To improve the computational efficiency and accuracy of multi-objective reliability estimation for aerospace engineering structural systems,the Intelligent Vectorial Surrogate Modeling(IVSM)concept is presented by fus...To improve the computational efficiency and accuracy of multi-objective reliability estimation for aerospace engineering structural systems,the Intelligent Vectorial Surrogate Modeling(IVSM)concept is presented by fusing the compact support region,surrogate modeling methods,matrix theory,and Bayesian optimization strategy.In this concept,the compact support region is employed to select effective modeling samples;the surrogate modeling methods are employed to establish a functional relationship between input variables and output responses;the matrix theory is adopted to establish the vector and cell arrays of modeling parameters and synchronously determine multi-objective limit state functions;the Bayesian optimization strategy is utilized to search for the optimal hyperparameters for modeling.Under this concept,the Intelligent Vectorial Neural Network(IVNN)method is proposed based on deep neural network to realize the reliability analysis of multi-objective aerospace engineering structural systems synchronously.The multioutput response function approximation problem and two engineering application cases(i.e.,landing gear brake system temperature and aeroengine turbine blisk multi-failures)are used to verify the applicability of IVNN method.The results indicate that the proposed approach holds advantages in modeling properties and simulation performances.The efforts of this paper can offer a valuable reference for the improvement of multi-objective reliability assessment theory.展开更多
In this paper,a surrogate-based modeling methodology is developed and presented to predict the elastic properties of three dimensional(3 D)four-directional braided composites.Using this approach,the prediction process...In this paper,a surrogate-based modeling methodology is developed and presented to predict the elastic properties of three dimensional(3 D)four-directional braided composites.Using this approach,the prediction process becomes feasible with only a limited number of training points.The surrogate models constructed using Finite Element(FE)method and Diffuse Approximation,reduce the computational time and cost for preparing experimental samples.In the FE model,multiscale method is applied to couple the computations of elastic properties at microscale and mesoscale.Subsequently,a parametric study is performed to analyze the effects of the three design parameters on the elastic properties.Satisfactory results are obtained via the surrogatebased modeling predictions,which are compared with the experimental measurements.Moreover,the predictions obtained from surrogate models concur well with the FE predictions.This study orients a new direction for predicting the mechanical properties based on surrogate models which can effectively reduce the sample preparation cost and computational efforts.展开更多
Practical experience has demonstrated that single objective functions, no matter how carefully chosen, prove to be inadequate in providing proper measurements for all of the characteristics of the observed data. One s...Practical experience has demonstrated that single objective functions, no matter how carefully chosen, prove to be inadequate in providing proper measurements for all of the characteristics of the observed data. One strategy to circumvent this problem is to define multiple fitting criteria that measure different aspects of system behavior, and to use multi-criteria optimization to identify non-dominated optimal solutions. Unfortunately, these analyses require running original simulation models thousands of times. As such, they demand prohibitively large computational budgets. As a result, surrogate models have been used in combination with a variety of multi- objective optimization algorithms to approximate the true Pareto-front within limited evaluations for the original model. In this study, multi-objective optimization based on surrogate modeling （multivariate adaptive regression splines, MARS） for a conceptual rainfall-runoff model （Xin＇anjiang model, XAJ） was proposed. Taking the Yanduhe basin of Three Gorges in the upper stream of the Yangtze River in China as a case study, three evaluation criteria were selected to quantify the goodness-of-fit of observations against calculated values from the simulation model. The three criteria chosen were the Nash-Sutcliffe efficiency coefficient, the relative error of peak flow, and runoff volume （REPF and RERV）. The efficacy of this method is demonstrated on the calibration of the XAJ model. Compared to the single objective optimization results, it was indicated that the multi-objective optimization method can infer the most probable parameter set. The results also demonstrate that the use of surrogate-modeling enables optimization that is much more efficient; and the total computational cost is reduced by about 92.5%, compared to optimization without using surrogate model- ing. The results obtained with the proposed method support the feasibility of applying parameter optimization to computationally intensive simulation models, via reducing the number of simulation runs required in the numerical model considerably.展开更多
