Jiexiang Hu

A variable fidelity information fusion method based on radial basis function

A variable-fidelity information fusion approach based on RBF is proposed.The low-fidelity output is taken as a prior-knowledge of the studied system.Cases study show the applicability and efficiency of the proposed approaches. Radial basis function (RBF) model has been widely used in complex engineering design process to replace the computational-intensive simulation models. This paper proposes a variable-fidelity metamodeling (VFM) approach based on RBF, in which different levels fidelity information can be integrated and fully exploited. In the proposed VFM approach, a RBF metamodel is constructed for the low-fidelity (LF) model as a start. Then by taking the constructed LF metamodel as a prior-knowledge and mapping the output space of the LF metamodel to that of the studied high-fidelity (HF) model, a variable fidelity (VF) metamodel is created to approximate the relationships between the design variables and corresponding output responses. A numerical illustrative example is adopted to make a detailed comparison between the VFM approach developed in this research and three existing scaling function based VFM approaches, considering different sample sizes and sample noises. Results illustrate that the proposed VFM approach outperforms the scaling function based VFM approaches both in global and local accuracy. Then the proposed VFM approach is applied to two engineering problems, modeling aerodynamic data for a three-dimensional aircraft and the prediction of weld bead profile in laser welding, to illustrate its ability in support of complex engineering design.

A sequential multi-fidelity metamodeling approach for data regression

Abstract Multi-fidelity (MF) metamodeling approaches have attracted significant attention recently for data regression because they can make a trade-off between high accuracy and low computational expense by integrating the information from high-fidelity (HF) and low-fidelity (LF) models. To facilitate the usage of the MF metamodeling approaches, there are still challenging issues on the sample size ratio between HF and LF models and the locations of samples since these two components have profound effects on the prediction accuracy of the MF metamodels. In this study, a sequential multi-fidelity (SMF) metamodeling approach is proposed to address the issues of 1) where to allocate the LF and HF sample points, and 2) how to obtain an optimal combination of the high and low-fidelity sample sizes for a given computational budget and a high-to-low simulation cost ratio. Firstly, sequential objective formulations, with the objective to reduce the estimation of prediction error of MF metamodel, are constructed to update the LF and HF sampling data. Secondly, a decision criterion is proposed to determine whether one HF experiment or several LF experiments with the equivalent computational cost should be selected to update the MF metamodel. The proposed criterion is developed according to which selection will have a greater potential value to improve the prediction accuracy of the MF metamodel. To demonstrate the effectiveness and merits of the proposed SMF metamodeling approach, two numerical examples and a practical aerospace application example are used. Results show that the proposed approach can generate more accurate MF metamodels by providing the optimal high-to-low sample size ratio and sample locations.

A multi-fidelity information fusion metamodeling assisted laser beam welding process parameter optimization approach

A multi-fidelity (MF) metamodel assisted welding parameter optimization is proposed.A 3D thermal finite element model is developed as a low-fidelity model.A laser welding physical experiment is taken as the high-fidelity model.The MF metamodel is built based on two different levels fidelity information fusion.Verification experiments illustrated the reliability of the final optima. Selecting reasonable laser beam welding (LBW) process parameters is very helpful for obtaining a good welding bead profile and hence a high quality of the welding joint. Existing process parameter optimization approaches for LBW either based on cost-expensive physical experiments or low-fidelity (LF) computer simulations. This paper proposes a multi-fidelity (MF) metamodel based LBW process parameter optimization approach, in which different levels fidelity information, both from LF computer simulations and high-fidelity (HF) physical experiments can be integrated and fully exploited. In the proposed approach, a three-dimensional thermal finite element model is developed as the LF model, which is fitted with a LF metamodel firstly. Then, by taking the LF metamodel as a base model and scaling it using the HF physical experiments, a MF metamodel is constructed to approximate the relationships between the LBW process parameters and the bead profile. Two metrics are adopted to compare the prediction accuracy of the MF metamodel with the single-fidelity metamodels solely constructed with physical experiments or computer simulations. Results illustrate that the MF metamodel outperforms the single-fidelity metamodels both in global and local accuracy. Finally, the fast elitist non-dominated sorting genetic algorithm (NSGA-II) is used to facilitate LBW process parameter space exploration and multi-objective Pareto optima search. LBW verification experiments verify the effectiveness and reliability of the obtained optimal process parameters.

An adaptive sampling method for variable-fidelity surrogate models using improved hierarchical kriging

ABSTRACT Variable-fidelity (VF) modelling methods have been widely used in complex engineering system design to mitigate the computational burden. Building a VF model generally includes two parts: design of experiments and metamodel construction. In this article, an adaptive sampling method based on improved hierarchical kriging (ASM-IHK) is proposed to refine the improved VF model. First, an improved hierarchical kriging model is developed as the metamodel, in which the low-fidelity model is varied through a polynomial response surface function to capture the characteristics of a high-fidelity model. Secondly, to reduce local approximation errors, an active learning strategy based on a sequential sampling method is introduced to make full use of the already required information on the current sampling points and to guide the sampling process of the high-fidelity model. Finally, two numerical examples and the modelling of the aerodynamic coefficient for an aircraft are provided to demonstrate the approximation capability of the proposed approach, as well as three other metamodelling methods and two sequential sampling methods. The results show that ASM-IHK provides a more accurate metamodel at the same simulation cost, which is very important in metamodel-based engineering design problems.

