Gradient-Enhanced Support Vector Regression for Robust Life-Cycle Production Optimization with Nonlinear-State Constraints

SPE Journal ◽  
2020 ◽  
pp. 1-24
Author(s):  
Zhe Liu ◽  
Albert C. Reynolds
Keyword(s):  
Support Vector Regression ◽  
State Constraints ◽  
Production Optimization ◽  
Support Vector ◽  
Computationally Efficient ◽  
Production Rates ◽  
Order Of Magnitude ◽  
Reservoir Simulator ◽  
The Cost ◽  
Nonlinear State

Summary In the context of production optimization, we consider the general problem of finding the well controls that maximize the net present value (NPV) of life-cycle production, where the well controls are either the bottomhole pressure (BHP) or a rate (oil, gas, water, or total liquid) at each well on a set of specified control steps (time intervals), with the limitations on surface facility considered as nonlinear-state constraints [e.g., field-liquid-production rates (FLRs), field-water-production rates (FWRs), and/or field-gas-production rates]. If the reservoir simulation used for reservoir management has sufficient adjoint capability to compute gradients of the objective function and all state constraints, we show that one can develop a significantly more computationally efficient procedure by replacing the adjoint-enhanced reservoir simulator by a proxy model and optimizing the proxy. Our methodology achieves computational efficiency by generating a set of output values of the cost and constraint functions and their associated derivative values by running the reservoir simulator for a broad set of input design variables (well controls) and then using the set of input/output data to train a proxy model to replace the reservoir simulator when computing values of cost and constraint functions and their derivatives during iterations of sequential quadratic programming (SQP). The derivation of the equations for computing the proxy-based model that uses both function and gradient information is similar to that of least-squares support vector regression (LS-SVR). However, this method is referred to as gradient-enhanced support vector regression (GE-SVR) because, unlike LS-SVR, the method uses derivative information, not just function values, to train the proxy. Similar to LS-SVR, improved (higher) estimated optimal NPV values can be obtained by using iterative resampling (IR). With IR, after each proxy-based optimization, one evaluates the cost and constraint functions and their derivatives at the estimated optimal controls using reservoir-simulator output, and then adds this new input/output information to the training set to update the proxy models for predicting NPV and constraints. Using the updated proxies, one applies SQP optimization again. IR continues until the simulator and proxy evaluated at the latest estimate of the optimal well controls give the same value of NPV within a specified percentage tolerance and the constraints evaluated by reservoir simulator at the latest optimal well controls are such that the constraints are satisfied within some small specified tolerance. Our results indicate that proxy-based optimization with iterative resampling might require up to an order of magnitude less computational time than pure reservoir-simulator-based optimization. By comparing the results generated with an LS-SVR proxy with the GE-SVR results, we find that GE-SVR is roughly an order of magnitude more computationally efficient than LS-SVR but also provides a better approximation of a complex cost-function surface so that it is possible to locate multiple optima in cases where LS-SVR fails to identify the multiple optima.

Robust Life-Cycle Production Optimization With a Support-Vector-Regression Proxy

SPE Journal ◽  
2018 ◽  
Vol 23 (06) ◽  
pp. 2409-2427 ◽  
Author(s):  
Zhenyu Guo ◽  
Albert C. Reynolds
Keyword(s):  
Life Cycle ◽  
Simulation Model ◽  
Support Vector Regression ◽  
Reservoir Simulation ◽  
Production Optimization ◽  
Forward Model ◽  
Support Vector ◽  
Well Control ◽  
Steepest Ascent ◽  
Reservoir Simulation Model

Summary We design a new and general work flow for efficient estimation of the optimal well controls for the robust production-optimization problem using support-vector regression (SVR), where the cost function is the net present value (NPV). Given a set of simulation results, an SVR model is built as a proxy to approximate a reservoir-simulation model, and then the estimated optimal controls are found by maximizing NPV using the SVR proxy as the forward model. The gradient of the SVR model can be computed analytically so the steepest-ascent algorithm can easily and efficiently be applied to maximize NPV. Then, the well-control optimization is performed using an SVR model as the forward model with a steepest-ascent algorithm. To the best of our knowledge, this is the first SVR application to the optimal well-control problem. We provide insight and information on proper training of the SVR proxy for life-cycle production optimization. In particular, we develop and implement a new iterative-sampling-refinement algorithm that is designed specifically to promote the accuracy of the SVR model for robust production optimization. One key observation that is important for reservoir optimization is that SVR produces a high-fidelity model near an optimal point, but at points far away, we only need SVR to produce reasonable approximations of the predicting output from the reservoir-simulation model. Because running an SVR model is computationally more efficient than running a full-scale reservoir-simulation model, the large computational cost spent on multiple forward-reservoir-simulation runs for robust optimization is significantly reduced by applying the proposed method. We compare the performance of the proposed method using the SVR runs with the popular stochastic simplex approximate gradient (StoSAG) and reservoir-simulations runs for three synthetic examples, including one field-scale example. We also compare the optimization performance of our proposed method with that obtained from a linear-response-surface model and multiple SVR proxies that are built for each of the geological models.

Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses

2003 ◽  
Author(s):  
Stella M. Clarke ◽  
Jan H. Griebsch ◽  
Timothy W. Simpson
Keyword(s):  
Support Vector Regression ◽  
Computer Code ◽  
Multivariate Adaptive Regression Splines ◽  
Great Promise ◽  
Support Vector ◽  
Computationally Efficient ◽  
Adaptive Regression ◽  
Complex Engineering ◽  
Function Approximations ◽  
Adaptive Regression Splines

A variety of metamodeling techniques have been developed in the past decade to reduce the computational expense of computer-based analysis and simulation codes. Metamodeling is the process of building a “model of a model” that provides a fast surrogate for a computationally expensive computer code. Common metamodeling techniques include response surface methodology, kriging, radial basis functions, and multivariate adaptive regression splines. In this paper, we present Support Vector Regression (SVR) as an alternative technique for approximating complex engineering analyses. The computationally efficient theory behind SVR is presented, and SVR approximations are compared against the aforementioned four metamodeling techniques using a testbed of 22 engineering analysis functions. SVR achieves more accurate and more robust function approximations than these four metamodeling techniques and shows great promise for future metamodeling applications.

Surrogate-assisted differential evolution for production optimization with nonlinear state constraints

2020 ◽  
Vol 194 ◽  
pp. 107441
Author(s):  
Xinggang Zhao ◽  
Kai Zhang ◽  
Guodong Chen ◽  
Xiaoming Xue ◽  
Chuanjin Yao ◽  
...  
Keyword(s):  
Differential Evolution ◽  
State Constraints ◽  
Production Optimization ◽  
Nonlinear State

Robust Multiobjective Nonlinear Constrained Optimization with Ensemble Stochastic Gradient Sequential Quadratic Programming-Filter Algorithm

SPE Journal ◽  
2021 ◽  
pp. 1-16
Author(s):  
Zhe Liu ◽  
Albert Reynolds
Keyword(s):  
Life Cycle ◽  
Sequential Quadratic Programming ◽  
State Constraints ◽  
Production Optimization ◽  
Pareto Optimal ◽  
Nonlinear Constraints ◽  
Water Production ◽  
Production Rates ◽  
Short Term ◽  
Lexicographic Method

Summary As the crucial step in closed-loop reservoir management, robust life-cycle production optimization is defined as maximizing/minimizing the expected value of a predefined objective (cost) function over geological uncertainties (i.e., uncertainties in the reservoir permeability, porosity, endpoint relative permeability, etc.). However, with robust optimization, there is no control over downside risk defined as the minimum net present value (NPV) among the individual NPVs of the different reservoir models. Yet, field operators generally wish to keep this minimum NPV reasonably large to try to ensure that the reservoir is commercially viable. In addition, the field operator may desire to maximize the NPV of production over a much shorter time period than the life of the reservoir under the limitation of surface facilities (e.g., field liquid and water production rates). Thus, it is important to consider multiobjective robust production optimization with nonlinear constraints and when geological uncertainties are incorporated. The three objectives considered in this paper are; to maximize the average life-cycle NPV, to maximize the average short-term NPV, and to maximize the minimum NPV of the set of realizations. Generally, these objectives are in conflict; for example, the well controls that give a global maximum for robust life-cycle production optimization do not usually correspond to the controls that maximize the short-term average NPV of production. Moreover, handling the nonlinear state constraints (e.g., field liquid production rates and field water production rates for the bottom-hole pressure controlled producers in the robust production optimization) is also a challenge because those nonlinear constraints should be satisfied at each control steps for each geological realization. To provide potential solutions to the multiobjective robust optimization problem with state constraints, we developed a modified lexicographic method with a minimizing-maximum scheme to attempt to obtain a set of Pareto optimal solutions and to satisfy all nonlinear constraints. We apply the sequential quadratic programming filter with modified stochastic gradients to solve a sequence of optimization problems, where each solution is designed to generate a single point on the Pareto front. In the modified lexicographic method, the objective is always considered to be the primary objective, and the other objectives are considered by specifying bounds on them to convert them to state constraints. The temporal damping and truncation schemes are applied to improve the quality of the stochastic gradient on nonlinear constraints, and the minimizing–maximum procedure is applied to enforce constraints on the normal state constraints. The main advantage that the modified lexicographic method has over the standard lexicographic method is that it allows for the generation of potential Pareto optimal points, which are uniformly spaced in the values of the second and/or third objective that one wishes to improve by multiobjective optimization.

