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Surrogate Modeling and Related Methods in Science and Engineering

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (28 February 2021) | Viewed by 13609

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Special Issue Editor

Dr. Giovanni Angiulli

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Department of Information Engineering, Infrastructure and Sustainable Energy, University Mediterranea, Via Graziella, loc. Feo di Vito, 89122 Reggio Calabria, Italy
Interests: computational electromagnetics; electromagnetic theory; metamaterials; microwave engineering; surrogate modeling; soft computing; NDT/E
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Special Issue Information

Dear Colleagues,

It is well known that, in the present day, there is an ever-growing demand to model real-world phenomena with an increasing level of accuracy and detail. Multiscale systems, multiphysics processes, and the design of advanced engineering systems are representative examples of this trend. Despite the fast increase of both the performances provided by modern CPUs and related solutions in terms of computer architectures, the reduction of the computational time required by the resolution of the mathematical models involved in the description of complex phenomena sometimes turns out to be insufficient for scientific or engineering purposes. As a result, surrogate modeling (SM) has emerged as a fundamental tool in pure and applied research, through the development of computationally tractable and reasonably accurate models that are able to replace the original time-consuming physical models. Surrogate models are currently employed for design automation, parametric studies, design space exploration, optimization, and sensitivity analysis in different fields of applied physics and engineering. The purpose of this Special Issue is to gather a collection of articles reflecting the latest developments in surrogate modeling and related fields of applications.

Prof. Dr. Giovanni Angiulli
Guest Editor

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Keywords

Design of experiments
Data fit surrogate models
Reduced-order surrogate models
Hybrid surrogate models
Surrogate-based optimization
Multifidelity surrogate models
Forward and inverse surrogate modeling.

Published Papers (5 papers)

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Research

25 pages, 30227 KiB

Open AccessArticle

High-Precision Kriging Modeling Method Based on Hybrid Sampling Criteria

by Junjun Shi, Jingfang Shen and Yaohui Li

Mathematics 2021, 9(5), 536; https://0-doi-org.brum.beds.ac.uk/10.3390/math9050536 - 04 Mar 2021

Viewed by 1708

Abstract

Finding new valuable sampling points and making these points better distributed in the design space is the key to determining the approximate effect of Kriging. To this end, a high-precision Kriging modeling method based on hybrid sampling criteria (HKM-HS) is proposed to solve this problem. In the HKM-HS method, two infilling sampling strategies based on MSE (Mean Square Error) are optimized to obtain new candidate points. By maximizing MSE (MMSE) of Kriging model, it can generate the first candidate point that is likely to appear in a sparse area. To avoid the ill-conditioned correlation matrix caused by the too close distance between any two sampling points, the MC (MSE and Correlation function) criterion formed by combining the MSE and the correlation function through multiplication and division is minimized to generate the second candidate point. Furthermore, a new screening method is used to select the final expensive evaluation point from the two candidate points. Finally, the test results of sixteen benchmark functions and a house heating case show that the HKM-HS method can effectively enhance the modeling accuracy and stability of Kriging in contrast with other approximate modeling methods. Full article

(This article belongs to the Special Issue Surrogate Modeling and Related Methods in Science and Engineering)

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15 pages, 2664 KiB

Open AccessArticle

Integration of Second-Order Sensitivity Method and CoKriging Surrogate Model

by Zebin Zhang, Martin Buisson, Pascal Ferrand and Manuel Henner

Mathematics 2021, 9(4), 401; https://0-doi-org.brum.beds.ac.uk/10.3390/math9040401 - 18 Feb 2021

Cited by 2 | Viewed by 5200

Abstract

The global exploring feature of the surrogate model makes it a useful intermedia for design optimization. The accuracy of the surrogate model is closely related with the efficiency of optima-search. The cokriging approach described in present studies can significantly improve the surrogate model accuracy and cut down the turnaround time spent on the modeling process. Compared to the universal Kriging method, the cokriging method interpolates not only the sampling data, but also on their associated derivatives. However, the derivatives, especially high order ones, are too computationally costly to be easily affordable, forming a bottleneck for the application of derivative enhanced methods. Based on the sensitivity analysis of Navier–Stokes equations, current study introduces a low-cost method to compute the high-order derivatives, making high order derivatives enhanced cokriging modeling practically achievable. For a methodological illustration, second-order derivatives of regression model and correlation models are proposed. A second-order derivative enhanced cokriging model-based optimization tool was developed and tested on the optimal design of an automotive engine cooling fan. This approach improves the modern optimal design efficiency and proposes a novel direction for the large scale optimization problems. Full article

(This article belongs to the Special Issue Surrogate Modeling and Related Methods in Science and Engineering)

