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The purpose of this paper is to propose physically based varying fidelity surrogates to be used in structural design optimization of space trusses. The main aim is to demonstrate its efficiency in reducing the number of high fidelity (HF) runs in the optimization process.

In this work, surrogate models are built for space truss structures. This study uses functional as well as physical surrogates. In the latter, a grid analogy of the space truss is used thereby reducing drastically the analysis cost. Global and local approaches are considered. The latter will require a globalization scheme (sequential approximate optimization (SAO)) to ensure convergence.

Physically based surrogates were proposed. Classical techniques, namely Taylor series and kriging, are also implemented for comparison purposes. A parameter study in kriging is necessary to select the best kriging model to be used as surrogate. A test case was considered for optimization and several surrogates were built. The CPU time is reduced when compared with the HF solution, for all surrogate‐based optimization performed. The best result was achieved combining the proposed physical model with additive corrections in a SAO strategy in which C1 continuity was imposed at each trust region center. Some guidance for other engineering applications was given.

This is the first time that physical‐based surrogates for optimum design of space truss systems are used in the SAO framework. Physical surrogates typically exhibit better generalization properties than other surrogates forms, produce faster solutions, and do not suffer from dimensionality curse when used in approximate optimization strategies.

Kriging model has been widely adopted to reduce the high computational costs of simulations in Reliability-based design optimization (RBDO). To construct the Kriging model accurately and efficiently in the region of significance, a local sampling method with variable radius (LSVR) is proposed. The paper aims to discuss these issues.

In LSVR, the sequential sampling points are mainly selected within the local region around the current design point. The size of the local region is adaptively defined according to the target reliability and the nonlinearity of the probabilistic constraint. Every probabilistic constraint has its own local region instead of all constraints sharing one local region. In the local sampling region, the points located on the constraint boundary and the points with high uncertainty are considered simultaneously.

The computational capability of the proposed method is demonstrated using two mathematical problems, a reducer design and a box girder design of a super heavy machine tool. The comparison results show that the proposed method is very efficient and accurate.

The main contribution of this paper lies in: a new local sampling region computational criterion is proposed for Kriging. The originality of this paper is using expected feasible function (EFF) criterion and the shortest distance to the existing sample points instead of the other types of sequential sampling criterion to deal with the low efficiency problem.

Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.

In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.

Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.

The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.

A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

The purpose of this paper is to develop an application software interpolation system based on Taylor Kriging (TK) metamodeling, and apply the developed software system to addressing some engineering interpolation problems.

TK is a novel Kriging model where Taylor expansion is used to identify the base functions of drift function in Kriging. The paper explains the methodology of TK, illustrates the development of software, and reports the results of two case studies by comparing TK with several regression methods.

TK has the advantage of interpolation accuracy, and the developed Kriging software system is useful and can be conveniently manipulated by users.

The developed software system can benefit practical engineering applications that need accurate interpolations under limited observations.

This paper develops an application software interpolation system based on a novel TK metamodel, and the practical engineering applications show that it can provide accurate interpolations under limited observations.

This paper aims to investigates several design strategies to solve multi-objective aerodynamic optimization problems using high-fidelity simulations. The purpose is to find strategies which reduce the overall optimization time while still maintaining accuracy at the high-fidelity level.

Design strategies are proposed that use an algorithmic framework composed of search space reduction, fast surrogate models constructed using a combination of physics-based surrogates and kriging and global refinement of the Pareto front with co-kriging. The strategies either search the full or reduced design space with a low-fidelity model or a physics-based surrogate.

Numerical investigations of airfoil shapes in two-dimensional transonic flow are used to characterize and compare the strategies. The results show that searching a reduced design space produces the same Pareto front as when searching the full space. Moreover, as the reduced space is two orders of magnitude smaller (volume-wise), the number of required samples to setup the surrogates can be reduced by an order of magnitude. Consequently, the computational time is reduced from over three days to less than half a day.

The proposed design strategies are novel and holistic. The strategies render multi-objective design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search spaces computationally tractable.