During the pre-design stage of buildings,reliable long-term prediction of thermal loads is significant for cool-ing/heating system configuration and efficient operation.This paper proposes a surrogate modeling method ...During the pre-design stage of buildings,reliable long-term prediction of thermal loads is significant for cool-ing/heating system configuration and efficient operation.This paper proposes a surrogate modeling method to predict all-year hourly cooling/heating loads in high resolution for retail,hotel,and office buildings.16384 surrogate models are simulated in EnergyPlus to generate the load database,which contains 7 crucial building features as inputs and hourly loads as outputs.K-nearest-neighbors(KNN)is chosen as the data-driven algorithm to approximate the surrogates for load prediction.With test samples from the database,performances of five different spatial metrics for KNN are evaluated and optimized.Results show that the Manhattan distance is the optimal metric with the highest efficient hour rates of 93.57%and 97.14%for cooling and heating loads in office buildings.The method is verified by predicting the thermal loads of a given district in Shanghai,China.The mean absolute percentage errors(MAPE)are 5.26%and 6.88%for cooling/heating loads,respectively,and 5.63%for the annual thermal loads.The proposed surrogate modeling method meets the precision requirement of engineering in the building pre-design stage and achieves the fast prediction of all-year hourly thermal loads at the district level.As a data-driven approximation,it does not require as much detailed building information as the commonly used physics-based methods.And by pre-simulation of sufficient prototypical models,the method overcomes the gaps of data missing in current data-driven methods.展开更多
Process-based reactive transport modeling(RTM)integrates thermodynamic and kinetically controlled fluid-rock interactions with fluid flow through porous media in the subsurface and surface environment.RTM is usually c...Process-based reactive transport modeling(RTM)integrates thermodynamic and kinetically controlled fluid-rock interactions with fluid flow through porous media in the subsurface and surface environment.RTM is usually conducted through numerical programs based on the first principle of physical processes.However,the calculation for complex chemical reactions in most available programs is an iterative process,where each iteration is in general computationally intensive.A workflow of neural networkbased surrogate model as a proxy for process-based reactive transport simulation is established in this study.The workflow includes(1)base case RTM design,(2)development of training experiments,(3)surrogate model construction based on machine learning,(4)surrogate model validation,and(5)prediction with the calibrated model.The training experiments for surrogate modeling are generated and run prior to the predictions using RTM.The results show that the predictions from the surrogate model agree well with those from processes-based RTM but with a significantly reduced computational time.The well-trained surrogate model is especially useful when a large number of realizations are required,such as the sensitivity analysis or model calibration,which can significantly reduce the computational time compared to that required by RTM.The benefits are(1)it automatizes the experimental design during the sensitivity analysis to get sufficient numbers and coverage of the training cases;(2)it parallelizes the calculations of RTM training cases during the sensitivity analysis to reduce the simulation time;(3)it uses the neural network algorithm to rank the sensitivity of the parameters and to search the optimal solution for model calibration.展开更多
Largely repeated cells such as SRAM cells usually require extremely low failure-rate to ensure a mod- erate chi yield. Though fast Monte Carlo methods such as importance sampling and its variants can be used for yield...Largely repeated cells such as SRAM cells usually require extremely low failure-rate to ensure a mod- erate chi yield. Though fast Monte Carlo methods such as importance sampling and its variants can be used for yield estimation, they are still very expensive if one needs to perform optimization based on such estimations. Typ- ically the process of yield calculation requires a lot of SPICE simulation. The circuit SPICE simulation analysis accounted for the largest proportion of time in the process yield calculation. In the paper, a new method is proposed to address this issue. The key idea is to establish an efficient mixture surrogate model. The surrogate model is based on the design variables and process variables. This model construction method is based on the SPICE simulation to get a certain amount of sample points, these points are trained for mixture surrogate model by the lasso algorithm. Experimental results show that the proposed model is able to calculate accurate yield successfully and it brings significant speed ups to the calculation of failure rate. Based on the model, we made a further accelerated algo- rithm to further enhance the speed of the yield calculation. It is suitable for high-dimensional process variables and multi-performance applications.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
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
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
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 andα)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
Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this wor...Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this work introduces a machine-learning-based,data-driven scheme to overcome the challenges encountered,with a trained neural network(NN)assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system.The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions,remaining robust across varying system sizes and pulse durations.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
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
