Comparative Study of Response Surface Designs with Errors-in-Variables Model

This paper investigates the scaled prediction variances in the errors-in-variables model and compares the performance with those in classic model of response surface designs for three factors.The ordinary least squares estimators of regression coefficients are derived from a second-order response surface model with errors in variables.Three performance criteria are proposed.The first is the difference between the empirical mean of maximum value of scaled prediction variance with errors and the maximum value of scaled prediction variance without errors.The second is the mean squared deviation from the mean of simulated maximum scaled prediction variance with errors.The last performance measure is the mean squared scaled prediction variance change with and without errors.In the simulations,1 000 random samples were performed following three factors with 20 experimental runs for central composite designs and 15 for Box-Behnken design.The independent variables are coded variables in these designs.Comparative results show that for the low level errors in variables,central composite face-centered design is optimal;otherwise,Box-Behnken design has a relatively better performance.

Design optimization of transonic compressor stage using CFD and response surface model

In order to shorten the design period, the paper describes a new optimization strategy for computationally expensive design optimization of turbomachinery, combined with design of experiment (DOE), response surface models (RSM), genetic algorithm (GA) and a 3-D Navier-Stokes solver(Numeca Fine). Data points for response evaluations were selected by improved distributed hypercube sampling (IHS) and the 3-D Navier-Stokes analysis was carried out at these sample points. The quadratic response surface model was used to approximate the relationships between the design variables and flow parameters. To maximize the adiabatic efficiency, the genetic algorithm was applied to the response surface model to perform global optimization to achieve the optimum design of NASA Stage 35. An optimum leading edge line was found, which produced a new 3-D rotor blade combined with sweep and lean, and a new stator one with skew. It is concluded that the proposed strategy can provide a reliable method for design optimization of turbomachinery blades at reasonable computing cost.

Dynamic finite element model updating using meta-model and genetic algorithm

Current dynamic finite element model updating methods are not efficient or restricted to the problem of local optima. To circumvent these, a novel updating method which integrates the meta-model and the genetic algorithm is proposed. Experimental design technique is used to determine the best sampling points for the estimation of polynomial coefficients given the order and the number of independent variables. Finite element analyses are performed to generate the sampling data. Regression analysis is then used to estimate the response surface model to approximate the functional relationship between response features and design parameters on the entire design space. In the fitness evaluation of the genetic algorithm, the response surface model is used to substitute the finite element model to output features with given design parameters for the computation of fitness for the individual. Finally, the global optima that corresponds to the updated design parameter is acquired after several generations of evolution. In the application example, finite element analysis and modal testing are performed on a real chassis model. The finite element model is updated using the proposed method. After updating, root-mean-square error of modal frequencies is smaller than 2%. Furthermore, prediction ability of the updated model is validated using the testing results of the modified structure. The root-mean-square error of the prediction errors is smaller than 2%.

Simulation of an aircraft thermal management system based on vapor cycle response surface model

The modern aircraft Thermal Management System(TMS)faces significant challenges due to increasing thermal loads and limited heat dissipation pathways.To optimize TMS during the conceptual design stage,the development of a modeling and simulation tool is crucial.In this study,a TMS simulation model library was created using MATLAB/SIMULINK.To simplify the complexity of the Vapor Cycle System(VCS)model,a Response Surface Model(RSM)was constructed using the Monte Carlo method and validated through simulation experiments.Taking the F-22 fighter TMS as an example,a thermal dynamic simulation model was constructed to analyze the variation of thermal response parameters in key subsystems and elucidate their coupling relationships.Furthermore,the impact of total fuel flow and ram air flow on the TMS was investigated.The findings demonstrate the existence of an optimal total fuel flow that achieves a balance between maximizing fuel heat sink utilization and minimizing bleed air demand.The adaptive distribution of fuel and ram air flow was found to enhance aircraft thermal management performance.This study contributes to improving modeling efficiency and enhancing the understanding of the thermal dynamic characteristics of TMS,thereby facilitating further optimization in aircraft TMS design.

