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Metamodels are widely used to replace simulation models in engineering design optimization to reduce the computational cost. The purpose of this paper is to develop a novel sequential sampling strategy (weighted accumulative error sampling, WAES) to obtain accurate metamodels and apply it to improve the quality of global optimization.

A sequential single objective formulation is constructed to adaptively select new sample points. In this formulation, the optimization objective is to select a sample point with the maximum weighted accumulative predicted error obtained by analyzing data from previous iterations, and a space-filling criterion is introduced and treated as a constraint to avoid generating clustered sample points. Based on the proposed sequential sampling strategy, a two-step global optimization approach is developed.

The proposed WAES approach and the global optimization approach are tested in several cases. A comparison has been made between the proposed approach and other existing approaches. Results illustrate that WAES approach performs the best in improving metamodel accuracy and the two-step global optimization approach has a great ability to avoid local optimum.

The proposed WAES approach overcomes the shortcomings of some existing approaches. Besides, the two-step global optimization approach can be used for improving the optimization results.

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 efficiently use as few sample points as possible to get a sufficiently explored design space and an accurate optimum for adaptive metamodel-based design optimization (AMBDO).

A parameterized lower confidence bounding (PLCB) scheme is proposed in which a cooling strategy is introduced to guarantee the balance between exploitation and exploration by varying weights of the predicting error and optimum of a metamodel. The proposed scheme is investigated by a set of test functions and a structural optimization problem, in which PLCB with four kinds of cooling control functions are studied. Moreover, other infill criteria (such as expected improvement and its extension versions) are taken into comparison.

Results show that the proposed PLCB (especially PLCB with the first cooling control function) based AMBDO method can find the optimum with fewer evaluations and maintain good accuracy, which means the proposed PLCB contributes to the excellent efficiency and accuracy in finding global optimal solutions.

The parameterized version of the lower confidence bound metric is proposed for AMBDO, typically used in the context of adaptive sampling in efficient global optimization.

Engineering design optimization involving computational simulations is usually a time-consuming, even computationally prohibitive process. To relieve the computational burden, the adaptive metamodel-based design optimization (AMBDO) approaches have been widely used. This paper aims to develop an AMBDO approach, a lower confidence bounding approach based on the coefficient of variation (CV-LCB) approach, to balance the exploration and exploitation objectively for obtaining a global optimum under limited computational budget.

In the proposed CV-LCB approach, the coefficient of variation (CV) of predicted values is introduced to indicate the degree of dispersion of objective function values, while the CV of predicting errors is introduced to represent the accuracy of the established metamodel. Then, a weighted formula, which takes the degree of dispersion and the prediction accuracy into consideration, is defined based on the already-acquired CV information to adaptively update the metamodel during the optimization process.

Ten numerical examples with different degrees of complexity and an AIAA aerodynamic design optimization problem are used to demonstrate the effectiveness of the proposed CV-LCB approach. The comparisons between the proposed approach and four existing approaches regarding the computational efficiency and robustness are made. Results illustrate the merits of the proposed CV-LCB approach in computational efficiency and robustness.

The proposed approach exhibits high efficiency and robustness in engineering design optimization involving computational simulations.

CV-LCB approach can balance the exploration and exploitation objectively.

The purpose of this paper is to present a modified bi-level integrated system collaborative optimization (BLISCO) to avoid the non-separability of the original BLISCO. Besides, to mitigate the computational burden caused by expensive simulation codes and employ both efficiently simplified and expensively detailed information in multidisciplinary design optimization (MDO), an effective framework combining variable fidelity metamodels (VFM) and modified BLISCO (MBLISCO) (VFM-MBLISCO) is proposed.

The concept of the quasi-separable MDO problems is introduced to limit range of applicability about the BLISCO method and then based on the quasi-separable MDO form, the modification of BLISCO method without any derivatives is presented to solve the problems of BLISCO. Besides, an effective framework combining VFM-MBLISCO is presented.

One mathematical problem conforms to the quasi-separable MDO form is tested and the overall results illustrate the feasibility and robustness of the MBLISCO. The design of a Small Waterplane Area Twin Hull catamaran demonstrates that the proposed VFM-MBLISCO framework is a feasible and efficient design methodology in support of design of engineering products.

The proposed approach exhibits great capability for MDO problems with tremendous computational costs.

A MBLISCO is proposed which can avoid the non-separability of the original BLISCO and an effective framework combining VFM-MBLISCO is presented to efficiently integrate the different fidelities information in MDO.

The purpose of this paper is to introduce a new method to carry out the design optimization of the tool head system in the heavy‐duty machine tool where closed hydrostatic guideways with multiple pockets are employed.

