Bamboo Fiber Modified Asphalt Mixture Proportion Design and Road Performances Based on Response Surface Method

In order to comprehensively utilize the remaining bamboo residue of bamboo products,this paper presents a research on recycling the bamboo fibers from bamboo residue for improving the performance of the asphalt mixtures.First of all,the basic performance parameters of sinocalamus affinis fiber,phyllostachys pubescens fiber,green bamboo fiber were tested and analyzed,and the optimal content and length were put forward.Then,the mix ratio design of the bamboo fiber modified asphalt mixture was further designed through the response surface method,and was verified the rationality of the mix ratio.Finally,the mixture specimens were made according to the experimental design mix ratio,and the high temperature,low temperature performance and moisture susceptibility of the bamboo fiber modified mixtures asphalt were tested.The results showed that the high temperature performance,low temperature performance and moisture susceptibility of bamboo fiber modified asphalt mixtures were improved compared with the performance of SBS modified asphalt mixture.When the length of bamboo fiber is 7.25 mm and the content of 0.22%,the road performance of the asphalt mixture was optimal.Consequentially,the decomposition of bamboo residue into bamboo fiber and its application in asphalt pavement can improve the reuse of bamboo waste,with remarkable environmental benefits and great promotion value.

Mechanical and Permeability Analysis and Optimization of Recycled Aggregate Pervious Concrete Based on Response Surface Method

In this paper,the effects of different influencing factors and factor interaction on the compressive strength and permeability of recycled aggregate pervious concrete(RAPC)were studied based on the response surface method(RSM).By selecting the maximum aggregate size,water cement ratio and target porosity as design variables,combined with laboratory tests and numerical analysis,the influences of three factors on the compressive strength and permeability coefficient of RAPC were revealed.The regression equation of compressive strength and permeability coefficient of recycled aggregate pervious concrete were established based on RSM,and the response surface model was optimized to determine the optimal ratio of RAPC under the conditions of meeting the mechanical and permeability properties.The results show that the mismatch item of the model is not significant,the model is credible,and the accuracy and reliability of the test are high,but the degree of uncorrelation between the test data and the model is not obvious.The sensitivity of the three factors to the compressive strength is water cement ratio>maximum coarse aggregate particle size>target porosity,and the sensitivity to the permeability coefficient is target porosity>maximum coarse aggregate particle size>water cement ratio.The absolute errors of the model prediction results and the model optimization results are 1.28 MPa and 0.19 mm/s,and the relative errors are 5.06%and 4.19%,respectively.With high accuracy,RSM can match the measured results of compressive strength and permeability coefficient of RAPC.

Optimization of Supercritical Extraction Process of Laoshan Black Tea by Response Surface Methodology

[Objectives]Laoshan black tea was subjected to supercritical CO_(2) extraction. [Methods]The extraction conditions of Laoshan black tea were studied by an orthogonal experiment and optimized by response surface methodology. [Results] The optimum extraction conditions of black tea extract by supercritical CO_(2) extraction were as follows: extraction pressure 23.53 MPa, extraction time 1.73 h, and extraction temperature 49.75 ℃, with which the extract yield could reach 5.15% theoretically. [Conclusions] Based on the traditional extraction process, a supercritical extraction method optimized by response surface methodology and a unique extraction process were formed, which enriches the extraction processes and methods of natural raw materials.

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.

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.

Optimization of High-Protein Glutinous Rice Flour Production Using Response Surface Method

A response surface method was employed to study the effect of α-amylase concentration, hydrolysis temperature and time on the production of high protein glutinous rice flour(HPGRF). The suspension of glutinous rice flour(15%) that contained 6.52% protein was gelatinized and subsequently hydrolyzed by thermostable α-amylase. The hydrolysis yielded 0.144–0.222 g/g HPGRF with 29.4%–45.4% protein content. Hydrolysis time exerted a significant effect, while enzyme concentration and hydrolysis temperature showed insignificant effect on the protein content and production yield of HPGRF. The result of response surface method showed that the optimum condition for the production of HPGRF that contained at least 36% protein was treating gelatinized 15% glutinous rice flour suspension with 0.90 Kilo Novo α-amylase Unit(KNU)/g α-amylase at 80 oC for 99 min. By carrying out the predicted hydrolysis condition, HPGRF with 35.9% protein and 61.8% carbohydrates was resulted. The process yielded 0.172 g/g HPGRF. HPGRF contained higher amount of essential amino acids compared to glutinous rice flour. HPGRF had higher solubility and lower swelling power, and also showed no pasting peak compared with glutinous rice flour.

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.

