Parameter identification and calibration of the Xin＇anjiang model using the surrogate modeling approach

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.

Surrogate modeling for long-term and high-resolution prediction of building thermal load with a metric-optimized KNN algorithm

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.

A novel surrogate modeling strategy of the mechanical properties of 3D braided composites

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.

An artificial-neural-network-based surrogate modeling workflow for reactive transport modeling

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.

Efficient SRAM yield optimization with mixture surrogate modeling

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.

Meta databases of steel frame buildings for surrogate modelling and machine learning-based feature importance analysis

Traditionally,nonlinear time history analysis(NLTHA)is used to assess the performance of structures under fu-ture hazards which is necessary to develop effective disaster risk management strategies.However,this method is computationally intensive and not suitable for analyzing a large number of structures on a city-wide scale.Surrogate models offer an efficient and reliable alternative and facilitate evaluating the performance of multiple structures under different hazard scenarios.However,creating a comprehensive database for surrogate mod-elling at the city level presents challenges.To overcome this,the present study proposes meta databases and a general framework for surrogate modelling of steel structures.The dataset includes 30,000 steel moment-resisting frame buildings,representing low-rise,mid-rise and high-rise buildings,with criteria for connections,beams,and columns.Pushover analysis is performed and structural parameters are extracted,and finally,incorporating two different machine learning algorithms,random forest and Shapley additive explanations,sensitivity and explain-ability analyses of the structural parameters are performed to identify the most significant factors in designing steel moment resisting frames.The framework and databases can be used as a validated source of surrogate modelling of steel frame structures in order for disaster risk management.

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.

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 of LiMn_2O_4 electrode properties in a gradient-and surrogate-based framework

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.

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.

Intelligent vectorial surrogate modeling framework for multi-objective reliability estimation of aerospace engineering structural systems

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.

Modeling of turbulent,isothermal and cryogenic cavitation under attached conditions

Cavitation is often triggered when the fluid pres- sure is lower than the vapor pressure at a local thermo- dynamic state. The present article reviews recent progress made toward developing modeling and computational strat- egies for cavitation predictions under both isothermal and cryogenic conditions, with an emphasis on the attached cav- ity. The review considers alternative cavitation models along Reynolds-averaged Navier-Stokes and very lager eddy simu- lation turbulence approaches to ensure that the computational tools can handle flows of engineering interests. Observing the substantial uncertainties associated with both modeling and experimental information, surrogate modeling strategies are reviewed to assess the implications and relative impor- tance of the various modeling and materials parameters. The exchange between static and dynamic pressures under the influence of the viscous effects can have a noticeable impact on the effective shape of a solid object, which can impact the cavitation structure. The thermal effect with respect to evaporation and condensation dynamics is examined to shed light on the fluid physics associated with cryogenic cav- itation. The surrogate modeling techniques are highlighted in the context of modeling sensitivity assessment. Keywords

Hybrid Data-Driven and Mechanistic Modeling Approaches for Multiscale Material and Process Design

The world’s increasing population requires the process industry to produce food,fuels,chemicals,and consumer products in a more efficient and sustainable way.Functional process materials lie at the heart of this challenge.Traditionally,new advanced materials are found empirically or through trial-and-error approaches.As theoretical methods and associated tools are being continuously improved and computer power has reached a high level,it is now efficient and popular to use computational methods to guide material selection and design.Due to the strong interaction between material selection and the operation of the process in which the material is used,it is essential to perform material and process design simultaneously.Despite this significant connection,the solution of the integrated material and process design problem is not easy because multiple models at different scales are usually required.Hybrid modeling provides a promising option to tackle such complex design problems.In hybrid modeling,the material properties,which are computationally expensive to obtain,are described by data-driven models,while the well-known process-related principles are represented by mechanistic models.This article highlights the significance of hybrid modeling in multiscale material and process design.The generic design methodology is first introduced.Six important application areas are then selected:four from the chemical engineering field and two from the energy systems engineering domain.For each selected area,state-ofthe-art work using hybrid modeling for multiscale material and process design is discussed.Concluding remarks are provided at the end,and current limitations and future opportunities are pointed out.

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.

A Double-Stage Surrogate-Based Shape Optimization Strategy for Blended-Wing-Body Underwater Gliders

In this paper,a Double-stage Surrogate-based Shape Optimization(DSSO)strategy for Blended-Wing-Body Underwater Gliders(BWBUGs)is proposed to reduce the computational cost.In this strategy,a double-stage surrogate model is developed to replace the high-dimensional objective in shape optimization.Specifically,several First-stage Surrogate Models(FSMs)are built for the sectional airfoils,and the second-stage surrogate model is constructed with respect to the outputs of FSMs.Besides,a Multi-start Space Reduction surrogate-based global optimization method is applied to search for the optimum.In order to validate the efficiency of the proposed method,DSSO is first compared with an ordinary One-stage Surrogate-based Optimization strategy by using the same optimization method.Then,the other three popular surrogate-based optimization methods and three heuristic algorithms are utilized to make comparisons.Results indicate that the lift-to-drag ratio of the BWBUG is improved by 9.35%with DSSO,which outperforms the comparison methods.Besides,DSSO reduces more than 50%of the time that other methods used when obtaining the same level of results.Furthermore,some considerations of the proposed strategy are further discussed and some characteristics of DSSO are identified.

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.