INTEGRATION SHAPE AND SIZING OPTIMIZATION OF COMPOSITE WING STRUCTURE BASED ON RESPONSE SURFACE METHOD

An effective optimization method for the shape/sizing design of composite wing structures is presented with satisfying weight-cutting results. After decoupling, a kind of two-layer cycled optimization strategy suitable for these integrated shape/sizing optimization is obtained. The uniform design method is used to provide sample points, and approximation models for shape design variables. And the results of sizing optimization are construct- ed with the quadratic response surface method （QRSM）. The complex method based on QRSM is used to opti- mize the shape design variables and the criteria method is adopted to optimize the sizing design variables. Compared with the conventional method, the proposed algorithm is more effective and feasible for solving complex composite optimization problems and has good efficiency in weight cutting.

Reliability-based design optimization for flexible mechanism with particle swarm optimization and advanced extremum response surface method

To improve the computational efficiency of the reliability-based design optimization(RBDO) of flexible mechanism, particle swarm optimization-advanced extremum response surface method(PSO-AERSM) was proposed by integrating particle swarm optimization(PSO) algorithm and advanced extremum response surface method(AERSM). Firstly, the AERSM was developed and its mathematical model was established based on artificial neural network, and the PSO algorithm was investigated. And then the RBDO model of flexible mechanism was presented based on AERSM and PSO. Finally, regarding cross-sectional area as design variable, the reliability optimization of flexible mechanism was implemented subject to reliability degree and uncertainties based on the proposed approach. The optimization results show that the cross-section sizes obviously reduce by 22.96 mm^2 while keeping reliability degree. Through the comparison of methods, it is demonstrated that the AERSM holds high computational efficiency while keeping computational precision for the RBDO of flexible mechanism, and PSO algorithm minimizes the response of the objective function. The efforts of this work provide a useful sight for the reliability optimization of flexible mechanism, and enrich and develop the reliability theory as well.

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.

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 Bead Geometry in CO₂Laser Welding of Ti 6Al 4V Using Response Surface Methodology

In the presented study, the laser butt-welding of Ti 6Al 4V is investigated using 2.2 kw CO2 laser. Ti 6Al 4V alloy has widespread application in various fields of industries including the medical, nuclear and aerospace. In this study, Response Surface Methodology (RSM) is employed to establish the design of experiments and to optimize the bead geometry. The relationships between the input laser-welding parameters (i.e. laser power, welding speed and focal point position) and the process responses (i.e. welded zone width, heat affected zone width, welded zone area, heat affected zone area and penetration depth) are investigated. The multi-response optimizations are used to optimize the welding process. The optimum welding conditions are identified in order to increase the productivity and minimize the total operating cost. The validation results demonstrate that the developed models are accurate with low percentages of error (less than 12.5%).

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.

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 ram/s, maximal thrust of 27.5 N, maximal efficiency of 43%, and thrust-weight ratio of 45.8.

Parametric Optimization to Minimise the Surface Roughness on the Machining of GFRP Composites

The present investigation focuses on the parametric influence of machining parameters on the surface finish obtained in turning of glass fiber reinforced polymer （GFRP） composites. The experiments were conducted based on Taguchi＇s experimental design technique. Response surface methodology and analysis of variance （ANOVA） were used to evaluate the composite machining process to perform the optimization. The results revealed that the feed rate was main influencing parameter on the surface roughness. The surface roughness increased with increasing the feed rate but decreased with increasing the cutting speed. Among the other parameters, depth of cut was more insensitive. The predicted values and measured values were fairly close to each other, which indicates that the developed model can be effectively used to predict the surface roughness on the machining of GFRP composites with 95% confidence intervals. Using such model could remarkablely save the time and cost.

Multivariate Rational Response Surface Approximation of Nodal Displacements of Truss Structures

Polynomial-basis response surface method has some shortcomings for truss structures in structural optimization,concluding the low fitting accuracy and the great computational effort. Based on the theory of approximation, a response surface method based on Multivariate Rational Function basis(MRRSM) is proposed. In order to further reduce the computational workload of MRRSM, focusing on the law between the cross-sectional area and the nodal displacements of truss structure, a conjecture that the determinant of the stiffness matrix and the corresponding elements of adjoint matrix involved in displacement determination are polynomials with the same order as their respective matrices, each term of which is the product of cross-sectional areas, is proposed. The conjecture is proved theoretically for statically determinate truss structure, and is shown corrected by a large number of statically indeterminate truss structures. The theoretical analysis and a large number of numerical examples show that MRRSM has a high fitting accuracy and less computational effort. Efficiency of the structural optimization of truss structures would be enhanced.

