Long-term deformation analysis of Shuibuya concrete face rockfill dam based on response surface method and improved genetic algorithm

Due to the size effects of rockfill materials, the settlement difference between numerical simulation and in situ monitoring of rockfill dams is a topic of general concern.The constitutive model parameters obtained from laboratory triaxial tests often underestimate the deformation of high rockfill dams.Therefore, constitutive model parameters obtained by back analysis were used to calculate and predict the long-term deformation of rockfill dams.Instead of using artificial neural networks (ANNs), the response surface method (RSM) was employed to replace the finite element simulation used in the optimization iteration.Only 27 training samples were required for RSM, improving computational efficiency compared with ANN, which required 300 training samples.RSM can be used to describe the relationship between the constitutive model parameters and dam settlements.The inversion results of the Shuibuya concrete face rockfill dam (CFRD) show that the calculated settlements agree with the measured data, indicating the accuracy and efficiency of RSM.

Response surface method using grey relational analysis for decision making in weapon system selection

A proper weapon system is very important for a na- tional defense system. Generally, it means selecting the optimal weapon system among many alternatives, which is a multiple- attribute decision making （MADM） problem. This paper proposes a new mathematical model based on the response surface method （RSM） and the grey relational analysis （GRA）. RSM is used to obtain the experimental points and analyze the factors that have a significant impact on the selection results. GRA is used to an- alyze the trend relationship between alternatives and reference series. And then an RSM model is obtained, which can be used to calculate all alternatives and obtain ranking results. A real world application is introduced to illustrate the utilization of the model for the weapon selection problem. The results show that this model can be used to help decision-makers to make a quick comparison of alternatives and select a proper weapon system from multiple alternatives, which is an effective and adaptable method for solving the weapon system selection problem.

Optimization on the Conversion of Bamboo Shoot Shell to Levulinic Acid with Environmentally Benign Acidic Ionic Liquid and Response Surface Analysis

Levulinic acid（LA） has been identified as a promising green,biomass derived platform chemical.Response surface analysis（RSA） with a four-factor-five-level central composite design（CCD） was applied to optimize the hydrolysis conditions for the conversion of bamboo（Phyllostachys Praecox f.preveynalis） shoot shell（BSS） to LA catalyzed with ionic liquid [C4mim]HSO4.The effects of four main reaction parameters including temperature,time,C[C4mim]HSO4（initial [C4mim]HSO4 concentration） and XBSS（initial BSS intake） on the hydrolysis reaction for yield of LA were analyzed.A quadratic equation model for yield of LA was established and fitted to the data with an R2 of 0.9868,and effects of main factors and their corresponding relationships were obtained with RSA.Model validation and results of CCD showed good correspondence between actual and predicted values.The analysis of variance（ANOVA） of the results indicated that the yield of LA in the range studied was significantly（P＆lt;0.05） affected by the four factors.The optimized reaction conditions were as follows：temperature of 145 ℃,time of 103.8 min,C[C4mim]HSO4 of 0.9 mol.L-1 and XBSS of 2.04%（by mass）,respectively.A high yield [（71±0.41）%（by mol）,triplicate experiment] was obtained at the optimum conditions of temperature of 145 ℃,time of 104 min,C[C4mim]HSO4 of 0.9 mol.L-1 and XBSS of 2%（by mass）,which obtained from the real experiments,concurred with the model prediction [73.8%（by mol） based on available C6 sugars in BSS or 17.9%（by mass） based on the mass of BSS],indicating that the model was adequate for the hydrolysis process.

General Response Surface Reliability Analysis for Fuzzy-Random Uncertainty both in Basic Variables and in State Variables

A general response surface（RS） method is presented for reliability analysis of complex structure/mechanism with fuzzy-random uncertainty both in basic variables and in failure state variables. On the basis of equivalent transformation from fuzzy basic variable to random basic variable, the fuzziness and randomness in the basic variables are considered simultaneously in the presented general RS method. Once the fuzzy basic variables are transformed into the random basic variables, the conventional RS method is employed to establish the general RS for the complex structure/mechanism with implicit limit state equation by finite element numerical simulation. Furthermore, the general failure probability is defined according to the probability formula for fuzzy-random event by taking the fuzziness and randomness in the failure-safety state into consideration, and an appropriate fuzzy operator is adopted to calculate the general failure probability for the complex structure/mechanism with multiple implicit failure modes. Finally, a general reliability analysis of an elastic linkage mechanism is introduced to illustrate the present method.

