Longchao Cao

Optimization of laser brazing onto galvanized steel based on ensemble of metamodels

Laser brazing (LB) provides a promising way to join the galvanized steel in automotive industry for its significant advantages including high speed, small heat-affected zone, and high welding seam quality. The process parameters of LB have significant effects on the bead profile and hence the quality of joint. Since the relationships between the process parameters and bead profile cannot be expressed explicitly, it is impractical to determine the optimal process parameters intuitively. This paper proposes an optimization methodology by combining genetic algorithm (GA) and ensemble of metamodels (EMs) to address the process parameters optimization of the bead profile in LB with crimping butt. Firstly, Taguchi experimental design is adopted to generate the experimental points. Secondly, the relationships between process parameters (i.e., welding speed, wire feed rate, gap) and the bead geometries are fitted using EMs based on the experimental data. The comparative results show that the EMs can take advantage of the prediction ability of each stand-alone metamodel and thus decrease the risk of adopting inappropriate metamodels. Then, the GA is used to facilitate design space exploration and global optimum search. Besides, the main effects and contribution rates of multiple process parameters on bead profile are analyzed. Eventually, the verification experiments are carried out to demonstrate the effectiveness and reliability of the obtained optimal parameters. Overall, the proposed hybrid approach, GA–EMs, exhibits great capability of guiding the actual LB processing and improving welding quality.

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.

Optimization of Process Parameters of Hybrid Laser–Arc Welding onto 316L Using Ensemble of Metamodels

Hybrid laser–arc welding (LAW) provides an effective way to overcome problems commonly encountered during either laser or arc welding such as brittle phase formation, cracking, and porosity. The process parameters of LAW have significant effects on the bead profile and hence the quality of joint. This paper proposes an optimization methodology by combining non-dominated sorting genetic algorithm (NSGA-II) and ensemble of metamodels (EMs) to address multi-objective process parameter optimization in LAW onto 316L. Firstly, Taguchi experimental design is adopted to generate the experimental samples. Secondly, the relationships between process parameters (i.e., laser power (P), welding current (A), distance between laser and arc (D), and welding speed (V)) and the bead geometries are fitted using EMs. The comparative results show that the EMs can take advantage of the prediction ability of each stand-alone metamodel and thus decrease the risk of adopting inappropriate metamodels. Then, the NSGA-II is used to facilitate design space exploration. Besides, the main effects and contribution rates of process parameters on bead profile are analyzed. Eventually, the verification experiments of the obtained optima are carried out and compared with the un-optimized weld seam for bead geometries, weld appearances, and welding defects. Results illustrate that the proposed hybrid approach exhibits great capability of improving welding quality in LAW.

A deterministic robust optimisation method under interval uncertainty based on the reverse model

Uncertainty is inevitable for real-world engineering optimisation. Most existing robust optimisation (RO) approaches consider many drastically different alternatives in an effort to design an engineering system under uncertainty. In this paper, a deterministic RO approach named variable adjustment robust optimisation (VARO) is proposed to improve the robustness of a preferred preexisting design. Firstly, a formulation to obtain design alternatives with acceptable difference from the preferred preexisting design is constructed. Secondly, the robustness indices, estimated sensitivity regions using worst-case scenario analysis, are generated by the reverse model that maps the given acceptable objective variations and feasibility variations into the space of variable variations. The obtained robustness indices are incorporated into the constructed formulation to evaluate the robustness of the design alternatives. Thirdly, metamodels are built for robustness indices to transform the nested optimisation structure of the proposed VARO approach into a single loop optimisation structure for the purpose of easing its computational burden. Seven examples with differing complexity are used to demonstrate the applicability and efficiency of the proposed approach. Verifications of robustness for the optimum obtained are also performed via design of experiment.

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 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.

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.

Cellular automaton modeling for dendritic growth during laser beam welding solidification process

A modified non-equilibrium cellular automaton (CA) model is proposed to simulate the dendrite growth along the fusion boundary under transient conditions during the solidification process of laser beam welding (LBW) pool. The main non-equilibrium solidification effects, including solute trapping, deviation of the liquidus line slope, and kinetic undercooling, are taken into consideration in this modified CA model. The evolution of dendrite morphology, concentration field, and velocity field was investigated. Four growth periods, i.e., the initial stable period, the instability period, the competitive growth period, and the short-term stable period, were observed during the solidification process of LBW pool. The dendrite growth patterns were different in these periods due to the transient solidification conditions. The solute distribution predicted by this modified CA model showed similar trends to that predicted by the previous phase field model. The dendrite tip velocity was significantly influenced by the thermal undercooling and constitutional undercooling in the LBW pool, and the tip velocity field can be divided into three stages, i.e., the planar growth stage, competitive stage, and short-term steady growth stage. In addition, further comparison between the simulated dendrite morphology and experimental dendrite morphology was performed. Results showed that the simulated morphology of dendrites agreed well with the experimental results. In particular, the primary dendrite arm spacing predicted by this model was in good agreement with that obtained from experiments.A modified non-equilibrium cellular automaton (CA) model is proposed to simulate the dendrite growth along the fusion boundary under transient conditions during the solidification process of laser beam welding (LBW) pool. The main non-equilibrium solidification effects, including solute trapping, deviation of the liquidus line slope, and kinetic undercooling, are taken into consideration in this modified CA model. The evolution of dendrite morphology, concentration field, and velocity field was investigated. Four growth periods, i.e., the initial stable period, the instability period, the competitive growth period, and the short-term stable period, were observed during the solidification process of LBW pool. The dendrite growth patterns were different in these periods due to the transient solidification conditions. The solute distribution predicted by this modified CA model showed similar trends to that predicted by the previous phase field model. The dendrite tip velocity was significantly influenced by ...

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...