Optimization of phenol degradation by Candida tropicalis Z-04 using Plackett-Burman design and response surface methodology

Statistical experimental designs were used to optimize the process of phenol degradation by Candida tropicalis Z-04, isolated from phenol-degrading aerobic granules. The most important factors influencing phenol degradation （p 〈 0.05）, as identified by a two-level Plackett-Burman design with 11 variables, were yeast extract, phenol, inoculum size, and temperature. Steepest ascent method was undertaken to determine the optimal regions of these four significant factors. Central composite design （CCD） and response surface analysis were adopted to further investigate the mutual interactions between these variables and to identify their optimal values that would generate maximum phenol degradation. The analysis results indicated that interactions between yeast extract and temperature, phenol and temperature, inocuhim size and temperature affected the response variable （phenol degradation） significantly. The predicted results showed that the maximum removal efficiency of phenol （99.10%） could be obtained under the optimum conditions of yeast extract 0.41 g/L, phenol 1.03 g/L, inoculum size 1.43% （V/V） and temperature 30.04℃. These predicted values were further verified by validation experiments. The excellent correlation between predicted and experimental values confirmed the validity and practicability of this statistical optimum strategy. This study indicated the excellent ability of C. tropicalis Z-04 in degrading high-strength phenol. Optimal conditions obtained in this experiment laid a solid foundation for further use of this microorganism in the treatment of highstrength phenol effluents.

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

Optimization of Sensor Orientation in Railway Wheel Detector, Using Kriging Method

Considering the importance of axle counter function in detecting the train wheels and determining the clearance or occupancy of a track section, it is important to ensure a safe and reliable performance of this system. In this paper, in order to improve the sensor performance, the authors have focused on the orientation of magnetic sensors’ coils. In order to improve the detection capability of the system, through measuring the induced voltage in the receiver coil, it is important to adjust the relative orientation of the transmitter and receiver coils. Due to the existence of infinite relative orientations, in order to determine the optimum orientation for the sensor coils, Kriging methods which is one of the Response Surface Methodologies (RSMs) is applied. Finite Element Method (FEM) is utilized to provide sample data, as inputs to the Kriging algorithm. The analysis not only provides the optimum relative orientation of the sensor coils, it also improves analysis time, comparing to field based measurements. The analysis results are validated by the laboratory based data implemented in the control and signaling laboratory of the school of railway engineering and also field based tests in Iranian railway.

Optimal Designs Technique for Locating the Optimum of a Second Order Response Function

A more efficient method of locating the optimum of a second order response function was of interest in this work. In order to do this, the principles of optimal designs of experiment is invoked and used for this purpose. At the end, it was discovered that the noticeable pitfall in response surface methodology (RSM) was circumvented by this method as the step length was obtained by taking the derivative of the response function rather than doing so by intuition or trial and error as is the case in RSM. A numerical illustration shows that this method is suitable for obtaining the desired optimizer in just one move which compares favourably with other known methods such as Newton-Raphson method which requires more than one iteration to reach the optimizer.

Hot Stamping Parameters Optimization of Boron Steel Using a Response Surface Methodology Based on Central Composite Design

The effect of hot stamping parameters on the mechanical properties of 22MnB5 steel sheet with thickness of 1.1 mm is studied. The considered parameters are austenization temperature （800- 1 000 ℃ ）, austenitizing soa king time （60-540 s）, initial deformation temperature （560-800 C） and tool temperature （20-220 ℃）. In order to obtain hot stamped parts with optimal mechanical properties, response surface methodology based on the central composite design has been employed to design the experiment matrix. Tensile strength of hot stamped parts is deter- mined as the relation in the mathematical model. The optimal condition and objective effects of parameters are deter mined via this relation. The statistical analysis showed that all four factors significantly affect the tensile strength of the hot stamped parts. The optimum austenization temperature is found to be 918.89 ℃ with the austenitizing soa- king time, initial deformation temperature and tool temperature of 279.45 s, 684.69 C and 21.85 ℃, respectively. These optimal hot stamping parameters prove to have high tensile strength （1 631.84 MPa） where deviation between predicted and actual response falls within 2 %.

Investigation on Multi-objective Performance Optimization Algorithm Application of Fan Based on Response Surface Method and Entropy Method

A multi-objective performance optimization method is proposed, and the problem that single structural parame- ters of small fan balance the optimization between the static characteristics and the aerodynamic noise is solved. In this method, three structural parameters are selected as the optimization variables. Besides, the static pressure efficiency and the aerodynamic noise of the fan are regarded as the multi-objective performance. Furthermore, the response surface method and the entropy method are used to establish the optimization function between the op- timization variables and the multi-objective performances. Finally, the optimized model is found when the opti- mization function reaches its maximttm value. Experimental data shows that the optimized model not only en- hances the static characteristics of the fan but also obviously reduces the noise. The results of the study will provide some reference for the optimization of multi-objective performance of other types of rotating machinery.

