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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.

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.

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.

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.

Metamodeling is an effective method to approximate the relations between input and output parameters when significant efforts of experiments and simulations are required to collect the data to build the relations. This paper aims to develop a new sequential sampling method for adaptive metamodeling by using the data with highly nonlinear relation between input and output parameters.

In this method, the Latin hypercube sampling method is used to sample the initial data, and kriging method is used to construct the metamodel. In this work, input parameter values for collecting the next output data to update the currently achieved metamodel are determined based on qualities of data in both the input and output parameter spaces. Uniformity is used to evaluate data in the input parameter space. Leave-one-out errors and sensitivities are considered to evaluate data in the output parameter space.

This new method has been compared with the existing methods to demonstrate its effectiveness in approximation. This new method has also been compared with the existing methods in solving global optimization problems. An engineering case is used at last to verify the method further.

This paper provides an effective sequential sampling method for adaptive metamodeling to approximate highly nonlinear relations between input and output parameters.

In writing this paper, the authors investigated the use of electromagnetic sensors in axle counter applications by means of train wheel detection. The purpose of this paper is to improve the detection capability of train wheel detectors, by installing them in the optimal orientation and position, using finite element modeling (FEM) in combination with metamodeling techniques. The authors compare three common metamodeling techniques for the special case of wheel detector orientation: response surface methodology; multivariate adaptive regression splines; and kriging.

After analyzing the effective parameters of a train wheel detector, an appropriate method for decreasing the system susceptibility to electromagnetic noises is presented.

The results were validated using a laboratory‐based system and also the results of field tests carried out on the Iranian railway network. The results of the study suggest that the FEM method and a metamodeling technique can reduce the computational efforts and processing time.

In this paper, combination of FEM and metamodeling approaches are used to optimize the railway axle counter coils orientation, which is more insusceptible to electromagnetic noise than initial arrangement used by some signallers.

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 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.

Large structures (e.g. plane, bridge, etc.) often include several hundreds of assembly points. Structural computations often use over-simplistic approximations for these points; among others, they do not take into account the thermo-mechanical history due to the assembling process. Running computations with each assembly point modelled completely would require too much time to achieve a simulation. There is thus a need to create equivalent elements for assembly points in order to: take into account the mechanical state of the assembly point in the design stage – while reducing the computational time cost at the same time. This paper aims to discuss these issues.

This paper introduces an innovative strategy based on a coupling procedure between a finite element tool for modelling the assembly process in order to access to the mechanical state of the assembly point and an optimisation algorithm, in order to identify the equivalent element parameters.

The strategy has proven to be successful. A connector model easier to use and much faster than the complete model, has been obtained. Results obtained with this element are in good agreement with experimental tests in the case of multipoint assemblies and with the simulation results of the complete numerical model. Finally the connector model appears to be easier to use and much faster than the complete model, more difficult to model properly.

The main innovative aspects of this strategy lie in the fact that the creation of this equivalent element is based on a complete numerical approach. The thermo-mechanical history due to the assembly process is considered – the element parameters are identified thanks to an evolution strategy based on the coupling between a finite element model and a zero-order minimisation algorithm.

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.