Parameter identification and global sensitivity analysis of Xin'anjiang model using meta-modeling approach

Parameter identification, model calibration, and uncertainty quantification are important steps in the model-building process, and are necessary for obtaining credible results and valuable information. Sensitivity analysis of hydrological model is a key step in model uncertainty quantification, which can identify the dominant parameters, reduce the model calibration uncertainty, and enhance the model optimization efficiency. There are, however, some shortcomings in classical approaches, including the long duration of time and high computation cost required to quantitatively assess the sensitivity of a multiple-parameter hydrological model. For this reason, a two-step statistical evaluation framework using global techniques is presented. It is based on （1） a screening method （Morris） for qualitative ranking of parameters, and （2） a variance-based method integrated with a meta-model for quantitative sensitivity analysis, i.e., the Sobol method integrated with the response surface model （RSMSobol）. First, the Morris screening method was used to qualitatively identify the parameters＇ sensitivity, and then ten parameters were selected to quantify the sensitivity indices. Subsequently, the RSMSobol method was used to quantify the sensitivity, i.e., the first-order and total sensitivity indices based on the response surface model （RSM） were calculated. The RSMSobol method can not only quantify the sensitivity, but also reduce the computational cost, with good accuracy compared to the classical approaches. This approach will be effective and reliable in the global sensitivity analysis of a complex large-scale distributed hydrological model.

Statistical Modeling Studies of Iron Recovery from Red Mud Using Thermal Plasma

Optimization studies of plasma smelting of red mud were carried out. Reduction of the dried red mud fines was done in an extended arc plasma reactor to recover the pig iron. Lime grit and low ash metallurgical （LAM） coke were used as the flux and reductant, respectively. 2level factorial design was used to study the influence of all parameters on the responses. Response surface modeling was done with the data obtained from statistically designed experiments. Metal recovery at optimum parameters was found to be 79.52%.

Performance Comparison of Two Meta-Model for the Application to Finite Element Model Updating of Structures

To investigate the application of meta-model for finite element( FE) model updating of structures,the performance of two popular meta-model,i. e.,Kriging model and response surface model( RSM),were compared in detail. Firstly,above two kinds of meta-model were introduced briefly. Secondly,some key issues of the application of meta-model to FE model updating of structures were proposed and discussed,and then some advices were presented in order to select a reasonable meta-model for the purpose of updating the FE model of structures. Finally,the procedure of FE model updating based on meta-model was implemented by updating the FE model of a truss bridge model with the measured modal parameters. The results showed that the Kriging model was more proper for FE model updating of complex structures.

PRINCIPAL COMPONENT DECOMPOSITION BASED FINITE ELEMENT MODEL UPDATING FOR STRAIN-RATE-DEPENDENCE NONLINEAR DYNAMIC PROBLEMS

Thin wail component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments （DOE） and principal component decomposition （PCD） approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.

VOC emission caps constrained by air quality targets based on response surface model:A case study in the Pearl River Delta Region,China

Because of the recent growth in ground-level ozone and increased emission of volatile organic compounds(VOCs),VOC emission control has become a major concern in China.In response,emission caps to control VOC have been stipulated in recent policies,but few of them were constrained by the co-control target of PM_(2.5)and ozone,and discussed the factor that influence the emission cap formulation.Herein,we proposed a framework for quantification of VOC emission caps constrained by targets for PM_(2.5)and ozone via a new response surface modeling(RSM)technique,achieving 50%computational cost savings of the quantification.In the Pearl River Delta(PRD)region,the VOC emission caps constrained by air quality targets varied greatly with the NOxemission reduction level.If control measures in the surrounding areas of the PRD region were not considered,there could be two feasible strategies for VOC emission caps to meet air quality targets(160μg/m^(3)for the maximum 8-hr-average 90th-percentile(MDA8-90%)ozone and 25μg/m^(3)for the annual average of PM_(2.5)):a moderate VOC emission cap with<20%NOxemission reductions or a notable VOC emission cap with>60%NOxemission reductions.If the ozone concentration target were reduced to 155μg/m^(3),deep NOxemission reductions is the only feasible ozone control measure in PRD.Optimization of seasonal VOC emission caps based on the Monte Carlo simulation could allow us to gain higher ozone benefits or greater VOC emission reductions.If VOC emissions were further reduced in autumn,MDA8-90%ozone could be lowered by 0.3-1.5μg/m^(3),equaling the ozone benefits of 10%VOC emission reduction measures.The method for VOC emission cap quantification and optimization proposed in this study could provide scientific guidance for coordinated control of regional PM_(2.5)and O_(3)pollution in China.