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
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
Multi-fidelity Data Fusion(MDF)frameworks have emerged as a prominent approach to producing economical but accurate surrogate models for aerodynamic data modeling by integrating data with different fidelity levels.How...Multi-fidelity Data Fusion(MDF)frameworks have emerged as a prominent approach to producing economical but accurate surrogate models for aerodynamic data modeling by integrating data with different fidelity levels.However,most existing MDF frameworks assume a uniform data structure between sampling data sources;thus,producing an accurate solution at the required level,for cases of non-uniform data structures is challenging.To address this challenge,an Adaptive Multi-fidelity Data Fusion(AMDF)framework is proposed to produce a composite surrogate model which can efficiently model multi-fidelity data featuring non-uniform structures.Firstly,the design space of the input data with non-uniform data structures is decomposed into subdomains containing simplified structures.Secondly,different MDF frameworks and a rule-based selection process are adopted to construct multiple local models for the subdomain data.On the other hand,the Enhanced Local Fidelity Modeling(ELFM)method is proposed to combine the generated local models into a unique and continuous global model.Finally,the resulting model inherits the features of local models and approximates a complete database for the whole design space.The validation of the proposed framework is performed to demonstrate its approximation capabilities in(A)four multi-dimensional analytical problems and(B)a practical engineering case study of constructing an F16C fighter aircraft’s aerodynamic database.Accuracy comparisons of the generated models using the proposed AMDF framework and conventional MDF approaches using a single global modeling algorithm are performed to reveal the adaptability of the proposed approach for fusing multi-fidelity data featuring non-uniform structures.Indeed,the results indicated that the proposed framework outperforms the state-of-the-art MDF approach in the cases of non-uniform data.展开更多
Polymer electrolyte membrane fuel cells(PEMFCs)are considered a promising alternative to internal combustion engines in the automotive sector.Their commercialization is mainly hindered due to the cost and effectivenes...Polymer electrolyte membrane fuel cells(PEMFCs)are considered a promising alternative to internal combustion engines in the automotive sector.Their commercialization is mainly hindered due to the cost and effectiveness of using platinum(Pt)in them.The cathode catalyst layer(CL)is considered a core component in PEMFCs,and its composition often considerably affects the cell performance(V_(cell))also PEMFC fabrication and production(C_(stack))costs.In this study,a data-driven multi-objective optimization analysis is conducted to effectively evaluate the effects of various cathode CL compositions on Vcelland Cstack.Four essential cathode CL parameters,i.e.,platinum loading(L_(Pt)),weight ratio of ionomer to carbon(wt_(I/C)),weight ratio of Pt to carbon(wt_(Pt/c)),and porosity of cathode CL(ε_(cCL)),are considered as the design variables.The simulation results of a three-dimensional,multi-scale,two-phase comprehensive PEMFC model are used to train and test two famous surrogates:multi-layer perceptron(MLP)and response surface analysis(RSA).Their accuracies are verified using root mean square error and adjusted R^(2).MLP which outperforms RSA in terms of prediction capability is then linked to a multi-objective non-dominated sorting genetic algorithmⅡ.Compared to a typical PEMFC stack,the results of the optimal study show that the single-cell voltage,Vcellis improved by 28 m V for the same stack price and the stack cost evaluated through the U.S department of energy cost model is reduced by$5.86/k W for the same stack performance.展开更多
In this study, the effects of discharge rate and LiMn2O4 cathode properties （thickness, porosity, particle size, and solid-state diffusivity and conductivity） on the gravimetric energy and power density of a lithium...In this study, the effects of discharge rate and LiMn2O4 cathode properties （thickness, porosity, particle size, and solid-state diffusivity and conductivity） on the gravimetric energy and power density of a lithium-ion battery cell are analyzed simultaneously using a cell-level model. Surrogate-based analysis tools are applied to simulation data to construct educed-order models, which are in turn used to perform global sensitivity analysis to compare the relative importance of cathode properties. Based on these results, the cell is then optimized for several distinct physical scenarios using gradient-based methods. The comple-mentary nature of the gradient-and surrogate-based tools is demonstrated by establishing proper bounds and constraints with the surrogate model, and then obtaining accurate optimized solutions with the gradient-based optimizer. These optimal solutions enable the quantification of the tradeoffs between energy and power density, and the effect of optimizing the electrode thickness and porosity. In conjunction with known guidelines, the numerical optimization frame-work developed herein can be applied directly to cell and pack design.展开更多
基金supported by the National Natural Science Foundation of China(No.51875465)the Shaanxi Province Postdoctoral Research Project Funding,Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(No.CX2023002)+1 种基金the Civil Aircraft Scientific Research Projectthe Fund of Shanghai Engineering Research Center of Civil Aircraft Health Monitoring(No.GCZX-2022-01).
