DeepSurNet-NSGA II:Deep Surrogate Model-Assisted Multi-Objective Evolutionary Algorithm for Enhancing Leg Linkage in Walking Robots

This research paper presents a comprehensive investigation into the effectiveness of the DeepSurNet-NSGA II(Deep Surrogate Model-Assisted Non-dominated Sorting Genetic Algorithm II)for solving complex multiobjective optimization problems,with a particular focus on robotic leg-linkage design.The study introduces an innovative approach that integrates deep learning-based surrogate models with the robust Non-dominated Sorting Genetic Algorithm II,aiming to enhance the efficiency and precision of the optimization process.Through a series of empirical experiments and algorithmic analyses,the paper demonstrates a high degree of correlation between solutions generated by the DeepSurNet-NSGA II and those obtained from direct experimental methods,underscoring the algorithm’s capability to accurately approximate the Pareto-optimal frontier while significantly reducing computational demands.The methodology encompasses a detailed exploration of the algorithm’s configuration,the experimental setup,and the criteria for performance evaluation,ensuring the reproducibility of results and facilitating future advancements in the field.The findings of this study not only confirm the practical applicability and theoretical soundness of the DeepSurNet-NSGA II in navigating the intricacies of multi-objective optimization but also highlight its potential as a transformative tool in engineering and design optimization.By bridging the gap between complex optimization challenges and achievable solutions,this research contributes valuable insights into the optimization domain,offering a promising direction for future inquiries and technological innovations.

Establishment and Optimization of Ablation Surrogate Model for Thermal Protection Material

The temperature response calculation of thermal protection materials,especially ablative thermal protection materials,usually adopts the ablation model,which is complicated in process and requires a large amount of calculation.Especially in the process of optimization calculation and parameter identification,the ablation model needs to be called many times,so it is necessary to construct an ablation surrogate model to improve the computational efficiency under the premise of ensuring the accuracy.In this paper,the Gaussian process model method is used to construct a thermal protection material ablation surrogate model,and the prediction accuracy of the surrogate model is improved through optimization.

ROBUST OPTIMIZATION OF AERODYNAMIC DESIGN USING SURROGATE MODEL

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.

Optimization on the Crosswind Stability of Trains Using Neural Network Surrogate Model

Under the influence of crosswinds,the running safety of trains will decrease sharply,so it is necessary to optimize the suspension parameters of trains.This paper studies the dynamic performance of high-speed trains under cross-wind conditions,and optimizes the running safety of train.A computational fluid dynamics simulation was used to determine the aerodynamic loads and moments experienced by a train.A series of dynamic models of a train,with different dynamic parameters were constructed,and analyzed,with safety metrics for these being determined.Finally,a surrogate model was built and an optimization algorithm was used upon this surrogate model,to find the minimum possible values for:derailment coefficient,vertical wheel-rail contact force,wheel load reduction ratio,wheel lateral force and overturning coefficient.There were 9 design variables,all associated with the dynamic parameters of the bogie.When the train was running with the speed of 350 km/h,under a crosswind speed of 15 m/s,the benchmark dynamic model performed poorly.The derailment coefficient was 1.31.The vertical wheel-rail contact force was 133.30 kN.The wheel load reduction rate was 0.643.The wheel lateral force was 85.67 kN,and the overturning coefficient was 0.425.After optimization,under the same running conditions,the metrics of the train were 0.268,100.44 kN,0.474,34.36 kN,and 0.421,respectively.This paper show that by combining train aerodynamics,vehicle system dynamics and many-objective optimization theory,a train’s stability can be more comprehensively analyzed,with more safety metrics being considered.

