data assimilation, surrogate model of subsurface flow problem may be utilized. In this work, a physics-informed neural network (PINN) based surrogate model is proposed for subsurface flow with uncertain model parameters. Training data generated by solving stochastic partial differential equations (SPDEs) are utilized to train the neural network. Besides the data mismatch term, the term that incorporates physics laws is added in the loss function. The trained neural network can predict the solutions of the subsurface flow problem with new stochastic parameters, which can serve as a surrogate for approximating the relationship between model output and model input. By incorporating physics laws, PINN can achieve high accuracy. Then an iterative ensemble smoother (ES) is introduced to implement the data assimilation task based on the PINN surrogate. Several subsurface flow cases are designed to test the performance of the proposed paradigm. The results show that the PINN surrogate can significantly improve the efficiency of data assimilation task while maintaining a high accuracy.</p>

Efficient Uncertainty Quantification and Data Assimilation via Theory-Guided Convolutional Neural Network

SPE Journal ◽  
1900 ◽  
pp. 1-29
Author(s):  
Nanzhe Wang ◽  
Haibin Chang ◽  
Dongxiao Zhang
Keyword(s):  
Neural Network ◽  
Data Assimilation ◽  
Convolutional Neural Network ◽  
Uncertainty Quantification ◽  
Reservoir Simulation ◽  
High Accuracy ◽  
Training Data ◽  
Flow Problems ◽  
Stochastic Parameter ◽  
Reservoir Flow

Summary A deep learning framework, called the theory-guided convolutional neural network (TgCNN), is developed for efficient uncertainty quantification and data assimilation of reservoir flow with uncertain model parameters. The performance of the proposed framework in terms of accuracy and computational efficiency is assessed by comparing it to classical approaches in reservoir simulation. The essence of the TgCNN is to take into consideration both the available data and underlying physical/engineering principles. The stochastic parameter fields and time matrix comprise the input of the convolutional neural network (CNN), whereas the output is the quantity of interest (e.g., pressure, saturation, etc.). The TgCNN is trained with available data while being simultaneously guided by theory (e.g., governing equations, other physical constraints, and engineering controls) of the underlying problem. The trained TgCNN serves as a surrogate that can predict the solutions of the reservoir flow problem with new stochastic parameter fields. Such approaches, including the Monte Carlo (MC) method and the iterative ensemble smoother (IES) method, can then be used to perform uncertainty quantification and data assimilation efficiently based on the TgCNN surrogate, respectively. The proposed paradigm is evaluated with dynamic reservoir flow problems. The results demonstrate that the TgCNN surrogate can be built with a relatively small number of training data and even in a label-free manner, which can approximate the relationship between model inputs and outputs with high accuracy. The TgCNN surrogate is then used for uncertainty quantification and data assimilation of reservoir flow problems, which achieves satisfactory accuracy and higher efficiency compared with state-of-the-art approaches. The novelty of the work lies in the ability to incorporate physical laws and domain knowledge into the deep learning process and achieve high accuracy with limited training data. The trained surrogate can significantly improve the efficiency of uncertainty quantification and data assimilation processes. NOTE: This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

scholarly journals Joint Estimation of Hydraulic and Biochemical Parameters for Reactive Transport Modelling with a Modified ILUES Algorithm

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2161
Author(s):  
Ruicheng Zhang ◽  
Nianqing Zhou ◽  
Xuemin Xia ◽  
Guoxian Zhao ◽  
Simin Jiang
Keyword(s):  
Reactive Transport ◽  
Biochemical Parameters ◽  
Transport Model ◽  
Joint Estimation ◽  
Model Parameters ◽  
Transport Modelling ◽  
Selection Scheme ◽  
Related Model ◽  
Ensemble Smoother ◽  
Iterative Ensemble Smoother

Multicomponent reactive transport modeling is a powerful tool for the comprehensive analysis of coupled hydraulic and biochemical processes. The performance of the simulation model depends on the accuracy of related model parameters whose values are usually difficult to determine from direct measurements. In this situation, estimates of these uncertain parameters can be obtained by solving inverse problems. In this study, an efficient data assimilation method, the iterative local updating ensemble smoother (ILUES), is employed for the joint estimation of hydraulic parameters, biochemical parameters and contaminant source characteristics in the sequential biodegradation process of tetrachloroethene (PCE). In the framework of the ILUES algorithm, parameter estimation is realized by updating local ensemble with the iterative ensemble smoother (IES). To better explore the parameter space, the original ILUES algorithm is modified by determining the local ensemble partly with a linear ranking selection scheme. Numerical case studies based on the sequential biodegradation of PCE are then used to evaluate the performance of the ILUES algorithm. The results show that the ILUES algorithm is able to achieve an accurate joint estimation of related model parameters in the reactive transport model.