文摘To improve the computational efficiency and accuracy of multi-objective reliability estimation for aerospace engineering structural systems,the Intelligent Vectorial Surrogate Modeling(IVSM)concept is presented by fusing the compact support region,surrogate modeling methods,matrix theory,and Bayesian optimization strategy.In this concept,the compact support region is employed to select effective modeling samples;the surrogate modeling methods are employed to establish a functional relationship between input variables and output responses;the matrix theory is adopted to establish the vector and cell arrays of modeling parameters and synchronously determine multi-objective limit state functions;the Bayesian optimization strategy is utilized to search for the optimal hyperparameters for modeling.Under this concept,the Intelligent Vectorial Neural Network(IVNN)method is proposed based on deep neural network to realize the reliability analysis of multi-objective aerospace engineering structural systems synchronously.The multioutput response function approximation problem and two engineering application cases(i.e.,landing gear brake system temperature and aeroengine turbine blisk multi-failures)are used to verify the applicability of IVNN method.The results indicate that the proposed approach holds advantages in modeling properties and simulation performances.The efforts of this paper can offer a valuable reference for the improvement of multi-objective reliability assessment theory.
基金financial support from National Natural Science Foundation of China(No.U1833116)the China Postdoctoral Science Foundation Funded Project(No.2018M642775)supported by Key Scientific Research Project of Colleges and Universities in Henan Province(No.20A460003)。
文摘In this paper,a surrogate-based modeling methodology is developed and presented to predict the elastic properties of three dimensional(3 D)four-directional braided composites.Using this approach,the prediction process becomes feasible with only a limited number of training points.The surrogate models constructed using Finite Element(FE)method and Diffuse Approximation,reduce the computational time and cost for preparing experimental samples.In the FE model,multiscale method is applied to couple the computations of elastic properties at microscale and mesoscale.Subsequently,a parametric study is performed to analyze the effects of the three design parameters on the elastic properties.Satisfactory results are obtained via the surrogatebased modeling predictions,which are compared with the experimental measurements.Moreover,the predictions obtained from surrogate models concur well with the FE predictions.This study orients a new direction for predicting the mechanical properties based on surrogate models which can effectively reduce the sample preparation cost and computational efforts.
基金Acknowledgements The work was supported by the National Basic Research Program of China （No. 2010CB951103）, the National Natural Science Foundation of China （Grant Nos. 41330854, 41371063 and 51309155） and the National Science ＆ Technology Pillar Program during the 12th Five-year Plan Period （2012BAC21B01 and 2012BAC19B03）. We are also thankful to anonymous reviewers and editors for their helpful comments and suggestions.
文摘Practical experience has demonstrated that single objective functions, no matter how carefully chosen, prove to be inadequate in providing proper measurements for all of the characteristics of the observed data. One strategy to circumvent this problem is to define multiple fitting criteria that measure different aspects of system behavior, and to use multi-criteria optimization to identify non-dominated optimal solutions. Unfortunately, these analyses require running original simulation models thousands of times. As such, they demand prohibitively large computational budgets. As a result, surrogate models have been used in combination with a variety of multi- objective optimization algorithms to approximate the true Pareto-front within limited evaluations for the original model. In this study, multi-objective optimization based on surrogate modeling （multivariate adaptive regression splines, MARS） for a conceptual rainfall-runoff model （Xin＇anjiang model, XAJ） was proposed. Taking the Yanduhe basin of Three Gorges in the upper stream of the Yangtze River in China as a case study, three evaluation criteria were selected to quantify the goodness-of-fit of observations against calculated values from the simulation model. The three criteria chosen were the Nash-Sutcliffe efficiency coefficient, the relative error of peak flow, and runoff volume （REPF and RERV）. The efficacy of this method is demonstrated on the calibration of the XAJ model. Compared to the single objective optimization results, it was indicated that the multi-objective optimization method can infer the most probable parameter set. The results also demonstrate that the use of surrogate-modeling enables optimization that is much more efficient; and the total computational cost is reduced by about 92.5%, compared to optimization without using surrogate model- ing. The results obtained with the proposed method support the feasibility of applying parameter optimization to computationally intensive simulation models, via reducing the number of simulation runs required in the numerical model considerably.