Multi-objective optimisation of a vehicle energy absorption structure based on surrogate model

In order to optimize the crashworthy characteristic of energy-absorbing structures, the surrogate models of specific energy absorption （SEA） and ratio of SEA to initial peak force （REAF） with respect to the design parameters were respectively constructed based on surrogate model optimization methods （polynomial response surface method （PRSM） and Kriging method （KM））. Firstly, the sample data were prepared through the design of experiment （DOE）. Then, the test data models were set up based on the theory of surrogate model, and the data samples were trained to obtain the response relationship between the SEA ＆amp; REAF and design parameters. At last, the structure optimal parameters were obtained by visual analysis and genetic algorithm （GA）. The results indicate that the KM, where the local interpolation method is used in Gauss correlation function, has the highest fitting accuracy and the structure optimal parameters are obtained as： the SEA of 29.8558 kJ/kg （corresponding toa=70 mm andt= 3.5 mm） and REAF of 0.2896 （corresponding toa=70 mm andt=1.9615 mm）. The basis function of the quartic PRSM with higher order than that of the quadratic PRSM, and the mutual influence of the design variables are considered, so the fitting accuracy of the quartic PRSM is higher than that of the quadratic PRSM.

Random dynamic analysis of vertical train–bridge systems under small probability by surrogate model and subset simulation with splitting

The response of the train–bridge system has an obvious random behavior.A high traffic density and a long maintenance period of a track will result in a substantial increase in the number of trains running on a bridge,and there is small likelihood that the maximum responses of the train and bridge happen in the total maintenance period of the track.Firstly,the coupling model of train–bridge systems is reviewed.Then,an ensemble method is presented,which can estimate the small probabilities of a dynamic system with stochastic excitations.The main idea of the ensemble method is to use the NARX(nonlinear autoregressive with exogenous input)model to replace the physical model and apply subset simulation with splitting to obtain the extreme distribution.Finally,the efficiency of the suggested method is compared with the direct Monte Carlo simulation method,and the probability exceedance of train responses under the vertical track irregularity is discussed.The results show that when the small probability of train responses under vertical track irregularity is estimated,the ensemble method can reduce both the calculation time of a single sample and the required number of samples.

Uncertain Multidisciplinary Design Optimization on Next Generation Subsea Production System by Using Surrogate Model and Interval Method

The innovative Next Generation Subsea Production System(NextGen SPS)concept is a newly proposed petroleum development solution in ultra-deep water areas.The definition of NextGen SPS involves several disciplines,which makes the design process difficult.In this paper,the definition of NextGen SPS is modeled as an uncertain multidisciplinary design optimization(MDO)problem.The deterministic optimization model is formulated,and three concerning disciplines—cost calculation,hydrodynamic analysis and global performance analysis are presented.Surrogate model technique is applied in the latter two disciplines.Collaborative optimization(CO)architecture is utilized to organize the concerning disciplines.A deterministic CO framework with two disciplinelevel optimizations is proposed firstly.Then the uncertainties of design parameters and surrogate models are incorporated by using interval method,and uncertain CO frameworks with triple loop and double loop optimization structure are established respectively.The optimization results illustrate that,although the deterministic MDO result achieves higher reduction in objective function than the uncertain MDO result,the latter is more reliable than the former.

Fluid Analysis and Structure Optimization of Impeller Based on Surrogate Model

The surrogate model technology has a good performance in solving black-box optimization problems,which is widely used in multi-domain engineering optimization problems.The adaptive surrogate model is the mainstream research direction of surrogate model technology,which can realize model fitting and global optimization of engineering problems by infilling criteria.Based on the idea of the adaptive surrogate model,this paper proposes an efficient global optimization algorithm based on the local remodeling method(EGO-LR),which aims at improving the accuracy and optimization efficiency of the model.The proposed algorithm firstly constructs the expectation improvement(EI)function in the local area and optimizes it to get the update points.Secondly,the obtained update points are added to the global region until the global accuracy of the model meets the requirements.Then the differential evolution algorithm is used for global optimization.Sixteen benchmark functions are used to compare the EGO-LR algorithm with the existing algorithms.The results show that the EGO-LR algorithm can quickly converge to the accuracy requirements of the model and find the optimal value efficiently when facing complex problems with many local extrema and large variable spaces.The proposed algorithm is applied to the optimization design of the structural parameter of the impeller,and the outflow field analysis of the impeller is realized through finite element analysis.The optimization with the maximum fluid pressure(MP value)of the impeller as the objective function is completed,which effectively reduces the pressure value of the impeller under load.