Comparative Study on Response Surfaces for Reliability Analysis of Spatially Variable Soil Slope

This paper focuses on the performance of the second-order polynomial-based response surfaces on the reliability of spatially variable soil slope. A single response surface constructed to approximate the slope system failure performance function G（X） （called single RS） and multiple response surfaces constructed on finite number of slip surfaces （called multiple RS） are developed, respectively. Single RS and multiple RS are applied to evaluate the system failure probability pf for a cohesive soil slope together with Monte Carlo simulation （MCS）. It is found thatpe calculated by single RS deviates significantly from that obtained by searching a large number of potential slip surfaces, and this deviation becomes insignificant with the decrease of the number of random variables or the increase of the scale of fluctuation. In other words, single RS cannot approximate G（X） with reasonable accuracy. The value of pc from multiple response surfaces fits well with that obtained by searching a large number of potential slip surfaces. That is, multiple RS can estimate G（X） with reasonable accuracy.

Deformation prediction and analysis of underground mining during stacking of dry gangue in open-pit based on response surface methodology

Deformation prediction and the analysis of underground goaf are important to the safe and efficient recovery of residual ore when shifting from open-pit mining to underground mining.To address the comprehensive problem of stability in the double mined-out area of the Tong-Lv-Shan(TLS)mine,which employed the dry stacked gangue technology,this paper applies the function fitting theory and a regression analysis method to screen the sensitive interval of four influencing factors based on single-factor experiments and the numerical simulation software FLAC3D.The influencing factors of the TLS mine consist of the column thickness(d),gob area span(D),boundary pillar thickness(h)and height of tailing gangue(H).The fitting degree between the four factors and the displacement of the gob roof(W)is reasonable because the correlation coefficient(R2)is greater than0.9701.After establishing29groups that satisfy the principles of Box-Behnken design(BBD),the dry gangue tailings process was re-simulated for the selected sensitive interval.Using a combination of an analysis of variance(ANOVA),regression equations and a significance analysis,the prediction results of the response surface methodology(RSM)show that the significant degree for the stability of the mined-out area for the factors satisfies the relationship of h>D>d>H.The importance of the four factors cannot be disregarded in a comparison of the prediction results of the engineering test stope in the TLS mine.By comparing the data of monitoring points and function prediction,the proposed method has shown promising results,and the prediction accuracy of RSM model is acceptable.The relative errors of the two test stopes are1.67%and3.85%,respectively,which yield satisfactory reliability and reference values for the mines.

Reliability analysis for aeroengine turbine disc fatigue life with multiple random variables based on distributed collaborative response surface method

The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables,such as applied load,working temperature,geometrical dimensions and material properties.In order to ameliorate reliability analysis efficiency without loss of reliability,the distributed collaborative response surface method(DCRSM) was proposed,and its basic theories were established in this work.Considering the failure dependency among the failure modes,the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random variables.Then,the failure modes were considered as the random variables of system response to obtain the distributed collaborative response surface model based on structure failure criterion.Finally,the given turbine disc structure was employed to illustrate the feasibility and validity of the presented method.Through the comparison of DCRSM,Monte Carlo method(MCM) and the traditional response surface method(RSM),the results show that the computational precision for DCRSM is more consistent with MCM than RSM,while DCRSM needs far less computing time than MCM and RSM under the same simulation conditions.Thus,DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables,and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode.

Distributed collaborative extremum response surface method for mechanical dynamic assembly reliability analysis

To make the dynamic assembly reliability analysis more effective for complex machinery of multi-object multi-discipline(MOMD),distributed collaborative extremum response surface method(DCERSM)was proposed based on extremum response surface method(ERSM).Firstly,the basic theories of the ERSM and DCERSM were investigated,and the strengths of DCERSM were proved theoretically.Secondly,the mathematical model of the DCERSM was established based upon extremum response surface function(ERSF).Finally,this model was applied to the reliability analysis of blade-tip radial running clearance(BTRRC)of an aeroengine high pressure turbine(HPT)to verify its advantages.The results show that the DCERSM can not only reshape the possibility of the reliability analysis for the complex turbo machinery,but also greatly improve the computational speed,save the computational time and improve the computational efficiency while keeping the accuracy.Thus,the DCERSM is verified to be feasible and effective in the dynamic assembly reliability(DAR)analysis of complex machinery.Moreover,this method offers an useful insight for designing and optimizing the dynamic reliability of complex machinery.