This paper aims to investigate three low-evaluation-budget optimization techniques: output space mapping (OSM), manifold mapping (MM) and Kriging-OSM. Kriging-OSM is an original approach having high-order mapping.

The electromagnetic device to be optimally sized is a five-phase linear induction motor, represented through two levels of modeling: coarse (Kriging model) and fine.The optimization comparison of the three techniques on the five-phase linear induction motor is discussed.

The optimization results show that the OSM takes more time and iteration to converge the optimal solution compared to MM and Kriging-OSM. This is mainly because of the poor quality of the initial Kriging model. In the case of a high-quality coarse model, the OSM technique would show its domination over the other two techniques. In the case of poor quality of coarse model, MM and Kriging-OSM techniques are more efficient to converge to the accurate optimum.

Kriging-OSM is an original approach having high-order mapping. An advantage of this new technique consists in its capability of providing a sufficiently accurate model for each objective and constraint function and makes the coarse model converge toward the fine model more effectively.

This study aims to propose a computationally efficient framework for multi-objective optimization (MO) of antennas involving nested kriging modeling technology. The technique is demonstrated through a two-objective optimization of a planar Yagi antenna and three-objective design of a compact wideband antenna.

The keystone of the proposed approach is the usage of recently introduced nested kriging modeling for identifying the design space region containing the Pareto front and constructing fast surrogate model for the MO algorithm. Surrogate-assisted design refinement is applied to improve the accuracy of Pareto set determination. Consequently, the Pareto set is obtained cost-efficiently, even though the optimization process uses solely high-fidelity electromagnetic (EM) analysis.

The optimization cost is dramatically reduced for the proposed framework as compared to other state-of-the-art frameworks. The initial Pareto set is identified more precisely (its span is wider and of better quality), which is a result of a considerably smaller domain of the nested kriging model and better predictive power of the surrogate.

The proposed technique can be generalized to accommodate low- and high-fidelity EM simulations in a straightforward manner. The future work will incorporate variable-fidelity simulations to further reduce the cost of the training data acquisition.

The fast MO optimization procedure with the use of the nested kriging modeling technology for approximation of the Pareto set has been proposed and its superiority over state-of-the-art surrogate-assisted procedures has been proved. To the best of the authors’ knowledge, this approach to multi-objective antenna optimization is novel and enables obtaining optimal designs cost-effectively even in relatively high-dimensional spaces (considering typical antenna design setups) within wide parameter ranges.

Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models.

In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels.

To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent.

The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.

This paper aims to introduce a method based on the optimizer of the particle swarm optimization (PSO) algorithm to improve the efficiency of a Kriging surrogate model.

PSO was first used to identify the best group of trend functions and to optimize the correlation parameter thereafter.

The Kriging surrogate model was used to resolve the fuselage optimization of an unmanned helicopter.

The optimization results indicated that an appropriate PSO scheme can improve the efficiency of the Kriging surrogate model.

Both the STANDARD PSO and the original PSO algorithms were chosen to show the effect of PSO on a Kriging surrogate model.

The purpose of study is to overcome the error estimation of standard deviation derived from Expected improvement (EI) criterion. Compared with other popular methods, a quantitative model assessment and analysis tool, termed high-dimensional model representation (HDMR), is suggested to be integrated with an EI-assisted sampling strategy.

To predict standard deviation directly, Kriging is imported. Furthermore, to compensate for the underestimation of error in the Kriging predictor, a Pareto frontier (PF)-EI (PFEI) criterion is also suggested. Compared with other surrogate-assisted optimization methods, the distinctive characteristic of HDMR is to disclose the correlations among component functions. If only low correlation terms are considered, the number of function evaluations for HDMR grows only polynomially with the number of input variables and correlative terms.

To validate the suggested method, various nonlinear and high-dimensional mathematical functions are tested. The results show the suggested method is potential for solving complicated real engineering problems.

In this study, the authors hope to integrate superiorities of PFEI and HDMR to improve optimization performance.