Surrogate model-assisted interactive genetic algorithms with individual’s fuzzy and stochastic fitness

We propose a surrogate model-assisted algorithm by using a directed fuzzy graph to extract a user’s cognition on evaluated individuals in order to alleviate user fatigue in interactive genetic algorithms with an individual’s fuzzy and stochastic fitness. We firstly present an approach to construct a directed fuzzy graph of an evolutionary population according to individuals’ dominance relations, cut-set levels and interval dominance probabilities, and then calculate an individual’s crisp fitness based on the out-degree and in-degree of the fuzzy graph. The approach to obtain training data is achieved using the fuzzy entropy of the evolutionary system to guarantee the credibilities of the samples which are used to train the surrogate model. We adopt a support vector regression machine as the surrogate model and train it using the sampled individuals and their crisp fitness. Then the surrogate model is optimized using the traditional genetic algorithm for some generations, and some good individuals are submitted to the user for the subsequent evolutions so as to guide and accelerate the evolution. Finally, we quantitatively analyze the performance of the presented algorithm in alleviating user fatigue and increasing more opportunities to find the satisfactory individuals, and also apply our algorithm to a fashion evolutionary design system to demonstrate its efficiency.

Optimization Design of High-speed Interior Permanent Magnet Motor with High Torque Performance Based on Multiple Surrogate Models

In order to obtain better torque performance of high-speed interior permanent magnet motor(HSIPMM) and solve the problem that electromagnetic optimization design is seriously limited by its mechanical strength, a complete optimization design method is proposed in this paper. The object of optimization design is a 15 kW、20000 r/min HSIPMM whose permanent magnets in rotor is segmented. Eight structural dimensions are selected as its optimization variables. After design of experiment(DOE), multiple surrogate models are fitted, a set of surrogate models with minimum error is selected by using error evaluation indexes to optimize, the NSGA-II algorithm is used to get the optimal solution. The optimal solution is verified by load test on a 15 kW, 20000 r/min HSIPMM prototype. This paper can be used as a reference for the optimization design of HSIPMM.

Optimal Design of Electrical Machines Assisted by Hybrid Surrogate Model Based Algorithm

In this paper,for design of large-scale electromagnetic problems,a novel robust global optimization algorithm based on surrogate models is presented.The proposed algorithm can automatically select a proper meta-model technique among multiple alternatives.In this paper,three representative meta-modeling techniques including ordinary Kriging,universal Kriging,and response surface method with multi-quadratic radial basis functions are applied.In each optimization iteration,the above three models are used for parallel calculation.The proposed hybrid surrogate model optimization algorithm synthesizes advantages of these different meta-models.Without verification of a specific meta-model,a suitable one for the engineering problem to be analyzed is automatically selected.Therefore,the proposed algorithm intends to make a better trade-off between numerical efficiency and searching accuracy for solving engineering problems,which are characterized by stronger non-linearity,higher complexity,non-convex feasible region,and expensive performance analysis.

Deep Learning-Based Surrogate Model for Flight Load Analysis

Flight load computations(FLC)are generally expensive and time-consuming.This paper studies deep learning(DL)-based surrogate models of FLC to provide a reliable basis for the strength design of aircraft structures.We mainly analyze the influence of Mach number,overload,angle of attack,elevator deflection,altitude,and other factors on the loads of key monitoring components,based on which input and output variables are set.The data used to train and validate the DL surrogate models are derived using aircraft flight load simulation results based on wind tunnel test data.According to the FLC features,a deep neural network(DNN)and a random forest(RF)are proposed to establish the surrogate models.The DNN meets the FLC accuracy requirement using rich data sources in the FLC;the RF can alleviate overfitting and evaluate the importance of flight parameters.Numerical experiments show that both the DNN-and RF-based surrogate models achieve high accuracy.The input variables importance analysis demonstrates that vertical overload and elevator deflection have a significant influence on the FLC.We believe that synthetic applications of these DL-based surrogate methods show a great promise in the field of FLC.

Evolutionary Algorithm with Ensemble Classifier Surrogate Model for Expensive Multiobjective Optimization

For many real-world multiobjective optimization problems,the evaluations of the objective functions are computationally expensive.Such problems are usually called expensive multiobjective optimization problems(EMOPs).One type of feasible approaches for EMOPs is to introduce the computationally efficient surrogates for reducing the number of function evaluations.Inspired from ensemble learning,this paper proposes a multiobjective evolutionary algorithm with an ensemble classifier(MOEA-EC)for EMOPs.More specifically,multiple decision tree models are used as an ensemble classifier for the pre-selection,which is be more helpful for further reducing the function evaluations of the solutions than using single inaccurate model.The extensive experimental studies have been conducted to verify the efficiency of MOEA-EC by comparing it with several advanced multiobjective expensive optimization algorithms.The experimental results show that MOEA-EC outperforms the compared algorithms.