An Intelligent Method for Structural Reliability Analysis Based on Response Surface

As water depth increases, the structural safety and reliability of a system become more and more important and challenging. Therefore, the structural reliability method must be applied in ocean engineering design such as offshore platform design. If the performance function is known in structural reliability analysis, the first-order second-moment method is often used. If the performance function could not be definitely expressed, the response surface method is always used because it has a very clear train of thought and simple programming. However, the traditional response surface method fits the response surface of quadratic polynomials where the problem of accuracy could not be solved, because the true limit state surface can be fitted well only in the area near the checking point. In this paper, an intelligent computing method based on the whole response surface is proposed, which can be used for the situation where the performance function could not be definitely expressed in structural reliability analysis. In this method, a response surface of the fuzzy neural network for the whole area should be constructed first, and then the structural reliability can be calculated by the genetic algorithm. In the proposed method, all the sample points for the training network come from the whole area, so the true limit state surface in the whole area can be fitted. Through calculational examples and comparative analysis, it can be known that the proposed method is much better than the traditional response surface method of quadratic polynomials, because, the amount of calculation of finite element analysis is largely reduced, the accuracy of calculation is improved, and the true limit state surface can be fitted very well in the whole area. So, the method proposed in this paper is suitable for engineering application.

Advanced response surface method for mechanical reliability analysis

Based on the classical response surface method （RSM）, a novel RSM using improved experimental points （EPs） is presented for reliability analysis. Two novel points are included in the presented method. One is the use of linear interpolation, from which the total EPs for determining the RS are selected to be closer to the actual failure surface; the other is the application of sequential linear interpolation to control the distance be- tween the surrounding EPs and the center EP, by which the presented method can ensure that the RS fits the actual failure surface in the region of maximum likelihood as the center EPs converge to the actual most probable point （MPP）. Since the fitting precision of the RS to the actual failure surface in the vicinity of the MPP, which has significant contribution to the probability of the failure surface being exceeded, is increased by the presented method, the precision of the failure probability calculated by RS is increased as well. Numerical examples illustrate the accuracy and efficiency of the presented method.

Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

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.

A new look at the response surface method for reliability analysis using chaos theory

To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.

Extraction Optimization of Polysaccharides from Rhizoma Polygonati by Response Surface Methodology and Content Determination

[Objectives]This study aimed to investigate the water extraction-alcohol precipitation technology and content determination method of polysaccharides in Rhizoma Polygonati.[Methods]Taking the content of polysaccharides in the extract as the indicator,the extraction process was optimized using single-factor tests and Box-Behnken Design.The content of polysaccharides extracted was determined by the anthrone-sulfuric acid method.Among the three factors in the test design,the solid/liquid ratio and extraction time had a significant effect(P<0.05,P<0.01),while the extraction temperature had no effect on the content of polysaccharides extracted(P>0.05).[Results]The optimal extraction process for polysaccharides in Rhizoma Polygonati was as follows:liquid/solid ratio 20∶1(mL/g),extraction time 2 h,and extraction temperature 85℃.Under the optimal extraction process,the content of polysaccharides in the extract reached 12.50%.[Conclusions]The extraction process optimized by response surface methodology for polysaccharides in Rhizoma Polygonati is reliable and has practical value,and can be used to guide production practices.

Fluidity Influencing Factor Analysis and Ratio Optimization of New Filling Slurry Based on the Response Surface Method

The filling mining method is important in realizing the green mining of mineral resources.Aiming at the problems of land resource occupation,environmental pollution,and rational utilization of coal-based solid wastes such as coal gangue,fly ash,and desulfurization gypsum,a new paste filling material was developed with coal gangue,fly ash,and desulfurization gypsum as raw materials.The microstructure of the raw materials was analyzed by XRD and SEM.Combined with the Box-Behnken experimental design,the effect of each component on the fluidity of the filling slurry was analyzed through the response surface analysis.The significance of each component on its bleeding and fluidity was determined,and the optimal ratio of the filling slurry was obtained.Experimental results show that the microcosmic morphology of coal gangue,desulfurization gypsum,and gasification slag presents an irregular block and rough particle surface;the microcosmic morphology of fly ash and bottom slag presents first out spherical or quasi spherical particles.Moreover,obvious sintering traces exist on the surface of the bottom slag.The main crystal mineral of coal gangue and fly ash is SiO_(2),the desulfurization gypsum is composed of Ca(SO_(4))(H_(2)O)and Ca(CO_(3))crystal minerals,the gasification slag is composed of carbon and nitrogen compounds,and the main crystal mineral components in the bottom slag sample are SiO_(2) and Al_(x)Si_(y)O_(z) compounds.The order of significance of each key factor on slurry fluidity is as follows:C(desulfurization gypsum)>D(gasification slag and bottom slag 1:1)>A(coal gangue)>B(fly ash).The order of the significance of each key factor on slurry bleeding is as follows:B(fly ash)>C(desulfurization gypsum)>D(gasification slag and bottom slag 1:1)>A(coal gangue).Considering the material preparation,field application,and other conditions,the mass percentage of each factor content of the new paste filling material is as follows:49.5%coal gangue,8.3%fly ash,4.1%desulfurization gypsum,6.2%gasification slag,and 6.2%bottom slag.

