The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is m...The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.展开更多
The Infrared Hyperspectral Atmospheric SounderⅡ(HIRAS-Ⅱ)is the key equipment on FengYun-3E(FY-3E)satellite,which can realize vertical atmospheric detection,featuring hyper spectral,high sensitivity and high precisio...The Infrared Hyperspectral Atmospheric SounderⅡ(HIRAS-Ⅱ)is the key equipment on FengYun-3E(FY-3E)satellite,which can realize vertical atmospheric detection,featuring hyper spectral,high sensitivity and high precision.To ensure its accuracy of detection,it is necessary to correlate their thermal models to in-orbit da⁃ta.In this work,an investigation of intelligent correlation method named Intelligent Correlation Platform for Ther⁃mal Model(ICP-TM)was established,the advanced Kriging surrogate model and efficient adaptive region opti⁃mization algorithm were introduced.After the correlation with this method for FY-3E/HIRAS-Ⅱ,the results indi⁃cate that compared with the data in orbit,the error of the thermal model has decreased from 5 K to within±1 K in cold case(10℃).Then,the correlated model is validated in hot case(20℃),and the correlated model exhibits good universality.This correlation precision is also much superiors to the general ones like 3 K in other similar lit⁃erature.Furthermore,the process is finished in 8 days using ICP-TM,the efficiency is much better than 3 months based on manual.The results show that the proposed approach significantly enhances the accuracy and efficiency of thermal model,this contributes to the precise thermal control of subsequent infrared optical payloads.展开更多
This study introduces a novel approach to addressing the challenges of high-dimensional variables and strong nonlinearity in reservoir production and layer configuration optimization.For the first time,relational mach...This study introduces a novel approach to addressing the challenges of high-dimensional variables and strong nonlinearity in reservoir production and layer configuration optimization.For the first time,relational machine learning models are applied in reservoir development optimization.Traditional regression-based models often struggle in complex scenarios,but the proposed relational and regression-based composite differential evolution(RRCODE)method combines a Gaussian naive Bayes relational model with a radial basis function network regression model.This integration effectively captures complex relationships in the optimization process,improving both accuracy and convergence speed.Experimental tests on a multi-layer multi-channel reservoir model,the Egg reservoir model,and a real-field reservoir model(the S reservoir)demonstrate that RRCODE significantly reduces water injection and production volumes while increasing economic returns and cumulative oil recovery.Moreover,the surrogate models employed in RRCODE exhibit lightweight characteristics with low computational overhead.These results highlight RRCODE's superior performance in the integrated optimization of reservoir production and layer configurations,offering more efficient and economically viable solutions for oilfield development.展开更多
Stratospheric airships are lighter-than-air vehicles capable of continuous flying for months.The energy balance of the airship is the key to long-duration flights.The stratospheric airship is entirely powered by the s...Stratospheric airships are lighter-than-air vehicles capable of continuous flying for months.The energy balance of the airship is the key to long-duration flights.The stratospheric airship is entirely powered by the solar array.It is necessary to accurately predict the output power of the array for any flight state.Because of the uneven solar radiation received by the solar array,the traditional model based on components has a slow simulation speed.In this study,a data-driven surrogate modeling approach for prediction the output power of the solar array is proposed.The surrogate model is trained using the samples obtained from the high-accuracy simulation model.By using the input parameter preprocessor,the accuracy of the surrogate model in predicting the output power of the solar array is improved to 98.65%.In addition,the predictive speed of the surrogate model is ten million times faster than the traditional simulation model.Finally,the surrogate model is used to predict the energy balance of stratospheric airships flying throughout the year under actual global wind fields.展开更多
Cobalt phosphide has been successfully used as a catalyst in the production of ammonia from nitric acid.Substituting appropriate atoms is expected to further improve its catalytic performance.Owing to the diversity of...Cobalt phosphide has been successfully used as a catalyst in the production of ammonia from nitric acid.Substituting appropriate atoms is expected to further improve its catalytic performance.Owing to the diversity of substituting elements,substitution sites,adsorption sites,and adsorption configurations,extensive time-consuming simulation calculations are required for the high-throughput screening method.Additionally,multi-objective attributes should be considered simultaneously in catalytic design.To tackle this challenge,this paper suggests a multi-objective cobalt phosphide catalytic material design method based on surrogate models.And the effectiveness of the proposed method was validated through comparative experiments.The proposed method led to the discovery of fifteen promising cobalt phosphide catalyst configurations.This study provides a new avenue for expediting the design of catalyst,with the potential for application in other systems.展开更多
The authors regret that the original publication of this paper did not include Jawad Fayaz as a co-author.After further discussions and a thorough review of the research contributions,it was agreed that his significan...The authors regret that the original publication of this paper did not include Jawad Fayaz as a co-author.After further discussions and a thorough review of the research contributions,it was agreed that his significant contributions to the foundational aspects of the research warranted recognition,and he has now been added as a co-author.展开更多
Coalbed methane(CBM)is a vital unconventional energy resource,and predicting its spatiotemporal pressure dynamics is crucial for efficient development strategies.This paper proposes a novel deep learningebased data-dr...Coalbed methane(CBM)is a vital unconventional energy resource,and predicting its spatiotemporal pressure dynamics is crucial for efficient development strategies.This paper proposes a novel deep learningebased data-driven surrogate model,AxialViT-ConvLSTM,which integrates AxialAttention Vision Transformer,ConvLSTM,and an enhanced loss function to predict pressure dynamics in CBM reservoirs.The results showed that the model achieves a mean square error of 0.003,a learned perceptual image patch similarity of 0.037,a structural similarity of 0.979,and an R^(2) of 0.982 between predictions and actual pressures,indicating excellent performance.The model also demonstrates strong robustness and accuracy in capturing spatialetemporal pressure features.展开更多
