Sequential Surrogate Modeling Research Articles

Research on surrogate model of dam numerical simulation with multiple outputs based on adaptive sampling.

Dam numerical simulation is an important method to research the dam structural behavior, but it often takes a lot of time for calculation when facing problems that require many simulations, such as structural parameter back analysis. The surrogate model is widely used as a technology to reduce computational cost. Although various methods have been widely investigated, there are still problems in designing the surrogate model's optimal Design of Experiments (DoE). In addition, most of the current DoE focuses on establishing a single-output problem. Designing a reasonable DoE for high-dimensional outputs is also a problem that needs to be solved. Based on the above issues, this research proposes a sequential surrogate model based on the radial basis function model (RBFM) with multi-outputs adaptive sampling. The benchmark function demonstrates the applicability of the proposed method to single-input & multi-outputs and multi-inputs & multi-outputs problems. Then, this method is applied to establishing a surrogate model for dam numerical simulation with multi-outputs. The result demonstrates that the proposed technique can be sampled adaptively and samples can be targeted based on the function form of the surrogate model, which significantly reduces the required sampling and calculation cost.

Lego-inspired reconfigurable modular blocks for automated construction of engineering structures

Reconfigurable modular structures are able to be assembled using prefabricated modules and reconfigured to promote automated construction and to improve sustainability and resilience of infrastructure, while the computer-aided design and modeling of the modules are unclear. This study develops a many-objective optimization approach to design the modules made using strain-hardening cementitious composite. The proposed approach integrates a sequential surrogate model, Latin hypercube sampling method, Unified Non-dominated Sorting Genetic Algorithm III, and Technique for Order of Preference by Similarity to Ideal Solution to predict and optimize the properties of assemblages of the modules. Four objective functions were defined using the load-carrying capacity, deformability, stiffness, and volume. Results showed that the proposed method had reasonable prediction accuracy. The optimal design increased the load-carrying capacity, deformability, and stiffness by 22.8%, 11.5%, and 129.2%, respectively, and reduced the volume by 51.6%. This study is expected to effectively improve the design of reconfigurable modular structures.

Variance-based adaptive sequential sampling for Polynomial Chaos Expansion

This paper presents a novel adaptive sequential sampling method for building Polynomial Chaos Expansion surrogate models. The technique enables one-by-one extension of an experimental design while trying to obtain an optimal sample at each stage of the adaptive sequential surrogate model construction process. The proposed sequential sampling strategy selects from a pool of candidate points by trying to cover the design domain proportionally to their local variance contribution. The proposed criterion for the sample selection balances both exploitation of the surrogate model and exploration of the design domain. The adaptive sequential sampling technique can be used in tandem with any user-defined sampling method, and here was coupled with commonly used Latin Hypercube Sampling and advanced Coherence D-optimal sampling in order to present its general performance. The obtained numerical results confirm its superiority over standard non-sequential approaches in terms of surrogate model accuracy and estimation of the output variance.

Deep Sequential Surrogate Model Enables New Work Flows

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 201775, “An End-to-End Deep Sequential Surrogate Model for High-Performance Reservoir Modeling: Enabling New Work Flows,” by Jiri Navratil, IBM; Giorgio De Paola, SPE, Repsol; and Georgos Kollias, IBM, et al., prepared for the 2020 SPE Annual Technical Conference and Exhibition, originally scheduled to be held in Denver, 5–7 October. The paper has not been peer reviewed. Despite considerable progress in the development of rapid evaluation methods for physics-based reservoir simulators, a significant gap still exists in the acceleration and accuracy needed to enable complex optimization methods. The complete paper describes an end-to-end deep surrogate model capable of modeling field and individual-well production rates given arbitrary sequences of actions (schedules), including varying well locations, controls, and completions. Results provide concrete measures of the efficacy of the deep surrogate model as an enabling technology for the development of optimization techniques previously out of reach because of computational complexity. Introduction Recent advances in machine learning, particularly in deep learning, have enabled breakthroughs in technically challenging areas such as computer vision, natural language processing, and speech processing. The authors expand on these powerful algorithms to develop a deep neural network (DNN) surrogate model for reservoir dynamics. The objective of the DNN surrogate model is to predict field rates and individual well rates. The field rates typically include aggregate oil and water production and water-injection rates reported at equidistant timesteps over a desired production horizon. Economic metrics such as net present value are computed using the field rates. The individual well rates are optional, and, typically, the oil production per well is the desired output. The contribution of this paper is twofold: It expands on the sequence-to-sequence approach by capturing additional varying inputs, namely well controls and completions, and it presents a thorough experimental analysis and validation on a publicly available synthetic reservoir model (SPE9) as well as a real large-scale reservoir model. Methods and Procedures Reservoir Models. SPE9 is a standard benchmark to validate and compare simulations of the black-oil model. The reservoir is described by a 24×25×15 grid, having a 10° dipping angle in the x direction and a heterogeneous geostatistically based permeability field. The grid has a uniform size of 300 ft in the x and y directions and is nonuniform along the z direction. The porosity values for each layer are constant and vary across layers. In this work, the original SPE9 benchmark has been modified to be suitable for field development plan (FDP) optimization. Different well-completion data and ranges have been used for the number of producer and injector wells. The areal well locations, the number of wells, and the well-drilling sequence are variables specified by a suitable FDP. A fixed well control has been used in all SPE9 simulations. In the original SPE9 benchmark, the field operating conditions led to free-gas formation and most of the wells switched from rate control to pressure control. The conditions that trigger the switch in well controls are provided as inputs to a reservoir model and are determined on the basis of operational logistics and geomechanical stability criteria. Neglecting such switches in well controls is disastrous in the real world. However, this is benign from the point of view of a numerical benchmark to test FDP optimization.