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14 pages, 1921 KiB

Open AccessArticle

Hybrid Assembly Path Planning for Complex Products by Reusing a Priori Data

by Guodong Yi, Chuanyuan Zhou, Yanpeng Cao and Hangjian Hu

Mathematics 2021, 9(4), 395; https://0-doi-org.brum.beds.ac.uk/10.3390/math9040395 - 17 Feb 2021

Cited by 3 | Viewed by 1688

Abstract

Assembly path planning (APP) for complex products is challenging due to the large number of parts and intricate coupling requirements. A hybrid assembly path planning method is proposed herein that reuses a priori paths to improve the efficiency and success ratio. The assembly path is initially segmented to improve its reusability. Subsequently, the planned assembly paths are employed as a priori paths to establish an a priori tree, which is expanded according to the bounding sphere of the part to create the a priori space for path searching. Three rapidly exploring random tree (RRT)-based algorithms are studied for path planning based on a priori path reuse. The RRT* algorithm establishes the new path exploration tree in the early planning stage when there is no a priori path to reuse. The static RRT* (S-RRT*) and dynamic RRT* (D-RRT*) algorithms form the connection between the exploration tree and the a priori tree with a pair of connection points after the extension of the exploration tree to a priori space. The difference between the two algorithms is that the S-RRT* algorithm directly reuses an a priori path and obtains a new path through static backtracking from the endpoint to the starting point. However, the D-RRT* algorithm further extends the exploration tree via the dynamic window approach to avoid collision between an a priori path and obstacles. The algorithm subsequently obtains a new path through dynamic and non-continuous backtracking from the endpoint to the starting point. A hybrid process combining the RRT*, S-RRT*, and D-RRT* algorithms is designed to plan the assembly path for complex products in several cases. The performances of these algorithms are compared, and simulations indicate that the S-RRT* and D-RRT* algorithms are significantly superior to the RRT* algorithm in terms of the efficiency and success ratio of APP. Therefore, hybrid path planning combining the three algorithms is helpful to improving the assembly path planning of complex products. Full article

(This article belongs to the Special Issue Surrogate Modeling and Related Methods in Science and Engineering)

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20 pages, 6572 KiB

Open AccessArticle

A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions

by Yaohui Li, Jingfang Shen, Ziliang Cai, Yizhong Wu and Shuting Wang

Mathematics 2021, 9(2), 149; https://0-doi-org.brum.beds.ac.uk/10.3390/math9020149 - 11 Jan 2021

Cited by 8 | Viewed by 1943

Abstract

The kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the number of expensive evaluations has been a wide concern. For this reason, a kriging-assisted multi-objective constrained global optimization (KMCGO) method has been proposed. The sample data obtained from the expensive function evaluation is first used to construct or update the kriging model in each cycle. Then, kriging-based estimated target, RMSE (root mean square error), and feasibility probability are used to form three objectives, which are optimized to generate the Pareto frontier set through multi-objective optimization. Finally, the sample data from the Pareto frontier set is further screened to obtain more promising and valuable sampling points. The test results of five benchmark functions, four design problems, and a fuel economy simulation optimization prove the effectiveness of the proposed algorithm. Full article

(This article belongs to the Special Issue Surrogate Modeling and Related Methods in Science and Engineering)

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13 pages, 1674 KiB

Open AccessArticle

An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization

by Bolin Liu and Liyang Xie

Mathematics 2020, 8(2), 209; https://0-doi-org.brum.beds.ac.uk/10.3390/math8020209 - 07 Feb 2020

Cited by 6 | Viewed by 2054

Abstract

The Kriging-based reliability method with a sequential design of experiments (DoE) has been developed in recent years for implicit limit state functions. Such methods include the efficient global reliability analysis, the active learning reliability method combining Kriging and MCS Simulations. In this research, a novel local approximation method based on the most probable failure point (MPFP) is proposed to improve such methods. In this method, the MPFP calculated in the last iteration is the center of the next sampling region. The size of the local region depends on the reliability index obtained by the First Order Reliability Method (FORM) and the deviation distance of the standard deviation. The proposed algorithm, which approximates the limit state function accurately near MPFP rather than in the whole design space, can avoid selecting samples in regions that have negligible effects on the reliability analysis results. In addition, a multi-point enrichment technique is also introduced to select multiple sample points in each iteration. After the high-quality approximation of limit state function is obtained, the failure probability is calculated by the Monte Carlo method. Four numerical examples are used to validate the accuracy and efficiency of the proposed method. Results show that the proposed method is very effective for an accurate evaluation of the failure probability. Full article

(This article belongs to the Special Issue Surrogate Modeling and Related Methods in Science and Engineering)

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