Artificial neural network-based sequential approximate optimization of metal sheet architecture and forming process

Han Seong-Sik,김흥규 한국CDE학회 2024 Journal of computational design and engineering Vol.11 No.3

This paper introduces a sequential approximate optimization method that combines the finite element method (FEM), dynamic differential evolution (DDE), and artificial neural network (ANN) surrogate models. The developed method is applied to address two optimization problems. The first involves metamaterial design optimization for metal sheet architecture with binary design variables. The second pertains to optimizing process parameters in multi-stage metal forming, where the discrete nature arises owing to changing tool geometries across stages. This process is highly non-linear, accumulating contact, geometric, and material non-linear effects discretely through forming stages. The efficacy of the proposed optimization method, utilizing ANN surrogate models, is compared with traditionally used polynomial response surface (PRS) surrogate models, primarily based on low-order polynomials. Efficient learning of ANN surrogate models is facilitated through the FEM and Python integration framework. Initial data for surrogate model training are collected via Latin hypercube sampling and FEM simulations. DDE is employed for sequential approximate optimization, optimizing ANN or PRS surrogate models to determine optimal design variables. PRS surrogate models encounter challenges in dealing with non-linear changes in sequential approximate optimization concerning discrete characteristics such as binary design variables and discrete non-linear behavior found in multi-stage metal forming processes. Owing to the discrete nature, PRS surrogate models require more data and iterations for optimal design variables. In contrast, ANN surrogate models adeptly predict non-linear behavior through the activation function’s characteristics. In the optimization problem of metal sheet architecture for design Target C, the ANN surrogate model required an average of 4.6 times fewer iterations to satisfy stopping criteria compared with the PRS surrogate model. Furthermore, in the optimization of multi-stage deep drawing processes, the ANN surrogate model required an average of 6.1 times fewer iterations to satisfy stopping criteria compared with the PRS surrogate model. As a result, the sequential global optimization method utilizing ANN surrogate models achieves optimal design variables with fewer iterations than PRS surrogate models. Further confirmation of the method’s efficiency is provided by comparing Pearson correlation coefficients and locus plots.

Surrogate-assisted modeling and optimization of a natural-gas liquefaction plant

Ali, Wahid,Khan, Mohd Shariq,Qyyum, Muhammad Abdul,Lee, Moonyong Elsevier 2018 Computers & chemical engineering Vol.118 No.-

<P><B>Abstract</B></P> <P>In this study, surrogate-assisted modeling and optimization of the single mixed refrigerant process of natural-gas liquefaction is presented. The mixed refrigerant liquefaction process is highly nonlinear owing to the involved thermodynamics that increase the computational burden of any optimization algorithm. To address the computational-burden issue and obtain the results in a reasonable time for the complex single mixed refrigerant process, an approximate surrogate model was developed using a radial basis function combined with a thin-plate spline approach. Even with the reduced model, all the results obtained were comparable with those by rigorous first-principle models. This confirms that all the important characteristics of the model are correctly captured, and the surrogate models of the liquefaction plant are acceptable replacements of first-principle models, especially in computationally demanding situations.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Hysys and Matlab model were linked by HDSS code. </LI> <LI> Surrogate model using RBF approach with thin plate spline kernel function was employed. </LI> <LI> Adaptation of feasible region and model identification was made. </LI> <LI> PSO and GA optimization algorithm were applied to both Hysys and surrogate model. </LI> <LI> Results obtained were found to be promising with less computational efforts. </LI> </UL> </P> <P><B>Graphical Abstract</B></P> <P>[DISPLAY OMISSION]</P>

An artificial neural network residual kriging based surrogate model for curvilinearly stiffened panel optimization

Sunny, Mohammed R.,Mulani, Sameer B.,Sanyal, Subrata,Kapania, Rakesh K. Techno-Press 2016 Advances in computational design Vol.1 No.3

We have performed a design optimization of a stiffened panel with curvilinear stiffeners using an artificial neural network (ANN) residual kriging based surrogate modeling approach. The ANN residual kriging based surrogate modeling involves two steps. In the first step, we approximate the objective function using ANN. In the next step we use kriging to model the residue. We optimize the panel in an iterative way. Each iteration involves two steps-shape optimization and size optimization. For both shape and size optimization, we use ANN residual kriging based surrogate model. At each optimization step, we do an initial sampling and fit an ANN residual kriging model for the objective function. Then we keep updating this surrogate model using an adaptive sampling algorithm until the minimum value of the objective function converges. The comparison of the design obtained using our optimization scheme with that obtained using a traditional genetic algorithm (GA) based optimization scheme shows satisfactory agreement. However, with this surrogate model based approach we reach optimum design with less computation effort as compared to the GA based approach which does not use any surrogate model.