This paper proposed a RIME-VMD-BiLSTM surrogate model to rapidly and precisely predict the seismic response of a nonlinear vehicle-track-bridge(VTB)system.The surrogate model employs the RIME algorithm to optimize the...This paper proposed a RIME-VMD-BiLSTM surrogate model to rapidly and precisely predict the seismic response of a nonlinear vehicle-track-bridge(VTB)system.The surrogate model employs the RIME algorithm to optimize the variational mode decomposition(VMD)parameters(k and α)and the architecture and hyperparameter of the bidirectional long-and short-term memory network(BiLSTM).After comparing different combinations and optimization algorithms,the surrogate model was trained and used to analyze a typical 9-span 32-m high-speed railway simply supported bridge system.A series of numerical examples considering the vehicle speed,bridge damping,seismic intensity,and training strategy on the prediction effect of the surrogate model were conducted on the extended OpenSees platform.The results show that the BiLSTM model performed better than the LSTM model,whereas the prediction effects of the single-LSTM and BiLSTM models were relatively poor.With the introduction of the VMD and RIME optimization techniques,the prediction effect of the proposed RIME-VMD-BiLSTM model was excellent.The abovementioned factors had a significant influence on the seismic response of a VTB system but little impact on the prediction effect of the surrogate model.The proposed surrogate model exhibits notable transferability and robustness for predicting the VTB’s nonlinear seismic response.展开更多
In the realm of subsurface flow simulations,deep-learning-based surrogate models have emerged as a promising alternative to traditional simulation methods,especially in addressing complex optimization problems.However...In the realm of subsurface flow simulations,deep-learning-based surrogate models have emerged as a promising alternative to traditional simulation methods,especially in addressing complex optimization problems.However,a significant challenge lies in the necessity of numerous high-fidelity training simulations to construct these deep-learning models,which limits their application to field-scale problems.To overcome this limitation,we introduce a training procedure that leverages transfer learning with multi-fidelity training data to construct surrogate models efficiently.The procedure begins with the pre-training of the surrogate model using a relatively larger amount of data that can be efficiently generated from upscaled coarse-scale models.Subsequently,the model parameters are finetuned with a much smaller set of high-fidelity simulation data.For the cases considered in this study,this method leads to about a 75%reduction in total computational cost,in comparison with the traditional training approach,without any sacrifice of prediction accuracy.In addition,a dedicated well-control embedding model is introduced to the traditional U-Net architecture to improve the surrogate model's prediction accuracy,which is shown to be particularly effective when dealing with large-scale reservoir models under time-varying well control parameters.Comprehensive results and analyses are presented for the prediction of well rates,pressure and saturation states of a 3D synthetic reservoir system.Finally,the proposed procedure is applied to a field-scale production optimization problem.The trained surrogate model is shown to provide excellent generalization capabilities during the optimization process,in which the final optimized net-present-value is much higher than those from the training data ranges.展开更多
Accurate acquisition of the rock stress is crucial for various rock engineering applications.The hollow inclusion (HI) technique is widely used for measuring in-situ rock stress.This technique calculates the stress te...Accurate acquisition of the rock stress is crucial for various rock engineering applications.The hollow inclusion (HI) technique is widely used for measuring in-situ rock stress.This technique calculates the stress tensor by measuring strain using an HI strain cell.However,existing analytical solutions for stress calculation based on an HI strain cell in a double-layer medium are not applicable when an HI strain cell is used in a three-layer medium,leading to erroneous stress calculations.To address this issue,this paper presents a method for calculating stress tensors in a three-layer medium using numerical simulations,specifically by obtaining a constitutive matrix that relates strain measurements to stress tensors in a three-layer medium.Furthermore,using Latin hypercube sampling (LHS) and orthogonal experimental design strategies,764 groups of numerical models encompassing various stress measurement scenarios have been established and calculated using FLAC^(3D)software.Finally,a surrogate model based on artificial neural network (ANN) was developed to predict constitutive matrices,achieving a goodness of fit (R^(2)) of 0.999 and a mean squared error (MSE) of 1.254.A software program has been developed from this surrogate model for ease of use in practical engineering applications.The method’s accuracy was verified through numerical simulations,analytical solution and laboratory experiment,demonstrating its effectiveness in calculating stress in a three-layer medium.The surrogate model was applied to calculate mining-induced stress in the roadway roof rock of a coal mine,a typical case for stress measurement in a three-layer medium.Errors in stress calculations arising from the use of existing analytical solutions were corrected.The study also highlights the significant errors associated with using double-layer analytical solutions in a three-layer medium,which could lead to inappropriate engineering design.展开更多
The surrogate model serves as an efficient simulation tool during the slope parameter inversion process.However,the creep constitutive model integrated with dynamic damage evolution poses challenges in development of ...The surrogate model serves as an efficient simulation tool during the slope parameter inversion process.However,the creep constitutive model integrated with dynamic damage evolution poses challenges in development of the required surrogate model.In this study,a novel physics knowledge-based surrogate model framework is proposed.In this framework,a Transformer module is employed to capture straindriven softening-hardening physical mechanisms.Positional encoding and self-attention are utilized to transform the constitutive parameters associated with shear strain,which are not directly time-related,into intermediate latent features for physical loss calculation.Next,a multi-layer stacked GRU(gated recurrent unit)network is built to provide input interfaces for time-dependent intermediate latent features,hydraulic boundary conditions,and water-rock interaction degradation equations,with static parameters introduced via external fully-connected layers.Finally,a combined loss function is constructed to facilitate the collaborative training of physical and data loss,introducing time-dependent weight adjustments to focus the surrogate model on accurate deformation predictions during critical phases.Based on the deformation of a reservoir bank landslide triggered by impoundment and subsequent restabilization,an elasto-viscoplastic constitutive model that considers water effect and sliding state dependencies is developed to validate the proposed surrogate model framework.The results indicate that the framework exhibits good performance in capturing physical mechanisms and predicting creep behavior,reducing errors by about 30 times compared to baseline models such as GRU and LSTM(long short-term memory),meeting the precision requirements for parameter inversion.Ablation experiments also confirmed the effectiveness of the framework.This framework can also serve as a reference for constructing other creep surrogate models that involve non-time-related across dimensions.展开更多