Improved Estimation and Forecasting Through Residual-Based Model Error Quantification

SPE Journal ◽  
2020 ◽  
Vol 25 (02) ◽  
pp. 951-968 ◽  
Author(s):  
Minjie Lu ◽  
Yan Chen
Keyword(s):  
History Matching ◽  
Historical Data ◽  
Total Error ◽  
Model Error ◽  
Complex Nature ◽  
Model Parameters ◽  
Observation Error ◽  
Model Errors ◽  
Ensemble Smoother ◽  
Iterative Ensemble Smoother

Summary Owing to the complex nature of hydrocarbon reservoirs, the numerical model constructed by geoscientists is always a simplified version of reality: for example, it might lack resolution from discretization and lack accuracy in modeling some physical processes. This flaw in the model that causes mismatch between actual observations and simulated data when “perfect” model parameters are used as model inputs is known as “model error”. Even in a situation when the model is a perfect representation of reality, the inputs to the model are never completely known. During a typical model calibration procedure, only a subset of model inputs is adjusted to improve the agreement between model responses and historical data. The remaining model inputs that are not calibrated and are likely fixed at incorrect values result in model error in a similar manner as the imperfect model scenario. Assimilation of data without accounting for model error can result in the incorrect adjustment to model parameters, the underestimation of prediction uncertainties, and bias in forecasts. In this paper, we investigate the benefit of recognizing and accounting for model error when an iterative ensemble smoother is used to assimilate production data. The correlated “total error” (a combination of model error and observation error) is estimated from the data residual after a standard history-matching using the Levenberg-Marquardt form of iterative ensemble smoother (LM-EnRML). This total error is then used in further data assimilations to improve the estimation of model parameters and quantification of prediction uncertainty. We first illustrate the method using a synthetic 2D five-spot example, where some model errors are deliberately introduced, and the results are closely examined against the known “true” model. Then, the Norne field case is used to further evaluate the method. The Norne model has previously been history-matched using the LM-EnRML (Chen and Oliver 2014), where cell-by-cell properties (permeability, porosity, net-to-gross, vertical transmissibility) and parameters related to fault transmissibility, depths of water/oil contacts, and relative permeability function are adjusted to honor historical data. In this previous study, the authors highlighted the importance of including large amounts of model parameters, the proper use of localization, and heuristic adjustment of data noise to account for modeling error. In this paper, we improve the last aspect by quantitatively estimating model error using residual analysis.

scholarly journals Accelerated System-Level Seismic Risk Assessment of Bridge Transportation Networks through Artificial Neural Network-Based Surrogate Model

2020 ◽  
Vol 10 (18) ◽  
pp. 6476
Author(s):  
Sungsik Yoon ◽  
Jeongseob Kim ◽  
Minsun Kim ◽  
Hye-Young Tak ◽  
Young-Joo Lee
Keyword(s):  
Neural Network ◽  
Risk Assessment ◽  
Artificial Neural Network ◽  
Surrogate Model ◽  
Seismic Risk ◽  
Transportation Networks ◽  
Training Data ◽  
System Level ◽  
High Dimensional ◽  
Seismic Risk Assessment

In this study, an artificial neural network (ANN)-based surrogate model is proposed to evaluate the system-level seismic risk of bridge transportation networks efficiently. To estimate the performance of a network, total system travel time (TSTT) was introduced as a performance index, and an ANN-based surrogate model was incorporated to evaluate a high-dimensional network with probabilistic seismic hazard analysis (PSHA) efficiently. To generate training data, the damage states of bridge components were considered as the input training data, and TSTT was selected as output data. An actual bridge transportation network in South Korea was considered as the target network, and the entire network map was reconstructed based on geographic information system data to demonstrate the proposed method. For numerical analysis, the training data were generated based on epicenter location history. By using the surrogate model, the network performance was estimated for various earthquake magnitudes at the trained epicenter with significantly-reduced computational time cost. In addition, 20 historical epicenters were adopted to confirm the robustness of the epicenter. Therefore, it was concluded that the proposed ANN-based surrogate model could be used as an alternative for efficient system-level seismic risk assessment of high-dimensional bridge transportation networks.