基金This work was supported by the National Natural Science Foundation of China(Grant No.51978481).
文摘During the pre-design stage of buildings,reliable long-term prediction of thermal loads is significant for cool-ing/heating system configuration and efficient operation.This paper proposes a surrogate modeling method to predict all-year hourly cooling/heating loads in high resolution for retail,hotel,and office buildings.16384 surrogate models are simulated in EnergyPlus to generate the load database,which contains 7 crucial building features as inputs and hourly loads as outputs.K-nearest-neighbors(KNN)is chosen as the data-driven algorithm to approximate the surrogates for load prediction.With test samples from the database,performances of five different spatial metrics for KNN are evaluated and optimized.Results show that the Manhattan distance is the optimal metric with the highest efficient hour rates of 93.57%and 97.14%for cooling and heating loads in office buildings.The method is verified by predicting the thermal loads of a given district in Shanghai,China.The mean absolute percentage errors(MAPE)are 5.26%and 6.88%for cooling/heating loads,respectively,and 5.63%for the annual thermal loads.The proposed surrogate modeling method meets the precision requirement of engineering in the building pre-design stage and achieves the fast prediction of all-year hourly thermal loads at the district level.As a data-driven approximation,it does not require as much detailed building information as the commonly used physics-based methods.And by pre-simulation of sufficient prototypical models,the method overcomes the gaps of data missing in current data-driven methods.
文摘Process-based reactive transport modeling(RTM)integrates thermodynamic and kinetically controlled fluid-rock interactions with fluid flow through porous media in the subsurface and surface environment.RTM is usually conducted through numerical programs based on the first principle of physical processes.However,the calculation for complex chemical reactions in most available programs is an iterative process,where each iteration is in general computationally intensive.A workflow of neural networkbased surrogate model as a proxy for process-based reactive transport simulation is established in this study.The workflow includes(1)base case RTM design,(2)development of training experiments,(3)surrogate model construction based on machine learning,(4)surrogate model validation,and(5)prediction with the calibrated model.The training experiments for surrogate modeling are generated and run prior to the predictions using RTM.The results show that the predictions from the surrogate model agree well with those from processes-based RTM but with a significantly reduced computational time.The well-trained surrogate model is especially useful when a large number of realizations are required,such as the sensitivity analysis or model calibration,which can significantly reduce the computational time compared to that required by RTM.The benefits are(1)it automatizes the experimental design during the sensitivity analysis to get sufficient numbers and coverage of the training cases;(2)it parallelizes the calculations of RTM training cases during the sensitivity analysis to reduce the simulation time;(3)it uses the neural network algorithm to rank the sensitivity of the parameters and to search the optimal solution for model calibration.
文摘Largely repeated cells such as SRAM cells usually require extremely low failure-rate to ensure a mod- erate chi yield. Though fast Monte Carlo methods such as importance sampling and its variants can be used for yield estimation, they are still very expensive if one needs to perform optimization based on such estimations. Typ- ically the process of yield calculation requires a lot of SPICE simulation. The circuit SPICE simulation analysis accounted for the largest proportion of time in the process yield calculation. In the paper, a new method is proposed to address this issue. The key idea is to establish an efficient mixture surrogate model. The surrogate model is based on the design variables and process variables. This model construction method is based on the SPICE simulation to get a certain amount of sample points, these points are trained for mixture surrogate model by the lasso algorithm. Experimental results show that the proposed model is able to calculate accurate yield successfully and it brings significant speed ups to the calculation of failure rate. Based on the model, we made a further accelerated algo- rithm to further enhance the speed of the yield calculation. It is suitable for high-dimensional process variables and multi-performance applications.
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.
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 andα)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supported by the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302100)the National Natural Science Foundation of China(Grant Nos.12361131576,92265205,and 92476205).
文摘Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this work introduces a machine-learning-based,data-driven scheme to overcome the challenges encountered,with a trained neural network(NN)assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system.The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions,remaining robust across varying system sizes and pulse durations.
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.
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.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(No.2020R1A6A1A03046811).This paper was also supported by Konkuk University Researcher Fund in 2021.