Vibration reliability analysis for aeroengine compressor blade based on support vector machine response surface method

To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method(SRSM) is proposed. SRSM integrates the advantages of support vector machine(SVM) and traditional response surface method(RSM), and utilizes experimental samples to construct a suitable response surface function(RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method(MCM); while SRSM(17.296 s) needs far less running time than MCM(10958 s) and RSM(9840 s). Therefore,under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.

A Study of Design Optimization Using Response Surface Analysis and Fabricaiton MEMS Probe Tip

In semiconductor manufacturing process, probe station that is testing equipment is important. Inspection step is for detecting defects on semiconductor before the packaging. Probe card is a part of probe station and contains probe tip that contacts to semiconductor. Through probe tip, it can inspect defects of semiconductor. In this paper, optimization method is used with response surface analysis to design MEMS type probe tip. And fabricating probe tip uses maskless lithography, electro-plating and lapping process.

Dynamic optimization analysis of hydraulic pipeline system based on a developed response surface method

When designing a complex pipeline with long distance and multi-supports for offshore platform,it is necessary to analyze the vibration characteristics of the complex pipeline system to ensure that there is no harmful resonance in the working conditions.Therefore,the optimal layout of support is an effective method to reduce the vibration response of hydraulic pipeline system.In this paper,a developed dynamic optimization method for the complex pipeline is proposed to investigate the vibration characteristics of complex pipeline with multi-elastic supports.In this method,the Kriging response surface model between the support position and pipeline is established.The position of the clamp in the model is parameterized and the optimal solution of performance index is obtained by genetic algorithm.The number of clamps and the interval between clamps are considered as the constraints of layout optimization,and the optimization objective is the natural frequencies of pipeline.Taking a typical offshore pipeline as example to demonstrate the effectiveness of the proposed method,the results show that the vibration performance of the hydraulic pipeline system is distinctly improved by the optimization procedure,which can provide reasonable guidance for the design of complex hydraulic pipeline system.

Optimization of Rhododendri Daurici oil liposome by Box-Behnken design and response surface method

Objective:To prepare the liposomes of mangrove oil,Optimization of the formulation of mangrove oil liposomes by Box Behnken response surface methodology.Methods:Preparation of Rhododendron oil liposomes by ethanol injection probe ultrasound,Determination of gemacrone by HPLC.The ratio of lecithin to cholesterol(X1),drug lipid ratio(X2)and phospholipid concentration(X3)were used as independent variables,and encapsulation efficiency(Y)was used as dependent variable,the formulation was optimized by Box Behnken response surface method,and the entrapment efficiency was predicted.The entrapment efficiency,particle size,polydispersity index(PDI),Zeta potential and drug loading of the optimized liposomes were evaluated.Results:The optimal prescription and preparation of Folium Rhododendri Daurici oil liposome was confirmed as follows:X1=7.28:1、X2=11.34:1、X3=9.32mg·mL-1,the encapsulation efficiency was(82.55±1.66)%,the particle size was(130.531±46)nm,the polydispersity index was 0.185±05,Zeta potential was(21.970±36)mV,the drug loading was(5.941±0.12)%.Conclusion:The Box Behnken response surface method is accurate to obtain the optimal formulation of mangrove oil liposomes,it has high precision and good prediction effect.And the preparation process of mangrove oil liposomes is stable and feasible.

Optimization of the extraction process of total flavonoids from Trichosanthis Fructus by Box-Behnken response surface method combined with differential spectrophotometry

Objective:To optimize the extraction process of total flavones in Trichosanthis Fructus(composed of Trichosanthis pericarpium and Trichosanthis semen in certain proportion).Methods:The effects of the mixture ratio of Trichosanthis pericarpium and Trichosanthis semen,ethanol concentration,ultrasonic extraction time and extraction temperature on the extraction rate of total flavonoids in Trichosanthis Fructus were investigated.The extraction process of total flavonoids in Trichosanthis Fructus was optimized by Box-Behnken response surface method combined with differential spectrophotometry.Results:The optimum extraction conditions of total flavonoids in Trichosanthis Fructus were as follows:The mixture ratio of Trichosanthis pericarpium and Trichosanthis semen was 4:6,the ethanol concentration was 70%,the ultrasonic extraction time was 60min and the extraction temperature was 40℃.Conclusion:Box-Behnken response surface method combined with differential spectrophotometry can optimize the extraction process of total flavonoids from Trichosanthis Fructus,which can provide reference for the extraction and application of total flavonoids in Trichosanthis Fructus.