Prediction of Aircraft＇s Longitudinal Motion Based on Aerodynamic Coefficients and Derivatives by Surrogate Model Approach

The accuracy of a flight simulation is highly dependent on the quality of the aerodynamic database and prediction accuracies of the aerodynamic coefficients and derivatives. A surrogate model is an approximation method that is used to predict unknown functions based on the sampling data obtained by the design of experiments. This model can also be used to predict aerodynamic coefficients/derivatives using several measured points. The objective of this paper is to develop an efficient digital flight simulation by solving the equation of motion to predict the aerodynamics data using a surrogate model. Accordingly, there is a need to construct and investigate aerodynamic databases and compare the accuracy of the surrogate model with the exact solution, and hence solve the equation of motion for the flight simulation analysis. In this study, sample datas for models are acquired from the USAF Stability and Control DATCOM, and a database is constructed for two input variables （the angle of attack and Mach number）, along with two derivatives of the X-force axis and three derivatives for the Z-force axis and pitching moment. Furthermore, a comparison of the value predicted by the Kriging model and the exact solution shows that its flight analysis prediction ability makes it possible to use the surrogate model in future analyses.

A systematic framework of constructing surrogate model for slider track peeling strength prediction

Peeling strength can comprehensively reflect slider track safety and is crucial in car seat safety assessments.Current methods for determining slider peeling strength are primarily physical testing and numerical simulation.However,these methods encounter the potential challenges of high costs and overlong time consumption which have not been adequately addressed.Therefore,the efficient and low-cost surrogate model emerges as a promising solution.Nevertheless,currently used surrogate models suffer from inefficiencies and complexity in data sampling,lack of robustness in local model predictions,and isolation between data sampling and model prediction.To overcome these challenges,this paper aims to set up a systematic framework for slider track peeling strength prediction,including sensitivity analysis,dataset sampling,and model prediction.Specifically,the interpretable linear regression is performed to identify the sensitivity of various geometric variables to peeling strength.Based on the variable sensitivity,a distance metric is constructed to measure the disparity of different variable groups.Then,the sparsity-targeted sampling(STS)is proposed to formulate a representative dataset.Finally,the sequentially selected local weighted linear regression(SLWLR)is designed to achieve accurate track peeling strength prediction.Additionally,a quantitative cost assessment of the supplementary dataset is proposed by utilizing the minimum adjacent sample distance as a mediator.Experimental results validate the efficacy of sequential selection and the weighting mechanism in enhancing localization robustness.Furthermore,the proposed SLWLR method surpasses similar approaches and other common surrogate methods in terms of prediction performance and data quantity requirements,achieving an average absolute error of 3.3 kN in the simulated test dataset.

Establishment and application of a surrogate model for human Ebola virus disease in BSL-2 laboratory

The Ebola virus(EBOV)is a member of the Orthoebolavirus genus,Filoviridae family,which causes severe hemorrhagic diseases in humans and non-human primates(NHPs),with a case fatality rate of up to 90%.The development of countermeasures against EBOV has been hindered by the lack of ideal animal models,as EBOV requires handling in biosafety level(BSL)-4 facilities.Therefore,accessible and convenient animal models are urgently needed to promote prophylactic and therapeutic approaches against EBOV.In this study,a recombinant vesicular stomatitis virus expressing Ebola virus glycoprotein(VSV-EBOV/GP)was constructed and applied as a surrogate virus,establishing a lethal infection in hamsters.Following infection with VSV-EBOV/GP,3-week-old female Syrian hamsters exhibited disease signs such as weight loss,multi-organ failure,severe uveitis,high viral loads,and developed severe systemic diseases similar to those observed in human EBOV patients.All animals succumbed at 2–3 days post-infection(dpi).Histopathological changes indicated that VSV-EBOV/GP targeted liver cells,suggesting that the tissue tropism of VSV-EBOV/GP was comparable to wild-type EBOV(WT EBOV).Notably,the pathogenicity of the VSV-EBOV/GP was found to be species-specific,age-related,gender-associated,and challenge route-dependent.Subsequently,equine anti-EBOV immunoglobulins and a subunit vaccine were validated using this model.Overall,this surrogate model represents a safe,effective,and economical tool for rapid preclinical evaluation of medical countermeasures against EBOV under BSL-2 conditions,which would accelerate technological advances and breakthroughs in confronting Ebola virus disease.