Research on Comparative of Multi-Surrogate Models to Optimize Complex Truss Structures

Chongjian Yang,Junle Yang,Yixiao Qin 대한토목학회 2024 KSCE Journal of Civil Engineering Vol.28 No.6

Surrogate models have been proven to be reliable and effective methods for the application of engineering problems. This article presents a comparative study of three common surrogate models Polynomial Response Surface (PRS), Radial Basis Function (RBF) neural network, and Kriging model in terms of optimization. For the optimization of plane 10-bar truss structure and 25 bar space truss, the effectiveness of the surrogate model algorithm is verified by different surrogate models. Finally for a typical complex truss structure such as lattice boom of crawler crane, the Optimal Latin Hypercube Design (OLHD) is used to sample the optimized sample points for fitting and interpolation of three surrogate models and analyzing their errors, in order to get better surrogate effect, PRS is combined with RBF Neural Network, and secondly, the global optimization algorithm (Multi-Island Genetic Algorithm, MIGA) and gradient algorithm (Modified Method of Feasible Directions, MMFD) are used to optimize the fitted four surrogate models. Through the comparison of the optimization results, the optimization of PRS-RBF combined surrogate model using MIGA-MMFD algorithm instead of finite element model optimization has good stability and reliability. The total mass of the optimized model has been reduced by 24.47%. The number of optimization iterations is within 250 generations. The new method proposed in this paper can greatly promote the reduction of the period of analysis and optimization of engineering structures.

Experimental validation of FE model updating based on multi-objective optimization using the surrogate model

황용문,진승섭,정호연,김세훈,이종재,정형조 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.2

In this paper, finite element (FE) model updating based on multi-objective optimization with the surrogate model for a steel plate girder bridge is investigated. Conventionally, FE model updating for bridge structures uses single-objective optimization with finite element analysis (FEA). In the case of the conventional method, computational burden occurs considerably because a lot of iteration are performed during the updating process. This issue can be addressed by replacing FEA with the surrogate model. The other problem is that the updating result from single-objective optimization depends on the condition of the weighting factors. Previous studies have used the trial-and-error strategy, genetic algorithm, or user’s preference to obtain the most preferred model; but it needs considerable computation cost. In this study, the FE model updating method consisting of the surrogate model and multi-objective optimization, which can construct the Pareto-optimal front through a single run without considering the weighting factors, is proposed to overcome the limitations of the single-objective optimization. To verify the proposed method, the results of the proposed method are compared with those of the single-objective optimization. The comparison shows that the updated model from the multi-objective optimization is superior to the result of single-objective optimization in calculation time as well as the relative errors between the updated model and measurement.

Crack identification based on Kriging surrogate model

Gao, Hai-Yang,Guo, Xing-Lin,Hu, Xiao-Fei Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.41 No.1

Kriging surrogate model provides explicit functions to represent the relationships between the inputs and outputs of a linear or nonlinear system, which is a desirable advantage for response estimation and parameter identification in structural design and model updating problem. However, little research has been carried out in applying Kriging model to crack identification. In this work, a scheme for crack identification based on a Kriging surrogate model is proposed. A modified rectangular grid (MRG) is introduced to move some sample points lying on the boundary into the internal design region, which will provide more useful information for the construction of Kriging model. The initial Kriging model is then constructed by samples of varying crack parameters (locations and sizes) and their corresponding modal frequencies. For identifying crack parameters, a robust stochastic particle swarm optimization (SPSO) algorithm is used to find the global optimal solution beyond the constructed Kriging model. To improve the accuracy of surrogate model, the finite element (FE) analysis soft ANSYS is employed to deal with the re-meshing problem during surrogate model updating. Specially, a simple method for crack number identification is proposed by finding the maximum probability factor. Finally, numerical simulations and experimental research are performed to assess the effectiveness and noise immunity of this proposed scheme.