Probabilistic assessment of rock slopes stability using the response surface approach——A case study

This paper examines the stability condition of a jointed rock slope in the south western region of Saudi Arabia using deterministic and probabilistic approaches,under both dry and wet conditions.The study area is characterized by complex geology in rugged terrains.The stability analysis is carried out using the code FLAC3D to generate a 3-dimensional,ubiquitous joint model,to determine the influence of the dominant,unfavourable discontinuity orientation with respect to the slope face.The deterministic analysis is first implemented using the mean values of the selected random variables,namely the dip,dip direction and friction angle of the dominant discontinuity set,and the stability condition is assessed with a factor of safety based on the classical frictional joint constitutive model.A Box-Behnken design(BBD)approach is then adopted to create the surface response function as a second order polynomial for the factor of safety.To do so,fifteen FLAC3D models are generated in accordance with the BBD.Based on this,10,000 simulations of different slope realizations are carried out using Monte-Carlo simulation technique,and the probability of unsatisfactory of performance of the rock slope is assessed.It is shown that the probabilistic approach provides more insight and confidence in the stability condition of the rock slope,both under dry and steady state heavy rainfall conditions.A discussion is presented on the significance of accepting lower safety factors when heavy rainfall conditions are encountered.

Distributed Collaborative Response Surface Method for Mechanical Dynamic Assembly Reliability Design

Because of the randomness of many impact factors influencing the dynamic assembly relationship of complex machinery, the reliability analysis of dynamic assembly relationship needs to be accomplished considering the randomness from a probabilistic perspective. To improve the accuracy and efficiency of dynamic assembly relationship reliability analysis, the mechanical dynamic assembly reliability（MDAR） theory and a distributed collaborative response surface method（DCRSM） are proposed. The mathematic model of DCRSM is established based on the quadratic response surface function, and verified by the assembly relationship reliability analysis of aeroengine high pressure turbine（HPT） blade-tip radial running clearance（BTRRC）. Through the comparison of the DCRSM, traditional response surface method（RSM） and Monte Carlo Method（MCM）, the results show that the DCRSM is not able to accomplish the computational task which is impossible for the other methods when the number of simulation is more than 100 000 times, but also the computational precision for the DCRSM is basically consistent with the MCM and improved by 0.40-4.63% to the RSM, furthermore, the computational efficiency of DCRSM is up to about 188 times of the MCM and 55 times of the RSM under 10000 times simulations. The DCRSM is demonstrated to be a feasible and effective approach for markedly improving the computational efficiency and accuracy of MDAR analysis. Thus, the proposed research provides the promising theory and method for the MDAR design and optimization, and opens a novel research direction of probabilistic analysis for developing the high-performance and high-reliability of aeroengine.

Optimizing electrocoagulation process for the treatment of biodiesel wastewater using response surface methodology

The production of biodiesel through a transesterification method produces a large amount of wastewater that contains high levels of chemical oxygen demand （COD） and oil and grease （O＆G）. Currently, flotation is the conventional primary treatment for O＆G removal prior to biological treatments. In this study, electrocoagulation （EC） was adopted to treat the biodiesel wastewater. The effects of initial pH, applied voltage, and reaction time on the EC process for the removal of COD, O＆G, and suspended solids （SS） were investigated using one factor at a time experiment. Furthermore, the Box-Behnken design, an experimental design for response surface methodology （RSM）, was used to create a set of 15 experimental runs needed for optimizing of the operating conditions. Quadratic regression models with estimated coefficients were developed to describe the pollutant removals. The experimental results show that EC could effectively reduce COD, O＆G, and SS by 55.43%, 98.42%, and 96.59%, respectively, at the optimum conditions of pH 6.06, applied voltage 18.2 V, and reaction time 23.5 min. The experimental observations were in reasonable agreement with the modeled values.