Optimizing building retrofit through data analytics:A study of multi-objective optimization and surrogate models derived from energy performance certificates

The building stock is responsible for a large share of global energy consumption and greenhouse gas emissions,therefore,it is critical to promote building retrofit to achieve the proposed carbon and energy neutrality goals.One of the policies implemented in recent years was the Energy Performance Certificate(EPC)policy,which proposes building stock benchmarking to identify buildings that require rehabilitation.However,research shows that these mechanisms fail to engage stakeholders in the retrofit process because it is widely seen as a mandatory and complex bureaucracy.This study makes use of an EPC database to integrate machine learning techniques with multi-objective optimization and develop an interface capable of(1)predicting a building’s,or household’s,energy needs;and(2)providing the user with optimum retrofit solutions,costs,and return on investment.The goal is to provide an open-source,easy-to-use interface that guides the user in the building retrofit process.The energy and EPC prediction models show a coefficient of determination(R2)of 0.84 and 0.79,and the optimization results for one case study EPC with a 2000€budget limit inÉvora,Portugal,show decreases of up to 60%in energy needs and return on investments of up to 7 in 3 years.

Optimal design of double-layer barrel vaults using genetic and pattern search algorithms and optimized neural network as surrogate model

This paper presents a combined method based on optimized neural networks and optimization algorithms to solve structural optimization problems.The main idea is to utilize an optimized artificial neural network(OANN)as a surrogate model to reduce the number of computations for structural analysis.First,the OANN is trained appropriately.Subsequently,the main optimization problem is solved using the OANN and a population-based algorithm.The algorithms considered in this step are the arithmetic optimization algorithm(AOA)and genetic algorithm(GA).Finally,the abovementioned problem is solved using the optimal point obtained from the previous step and the pattern search(PS)algorithm.To evaluate the performance of the proposed method,two numerical examples are considered.In the first example,the performance of two algorithms,OANN+AOA+PS and OANN+GA+PS,is investigated.Using the GA reduces the elapsed time by approximately 50%compared with using the AOA.Results show that both the OANN+GA+PS and OANN+AOA+PS algorithms perform well in solving structural optimization problems and achieve the same optimal design.However,the OANN+GA+PS algorithm requires significantly fewer function evaluations to achieve the same accuracy as the OANN+AOA+PS algorithm.

Reliability-based design optimization of offshore wind turbine support structures using RBF surrogate model

An efficient reliability-based design optimization method for the support structures of monopile offshore wind turbines is proposed herein.First,parametric finite element analysis(FEA)models of the support structure are established by considering stochastic variables.Subsequently,a surrogate model is constructed using a radial basis function(RBF)neural network to replace the time-consuming FEA.The uncertainties of loads,material properties,key sizes of structural components,and soil properties are considered.The uncertainty of soil properties is characterized by the variabilities of the unit weight,friction angle,and elastic modulus of soil.Structure reliability is determined via Monte Carlo simulation,and five limit states are considered,i.e.,structural stresses,tower top displacements,mudline rotation,buckling,and natural frequency.Based on the RBF surrogate model and particle swarm optimization algorithm,an optimal design is established to minimize the volume.Results show that the proposed method can yield an optimal design that satisfies the target reliability and that the constructed RBF surrogate model significantly improves the optimization efficiency.Furthermore,the uncertainty of soil parameters significantly affects the optimization results,and increasing the monopile diameter is a cost-effective approach to cope with the uncertainty of soil parameters.

Multi-objective optimization of the cathode catalyst layer micro-composition of polymer electrolyte membrane fuel cells using a multi-scale,two-phase fuel cell model and data-driven surrogates

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.