결정계수와 유전자 알고리즘을 이용한 Optimized-order Trended Kriging 모델 개발

이학진(Hakjin Lee),이덕주(Duck-Joo Lee) 한국항공우주학회 2016 한국항공우주학회 학술발표회 논문집 Vol.2016 No.4

전산최적설계에서 근사 모델 기법은 목적함수 평가를 간단한 수학식으로 대체함으로써 목적함수 평가에 소모되는 계산 자원을 획기적으로 완화할 수 있는 방법이다. 본 연구에서는 기존의 Kriging 근사 모델에 대한 정확도를 향상시키기 위해 고정된 형태의 회귀 다항식이 아닌 최적화된 회귀 다항식을 평균항 함수로 이용하는 Optimized-order Trended Kriging (OTKG) 모델을 제안한다. 회귀분석을 통해 계산된 결정계수를 이용하여 실제 함수의 경향성을 파악하고 가장 적합한 회귀 다항식의 차수를 결정한다. 또한, 회귀 다항식 항들 중 실제 함수 근사에 도움이 되는 항만을 결정하기 위해 유전자 알고리즘을 이용한다. 경향성이 서로 다른 3개의 해석적인 함수에 대해 제안한 모델과 Ordinary, Universal Kriging을 적용하고 정확성을 비교한 결과, OTKG 모델의 정확도가 가장 우수함을 확인할 수 있었다. The surrogate model or metamodeling is an efficient way of alleviating the expensive computation burden for function evaluation in the design optimization. A simple mathematical form of surrogate model is used to substitute the function evaluation. Therefore, an accuracy of surrogate model is important factor that will directly affects a result of design optimization. In this study, an enhanced Kriging model called the Optimized-order Trended Kriging (OTKG) model is suggested to improve the accuracy of model. In the OTKG model, the optimal subset of basis function instead of the full set of basis function is used as a drift function. The order and optimal subset of basis function are determined by Coefficient of determination and Genetic Algorithm. The validation results show that the OTKG model yields more accurate results compared with other Kriging models.

Experimental validation of FE model updating based on multi-objective optimization using the surrogate model

Hwang, Yongmoon,Jin, Seung-seop,Jung, Ho-Yeon,Kim, Sehoon,Lee, Jong-Jae,Jung, Hyung-Jo Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.2

In this paper, finite element (FE) model updating based on multi-objective optimization with the surrogate model for a steel plate girder bridge is investigated. Conventionally, FE model updating for bridge structures uses single-objective optimization with finite element analysis (FEA). In the case of the conventional method, computational burden occurs considerably because a lot of iteration are performed during the updating process. This issue can be addressed by replacing FEA with the surrogate model. The other problem is that the updating result from single-objective optimization depends on the condition of the weighting factors. Previous studies have used the trial-and-error strategy, genetic algorithm, or user's preference to obtain the most preferred model; but it needs considerable computation cost. In this study, the FE model updating method consisting of the surrogate model and multi-objective optimization, which can construct the Pareto-optimal front through a single run without considering the weighting factors, is proposed to overcome the limitations of the single-objective optimization. To verify the proposed method, the results of the proposed method are compared with those of the single-objective optimization. The comparison shows that the updated model from the multi-objective optimization is superior to the result of single-objective optimization in calculation time as well as the relative errors between the updated model and measurement.

Development of an optimized trend kriging model using regression analysis and selection process for optimal subset of basis functions

Lee, Hakjin,Lee, Duck-Joo,Kwon, Hyungil Elsevier 2018 AEROSPACE SCIENCE AND TECHNOLOGY Vol.77 No.-

<P><B>Abstract</B></P> <P>Surrogate modeling, or metamodeling, is an efficient way of alleviating the high computational cost and complexity for iterative function evaluation in design optimization. Accuracy is significantly important because optimization algorithms rely heavily on the function response calculated by surrogate model and the optimum solution is directly affected by the quality of surrogate model. In this study, an optimized trend kriging model is proposed to improve the accuracy of the existing kriging models. Within the framework of the proposed model, regression analysis is carried out to approximate the unknown trend of the true function and to determine the order of the universal kriging model, which has a fixed form with a mean structure dependent on the order of model. In addition, the selection of an optimal basis function is conducted to separate the useful basis function terms from the full set of the basis function. The optimal subset of the basis function is selected with the global optimization algorithm; which can accurately represent the trend of true response surface. The mean structure of proposed model has been optimized to maximize the accuracy of kriging model depending on the trend of true function. Two- and three-dimensional analytic functions and a practical engineering problem are chosen to validate the proposed model. The results showed that the OTKG model yield the most accurate responses regardless of the number of initial sample points, and can conversed into well-trained model with few additional sample points.</P>

Crack identification based on Kriging surrogate model

Hai-yang Gao,Xing-lin Guo,Xiao-fei Hu 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.41 No.1

Kriging surrogate model provides explicit functions to represent the relationships between the inputs and outputs of a linear or nonlinear system, which is a desirable advantage for response estimation and parameter identification in structural design and model updating problem. However, little research has been carried out in applying Kriging model to crack identification. In this work, a scheme for crack identification based on a Kriging surrogate model is proposed. A modified rectangular grid (MRG) is introduced to move some sample points lying on the boundary into the internal design region, which will provide more useful information for the construction of Kriging model. The initial Kriging model is then constructed by samples of varying crack parameters (locations and sizes) and their corresponding modal frequencies. For identifying crack parameters, a robust stochastic particle swarm optimization (SPSO) algorithm is used to find the global optimal solution beyond the constructed Kriging model. To improve the accuracy of surrogate model, the finite element (FE) analysis soft ANSYS is employed to deal with the re-meshing problem during surrogate model updating. Specially, a simple method for crack number identification is proposed by finding the maximum probability factor. Finally, numerical simulations and experimental research are performed to assess the effectiveness and noise immunity of this proposed scheme.