A more accurate method of pressure calculation for closed hydrostatic guideways is introduced. Then, a multidisciplinary design optimization (MDO) model is formulated for design of a tool head system, which minimizes the highest pocket pressure under some constraints from machining accuracy and vibration resistance requirements as well as constraints from ballscrew design specifications. Finally, a metamodel‐based design space alternation (DSA) strategy is proposed to solve the optimization problem.

The results show that the maximum pocket pressure in a tool head system can be reduced over 47 percent with a proper design while all the constraints are satisfied. As a consequence, the tool head system can safely work under the maximum output pressure of oil supply system.

This paper introduces a more accurate method of pressure calculation for multi‐pocket closed hydrostatic guideways, develops a metamodel‐based MDO model for the tool head system, and proposes a DSA strategy to solve the MDO problem.

Extreme support vector regression (ESVR) has been widely used in the design, analysis and optimization of engineering systems of its fast training speed and good computational ability. However, the ESVR model is only able to utilize one-fidelity information of engineering system. To solve this issue, this paper extends extreme support vector regression (ESVR) to a multi-fidelity surrogate (MFS) model which can make use of a few expensive but higher-fidelity (HF) samples and a lot of inaccurate but cheap low-fidelity (LF) samples, named ESVR-MFS.

In the ESVR-MFS model, a kernel matrix is designed to evaluate the relationship between the HF and LF samples. The root mean square error of HF samples is used as the training error metric, and the optimal hyper-parameters of the kernel matrix are obtained through a heuristic algorithm.

A number of numerical problems and three engineering problems are used to compare the ESVR-MFS model with the single-fidelity ESVR model and two benchmark MFS models. The results show that the ESVR-MFS model exhibits competitive performance in both numerical cases and practical cases tested in this work.

The proposed approach exhibits great capability for practical multi-fidelity engineering design problems.

A MFS model is proposed based on ESVR, which can make full use of the advantages of both HF data and LF data to achieve optimal results at same or lower cost.

In the dynamical analysis of engineering systems, running a detailed high‐resolution finite element model can be expensive even for obtaining the dynamic response at few frequency points. To address this problem, this paper aims to investigate the possibility of representing the output of an expensive computer code as a Gaussian stochastic process.

The Gaussian process emulator method is discussed and then applied to both simulated and experimentally measured data from the frequency response of a cantilever plate excited by a harmonic force. The dynamic response over a frequency range is approximated using only a small number of response values, obtained both by running a finite element model at carefully selected frequency points and from experimental measurements. The results are then validated applying some adequacy diagnostics.

It is shown that the Gaussian process emulator method can be an effective predictive tool for medium and high‐frequency vibration problems, whenever the data are expensive to obtain, either from a computer‐intensive code or a resource‐consuming experiment.

Although Gaussian process emulators have been used in other disciplines, there is no knowledge of it having been implemented for structural dynamic analyses and it has good potential for this area of engineering.

This paper aims to propose hybrid global optimization based on multiple metamodels for improving the efficiency of global optimization.

The method has fully utilized the information provided by different metamodels in the optimization process. It not only imparts the expected improvement criterion of kriging into other metamodels but also intelligently selects appropriate metamodeling techniques to guide the search direction, thus making the search process very efficient. Besides, the corresponding local search strategies are also put forward to further improve the optimizing efficiency.

To validate the method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the global optimization efficiency of the proposed method is higher than that of the other methods for most situations.

The proposed method sufficiently utilizes multiple metamodels in the optimizing process. Thus, good optimizing results are obtained, showing great applicability in engineering design optimization problems which involve costly simulations.

Uncertainty is inevitable in real-world engineering optimization. With an outer-inner optimization structure, most previous robust optimization (RO) approaches under interval uncertainty can become computationally intractable because the inner level must perform robust evaluation for each design alternative delivered from the outer level. This paper aims to propose an on-line Kriging metamodel-assisted variable adjustment robust optimization (OLK-VARO) to ease the computational burden of previous VARO approach.

In OLK-VARO, Kriging metamodels are constructed for replacing robust evaluations of the design alternative delivered from the outer level, reducing the nested optimization structure of previous VARO approach into a single loop optimization structure. An on-line updating mechanism is introduced in OLK-VARO to exploit the obtained data from previous iterations.

One nonlinear numerical example and two engineering cases have been used to demonstrate the applicability and efficiency of the proposed OLK-VARO approach. Results illustrate that OLK-VARO is able to obtain comparable robust optimums as to that obtained by previous VARO, while at the same time significantly reducing computational cost.

The proposed approach exhibits great capability for practical engineering design optimization problems under interval uncertainty.

The main contribution of this paper lies in the following: an OLK-VARO approach under interval uncertainty is proposed, which can significantly ease the computational burden of previous VARO approach.