The rapid development of evolutionary deep learning has led to the emergence of various Neural Architecture Search(NAS)algorithms designed to optimize neural network structures.However,these algorithms often face sign...The rapid development of evolutionary deep learning has led to the emergence of various Neural Architecture Search(NAS)algorithms designed to optimize neural network structures.However,these algorithms often face significant computational costs due to the time-consuming process of training neural networks and evaluating their performance.Traditional NAS approaches,which rely on exhaustive evaluations and large training datasets,are inefficient for solving complex image classification tasks within limited time frames.To address these challenges,this paper proposes a novel NAS algorithm that integrates a hierarchical evaluation strategy based on Surrogate models,specifically using supernet to pre-trainweights and randomforests as performance predictors.This hierarchical framework combines rapid Surrogate model evaluations with traditional,precise evaluations to balance the trade-off between performance accuracy and computational efficiency.The algorithm significantly reduces the time required for model evaluation by predicting the fitness of candidate architectures using a random forest Surrogate model,thus alleviating the need for full training cycles for each architecture.The proposed method also incorporates evolutionary operations such as mutation and crossover to refine the search process and improve the accuracy of the resulting architectures.Experimental evaluations on the CIFAR-10 and CIFAR-100 datasets demonstrate that the proposed hierarchical evaluation strategy reduces the search time and costs compared to traditional methods,while achieving comparable or even superior model performance.The results suggest that this approach can efficiently handle resourceconstrained tasks,providing a promising solution for accelerating the NAS process without compromising the quality of the generated architectures.展开更多
This study proposes a multi-objective optimization framework for electric winches in fiber-reinforced plastic(FRP)fishing vessels to address critical limitations of conventional designs,including excessive weight,mate...This study proposes a multi-objective optimization framework for electric winches in fiber-reinforced plastic(FRP)fishing vessels to address critical limitations of conventional designs,including excessive weight,material inefficiency,and performance redundancy.By integrating surrogate modeling techniques with a multi-objective genetic algorithm(MOGA),we have developed a systematic approach that encompasses parametric modeling,finite element analysis under extreme operational conditions,and multi-fidelity performance evaluation.Through a 10-t electric winch case study,the methodology’s effectiveness is demonstrated via parametric characterization of structural integrity,stiffness behavior,and mass distribution.The comparative analysis identified optimal surrogate models for predicting key performance metrics,which enabled the construction of a robust multi-objective optimization model.The MOGA-derived Pareto solutions produced a design configuration achieving 7.86%mass reduction,2.01%safety factor improvement,and 23.97%deformation mitigation.Verification analysis confirmed the optimization scheme’s reliability in balancing conflicting design requirements.This research establishes a generalized framework for marine deck machinery modernization,particularly addressing the structural compatibility challenges in FRP vessel retrofitting.The proposed methodology demonstrates significant potential for facilitating sustainable upgrades of fishing vessel equipment through systematic performance optimization.展开更多
Self-propelled robots have attracted significant attention due to their remarkable ability to navigate confined terrains.These robots usually have deformable structures while having discontinuous contact forces with t...Self-propelled robots have attracted significant attention due to their remarkable ability to navigate confined terrains.These robots usually have deformable structures while having discontinuous contact forces with the ground,resulting in a complex nonlinear system.To provide a solid foundation for the locomotion prediction and optimization for the self-propelled robots,it is necessary to conduct dynamic modelling and locomotion analysis of the robot.Motivated by these issues,this paper proposes a vibration-driven surrogate dynamic model for a deformable self-propelled robot and presents a detailed dynamic analysis.The surrogate dynamic model is employed to classify various types of stick-slip locomotion.Subsequently,the corresponding experiment demonstrates that the surrogate dynamic model effectively predicts the locomotion of the robot,particularly three types of stick-slip locomotion induced by discontinuous friction.Finally,a multi-objective coordinated optimization regarding the locomotion velocity,the cost of transport,and the energy conversion rate of the self-propelled robot is conducted,aiming to comprehensively enhance the robot’s locomotion performance.Additionally,suggestions for the selection of actuation parameters are presented.展开更多
To reduce the high computational cost of the uncertainty analysis, a procedure is proposed for the aerodynamic optimization under uncertainties, in which the surrogate model is used to simplify the computation of the ...To reduce the high computational cost of the uncertainty analysis, a procedure is proposed for the aerodynamic optimization under uncertainties, in which the surrogate model is used to simplify the computation of the uncertainty analysis. The surrogate model is constructed by using the Latin Hypercube design and the Kriging model. The random parameters are used to account for the small manufacturing errors and the variations of operating conditions. Based on the surrogate model, an uncertainty analysis approach, called the Monte Carlo simulation, is used to compute the mean value and the variance of the predicated performance. The robust optimization for aerodynamic design is formulated, and solved by the genetic algorithm. And then, an airfoil optimization problem is used to test the proposed procedure. Results show that the optimal solutions obtained from the uncertainty-based optimization formulation are less sensitive to uncertainties. And the design constraints are still satisfied under the uncertainties.展开更多
This study investigates the uncertain dynamic characterization of hybrid composite plates by employing advanced machine-assisted finite element methodologies.Hybrid composites,widely used in aerospace,automotive,and s...This study investigates the uncertain dynamic characterization of hybrid composite plates by employing advanced machine-assisted finite element methodologies.Hybrid composites,widely used in aerospace,automotive,and structural applications,often face variability in material properties,geometric configurations,and manufacturing processes,leading to uncertainty in their dynamic response.To address this,three surrogate-based machine learning approaches like radial basis function(RBF),multivariate adaptive regression splines(MARS),and polynomial neural networks(PNN)are integrated with a finite element framework to efficiently capture the stochastic behavior of these plates.The research focuses on predicting the first three natural frequencies under material uncertainties,which are critical to ensuring structural reliability.Monte Carlo simulation(MCS)is used as a benchmark for generating probabilistic datasets,including mean values,standard deviations,and probability density functions.The surrogate models are then trained and validated against these datasets,enabling accurate representation of uncertainty with substantially fewer samples compared to conventionalMCS.Among the methods studied,the RBFmodel demonstrates superior performance,closely approximating MCS results with a reduced sample size,thereby achieving significant computational savings.The proposed framework not only reduces computational time and costs but also maintains high predictive accuracy,making it well-suited for complex engineering systems.Beyond free vibration analysis,the methodology can be extended to more sophisticated scenarios,such as forced vibration,damping effects,and nonlinear structural responses.Overall,this work presents a computationally efficient and robust approach for surrogate-based uncertainty quantification,advancing the analysis and design of hybrid composite structures under uncertainty.展开更多