Convolutional Neural Network Considering the Effects of Noise for Bearing Fault Diagnosis

2020 ◽  
Author(s):  
Ilyoung Han ◽  
Jangbom Chai ◽  
Chanwoo Lim ◽  
Taeyun Kim
Keyword(s):  
Neural Network ◽  
Fault Diagnosis ◽  
Convolutional Neural Network ◽  
High Accuracy ◽  
Training Data ◽  
Bearing Fault ◽  
Bearing Fault Diagnosis ◽  
System Noise ◽  
Novel Method ◽  
Maintenance Activities

Abstract Convolutional Neural Network (CNN) is, in general, good at finding principal components of data. However, the characteristic components of the signals could often be obscured by system noise. Therefore, even though the CNN model is well-trained and predict with high accuracy, it may detect only the primary patterns of data which could be formed by system noise. They are, in fact, highly vulnerable to maintenance activities such as reassembly. In other words, CNN models could misdiagnose even with excellent performances. In this study, a novel method that combines the classification using CNN with the data preprocessing is proposed for bearing fault diagnosis. The proposed method is demonstrated by the following steps. First, training data is preprocessed so that the noise and the fault signature of the bearings are separated. Then, CNN models are developed and trained to learn significant features containing information of defects. Lastly, the CNN models are examined and validated whether they learn and extract the meaningful features or not.

Artificial Neural Network Approach for Solving Power Flow Problem: A Case Study of Ayede 132 KV Power System, Nigeria

2011 ◽  
Vol 367 ◽  
pp. 133-141
Author(s):  
P.B. Osofisan ◽  
J.O. Ilevbare
Keyword(s):  
Neural Network ◽  
Power System ◽  
Test Data ◽  
Power Flow ◽  
Flow Problem ◽  
High Accuracy ◽  
Voltage Phase ◽  
Phase Angles ◽  
Very High ◽  
Power Flow Problem

The main objective of this research work was to use Artificial Neural Network (ANN) based method for solving Power Flow Problem for a power system in Nigeria. This was achieved using the Backpropagation (multilayered feed-forward) Neural Network model. Two Backpropagation neural networks were designed and trained; one for computing voltage magnitudes on all buses and the other for computing voltage phase angles on all PV and PQ buses for different load and generation conditions for a 7-bus 132 kV power system in South-West Nigeria (Ayede). Due to unavailability of historical field records, data representing different scenarios of loading and/or generation conditions had to be generated using Newton-Raphson non-linear iterative method. A total of 250 scenarios were generated out of which 50% were used to train the ANNs, 25% were used for validation and the remaining 25% were used as test data for the ANNs. The test data results showed very high accuracy for the ANN used for computing voltage magnitudes for all test data with a Mean Square Error (MSE) of less than 10-6. Also, the ANN used for computing voltage phase angles showed very high accuracy in about 80% of the test data and acceptable results in about 97% of the test data. The MSE for all the test data results for the ANN computing voltage phase angles was less than 10-2.

scholarly journals Revising the stochastic iterative ensemble smoother

2019 ◽  
Author(s):  
Patrick N. Raanes ◽  
Andreas S. Stordal ◽  
Geir Evensen
Keyword(s):  
Data Assimilation ◽  
History Matching ◽  
Kalman Smoother ◽  
Multiple Data ◽  
Current Formulation ◽  
Ensemble Smoother ◽  
Careful Treatment ◽  
Randomized Maximum Likelihood ◽  
Iterative Ensemble Smoother ◽  
Lorenz 96

Abstract. Ensemble randomized maximum likelihood (EnRML) is an iterative (stochastic) ensemble smoother, used for large and nonlinear inverse problems, such as history matching and data assimilation. Its current formulation is overly complicated and has issues with computational costs, noise, and covariance localization, even causing some practitioners to omit crucial prior information. This paper resolves these difficulties and streamlines the algorithm, without changing its output. These simplifications are achieved through the careful treatment of the linearizations and subspaces. For example, it is shown (a) how ensemble linearizations relate to average sensitivity, and (b) that the ensemble does not loose rank during updates. The paper also draws significantly on the theory of the (deterministic) iterative ensemble Kalman smoother (IEnKS). Comparative benchmarks are obtained with the Lorenz-96 model with these two smoothers and the ensemble smoother using multiple data assimilation (ES-MDA).

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