scholarly journals State Evaluation Method of Robot Lubricating Oil Based on Support Vector Regression

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Dongdong Guo ◽  
Xiangqun Chen ◽  
Haitao Ma ◽  
Zimei Sun ◽  
Zongrui Jiang
Keyword(s):  
Support Vector Regression ◽  
Evaluation Method ◽  
Prediction Models ◽  
Sample Volume ◽  
Spare Parts ◽  
Small Sample ◽  
Industrial Robots ◽  
Lubricating Oil ◽  
Support Vector ◽  
The Cost

Recently, the development of the Industrial Internet of Things (IIoT) has led enterprises to re-examine the research of the equipment-state-prediction models and intelligent manufacturing applications. Take industrial robots as typical example. Under the effect of scale, robot maintenance decision seriously affects the cost of spare parts and labor deployment. In this paper, an evaluation method is proposed to predict the state of robot lubricating oil based on support vector regression (SVR). It would be the proper model to avoid the structural risks and minimize the effect of small sample volume. IIoT technology is used to collect and store the valuable robot running data. The key features of the running state of the robot are extracted, and the machine learning model is applied according to the measured element contents of the lubricating oil. As a result, the cost of spare parts consumption can be saved for more than two million CNY per year.

Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses

2004 ◽  
Vol 127 (6) ◽  
pp. 1077-1087 ◽  
Author(s):  
Stella M. Clarke ◽  
Jan H. Griebsch ◽  
Timothy W. Simpson
Keyword(s):  
Support Vector Regression ◽  
Computer Code ◽  
Multivariate Adaptive Regression Splines ◽  
Support Vector ◽  
Test Bed ◽  
Computationally Efficient ◽  
Empirical Performance ◽  
Adaptive Regression ◽  
Complex Engineering ◽  
Function Approximations

A variety of metamodeling techniques have been developed in the past decade to reduce the computational expense of computer-based analysis and simulation codes. Metamodeling is the process of building a “model of a model” to provide a fast surrogate for a computationally expensive computer code. Common metamodeling techniques include response surface methodology, kriging, radial basis functions, and multivariate adaptive regression splines. In this paper, we investigate support vector regression (SVR) as an alternative technique for approximating complex engineering analyses. The computationally efficient theory behind SVR is reviewed, and SVR approximations are compared against the aforementioned four metamodeling techniques using a test bed of 26 engineering analysis functions. SVR achieves more accurate and more robust function approximations than the four metamodeling techniques, and shows great potential for metamodeling applications, adding to the growing body of promising empirical performance of SVR.

Local and Regional Hour-Ahead Forecasts of Solar Irradiance with Training Data Selection and Support Vector Regression

2016 ◽  
Vol 136 (12) ◽  
pp. 898-907 ◽  
Author(s):  
Joao Gari da Silva Fonseca Junior ◽  
Hideaki Ohtake ◽  
Takashi Oozeki ◽  
Kazuhiko Ogimoto
Keyword(s):  
Support Vector Regression ◽  
Solar Irradiance ◽  
Training Data ◽  
Data Selection ◽  
Support Vector ◽  
Training Data Selection

Data Analytics to Help Improve Hydraulic Fracture Geometry Prediction Using Support Vector Regression: Case Study

2020 ◽  
Author(s):  
Avinash Wesley ◽  
Bharat Mantha ◽  
Ajay Rajeev ◽  
Aimee Taylor ◽  
Mohit Dholi ◽  
...  
Keyword(s):  
Support Vector Regression ◽  
Hydraulic Fracture ◽  
Data Analytics ◽  
Support Vector ◽  
Fracture Geometry
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