The roller is one of the fundamental elements of ore belt conveyor systems since it supports,guides,and directs material on the belt.This component comprises a body(the external tube)that rotates around a fixed shaft ...The roller is one of the fundamental elements of ore belt conveyor systems since it supports,guides,and directs material on the belt.This component comprises a body(the external tube)that rotates around a fixed shaft supported by easels.The external tube and shaft of rollers used in ore conveyor belts are mostly made of steel,resulting in high mass,hindering maintenance and replacement.Aiming to achieve mass reduction,we conducted a structural optimization of a roller with a polymeric external tube(hereafter referred to as a polymeric roller),seeking the optimal values for two design parameters:the inner diameter of the external tube and the shaft diameter.The optimization was constrained by admissible values for maximum stress,maximum deflection and misalignment angle between the shaft and bearings.A finite element model was built in Ansys Workbench to obtain the structural response of the system.The roller considered is composed of an external tube made of high-density polyethylene(HDPE),bearing seats of polyamide 6(PA6),and a steel shaft.To characterize the polymeric materials(HDPE and PA6),stress relaxation tests were conducted,and the data on shear modulus variation over time were inserted into the model to calculate Prony series terms to account for viscoelastic effects.The roller optimization was performed using surrogate modeling based on radial basis functions,with the Globalized Bounded Nelder-Mead(GBNM)algorithm as the optimizer.Two optimization cases were conducted.In the first case,concerning the roller’s initial material settings,the designs found violated the constraints and could not reduce mass.In the second case,by using PA6 in both bearing seats and the tube,a design configuration was found that respected all constraints and reduced the roller mass by 15.5%,equivalent to 5.15 kg.This study is among the first to integrate experimentally obtained viscoelastic data into the surrogate-based optimization of polymeric rollers,combining methodological innovation with industrial relevance.展开更多
A Hybrid Free-Form Deformation(HFFD)method is developed to improve shape preservation in mesh deformation for perforated surfaces,which traditional Free-Form Deformation(FFD)techniques struggle to handle effectively.T...A Hybrid Free-Form Deformation(HFFD)method is developed to improve shape preservation in mesh deformation for perforated surfaces,which traditional Free-Form Deformation(FFD)techniques struggle to handle effectively.The proposed method enables high-fidelity parameterized deformation for both flat and curved perforated surfaces while maintaining mesh quality with minimal geometric distortion.To evaluate its effectiveness,comparative studies between HFFD and conventional FFD methods are conducted,demonstrating superior performance in mesh quality and geometric fidelity.The HFFD-based framework is further applied to the Multidisciplinary Design Optimization(MDO)of a double-wall turbine blade leading edge.Results indicate an 11.6%increase in cooling efficiency and a 16.21%reduction in maximum stress.Additionally,compared to traditional geometry-based parameterization in MDO,the HFFD approach improves model processing efficiency by 84.15%and overall optimization efficiency by20.05%.These findings demonstrate HFFD's potential to significantly improve complex engineering design optimization by achieving precise shape preservation and improving computational efficiency.展开更多
Abstract Based on computational fluid dynamics （CFD） method, electromagnetic high-frequency method and surrogate model optimization techniques, an integration design method about aerody- namic/stealth has been estab...Abstract Based on computational fluid dynamics （CFD） method, electromagnetic high-frequency method and surrogate model optimization techniques, an integration design method about aerody- namic/stealth has been established for helicopter rotor. The developed integration design method is composed of three modules： integrated grids generation （the moving-embedded grids for CFD sol- ver and the blade grids for radar cross section （RCS） solver are generated by solving Poisson equa- tions and folding approach）, aerodynamic/stealth solver （the aerodynamic characteristics are simulated by CFD method based upon NavieStokes equations and Spalart-Allmaras （S-A） tur- bulence model）, and the stealth characteristics are calculated by using a panel edge method combining the method of physical optics （PO）, equivalent currents （MEC） and quasi-stationary （MQS）, and integrated optimization analysis （based upon the surrogate model optimization technique with full factorial design （FFD） and radial basis function （RBF）, an integrated optimization analyses on aerodynamic/stealth characteristics of rotor are conducted. Firstly, the scattering characteristics of the rotor with different blade-tip swept and twist angles have been carried out, then timfrequency domain grayscale with strong scattering regions of rotor have been given. Meanwhile, the effects of swept-tip and twist angles on the aerodynamic characteristic of rotor have been performed. Furthermore, by choosing suitable object function and constraint condition, the compromised design about swept and twist combinations of rotor with high aerodynamic performances and low scattering characteristics has been given at last.展开更多
An efficient method employing a Principal Component Analysis(PCA)-Deep Belief Network(DBN)-based surrogate model is developed for robust aerodynamic design optimization in this study.In order to reduce the number of d...An efficient method employing a Principal Component Analysis(PCA)-Deep Belief Network(DBN)-based surrogate model is developed for robust aerodynamic design optimization in this study.In order to reduce the number of design variables for aerodynamic optimizations,the PCA technique is implemented to the geometric parameters obtained by parameterization method.For the purpose of predicting aerodynamic parameters,the DBN model is established with the reduced design variables as input and the aerodynamic parameters as output,and it is trained using the k-step contrastive divergence algorithm.The established PCA-DBN-based surrogate model is validated through predicting lift-to-drag ratios of a set of airfoils,and the results indicate that the PCA-DBN-based surrogate model is reliable and obtains more accurate predictions than three other surrogate models.Then the efficient optimization method is established by embedding the PCA-DBN-based surrogate model into an improved Particle Swarm Optimization(PSO)framework,and applied to the robust aerodynamic design optimizations of Natural Laminar Flow(NLF)airfoil and transonic wing.The optimization results indicate that the PCA-DBN-based surrogate model works very well as a prediction model in the robust optimization processes of both NLF airfoil and transonic wing.By employing the PCA-DBN-based surrogate model,the developed efficient method improves the optimization efficiency obviously.展开更多
基金supported by the Science and Technology Research Project of Henan Province(242102241055)the Industry-University-Research Collaborative Innovation Base on Automobile Lightweight of“Science and Technology Innovation in Central Plains”(2024KCZY315)the Opening Fund of State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment(GZ2024A03-ZZU).