Reliability analysis of slopes considering spatial variability of soil properties based on efficiently identified representative slip surfaces

Slope reliability analysis considering inherent spatial variability(ISV)of soil properties is timeconsuming when response surface method(RSM)is used,because of the"curse of dimensionality".This paper proposes an effective method for identification of representative slip surfaces(RSSs)of slopes with spatially varied soils within the framework of limit equilibrium method(LEM),which utilizes an adaptive K-means clustering approach.Then,an improved slope reliability analysis based on the RSSs and RSM considering soil spatial variability,in perspective of computation efficiency,is established.The detailed implementation procedure of the proposed method is well documented,and the ability of the method in identifying RSSs and estimating reliability is investigated via three slope examples.Results show that the proposed method can automatically identify the RSSs of slope with only one evaluation of the conventional deterministic slope stability model.The RSSs are invariant with the statistics of soil properties,which allows parametric studies that are often required in slope reliability analysis to be efficiently achieved with ease.It is also found that the proposed method provides comparable values of factor of safety(FS)and probability of failure(Pf)of slopes with those obtained from direct analysis and lite rature.

Optimization of a fermented pumpkin-based beverage to improve Lactobacillus mali survival and-glucosidase inhibitory activity:A response surface methodology approach

The aim of this research was to develop an optimum fermentation and composition model for a new fermented pumpkin-based beverage with high probiotic survival and-glucosidase inhibitory activity.Relationship between fermentation temperature,inoculum and ingredient concentration with response variables(fermentation time at the fermentation endpoint pH 4.5,survival rate of Lactobacillus mali K8 in pumpkin-based beverage treated with simulated gastrointestinal tract enzyme fluids,-glucosidase inhibitory activity and sensory overall acceptability after 4 weeks of refrigerated storage)was investigated using response surface methodology.Optimal formulation was obtained at an approximation of 40%pumpkin puree concentration,8 Log CFU/mL inoculum and at 35℃.The product derived from this optimum formula reached the fermentation endpoint after 28.34±0.10 h and the quality change during 4 weeks storage was studied.The product achieved 88.56±0.67%of L.mali survival after treatment with simulated gastric and intestinal juices;demonstrated 95.89±0.30% α-glucosidase inhibitory activity,as well as scored 6.99±0.40 on sensory overall acceptability after 4 weeks of storage.These findings illustrated that the model is effective in improving probiotic survival and α-glucosidase inhibitory activity with excellent sensory acceptability,thus may offer a dietary means for the management of hyperglycaemia.

Multiple-response optimization for melting process of aluminum melting furnace based on response surface methodology with desirability function

To reduce the fuel consumption and emissions and also enhance the molten aluminum quality, a mathematical model with user-developed melting model and burning capacity model, were established according to the features of melting process of regenerative aluminum melting furnaces. Based on validating results by heat balance test for an aluminum melting furnace, CFD （computational fluid dynamics） technique, in association with statistical experimental design were used to optimize the melting process of the aluminum melting furnace. Four important factors influencing the melting time, such as horizontal angle between burners, height-to-radius ratio, natural gas mass flow and air preheated temperature, were identified by PLACKETT-BURMAN design. A steepest descent method was undertaken to determine the optimal regions of these factors. Response surface methodology with BOX-BEHNKEN design was adopted to further investigate the mutual interactions between these variables on RSD （relative standard deviation） of aluminum temperature, RSD of furnace temperature and melting time. Multiple-response optimization by desirability function approach was used to determine the optimum melting process parameters. The results indicate that the interaction between the height-to-radius ratio and horizontal angle between burners affects the response variables significantly. The predicted results show that the minimum RSD of aluminum temperature （12.13%）, RSD of furnace temperature （18.50%） and melting time （3.9 h） could be obtained under the optimum conditions of horizontal angle between burners as 64°, height-to-radius ratio as 0.3, natural gas mass flow as 599 m3/h, and air preheated temperature as 639 ℃. These predicted values were further verified by validation experiments. The excellent correlation between the predicted and experimental values confirms the validity and practicability of this statistical optimum strategy.

Comparison of Response Surface Methodology and Artificial Neural Network in Predicting the Microwave-Assisted Extraction Procedure to Determine Zinc in Fish Muscles

In this paper, the estimation capacities of the response surface methodology (RSM) and artificial neural network (ANN), in a microwave-assisted extraction method to determine the amount of zinc in fish samples were investigated. The experiments were carried out based on a 3-level, 4-variable Box–Behnken design. The amount of zinc was considered as a function of four independent variables, namely irradiation power, irradiation time, nitric acid concentration, and temperature. The RSM results showed the quadratic polynomial model can be used to describe the relationship between the various factors and the response. Using the ANN analysis, the optimal configuration of the ANN model was found to be 4-10-1. After predicting the model using RSM and ANN, two methodologies were then compared for their predictive capabilities. The results showed that the ANN model is much more accurate in prediction as compared to the RSM.