An active learning radial basis function modeling method based on self-organization maps for simulation-based design problems

Abstract The radial basis function has been widely used in constructing metamodels as response surfaces. Yet, it often faces the challenge of accuracy if a sequential sampling strategy is used to insert samples sequentially and refine the models, especially under the constraint of computational resources. In this paper, a sensitive region pursuing based active learning radial basis function (SRP-ALRBF) metamodeling approach is proposed to sequentially exploit the already-acquired knowledge in the modeling process for obtaining a desirable estimation of the relationship between the input design variables and the output response. In this method, the leave-one-out (LOO) errors of each sample point are taken to identify the boundaries of sensitive regions. According to the obtained LOO information, the original design space is divided into some subspaces by adopting the self-organization maps (SOMs). The boundary of the most sensitive region, where the output response is multi-modal or non-smooth with abrupt changes, is determined by the topological graph generated by cluster analysis in SOMs. In the most sensitive region, infill sample point searching is performed based on an optimization formulation. Ten numerical examples are used to compare the proposed SRP-ALRBF with four existing active learning RBF metamodeling approaches. Results show the advantage of the proposed SRP-ALRBF approach in both prediction accuracy and robustness. It is also applied to three engineering cases to illustrate its ability to support complex engineering design.

An on-line Kriging metamodel assisted robust optimization approach under interval uncertainty

Purpose 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. Design/methodology/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. Findings 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. Practical implications The proposed approach exhibits great capability for practical engineering design optimization problems under interval uncertainty. Originality/value 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.

An on-line variable fidelity metamodel assisted Multi-objective Genetic Algorithm for engineering design optimization

Abstract Population-based algorithms, which require a large number of fitness evaluations, can become computationally intractable when applied in engineering design optimization problems involving computational expensive simulations. To address this challenge, this paper proposes an on-line variable-fidelity metamodel assisted Multi-Objective Genetic Algorithm (OLVFM-MOGA) approach. In OLVFM-MOGA, the variable-fidelity metamodel (VFM) is constructed to replace the expensive simulation models to ease the computational burden. Besides, a novel model updating strategy is developed to address the issues of 1) which sample points should be sent for simulation analysis to improve the optimization quality, and 2) whether the low-fidelity (LF) model or the high-fidelity (HF) model should be selected to run for a selected sample point. Six numerical examples and an engineering case with different degrees of complexity are used to demonstrate the applicability and efficiency of the proposed approach. Results illustrate that the proposed OLVFM-MOGA is able to obtain comparable convergence and diversity of the Pareto frontier as to that obtained by MOGA with HF model, while at the same time significantly reducing the computational cost.

A space mapping method based on Gaussian process model for variable fidelity metamodeling

Abstract Computational simulation models with different fidelities are usually available in the design of engineering products for obtaining the quantity of interest (QOI). To integrate and fully exploit variable fidelity information, a space mapping based variable-fidelity metamodeling (VFM) approach is developed in this work. Firstly, a Gaussian process (GP) model is constructed for the low-fidelity (LF) model. Secondly, a variable-fidelity metamodel is constructed by taking the predicted information from this GP model as a prior-knowledge of the QOI and directly mapped into the outputs space of the high-fidelity (HF) model. This space mapping process is performed by constructing another GP model. A mathematic example is first adopted for illustrating how the proposed approach works under different sample sizes and sample noises. Then, the proposed approach is applied to two real-life cases, modeling of the maximum stress for the structure of a Small Waterplane Area Twin Hull (SWATH) catamaran and predicting weld geometry in fiber laser keyhole welding, to illustrate its ability in support of complex engineering design.

Comparative studies of error metrics in variable fidelity model uncertainty quantification

ABSTRACT Variable-fidelity (VF) surrogate models which integrate different fidelities of date are wildly used in simulation-based modelling due to a good balance of modelling expense and modelling accuracy. However, VF surrogate models built by limited sample points inevitably have large prediction uncertainty. Using inaccurate VF models in the design and optimisation process may lead to distort predictions or optimal solutions that locate in unfeasible region. Besides, if inappropriate error metrics are utilised in the uncertainty quantifying of a surrogate model, misleading or erroneous evaluation results will be obtained, which may lead to the wrong usage of it in design process. In this paper, the performance of four error metrics (bootstrap error, leave-one-out (LOO) error, mean square error (MSE) and predictive estimation of model fidelity (PEMF error) is systematically compared in uncertainty quantification of VF surrogate model. A set of numerical examples with different features and a long cylinder pressure vessel design problem are utilised to test the performance of the error metrics. The error metrics are evaluated from different aspects, including the number of sample points, sampling methods, and dimension of the test problems etc. Results show that in low dimensional problems, MSE shows excellent error prediction capability not only in efficiency but also in effectiveness while LOO error performs the best in high dimensional problems. Based on the comparison results, a useful guideline for selecting the most appropriate error metric for the problems with different characteristics is provided.

A multi-objective robust optimization approach for engineering design under interval uncertainty

Purpose Engineering system design and optimization problems are usually multi-objective, 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. In this paper, a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) is proposed to obtain the robust Pareto set under the interval uncertainty. Design/methodology/approach 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 pre...