文摘The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.
基金Supported by the National Key Research and Development Program of China(2022YFB3904803)。
文摘The Infrared Hyperspectral Atmospheric SounderⅡ(HIRAS-Ⅱ)is the key equipment on FengYun-3E(FY-3E)satellite,which can realize vertical atmospheric detection,featuring hyper spectral,high sensitivity and high precision.To ensure its accuracy of detection,it is necessary to correlate their thermal models to in-orbit da⁃ta.In this work,an investigation of intelligent correlation method named Intelligent Correlation Platform for Ther⁃mal Model(ICP-TM)was established,the advanced Kriging surrogate model and efficient adaptive region opti⁃mization algorithm were introduced.After the correlation with this method for FY-3E/HIRAS-Ⅱ,the results indi⁃cate that compared with the data in orbit,the error of the thermal model has decreased from 5 K to within±1 K in cold case(10℃).Then,the correlated model is validated in hot case(20℃),and the correlated model exhibits good universality.This correlation precision is also much superiors to the general ones like 3 K in other similar lit⁃erature.Furthermore,the process is finished in 8 days using ICP-TM,the efficiency is much better than 3 months based on manual.The results show that the proposed approach significantly enhances the accuracy and efficiency of thermal model,this contributes to the precise thermal control of subsequent infrared optical payloads.
基金supported by the National Natural Science Foundation of China under Grant 52325402,52274057,and 52074340the National Key R&D Program of China under Grant 2023YFB4104200+2 种基金the Major Scientific and Technological Projects of CNOOC under Grant CCL2022RCPS0397RSN111 Project under Grant B08028China Scholarship Council under Grant 202306450108.
文摘This study introduces a novel approach to addressing the challenges of high-dimensional variables and strong nonlinearity in reservoir production and layer configuration optimization.For the first time,relational machine learning models are applied in reservoir development optimization.Traditional regression-based models often struggle in complex scenarios,but the proposed relational and regression-based composite differential evolution(RRCODE)method combines a Gaussian naive Bayes relational model with a radial basis function network regression model.This integration effectively captures complex relationships in the optimization process,improving both accuracy and convergence speed.Experimental tests on a multi-layer multi-channel reservoir model,the Egg reservoir model,and a real-field reservoir model(the S reservoir)demonstrate that RRCODE significantly reduces water injection and production volumes while increasing economic returns and cumulative oil recovery.Moreover,the surrogate models employed in RRCODE exhibit lightweight characteristics with low computational overhead.These results highlight RRCODE's superior performance in the integrated optimization of reservoir production and layer configurations,offering more efficient and economically viable solutions for oilfield development.
基金supported by the National Natural Science Foundation of China(Nos.51775021,52302511)the Fundamental Research Funds for the Central Universities,China(Nos.YWF-23-JC-01,YWF-23-JC-04,YWF-23-JC-09)。
文摘Stratospheric airships are lighter-than-air vehicles capable of continuous flying for months.The energy balance of the airship is the key to long-duration flights.The stratospheric airship is entirely powered by the solar array.It is necessary to accurately predict the output power of the array for any flight state.Because of the uneven solar radiation received by the solar array,the traditional model based on components has a slow simulation speed.In this study,a data-driven surrogate modeling approach for prediction the output power of the solar array is proposed.The surrogate model is trained using the samples obtained from the high-accuracy simulation model.By using the input parameter preprocessor,the accuracy of the surrogate model in predicting the output power of the solar array is improved to 98.65%.In addition,the predictive speed of the surrogate model is ten million times faster than the traditional simulation model.Finally,the surrogate model is used to predict the energy balance of stratospheric airships flying throughout the year under actual global wind fields.
基金supported by the Jiangxi Provincial Natural Science Foundation(No.20224BAB212022)Science and Technology Project of Education Department of Jiangxi Province(No.GJJ211435)+3 种基金the National Key Research and Development Program of China(No.2021YFA1400204)the Project of China Postdoctoral Science Foundation(No.2022M712909)the Natural Science Foundation of China(No.21603109)the Henan Joint Fund of the National Natural Science Foundation of China(No.U1404216)。
文摘Cobalt phosphide has been successfully used as a catalyst in the production of ammonia from nitric acid.Substituting appropriate atoms is expected to further improve its catalytic performance.Owing to the diversity of substituting elements,substitution sites,adsorption sites,and adsorption configurations,extensive time-consuming simulation calculations are required for the high-throughput screening method.Additionally,multi-objective attributes should be considered simultaneously in catalytic design.To tackle this challenge,this paper suggests a multi-objective cobalt phosphide catalytic material design method based on surrogate models.And the effectiveness of the proposed method was validated through comparative experiments.The proposed method led to the discovery of fifteen promising cobalt phosphide catalyst configurations.This study provides a new avenue for expediting the design of catalyst,with the potential for application in other systems.
文摘The authors regret that the original publication of this paper did not include Jawad Fayaz as a co-author.After further discussions and a thorough review of the research contributions,it was agreed that his significant contributions to the foundational aspects of the research warranted recognition,and he has now been added as a co-author.
基金the National Natural Science Foundation of China(No.52474068)the Major Collab-orative Innovation Project of Prospecting Breakthrough Stra-tegic Action in Guizhou Province(No.[2022]ZD001-003).
文摘Coalbed methane(CBM)is a vital unconventional energy resource,and predicting its spatiotemporal pressure dynamics is crucial for efficient development strategies.This paper proposes a novel deep learningebased data-driven surrogate model,AxialViT-ConvLSTM,which integrates AxialAttention Vision Transformer,ConvLSTM,and an enhanced loss function to predict pressure dynamics in CBM reservoirs.The results showed that the model achieves a mean square error of 0.003,a learned perceptual image patch similarity of 0.037,a structural similarity of 0.979,and an R^(2) of 0.982 between predictions and actual pressures,indicating excellent performance.The model also demonstrates strong robustness and accuracy in capturing spatialetemporal pressure features.
