Kinds Of Surrogate Models Research Articles

Framework and application of ship berthing methods optimization in high-pile wharf based on surrogate models

Reasonable ship berthing methods are crucial to the safe operation of docks. Currently, the operational recommendations for ship berthing given in national codes are rather general and do not provide requirements for specific docks and ship berthing, which cannot meet the actual needs. In this study, a novel framework for the optimization of ship berthing methods (OSBM) is proposed, which uses the "berthing characteristics-dock response" dataset collected in the field or obtained from finite element analysis, constructs four kinds of surrogate models with low sample requirements and performs the optimal selection, and then quickly inverts the feasible domains of berthing based on the surrogate models. Finally, the reliability and practicability of the proposed method are verified with an example of a high-pile wharf in Jiangsu Province, China. The results show that the surrogate model can replace the finite element model for berthing response analysis, which greatly improves the computational efficiency; it can quickly investigate and judge for different ship types and specific docks and give more accurate and reasonable regions of berthing.

Combining Reduced-Order Model With Data-Driven Model for Parameter Estimation of Lithium-Ion Battery

The parameters of a lithium-ion battery are important to construct an effective battery management system. Parameter estimation assisted by the pseudo-two-dimensional (P2D) model is much more cost-effective than direct measurement methods. However, this is a nontrivial task, because the simulation of the P2D model is time-consuming. Alternatively, surrogate models such as reduced-order/data-driven models are often used to accelerate the parameter estimation process. Each category of surrogate models has its own strengths and weaknesses. Traditionally, reduced-order models run faster than data-driven models, while data-driven models are more accurate than reduced-order models. To leverage the complementary advantages of these two kinds of surrogate models, we make an interesting attempt to combine them compactly, thus proposing a two-phase surrogate model-assisted parameter estimation algorithm (TPSMA-PEAL). In the first phase, a fast reduced-order model is designed for parameter prescreening. In the second phase, a high-fidelity data-driven model is developed for fine estimation. In TPSMA-PEAL, except the time-consuming simulation, the other two challenges (i.e., the overfitting problem and the low observability of some parameters) are also considered from the perspective of optimization. Note that TPSMA-PEAL takes advantage of differential evolution and parameter sensitivity analysis to address them. Simulations and experiments verify that TPSMA-PEAL is efficient and accurate.

Uncertainty quantification of dynamical systems by a POD–Kriging surrogate model

Uncertainty quantification (UQ) of dynamical systems with a surrogate model is difficult as the surrogate model parameters often need to be computed at each time step. For that reason, a different kind of surrogate model is presented in this article by representing the stochastic response quantity using lower number of bases. Proper orthogonal decomposition (POD) is used to project the response quantity with low number of POD bases and the uncertainty is propagated using the Kriging model. The combined POD–Kriging model is used for UQ of four dynamical systems and all the results are compared with the Monte Carlo simulation results. The first three problems are long time integration problems and the time-dependent statistical moments are predicted well by the POD–Kriging model using low number of model evaluations. For the last example (a building subjected to Gaussian white noise base acceleration), the prediction accuracy of the POD–Kriging model is also high as compared to a similar surrogate model.

Surrogate-assisted inversion for large-scale history matching: Comparative study between projection-based reduced-order modeling and deep neural network

History matching can play a key role in improving geological characterization and reducing the uncertainty of reservoir model predictions. Application of reservoir history matching is restricted by the huge computational cost by amongst others the many runs of the full model. Surrogate models with a reduced complexity are therefore used to reduce the computational demands. This paper presents an efficient surrogate-assisted deterministic inversion framework to primarily explore the possibility of applying deep neural network (DNN) surrogate to approximate the gradient of large-scale history matching by using auto-differentiation (AD). In combination with the deep neural network model, the AD enables us to evaluate the gradients efficiently in a parallel manner. Furthermore, the benefits of using stochastic gradient optimizers in the deep learning practice, instead of full gradient optimizers in conventional deterministic inversions, is investigated as well. Numerical experiments are conducted on a 3D benchmark reservoir model in the context of a water-flooding production scenario. The quantity of interest, e.g., dynamic saturation for an ensemble of test models, can be accurately predicted. The proposed surrogate-assisted inversion with stochastic gradient optimizer obtains a very quick convergence rate against the model and data noise for the high-dimensional history matching problem with a large number of data and parameters. In addition, we also conduct several comparisons and evaluations with our previously proposed projection-based subdomain POD-TPWL approach in terms of computational efficiency and accuracy. The subdomain POD-TPWL constructs a local surrogate model, which is repeatedly reconstructed a number of times for maintaining a satisfactory accuracy, while DNN constructs a global surrogate model based on the entire training data and generally does not require additional reconstructions. The subdomain POD-TPWL is very sensitive to how the domain is decomposed, increasing the training samples does not infinitely improve the history matching results by a fixed decomposition. Overall, these two kinds of surrogate models have demonstrated great potential in solving large-scale history matching problem. The DNN surrogate is particularly useful to generate multiple posteriors for model uncertainty quantification. • Deep neural network is used to approximate the gradient of seismic history matching by using auto-differentiation (AD). • Deep-learning inversion with stochastic gradient optimizer demonstrates good convergence performance against both model and data noise. • This method demonstrates a significant reduction in computational cost while reasonable accuracy remains for seismic history matching.