A numerical simulation study of CO2 injection for enhancing hydrocarbon recovery and sequestration in liquid-rich shales

Less than 10% of oil is usually recovered from liquid-rich shales and this leaves much room for improvement, while water injection into shale formation is virtually impossible because of the extremely low permeability of the formation matrix. Injecting carbon dioxide（CO2） into oil shale formations can potentially improve oil recovery. Furthermore, the large surface area in organicrich shale could permanently store CO2 without jeopardizing the formation integrity. This work is a mechanism study of evaluating the effectiveness of CO2-enhanced oil shale recovery and shale formation CO2 sequestration capacity using numerical simulation. Petrophysical and fluid properties similar to the Bakken Formation are used to set up the base model for simulation. Result shows that the CO_2 injection could increase the oil recovery factor from7.4% to 53%. In addition, petrophysical characteristics such as in situ stress changes and presence of a natural fracture network in the shale formation are proven to have impacts on subsurface CO2 flow. A response surface modeling approach was applied to investigate the interaction between parameters and generate a proxy model for optimizing oil recovery and CO2 injectivity.

Response surface modeling-based source contribution analysis and VOC emission control policy assessment in a typical ozone-polluted urban Shunde,China

To develop a sound ozone（O_3） pollution control strategy,it is important to well understand and characterize the source contribution due to the complex chemical and physical formation processes of O_3.Using the ＂Shunde＂ city as a pilot summer case study,we apply an innovative response surface modeling（RSM） methodology based on the Community Multi-Scale Air Quality（CMAQ） modeling simulations to identify the O_3 regime and provide dynamic analysis of the precursor contributions to effectively assess the O_3 impacts of volatile organic compound（VOC） control strategy.Our results show that Shunde is a typical VOC-limited urban O_3 polluted city.The ＂Jiangmen＂ city,as the main upper wind area during July 2014,its VOCs and nitrogen oxides（NO_x） emissions make up the largest contribution（9.06%）.On the contrary,the contribution from local（Shunde） emission is lowest（6.35%） among the seven neighbor regions.The local VOCs industrial source emission has the largest contribution comparing to other precursor emission sectors in Shunde.The results of dynamic source contribution analysis further show that the local NO_x control could slightly increase the ground O_3 under low（10.00%） and medium（40.00%）reduction ratios,while it could start to turn positive to decrease ground O_3 under the high NO_x abatement ratio（75.00%）.The real-time assessment of O_3 impacts from VOCs control strategies in Pearl River Delta（PRD） shows that the joint regional VOCs emission control policy will effectively reduce the ground O_3 concentration in Shunde.

Enhancement of the polynomial functions response surface model for real-time analyzing ozone sensitivity

Quantification of the nonlinearities between ambient ozone(O3)and the emissions of nitrogen oxides(NOx)and volatile organic compound(VOC)is a prerequisite for an effective O3 control strategy.An Enhanced polynomial functions Response Surface Model(Epf-RSM)with the capability to analyze O3-NOx-VOC sensitivities in real time was developed by integrating the hill-climbing adaptive method into the optimized Extended Response Surface Model(ERSM)system.The Epf-RSM could single out the best suited polynomial function for each grid cell to quantify the responses of O3 concentrations to precursor emission changes.Several comparisons between Epf-RSM and pf-ERSM(polynomial functions based ERSM)were performed using out-of-sample validation,together with comparisons of the spatial distribution and the Empirical Kinetic Modeling Approach diagrams.The comparison results showed that Epf-RSM effectively addressed the drawbacks of pf-ERSM with respect to overfitting in the margin areas and high biases in the transition areas.The O3 concentrations predicted by Epf-RSM agreed well with Community Multi-scale Air Quality simulation results.The case study results in the Pearl River Delta and the north-western area of the Shandong province indicated that the O3 formations in the central areas of both the regions were more sensitive to anthropogenic VOC in January,April,and October,while more NOx-sensitive in July.

Finite element model validation of bridge based on structural health monitoring——Part I: Response surface-based finite element model updating

In the engineering practice, merging statistical analysis into structural evaluation and assessment is a tendency in the future. As a combination of mathematical and statistical techniques, response surface （RS） methodology has been successfully applied to design optimization, response prediction and model validation. With the aid of RS methodology, these two serial papers present a finite element （FE） model updating and validation method for bridge structures based on structural health monitoring. The key issues to implement such a model updating are discussed in this paper, such as design of experiment, parameter screening, construction of high-order polynomial response surface model, optimization methods and precision inspection of RS model. The proposed procedure is illustrated by a prestressed concrete continuous rigid-frame bridge monitored under operational conditions. The results from the updated FE model have been compared with those obtained from online health monitoring system. The real application to a full-size bridge has demonstrated that the FE model updating process is efficient and convenient. The updated FE model can relatively reflect the actual condition of Xiabaishi Bridge in the design space of parameters and can be further applied to FE model validation and damage identification.