Genetic optimization method of ship strong frame based on sequential surrogate model

Objectives The optimization design of a ship strong frame structure under the requirements of common structural rules (CSR) is a complex and time-consuming problem, moreover, it has tremendous constraints so that the feasibility of a design scheme is hard to identify. When adopting the static surrogate assisted evolutionary algorithm to solve this problem, since the approach aims at global accuracy, the prediction of key area will be distorted in the case of small size samples. However, the active-learning surrogate-based approach can solve this bottleneck since it can improve the accuracy of key area sequentially by adding samples to refine the surrogate model purposely. Therefore, this method can obtain better optimization scheme and save computational burden compared with the former one. Methods Aiming at the problem, an optimization method for strong frame based on sequential surrogate assisted genetic algorithm is proposed. Firstly, the constraints on strong frame structure based on CSR are analyzed, and all 675 constraints are reduced to 2 positive constraints according to the type of constraints. Then surrogates for objective function and constraints functions are constructed. Next, feasibility principle based genetic algorithm is adopted to solve it. After optimized solution is obtained, its true response is calculated and surrogates will be updated. In addition, expected feasibility function criterion is applied to update constraints surrogates, the purpose of which is to refine the prediction accuracy at the constraints boundary. Iterate the above procedures for several times, the optimized global feasible solution will be obtained finally. Results It is found that the proposed method is able to get better solution than static surrogate based algorithm with less computation resource and the weight of design area is reduced by 15.55% finally. Conclusions Proposed sequential surrogate based algorithm is superior to static surrogate based algorithm and has good application value in the optimization of ship structure under complex constraints.

Accelerating Gaussian Process surrogate modeling using Compositional Kernel Learning and multi-stage sampling framework

Surrogate modeling is becoming a popular tool to approximate computationally-expensive simulations for complex engineering problems. In practice, there are still difficulties in surrogate modeling as follows: (1) efficient learning for functional relationship of simulation models and (2) diagnostics for the surrogate model. In order to address these difficulties simultaneously, this paper proposes a new sequential surrogate modeling by integrating a Compositional Kernel Learning (CKL) method for Gaussian process into a sequential sampling strategy termed the Progressive Latin Hypercube Sampling (PLHS). The CKL enables efficient learning capability for complex response surfaces based on richly structured kernels, while the PLHS sequentially generates nested samples by maintaining desired properties for distribution. Furthermore, this sequential sampling framework allows users to monitor the diagnostics of the surrogate model and assess the stopping criteria for further sampling. In order to demonstrate useful features of the proposed method, nine test functions were assembled for numerical experiments to cover different types of problems (i.e., scale and complexity). The proposed method was evaluated with a set of surrogate modeling techniques and sampling methods in terms of performance, diagnostics and computational cost. The results show that (1) the proposed method can learn various response surfaces with fewer training samples than other methods; and (2) the proposed method only provides a reliable diagnostic measure for global accuracy over different types of problems.

A reliability-based optimization method using sequential surrogate model and Monte Carlo simulation

This paper presents a sequential surrogate model method for reliability-based optimization (SSRBO), which aims to reduce the number of the expensive black-box function calls in reliability-based optimization. The proposed method consists of three key steps. First, the initial samples are selected to construct radial basis function surrogate models for the objective and constraint functions, respectively. Second, by solving a series of special optimization problems in terms of the surrogate models, local samples are identified and added in the vicinity of the current optimal point to refine the surrogate models. Third, by solving the optimization problem with the shifted constraints, the current optimal point is obtained. Then, at the current optimal point, the Monte Carlo simulation based on the surrogate models is carried out to obtain the cumulative distribution functions (CDFs) of the constraints. The CDFs and target reliabilities are used to update the offsets of the constraints for the next iteration. Therefore, the original problem is decomposed to serial cheap surrogate-based deterministic problems and Monte Carlo simulations. Several examples are adopted to verify SSRBO. The results show that the number of the expensive black-box function calls is reduced exponentially without losing of precision compared to the alternative methods, which illustrates the efficiency and accuracy of the proposed method.