Rapidly Tuning the PID Controller Based on the Regional Surrogate Model Technique in the UAV Formation.

The leader–follower structure is widely used in unmanned aerial vehicle formation. This paper adopts the proportional-integral-derivative (PID) and the linear quadratic regulator controllers to construct the leader–follower formation. Tuning the PID controllers is generally empirical; hence, various surrogate models have been introduced to identify more refined parameters with relatively lower cost. However, the construction of surrogate models faces the problem that the singular points may affect the accuracy, such that the global surrogate models may be invalid. Thus, to tune controllers quickly and accurately, the regional surrogate model technique (RSMT), based on analyzing the regional information entropy, is proposed. The proposed RSMT cooperates only with the successful samples to mitigate the effect of singular points along with a classifier screening failed samples. Implementing the RSMT with various kinds of surrogate models, this study evaluates the Pareto fronts of the original simulation model and the RSMT to compare their effectiveness. The results show that the RSMT can accurately reconstruct the simulation model. Compared with the global surrogate models, the RSMT reduces the run time of tuning PID controllers by one order of magnitude, and it improves the accuracy of surrogate models by dozens of orders of magnitude.

Universal Prediction Distribution for Surrogate Models

The use of surrogate models instead of computationally expensive simulation codes is very convenient in engineering. Roughly speaking, there are two kinds of surrogate models: the deterministic and the probabilistic ones. These last are generally based on Gaussian assumptions. The main advantage of probabilistic approach is that it provides a measure of uncertainty associated with the surrogate model in the whole space. This uncertainty is an efficient tool to construct strategies for various problems such as prediction enhancement, optimization or inversion. In this paper, we propose a universal method to define a measure of uncertainty suitable for any surrogate model either deterministic or probabilistic. It relies on Cross-Validation (CV) sub-models predictions. This empirical distribution may be computed in much more general frames than the Gaussian one. So that it is called the Universal Prediction distribution (UP distribution). It allows the definition of many sampling criteria. We give and study adaptive sampling techniques for global refinement and an extension of the so-called Efficient Global Optimization (EGO) algorithm. We also discuss the use of the UP distribution for inversion problems. The performances of these new algorithms are studied both on toys models and on an engineering design problem.

Strength Reliability Analysis of Turbine Blade Using Surrogate Models

There are many stochastic parameters that have an effect on the reliability of steam turbine blades performance in practical operation. In order to improve the reliability of blade design, it is necessary to take these stochastic parameters into account. In this study, a variable cross-section twisted blade is investigated and geometrical parameters, material parameters and load parameters are considered as random variables. A reliability analysis method as a combination of a Finite Element Method (FEM), a surrogate model and Monte Carlo Simulation (MCS), is applied to solve the blade reliability analysis. Based on the blade finite element parametrical model and the experimental design, two kinds of surrogate models, Polynomial Response Surface (PRS) and Artificial Neural Network (ANN), are applied to construct the approximation analytical expressions between the blade responses (including maximum stress and deflection) and random input variables, which act as a surrogate of finite element solver to drastically reduce the number of simulations required. Then the surrogate is used for most of the samples needed in the Monte Carlo method and the statistical parameters and cumulative distribution functions of the maximum stress and deflection are obtained by Monte Carlo simulation. Finally, the probabilistic sensitivities analysis, which combines the magnitude of the gradient and the width of the scatter range of the random input variables, is applied to evaluate how much the maximum stress and deflection of the blade are influenced by the random nature of input parameters.

Sequential design for computer experiments with a flexible Bayesian additive model

AbstractIn computer experiments, a mathematical model implemented on a computer is used to represent complex physical phenomena. These models, known as computer simulators, enable experimental study of a virtual representation of the complex phenomena. Simulators can be thought of as complex functions that take many inputs and provide an output. Often these simulators are themselves expensive to compute, and may be approximated by “surrogate models” such as statistical regression models. In this paper we consider a new kind of surrogate model, a Bayesian ensemble of trees (Chipman, George, & McCulloch, 2010), with the specific goal of learning enough about the simulator that a particular feature of the simulator can be estimated. We focus on identifying the simulator's global minimum. Utilizing the Bayesian version of the expected improvement criterion (Jones, Schonlau, & Welch, 1998), we show that this ensemble is particularly effective when the simulator is ill‐behaved, exhibiting nonstationarity or abrupt changes in the response. A number of illustrations of the approach are given, including a tidal power application. The Canadian Journal of Statistics 40: 663–678; 2012 © 2012 Statistical Society of Canada