基金Project(52108433)supported by the National Natural Science Foundation of ChinaProject(HSR202004)supported by the Open Foundation of National Engineering Research Center of High-Speed Railway Construction Technology(CSU),China+3 种基金Projects(2024RC3170,2021RC4031)supported by the Science and Technology Innovation Program of Hunan Province,ChinaProjects(2024JJ5018,2024JJ5427)supported by the Hunan Provincial Natural Science Foundation,ChinaProject(KQ2402027)supported by the Changsha City Natural Science Foundation,ChinaProjects(2021-Special-08,2022-Special-09)supported by the Science and Technology Research and Development Program Project of China Railway Group Limited。
文摘This paper proposed a RIME-VMD-BiLSTM surrogate model to rapidly and precisely predict the seismic response of a nonlinear vehicle-track-bridge(VTB)system.The surrogate model employs the RIME algorithm to optimize the variational mode decomposition(VMD)parameters(k and α)and the architecture and hyperparameter of the bidirectional long-and short-term memory network(BiLSTM).After comparing different combinations and optimization algorithms,the surrogate model was trained and used to analyze a typical 9-span 32-m high-speed railway simply supported bridge system.A series of numerical examples considering the vehicle speed,bridge damping,seismic intensity,and training strategy on the prediction effect of the surrogate model were conducted on the extended OpenSees platform.The results show that the BiLSTM model performed better than the LSTM model,whereas the prediction effects of the single-LSTM and BiLSTM models were relatively poor.With the introduction of the VMD and RIME optimization techniques,the prediction effect of the proposed RIME-VMD-BiLSTM model was excellent.The abovementioned factors had a significant influence on the seismic response of a VTB system but little impact on the prediction effect of the surrogate model.The proposed surrogate model exhibits notable transferability and robustness for predicting the VTB’s nonlinear seismic response.
基金funding support from the National Natural Science Foundation of China(No.52204065,No.ZX20230398)supported by a grant from the Human Resources Development Program(No.20216110100070)of the Korea Institute of Energy Technology Evaluation and Planning(KETEP)。
文摘In the realm of subsurface flow simulations,deep-learning-based surrogate models have emerged as a promising alternative to traditional simulation methods,especially in addressing complex optimization problems.However,a significant challenge lies in the necessity of numerous high-fidelity training simulations to construct these deep-learning models,which limits their application to field-scale problems.To overcome this limitation,we introduce a training procedure that leverages transfer learning with multi-fidelity training data to construct surrogate models efficiently.The procedure begins with the pre-training of the surrogate model using a relatively larger amount of data that can be efficiently generated from upscaled coarse-scale models.Subsequently,the model parameters are finetuned with a much smaller set of high-fidelity simulation data.For the cases considered in this study,this method leads to about a 75%reduction in total computational cost,in comparison with the traditional training approach,without any sacrifice of prediction accuracy.In addition,a dedicated well-control embedding model is introduced to the traditional U-Net architecture to improve the surrogate model's prediction accuracy,which is shown to be particularly effective when dealing with large-scale reservoir models under time-varying well control parameters.Comprehensive results and analyses are presented for the prediction of well rates,pressure and saturation states of a 3D synthetic reservoir system.Finally,the proposed procedure is applied to a field-scale production optimization problem.The trained surrogate model is shown to provide excellent generalization capabilities during the optimization process,in which the final optimized net-present-value is much higher than those from the training data ranges.
基金funding support from the National Natural Science Foundation of China (Nos. 42477208 and 52079134)the Natural Science Foundation of Hubei Province, China (No. 2024AFA072)+2 种基金the Youth Innovation Promotion Association CAS (No. 2022332)the National Key R&D Program of China (No. 2024YFF0508203)the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering Safety (Nos. SKLGME-JBGS2402 and SKLGME022022)。
文摘Accurate acquisition of the rock stress is crucial for various rock engineering applications.The hollow inclusion (HI) technique is widely used for measuring in-situ rock stress.This technique calculates the stress tensor by measuring strain using an HI strain cell.However,existing analytical solutions for stress calculation based on an HI strain cell in a double-layer medium are not applicable when an HI strain cell is used in a three-layer medium,leading to erroneous stress calculations.To address this issue,this paper presents a method for calculating stress tensors in a three-layer medium using numerical simulations,specifically by obtaining a constitutive matrix that relates strain measurements to stress tensors in a three-layer medium.Furthermore,using Latin hypercube sampling (LHS) and orthogonal experimental design strategies,764 groups of numerical models encompassing various stress measurement scenarios have been established and calculated using FLAC^(3D)software.Finally,a surrogate model based on artificial neural network (ANN) was developed to predict constitutive matrices,achieving a goodness of fit (R^(2)) of 0.999 and a mean squared error (MSE) of 1.254.A software program has been developed from this surrogate model for ease of use in practical engineering applications.The method’s accuracy was verified through numerical simulations,analytical solution and laboratory experiment,demonstrating its effectiveness in calculating stress in a three-layer medium.The surrogate model was applied to calculate mining-induced stress in the roadway roof rock of a coal mine,a typical case for stress measurement in a three-layer medium.Errors in stress calculations arising from the use of existing analytical solutions were corrected.The study also highlights the significant errors associated with using double-layer analytical solutions in a three-layer medium,which could lead to inappropriate engineering design.
基金supported by the National Natural Science Foundation of China(Grant No.41961134032).
文摘The surrogate model serves as an efficient simulation tool during the slope parameter inversion process.However,the creep constitutive model integrated with dynamic damage evolution poses challenges in development of the required surrogate model.In this study,a novel physics knowledge-based surrogate model framework is proposed.In this framework,a Transformer module is employed to capture straindriven softening-hardening physical mechanisms.Positional encoding and self-attention are utilized to transform the constitutive parameters associated with shear strain,which are not directly time-related,into intermediate latent features for physical loss calculation.Next,a multi-layer stacked GRU(gated recurrent unit)network is built to provide input interfaces for time-dependent intermediate latent features,hydraulic boundary conditions,and water-rock interaction degradation equations,with static parameters introduced via external fully-connected layers.Finally,a combined loss function is constructed to facilitate the collaborative training of physical and data loss,introducing time-dependent weight adjustments to focus the surrogate model on accurate deformation predictions during critical phases.Based on the deformation of a reservoir bank landslide triggered by impoundment and subsequent restabilization,an elasto-viscoplastic constitutive model that considers water effect and sliding state dependencies is developed to validate the proposed surrogate model framework.The results indicate that the framework exhibits good performance in capturing physical mechanisms and predicting creep behavior,reducing errors by about 30 times compared to baseline models such as GRU and LSTM(long short-term memory),meeting the precision requirements for parameter inversion.Ablation experiments also confirmed the effectiveness of the framework.This framework can also serve as a reference for constructing other creep surrogate models that involve non-time-related across dimensions.