The Multiple-Update-Infill Sampling Method Using Minimum Energy Design for Sequential Surrogate Modeling

Computer experiments are widely used to evaluate the performance and reliability of engineering systems with the lowest possible time and cost. Sometimes, a high-fidelity model is required to ensure predictive accuracy; this becomes computationally intensive when many computational analyses are required (for example, inverse analysis or uncertainty analysis). In this context, a surrogate model can play a valuable role in addressing computational issues. Surrogate models are fast approximations of high-fidelity models. One efficient way for surrogate modeling is the sequential sampling (SS) method. The SS method sequentially adds samples to refine the surrogate model. This paper proposes a multiple-update-infill sampling method using a minimum energy design to improve the global quality of the surrogate model. The minimum energy design was recently developed for global optimization to find multiple optima. The proposed method was evaluated with other multiple-update-infill sampling methods in terms of convergence, accuracy, sampling efficiency, and computational cost.

Self-adaptive sampling for sequential surrogate modeling of time-consuming finite element analysis

This study presents a new approach of surrogate modeling for time-consuming finite element analysis. A surrogate model is widely used to reduce the computational cost under an iterative computational analysis. Although a variety of the methods have been widely investigated, there are still difficulties in surrogate modeling from a practical point of view: (1) How to derive optimal design of experiments (i.e., the number of training samples and their locations); and (2) diagnostics of the surrogate model. To overcome these difficulties, we propose a sequential surrogate modeling based on Gaussian process model (GPM) with self-adaptive sampling. The proposed approach not only enables further sampling to make GPM more accurate, but also evaluates the model adequacy within a sequential framework. The applicability of the proposed approach is first demonstrated by using mathematical test functions. Then, it is applied as a substitute of the iterative finite element analysis to Monte Carlo simulation for a response uncertainty analysis under correlated input uncertainties. In all numerical studies, it is successful to build GPM automatically with the minimal user intervention. The proposed approach can be customized for the various response surfaces and help a less experienced user save his/her efforts.

Sequential surrogate modeling for efficient finite element model updating

Despite the numerous studies concerning finite element model updating (FEMU), a challenging computational cost issue persists. Therefore, surrogate modeling has recently gained considerable attention in FEMU. Conventionally, surrogate models are constructed by identical samples for all outputs. It is very inefficient and subjective, if various response-surfaces exhibit even for identical parameters. Accordingly, we propose a sequential surrogate modeling for FEMU. It uses infill criteria to guide sampling for updating surrogate models automatically. The proposed method is successful to construct the different response-surfaces and apply FEMU. It is promising for constructing surrogate models with minimal user intervention and tremendous computational efficiency.

Comments on “Exposure assessment of mobile phone base station radiation in an outdoor environment using sequential surrogate modeling” by Aerts et al.

Comments on “Exposure assessment of mobile phone base station radiation in an outdoor environment using sequential surrogate modeling” by Aerts et al.

Response to comments by Beekhuizen et al. on “Exposure assessment of mobile phone base station radiation in an outdoor environment using sequential surrogate modeling”

Response to comments by Beekhuizen et al. on “Exposure assessment of mobile phone base station radiation in an outdoor environment using sequential surrogate modeling”

Exposure assessment of mobile phone base station radiation in an outdoor environment using sequential surrogate modeling

Human exposure to background radiofrequency electromagnetic fields (RF-EMF) has been increasing with the introduction of new technologies. There is a definite need for the quantification of RF-EMF exposure but a robust exposure assessment is not yet possible, mainly due to the lack of a fast and efficient measurement procedure. In this article, a new procedure is proposed for accurately mapping the exposure to base station radiation in an outdoor environment based on surrogate modeling and sequential design, an entirely new approach in the domain of dosimetry for human RF exposure. We tested our procedure in an urban area of about 0.04 km(2) for Global System for Mobile Communications (GSM) technology at 900 MHz (GSM900) using a personal exposimeter. Fifty measurement locations were sufficient to obtain a coarse street exposure map, locating regions of high and low exposure; 70 measurement locations were sufficient to characterize the electric field distribution in the area and build an accurate predictive interpolation model. Hence, accurate GSM900 downlink outdoor exposure maps (for use in, e.g., governmental risk communication and epidemiological studies) are developed by combining the proven efficiency of sequential design with the speed of exposimeter measurements and their ease of handling.

A robust optimization using the statistics based on kriging metamodel

Robust design technology has been applied to versatile engineering problems to ensure consistency in product performance. Since 1980s, the concept of robust design has been introduced to numerical optimization field, which is called the robust optimization. The robustness in the robust optimization is determined by a measure of insensitiveness with respect to the variation of a response. However, there are significant difficulties associated with the calculation of variations represented as its mean and variance. To overcome the current limitation, this research presents an implementation of the approximate statistical moment method based on kriging metamodel. Two sampling methods are simultaneously utilized to obtain the sequential surrogate model of a response. The statistics such as mean and variance are obtained based on the reliable kriging model and the second-order statistical approximation method. Then, the simulated annealing algorithm of global optimization methods is adopted to find the global robust optimum. The mathematical problem and the two-bar design problem are investigated to show the validity of the proposed method.