Leshi Shu

An adaptive global variable fidelity metamodeling strategy using a support vector regression based scaling function

Abstract Computational simulation models with variable fidelity have been widely used in complex systems design. However, running the most accurate simulation models tends to be very time-consuming and can therefore only be used sporadically, while incorporating less accurate, inexpensive models into the design process may result in inaccurate design alternatives. To make a trade-off between high accuracy and low expense, variable fidelity (VF) metamodeling approaches that aim to integrate information from both low-fidelity (LF) and high-fidelity (HF) models have gained increasing popularity. In this paper, an adaptive global VF metamodeling approach named difference adaptive decreasing variable-fidelity metamodeling (DAD-VFM) is proposed, in which the one-shot VF metamodeling process is transformed into an iterative process to utilize the already-acquired information of difference characteristics between the HF and LF models. In DAD-VFM, support vector regression (SVR) is adopted to map the difference between the HF and LF models. Besides, a generalized objective-oriented sampling strategy is introduced to adaptively probe and sample more points in the interesting regions where the differences between the HF and LF models are multi-model, non-smooth and have abrupt changes. Several numerical cases and a long cylinder pressure vessel optimization design problem verify the applicability of the proposed VF metamodeling approach.

An active learning variable-fidelity metamodelling approach based on ensemble of metamodels and objective-oriented sequential sampling

ABSTRACT Computational simulation models with different fidelity have been widely used in complex systems design. However, running the high-fidelity (HF) simulation models tends to be very time-consuming, while incorporating low-fidelity (LF), inexpensive models into the design process may result in inaccurate design alternatives. To make a trade-off between high accuracy and low expense, an active learning variable-fidelity (VF) metamodelling approach aiming to integrate information from both LF and HF models is proposed. In the proposed VF metamodelling approach, a model fusion technology based on ensemble of metamodels is employed to map the difference between the HF and LF models. Furthermore, an active learning strategy based on a generalised objective-oriented sequential sampling strategy is introduced to make full use of the already-acquired information of difference characteristics between the HF and LF models. Several numerical and engineering cases verify the applicability of the proposed VF metamodelling approach. Different types of test cases, sample sizes, and metamodel performance evaluation measures including accuracy and robustness are considered.

An active learning metamodeling approach by sequentially exploiting difference information from variable-fidelity models

We propose an active learning variable-fidelity metamodeling approach (AL-VFM).Information from high-fidelity and low-fidelity models is integrated in AL-VFM.An active learning strategy is introduced to use the already-acquired information.Numerical and engineering cases verify the applicability of the proposed approach. Complex system engineering design optimization based on simulation is a very time-consuming, even computationally prohibitive process. To relieve the computational burden, metamodels are commonly used to replace the computation-intensive simulations. In this paper, an active learning variable fidelity (VF) metamodeling approach (AL-VFM) is proposed for the purpose of integrating information from both low-fidelity (LF) and high-fidelity (HF) models. In AL-VFM, Kriging metamodel is adopted to map the difference between the HF and LF models aiming to approach the HF model on the entire domain. Besides, a general active learning strategy is introduced in AL-VFM to make full use of the already-acquired information to guide the VF metamodeling. The already-acquired information represents the location of regions where the differences between the HF and LF models are multi-model, non-smooth and have abrupt changes. Several numerical and engineering cases with different degrees of difficulty verify the applicability of the proposed VF metamodeling approach.

Optimization of laser welding process parameters of stainless steel 316L using FEM, Kriging and NSGA-II

Multi-objective laser welding process parameters optimization approach is proposed.The effects of process parameters on bead profile in light of Kriging are analyzed.Experiment results show the efficiency of the proposed approach. Laser welding process parameters have significant effects on the welding bead profile and quality of the welding joint. This paper proposes an integration method of process parameters optimization using finite element method (FEM), Kriging metamodels and nondominated sorting genetic algorithm II (NSGA-II) in laser welding for stainless steel 316L. The process parameters in this study are laser power (LP), welding speed (WS) and laser focal position (LF). Firstly, a three-dimensional thermal finite element model is developed to obtain the simulated results of bead width (BW) and depth of penetration (DP). Then, Kriging metamodels are constructed to reflect the relationship between input process parameters and output responses. Finally, NSGA-II is used to search for multi-objective Pareto optimal solutions. In addition, the main effects and contribution rates of multiple process parameters on welding bead profile are analyzed. The results of verification experiments indicate that the optimal process parameters are effective and reliable for producing expected welding bead profile.

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.

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...

Metamodel-based design optimization employing a novel sequential sampling strategy

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

An adaptive sampling strategy for Kriging metamodel based on Delaunay triangulation and TOPSIS

Metamodels have been widely used in engineering design and optimization. Sampling method plays an important role in the constructing of metamodels. This paper proposes an adaptive sampling strategy for Kriging metamodel based on Delaunay triangulation and TOPSIS (KMDT). In the proposed KMDT, Delaunay triangulation is employed to partition the design space according to current sample points. The area of each partitioned triangle is used to indicate the degree of dispersion of sample points, and the prediction error of Kriging metamodel at each triangle’s centroid is used to represent the local error of each triangle region. By calculating the weight of the area and prediction error for each triangle region using the entropy method and TOPSIS, the degree of dispersion of sample points and local errors of metamodel are taken into consideration to make a trade-off between global exploration and local exploitation during the sequential sampling process. As a demonstration, the proposed approach is compared to other three sampling methods using several numerical cases and the modeling of the aerodynamic coefficient for a three-dimensional aircraft. The result reveals that the proposed approach provides more accurate metamodel at the same simulation cost, which is very important in metamodel-based engineering design problems.

A variable-fidelity modeling method based on self-organizing maps spatial reduction

Variable-fidelity (VF) approximation models are wildly used to replace computational expensive simulation models in complex engineering designs. In this paper, a design space reduction variable-fidelity metamodeling (DSR-VFM) approach is proposed. In the proposed DSR-VFM, addition scaling Kriging (ASK) is chosen as the approximation model and self-organizing maps (SOM) is adopt to reduce the design space and select the key areas. Then new sample points are selected though the maximum distance method within the key areas and added to the sample set to update the approximate model. A numerical case and the modeling of the drag coefficient of an aircraft are utilized to verify the applicability of the proposed approach.