文摘Multi-fidelity Data Fusion(MDF)frameworks have emerged as a prominent approach to producing economical but accurate surrogate models for aerodynamic data modeling by integrating data with different fidelity levels.However,most existing MDF frameworks assume a uniform data structure between sampling data sources;thus,producing an accurate solution at the required level,for cases of non-uniform data structures is challenging.To address this challenge,an Adaptive Multi-fidelity Data Fusion(AMDF)framework is proposed to produce a composite surrogate model which can efficiently model multi-fidelity data featuring non-uniform structures.Firstly,the design space of the input data with non-uniform data structures is decomposed into subdomains containing simplified structures.Secondly,different MDF frameworks and a rule-based selection process are adopted to construct multiple local models for the subdomain data.On the other hand,the Enhanced Local Fidelity Modeling(ELFM)method is proposed to combine the generated local models into a unique and continuous global model.Finally,the resulting model inherits the features of local models and approximates a complete database for the whole design space.The validation of the proposed framework is performed to demonstrate its approximation capabilities in(A)four multi-dimensional analytical problems and(B)a practical engineering case study of constructing an F16C fighter aircraft’s aerodynamic database.Accuracy comparisons of the generated models using the proposed AMDF framework and conventional MDF approaches using a single global modeling algorithm are performed to reveal the adaptability of the proposed approach for fusing multi-fidelity data featuring non-uniform structures.Indeed,the results indicated that the proposed framework outperforms the state-of-the-art MDF approach in the cases of non-uniform data.
基金supported by the Technology Innovation Program of the Korea Evaluation Institute of Industrial Technology (KEIT)under the Ministry of Trade,Industry and Energy (MOTIE)of Republic of Korea (20012121)by the National Research Foundation of Korea (NRF)grant funded by the Korea government (MSIT) (2022M3J7A106294)。
文摘Polymer electrolyte membrane fuel cells(PEMFCs)are considered a promising alternative to internal combustion engines in the automotive sector.Their commercialization is mainly hindered due to the cost and effectiveness of using platinum(Pt)in them.The cathode catalyst layer(CL)is considered a core component in PEMFCs,and its composition often considerably affects the cell performance(V_(cell))also PEMFC fabrication and production(C_(stack))costs.In this study,a data-driven multi-objective optimization analysis is conducted to effectively evaluate the effects of various cathode CL compositions on Vcelland Cstack.Four essential cathode CL parameters,i.e.,platinum loading(L_(Pt)),weight ratio of ionomer to carbon(wt_(I/C)),weight ratio of Pt to carbon(wt_(Pt/c)),and porosity of cathode CL(ε_(cCL)),are considered as the design variables.The simulation results of a three-dimensional,multi-scale,two-phase comprehensive PEMFC model are used to train and test two famous surrogates:multi-layer perceptron(MLP)and response surface analysis(RSA).Their accuracies are verified using root mean square error and adjusted R^(2).MLP which outperforms RSA in terms of prediction capability is then linked to a multi-objective non-dominated sorting genetic algorithmⅡ.Compared to a typical PEMFC stack,the results of the optimal study show that the single-cell voltage,Vcellis improved by 28 m V for the same stack price and the stack cost evaluated through the U.S department of energy cost model is reduced by$5.86/k W for the same stack performance.
基金supported by the General Motors and University of Michigan Advanced Battery Coalition for Drivetrains (ABCD)
文摘In this study, the effects of discharge rate and LiMn2O4 cathode properties （thickness, porosity, particle size, and solid-state diffusivity and conductivity） on the gravimetric energy and power density of a lithium-ion battery cell are analyzed simultaneously using a cell-level model. Surrogate-based analysis tools are applied to simulation data to construct educed-order models, which are in turn used to perform global sensitivity analysis to compare the relative importance of cathode properties. Based on these results, the cell is then optimized for several distinct physical scenarios using gradient-based methods. The comple-mentary nature of the gradient-and surrogate-based tools is demonstrated by establishing proper bounds and constraints with the surrogate model, and then obtaining accurate optimized solutions with the gradient-based optimizer. These optimal solutions enable the quantification of the tradeoffs between energy and power density, and the effect of optimizing the electrode thickness and porosity. In conjunction with known guidelines, the numerical optimization frame-work developed herein can be applied directly to cell and pack design.