文摘The rapid development of evolutionary deep learning has led to the emergence of various Neural Architecture Search(NAS)algorithms designed to optimize neural network structures.However,these algorithms often face significant computational costs due to the time-consuming process of training neural networks and evaluating their performance.Traditional NAS approaches,which rely on exhaustive evaluations and large training datasets,are inefficient for solving complex image classification tasks within limited time frames.To address these challenges,this paper proposes a novel NAS algorithm that integrates a hierarchical evaluation strategy based on Surrogate models,specifically using supernet to pre-trainweights and randomforests as performance predictors.This hierarchical framework combines rapid Surrogate model evaluations with traditional,precise evaluations to balance the trade-off between performance accuracy and computational efficiency.The algorithm significantly reduces the time required for model evaluation by predicting the fitness of candidate architectures using a random forest Surrogate model,thus alleviating the need for full training cycles for each architecture.The proposed method also incorporates evolutionary operations such as mutation and crossover to refine the search process and improve the accuracy of the resulting architectures.Experimental evaluations on the CIFAR-10 and CIFAR-100 datasets demonstrate that the proposed hierarchical evaluation strategy reduces the search time and costs compared to traditional methods,while achieving comparable or even superior model performance.The results suggest that this approach can efficiently handle resourceconstrained tasks,providing a promising solution for accelerating the NAS process without compromising the quality of the generated architectures.
基金supported by the Basic Public Welfare Research Program of Zhejiang Province(No.LGN22E050005).
文摘This study proposes a multi-objective optimization framework for electric winches in fiber-reinforced plastic(FRP)fishing vessels to address critical limitations of conventional designs,including excessive weight,material inefficiency,and performance redundancy.By integrating surrogate modeling techniques with a multi-objective genetic algorithm(MOGA),we have developed a systematic approach that encompasses parametric modeling,finite element analysis under extreme operational conditions,and multi-fidelity performance evaluation.Through a 10-t electric winch case study,the methodology’s effectiveness is demonstrated via parametric characterization of structural integrity,stiffness behavior,and mass distribution.The comparative analysis identified optimal surrogate models for predicting key performance metrics,which enabled the construction of a robust multi-objective optimization model.The MOGA-derived Pareto solutions produced a design configuration achieving 7.86%mass reduction,2.01%safety factor improvement,and 23.97%deformation mitigation.Verification analysis confirmed the optimization scheme’s reliability in balancing conflicting design requirements.This research establishes a generalized framework for marine deck machinery modernization,particularly addressing the structural compatibility challenges in FRP vessel retrofitting.The proposed methodology demonstrates significant potential for facilitating sustainable upgrades of fishing vessel equipment through systematic performance optimization.
基金supported by the National Natural Science Foundation of China(Grant Nos.11932015,12072237,and 12372022)the Shanghai Gaofeng Project for University Academic Program Development,and the Fundamental Research Funds for the Central Universities(Grant No.22120220590).
文摘Self-propelled robots have attracted significant attention due to their remarkable ability to navigate confined terrains.These robots usually have deformable structures while having discontinuous contact forces with the ground,resulting in a complex nonlinear system.To provide a solid foundation for the locomotion prediction and optimization for the self-propelled robots,it is necessary to conduct dynamic modelling and locomotion analysis of the robot.Motivated by these issues,this paper proposes a vibration-driven surrogate dynamic model for a deformable self-propelled robot and presents a detailed dynamic analysis.The surrogate dynamic model is employed to classify various types of stick-slip locomotion.Subsequently,the corresponding experiment demonstrates that the surrogate dynamic model effectively predicts the locomotion of the robot,particularly three types of stick-slip locomotion induced by discontinuous friction.Finally,a multi-objective coordinated optimization regarding the locomotion velocity,the cost of transport,and the energy conversion rate of the self-propelled robot is conducted,aiming to comprehensively enhance the robot’s locomotion performance.Additionally,suggestions for the selection of actuation parameters are presented.
文摘To reduce the high computational cost of the uncertainty analysis, a procedure is proposed for the aerodynamic optimization under uncertainties, in which the surrogate model is used to simplify the computation of the uncertainty analysis. The surrogate model is constructed by using the Latin Hypercube design and the Kriging model. The random parameters are used to account for the small manufacturing errors and the variations of operating conditions. Based on the surrogate model, an uncertainty analysis approach, called the Monte Carlo simulation, is used to compute the mean value and the variance of the predicated performance. The robust optimization for aerodynamic design is formulated, and solved by the genetic algorithm. And then, an airfoil optimization problem is used to test the proposed procedure. Results show that the optimal solutions obtained from the uncertainty-based optimization formulation are less sensitive to uncertainties. And the design constraints are still satisfied under the uncertainties.
文摘This study investigates the uncertain dynamic characterization of hybrid composite plates by employing advanced machine-assisted finite element methodologies.Hybrid composites,widely used in aerospace,automotive,and structural applications,often face variability in material properties,geometric configurations,and manufacturing processes,leading to uncertainty in their dynamic response.To address this,three surrogate-based machine learning approaches like radial basis function(RBF),multivariate adaptive regression splines(MARS),and polynomial neural networks(PNN)are integrated with a finite element framework to efficiently capture the stochastic behavior of these plates.The research focuses on predicting the first three natural frequencies under material uncertainties,which are critical to ensuring structural reliability.Monte Carlo simulation(MCS)is used as a benchmark for generating probabilistic datasets,including mean values,standard deviations,and probability density functions.The surrogate models are then trained and validated against these datasets,enabling accurate representation of uncertainty with substantially fewer samples compared to conventionalMCS.Among the methods studied,the RBFmodel demonstrates superior performance,closely approximating MCS results with a reduced sample size,thereby achieving significant computational savings.The proposed framework not only reduces computational time and costs but also maintains high predictive accuracy,making it well-suited for complex engineering systems.Beyond free vibration analysis,the methodology can be extended to more sophisticated scenarios,such as forced vibration,damping effects,and nonlinear structural responses.Overall,this work presents a computationally efficient and robust approach for surrogate-based uncertainty quantification,advancing the analysis and design of hybrid composite structures under uncertainty.