The elementary explore of multiple regression techniques about the fiberglass filter paper＇s influence on the PM2.5 assaying

The thesis had a deep research about the fiberglass filter paper＇s influence on the PM2.5 assaying. It has chosen XRF to make a quantitative analysis. Based on multiple regression theory it regard fiberglass filter paper＇s quality, element content and the quality of the loaded sample as independent variable, while the element＇s quality that the sample has collected as dependent variable. Furthermore, it has established four multiple quadric response surface models which concerning Ca by using of Mathematica and Matlab： Y = 0.8649-2.094x1-2.08x2 -1.375x3-10.58x1x2＋8.53x1x3＋1.549x2x3-3.443x1^2＋6.555x2^2＋6. 547x3^2; Y = 0.8649-2.094x1-2.08x2-1.375x3; Y = 0.8649 -2.094x2-2.08x2-1.375x3-3.443x1^2＋6.525x2^2＋6.547x3^2 ; Y =0.8649-2.094x1-2.08x2-1.375x3-10.58x1x2＋8.53x1x3＋1.549x2x3. After comparison it has finally found the best model. In combining with the sample it present a multiple data fitting analysis method which could adjust the fiberglass filter paper model accordingly.

Finite element model updating of a rod-type ultrasonicmotor based on response surface method

The conventional finite element model （FEM） of a rod-type ultrasonic motor is usually simplified by means of continuous composite structure. Because the actual contact characteristics between the parts of the ultrasonic motor is ignored, there is bigger error between the calculated values and experimental results. Aiming at solving problem, a new modeling method of a rod-type ultrasonic motor is presented to obtain a high-accuracy FEM. The bolt pretension and the normal contact stiffness and friction coefficient of the contact surface of ultrasonic motor are all considered in this method, and the significant parameters of working mode of the motor are selected by the response surface method, and the goal of calculating the structural response rapidly is realized by building the response surface model to replace the FEM. The result of finite element model updating shows that the average error of modal frequencies of updated model drops to 0.21% from 1.20%. The accuracy of FEM is obviously improved, which indicates that the FEM updating based on response surface method is of great application value on the design for a rod-type ultrasonic motor.

Modelling air change rate of naturally ventilated dairy buildings using response surface methodology and numerical simulation

The air change rate(ACR)of naturally ventilated dairy buildings(NVDBs)plays an important part in the design and control of the ventilation system,as well as in the estimation of the gaseous emission rate.The objectives of this research were to model the ACR based on a quantitative investigation of the relationship between the ACR and its potential influencing factors,including the opening ratio(r),the building length to width ratio(a),the wind speed(U),and the wind direction(0).The investigations were performed using the response surface methodology integrated with the Box-Behnken design and Computational Fluid Dynamics(CFD)simulations.Three response surface models of the ACR of NVDBs were established for three opening ratio ranges of 5%-42.5%,42.5%-80%,and 5%-80%,respectively.It was found that the selection of the opening ratio range had almost no effect on the developed response surface models.The results showed that the ACR of NVDBs was not influenced by a,but was significantly affected by r,U,6,and interaction effects between every two of the three factors.The highest ACR was 6.7 s^(-1),6.0 s^(-1),and 4.0 s^(-1)when 0,U,and r was at their respective medium value while the rest parameters were at the highest values,indicating that the r played an important role in the value of ACR.It was concluded that in the prediction of the ACR of a building,the influences of both individual and interactional effects of 0,U,and r should be considered.

Quantitative Modeling for Corrosion Behavior in Complex Coupled Environment by Response Surface Methodology

Response surface methodology（RSM） is introduced into corrosion research as a tool to assess the effects of environmental factors and their interactions on corrosion behavior and establish a model for corrosion prediction in complex coupled environment（CCE）. In this study, a typical CCE, that is, the corrosion environment of pipelines in gas field is taken as an example. The effects of environmental factors such as chloride concentration, pH value and pressure as well as their interactions on critical pitting temperature（CPT） were evaluated, and a quadratic polynomial model was developed for corrosion prediction by RSM. The results showed that the model was excellent in corrosion prediction with R2= 0.9949. CPT was mostly affected by single environmental factor rather than interaction, and among the whole factors, chloride concentration was the most influential factor of CPT.