The Optimization of Ultrasonic Extraction Process of Total Flavonoids from Rhodiola Crenulata by Response Surface Method

[Objectives]To study the optimal extraction process of total flavonoids in Rhodiola rosea L.,and further facilitate the development and utilization of Rhodiola rosea L. [Methods]With Rhodiola crenulata as raw material,ethanol as extractant,ultrasonic extraction as the extraction method,the single factor method was first used for preliminary investigation of effect of ethanol volume fraction,solid-liquid ratio,extraction temperature and extraction time on the flavonoids extraction rate,and then the Box-Behnken response surface method was used to optimize the extraction process of total flavonoids in R. crenulata. [Results] The optimal extraction conditions: ethanol concentration of 72%;solid-liquid ratio of 1∶ 43; extraction temperature of 66℃; extraction time of 50 min. Under these conditions,the extraction rate of total flavonoids from R. crenulata was 2. 591%. [Conclusions] The results showed that the method of response surface was reasonable and feasible for the optimization of ultrasonic extraction of total flavonoids from R. crenulata.

Optimization of Extraction Conditions for SOD in Sedum aizoon by the Response Surface Method

This paper aimed to optimize extracting conditions of SOD in Sedum aizoon by response surface method. First,the single factor optimization tests were carried out. Three single factors were time,p H and liquid-solid ratio respectively. By Design expert 8. 0. 5 software,17 kinds of test scheme were designed. The protein yield of each scheme was obtained,and Design expert 8. 0. 5 software was used to conduct variance analysis and interactive analysis among factors,to obtain the corresponding mathematical model. The results showed that in single factor experiments,the optimal time was 1 h,p H was 7. 8,and liquid-solid ratio was 15:1. The interactive analysis indicated that the optimal scheme for extracting SOD in Sedum aizoon was time of 0. 98 h,p H of 7. 79,liquid-solid ratio of 13. 71:1. By the method of pyrogallol autoxidation,the extracted SOD enzyme activity was measured,namely 12 U/g. The results could provide a reference for further utilization and research of Sedum aizoon resource.

Influence of Operating Parameters on Unbalance in Rotating Machinery Using Response Surface Method

Wide range of rotating machinery contains an inherent amount of unbalance which leads to increase in the vibration level and related faults.In this work,the effect of different operating conditions viz.the unbalanced weight,radius,speed and position of the rotor disc on the unbalance in rotating machine are studied experimentally and analyzed by using Response Surface Methodology(RSM).RSM is a technique which consists of mathematical and statistical methods to develop the relationship between the inputs and outputs of a system by distinct functions.L27 Orthogonal Array(OA)was developed by using Design of Experiments(DOE)according to which experimentation has been carried out.Three accelerometer sensors were mounted to record the vibration responses(accelerations)in radially vertical,horizontal and axial directions.The responses recorded as root mean square values are then analysed using RSM.The relationship between response and operating factors has been established by developing a second order,non-linear mathematical model.Analysis of variance(ANOVA)has been performed for verification of the developed mathematical models.Results obtained from the analysis show that the unbalance weight and speed are most significant operating conditions that contribute the most to the effect the unbalance has on the rotating spindle.

Extremum response surface method of reliability analysis on two-link flexible robot manipulator

In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.

Improved response surface method and its application in stability reliability degree analysis of tunnel surrounding rock

An approach of limit state equation for surrounding rock was put forward based on deformation criterion.A method of symmetrical sampling of basic random variables adopted by classical response surface method was mended, and peak value and deflection degree of basic random variables distribution curve were took into account in the mended sampling method. A calculation way of probability moment, based on mended Rosenbluth method, suitable for non-explicit performance function was put forward. The first, second, third and fourth order moments of functional function value were calculated by mended Rosenbluth method through the first, second, third and fourth order moments of basic random variable. A probability density the function(PDF) of functional function was deduced through its first, second, third and fourth moments, the PDF in the new method took the place of the method of quadratic polynomial to approximate real functional function and reliability probability was calculated through integral by the PDF for random variable of functional function value in the new method. The result shows that the improved response surface method can adapt to various statistic distribution types of basic random variables, its calculation process is legible and need not iterative circulation. In addition, a stability probability of surrounding rock for a tunnel was calculated by the improved method, whose workload is only 30% of classical method and its accuracy is comparative.

Optimal design of butterfly-shaped linear ultrasonic motor using finite element method and response surface methodology

A new method for optimizing a butterfly-shaped linear ultrasonic motor was proposed to maximize its mechanical output. The finite element analysis technology and response surface methodology were combined together to realize the optimal design of the butterfly-shaped linear ultrasonic motor. First, the operation principle of the motor was introduced. Second, the finite element parameterized model of the stator of the motor was built using ANSYS parametric design language and some structure parameters of the stator were selected as design variables. Third, the sample points were selected in design variable space using latin hypercube Design. Through modal analysis and harmonic response analysis of the stator based on these sample points, the target responses were obtained. These sample points and response values were combined together to build a response surface model. Finally, the simplex method was used to find the optimal solution. The experimental results showed that many aspects of the design requirements of the butterfly-shaped linear ultrasonic motor have been fulfilled. The prototype motor fabricated based on the optimal design result exhibited considerably high dynamic performance, such as no-load speed of 873 mm/s, maximal thrust of 27.5 N, maximal efficiency of 43%, and thrust-weight ratio of 45.8.