基金funded by Vale S.A.company(www.vale.com)and the Institute of Technology Vale(ITV—www.itv.org),grant number SAP 4600048682.
文摘The roller is one of the fundamental elements of ore belt conveyor systems since it supports,guides,and directs material on the belt.This component comprises a body(the external tube)that rotates around a fixed shaft supported by easels.The external tube and shaft of rollers used in ore conveyor belts are mostly made of steel,resulting in high mass,hindering maintenance and replacement.Aiming to achieve mass reduction,we conducted a structural optimization of a roller with a polymeric external tube(hereafter referred to as a polymeric roller),seeking the optimal values for two design parameters:the inner diameter of the external tube and the shaft diameter.The optimization was constrained by admissible values for maximum stress,maximum deflection and misalignment angle between the shaft and bearings.A finite element model was built in Ansys Workbench to obtain the structural response of the system.The roller considered is composed of an external tube made of high-density polyethylene(HDPE),bearing seats of polyamide 6(PA6),and a steel shaft.To characterize the polymeric materials(HDPE and PA6),stress relaxation tests were conducted,and the data on shear modulus variation over time were inserted into the model to calculate Prony series terms to account for viscoelastic effects.The roller optimization was performed using surrogate modeling based on radial basis functions,with the Globalized Bounded Nelder-Mead(GBNM)algorithm as the optimizer.Two optimization cases were conducted.In the first case,concerning the roller’s initial material settings,the designs found violated the constraints and could not reduce mass.In the second case,by using PA6 in both bearing seats and the tube,a design configuration was found that respected all constraints and reduced the roller mass by 15.5%,equivalent to 5.15 kg.This study is among the first to integrate experimentally obtained viscoelastic data into the surrogate-based optimization of polymeric rollers,combining methodological innovation with industrial relevance.
基金supported by the National Science and Technology Major Project,China(No.2017-II-0006-0019)the National Natural Science Foundation of China(No.52375266)the Shaanxi Science Foundation for Distinguished Young Scholars,China(No.2022JC-36)。
文摘A Hybrid Free-Form Deformation(HFFD)method is developed to improve shape preservation in mesh deformation for perforated surfaces,which traditional Free-Form Deformation(FFD)techniques struggle to handle effectively.The proposed method enables high-fidelity parameterized deformation for both flat and curved perforated surfaces while maintaining mesh quality with minimal geometric distortion.To evaluate its effectiveness,comparative studies between HFFD and conventional FFD methods are conducted,demonstrating superior performance in mesh quality and geometric fidelity.The HFFD-based framework is further applied to the Multidisciplinary Design Optimization(MDO)of a double-wall turbine blade leading edge.Results indicate an 11.6%increase in cooling efficiency and a 16.21%reduction in maximum stress.Additionally,compared to traditional geometry-based parameterization in MDO,the HFFD approach improves model processing efficiency by 84.15%and overall optimization efficiency by20.05%.These findings demonstrate HFFD's potential to significantly improve complex engineering design optimization by achieving precise shape preservation and improving computational efficiency.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions of China
文摘Abstract Based on computational fluid dynamics （CFD） method, electromagnetic high-frequency method and surrogate model optimization techniques, an integration design method about aerody- namic/stealth has been established for helicopter rotor. The developed integration design method is composed of three modules： integrated grids generation （the moving-embedded grids for CFD sol- ver and the blade grids for radar cross section （RCS） solver are generated by solving Poisson equa- tions and folding approach）, aerodynamic/stealth solver （the aerodynamic characteristics are simulated by CFD method based upon NavieStokes equations and Spalart-Allmaras （S-A） tur- bulence model）, and the stealth characteristics are calculated by using a panel edge method combining the method of physical optics （PO）, equivalent currents （MEC） and quasi-stationary （MQS）, and integrated optimization analysis （based upon the surrogate model optimization technique with full factorial design （FFD） and radial basis function （RBF）, an integrated optimization analyses on aerodynamic/stealth characteristics of rotor are conducted. Firstly, the scattering characteristics of the rotor with different blade-tip swept and twist angles have been carried out, then timfrequency domain grayscale with strong scattering regions of rotor have been given. Meanwhile, the effects of swept-tip and twist angles on the aerodynamic characteristic of rotor have been performed. Furthermore, by choosing suitable object function and constraint condition, the compromised design about swept and twist combinations of rotor with high aerodynamic performances and low scattering characteristics has been given at last.
基金co-supported by Aeronautical Science Foundation of China(No.2015ZBP9002)China Scholarship Council。
文摘An efficient method employing a Principal Component Analysis(PCA)-Deep Belief Network(DBN)-based surrogate model is developed for robust aerodynamic design optimization in this study.In order to reduce the number of design variables for aerodynamic optimizations,the PCA technique is implemented to the geometric parameters obtained by parameterization method.For the purpose of predicting aerodynamic parameters,the DBN model is established with the reduced design variables as input and the aerodynamic parameters as output,and it is trained using the k-step contrastive divergence algorithm.The established PCA-DBN-based surrogate model is validated through predicting lift-to-drag ratios of a set of airfoils,and the results indicate that the PCA-DBN-based surrogate model is reliable and obtains more accurate predictions than three other surrogate models.Then the efficient optimization method is established by embedding the PCA-DBN-based surrogate model into an improved Particle Swarm Optimization(PSO)framework,and applied to the robust aerodynamic design optimizations of Natural Laminar Flow(NLF)airfoil and transonic wing.The optimization results indicate that the PCA-DBN-based surrogate model works very well as a prediction model in the robust optimization processes of both NLF airfoil and transonic wing.By employing the PCA-DBN-based surrogate model,the developed efficient method improves the optimization efficiency obviously.