Damage identification method of girder bridges based on finite element model updating and modal strain energy

A timely and accurate damage identification for bridge structures is essential to prevent sudden failures/collapses and other catastrophic accidents.Based on response surface model(RSM)updating and element modal strain energy(EMSE)damage index,this paper proposes a novel damage identification method for girder bridge structures.The effectiveness of the proposed damage identification method is investigated using experiments on four simply supported steel beams.With Xiabaishi Bridge,a prestressed continuous rigid frame bridge with large span,as the engineering background,the proposed damage identification method is validated by using numerical simulation to generate different bearing damage scenarios.Finally,the efficiency of the method is justified by considering its application to identifying cracking damage for a real continuous beam bridge called Xinyihe Bridge.It is concluded that the EMSE damage index is sensitive to the cracking damage and the bearing damage.The locations and levels of multiple cracking damages and bearing damages can be also identified.The results illuminate a great potential of the proposed method in identifying damages of real bridge structures.

A case study of development and application of a streamlined control and response modeling system for PM_(2.5)attainment assessment in China

This article describes the development and application of a streamlined air control and response modeling system with a novel response surface modeling-linear coupled fitting method and a new module to provide streamlined model data for PM_（2.5） attainment assessment in China.This method is capable of significantly reducing the dimensions required to establish a response surface model,as well as capturing more realistic response of PM_（2.5） to emission changes with a limited number of model simulations.The newly developed module establishes a data link between the system and the Software for Model Attainment Test—Community Edition（SMAT-CE）,and has the ability to rapidly provide model responses to emission control scenarios for SMAT-CE using a simple interface.The performance of this streamlined system is demonstrated through a case study of the Yangtze River Delta（YRD） in China.Our results show that this system is capable of reproducing the Community Multi-Scale Air Quality（CMAQ） model simulation results with maximum mean normalized error 〈 3.5%.It is also demonstrated that primary emissions make a major contribution to ambient levels of PM_（2.5） in January and August（e.g.,more than50%contributed by primary emissions in Shanghai）,and Shanghai needs to have regional emission control both locally and in its neighboring provinces to meet China＇s annual PM_（2.5）National Ambient Air Quality Standard.The streamlined system provides a real-time control/response assessment to identify the contributions of major emission sources to ambient PM_（2.5）（and potentially O_3 as well） and streamline air quality data for SMAT-CE to perform attainment assessments.

Synergetic PM_(2.5) and O_(3) control strategy for the Yangtze River Delta,China

PM_(2.5)concentrations have dramatically reduced in key regions of China during the period 2013-2017,while O_(3)has increased.Hence there is an urgent demand to develop a synergetic regional PM_(2.5)and O_(3)control strategy.This study develops an emission-to-concentration response surface model and proposes a synergetic pathway for PM_(2.5)and O_(3)control in the Yangtze River Delta(YRD)based on the framework of the Air Benefit and Cost and Attainment Assessment System(ABaCAS).Results suggest that the regional emissions of NOx,SO_(2),NH3,VOCs(volatile organic compounds)and primary PM_(2.5)should be reduced by 18%,23%,14%,17%and 33%compared with 2017 to achieve 25%and 5% decreases of PM_(2.5)and O_(3)in 2025,and that the emission reduction ratios will need to be 50%,26%,28%,28% and 55%to attain the National Ambient Air Quality Standard.To effectively reduce the O_(3) pollution in the central and eastern YRD,VOCs controls need to be strengthened to reduce O_(3)by 5%,and then NOx reduction should be accelerated for air quality attainment.Meanwhile,control of primary PM_(2.5)emissions shall be prioritized to address the severe PM_(2.5)pollution in the northern YRD.For most cities in the YRD,the VOCs emission reduction ratio should be higher than that for NOx in Spring and Autumn.NOx control should be increased in summer rather than winter when a strong VOC-limited regime occurs.Besides,regarding the emission control of industrial processes,on-road vehicle and residential sources shall be prioritized and the joint control area should be enlarged to include Shandong,Jiangxi and Hubei Province for effective O_(3)control.