Optimization of rare earth carbonate reactive-crystallization process based on response surface method

Rare earth carbonate precipitation is mainly amorphous,of large volume and difficult to filter.To prepare crystalline rare earth carbonate,mother liquor of heavy rare earth was taken as research object,and the experimental scheme was designed based on the response surface central composite design(CCD)method.The concentration of mother liquor,aging time and seed crystal dosage were taken as independent variables,and the particle size of rare earth carbonate was taken as the response value to establish a quadratic polynomial numerical model to optimize the reactive-crystallization process of rare earth carbonate.The results show that these three factors have significant effect on the particle size of rare earth carbonate,and the influence order is mother liquid concentration>aging time>seed crystal dosage.Moreover,the interaction between mother liquor concentration and seed crystal dosage has a significant effect on the size of rare earth carbonate particles.The optimal parameters predicted by the model are as follows:the concentration of mother liquid is 1.75 g/L,seed crystal dosage is 13.56 wt%,and aging time is 8 h.Under these conditions,the predicted particle size is 28.74μm,and the experiment particle size is 28.23μm,between both,the relative error is 0.73%,which indicates that the established response surface model has a good prediction effect and a certain practical significance to guide the reactive-crystallization process of rare earth carbonate.The obtained rare earth carbonate has a crystallinity of 97.82%,uniform particles size,and low-hydrated crystals with a tengerite structure.

Multi-Objective Optimization of Surface-Mounted and Interior Permanent Magnet Synchronous Motor Based on Taguchi Method and Response Surface Method

The surface-mounted and interior permanent magnet synchronous motor(SIPMSM)has the characteristics of multiple variables,strong coupling and nonlinearity.In order to improve the performance of SIPMSM,this paper presents a multi-objective optimal design process using Taguchi and response surface methodology(RSM).The peak value of cogging torque(PVCT),ratio value of average torque and permanent magnet weight(RTW),torque ripple and back-EMF total harmonics distortion(ETHD)are selected as optimization goals.The experiment matrix is established by Taguchi method,and analyzed the tendency and proportion of the effect of the optimization parameters on SIPMSM performance.The rules of choosing multi-objective optimization parameters are obtained.The least-squares method is used to establish the optimal objective function,and RSM is used to obtain the resolutions of the optimization objective function.Comparing the initial performance with optimized performance verifies the effectiveness of the proposed method.

Robust optimization of the billet for isothermal local loading transitional region of a Ti-alloy rib-web component based on dual-response surface method

Billet optimization can greatly improve the forming quality of the transitional region in the isothermal local loading forming （ILLF） of large-scale Ti-alloy ribweb components. However, the final quality of the transitional region may be deteriorated by uncontrollable factors, such as the manufacturing tolerance of the preforming billet, fluctuation of the stroke length, and friction factor. Thus, a dual-response surface method （RSM）-based robust optimization of the billet was proposed to address the uncontrollable factors in transi- tional region of the ILLF. Given that the die underfilling and folding defect are two key factors that influence the forming quality of the transitional region, minimizing the mean and standard deviation of the die underfilling rate and avoiding folding defect were defined as the objective function and constraint condition in robust optimization. Then, the cross array design was constructed, a dual-RSM model was established for the mean and standard deviation of the die underfilling rate by considering the size parameters of the billet and uncontrollable factors. Subsequently, an optimum solution was derived to achieve the robust optimization of the billet. A case study on robust optimization was conducted. Good results were attained for improving the die filling and avoiding folding defect, suggesting that the robust optimization of the billet in the transitional region of the ILLF was efficient and reliable.

Reliability Based Optimization of Composite Laminates for Frequency Constraint

The reliability based optimization （RBO） issue of composite laminates trader fundamental frequency constraint is studied. Considering the tmcertainties of material properties, the frequency constraint reliability of the structure is evaluated by the combination of response surface method （RSM） and finite element method. An optimization algorithm is developed based on the mechanism of laminate frequency characteristics, to optimize the laminate in terms of the ply amount and orientation angles. Numerical examples of composite laminates and cylindrical shell illustrate the advantages of the present optimization algorithm on the efficiency and applicability respects. The optimal solutions of RBO are obviously different from the deterministic optimization results, and the necessity of considering material property uncertainties in the composite structural frequency constraint optimization is revealed.

Effect of Variable Selection on Multidisciplinary Design Optimization:a Flight Vehicle Example

Different multidisciplinary design optimization （MDO） problems are formulated and compared. Two MDO formulations are applied to a sounding rocket in order to optimize the performance of the rocket. In the MDO of the referred vehicle, three disciplines have been considered, which are trajectory, propulsion and aerodynamics. A special design structure matrix is developed to assist data exchange between disciplines. This design process uses response surface method （RSM） for multidisciplinary optimization of the rocket. The RSM is applied to the design in two categories： the propulsion model and the system level. In the propulsion model, RSM determines an approximate mathematical model of the engine output parameters as a function of design variables. In the system level, RSM fits a surface of objective function versus design variables. In the first MDO problem formulation, two design variables are selected to form propulsion discipline. In the second one, three new design variables from geometry are added and finally, an optimization method is applied to the response surface in the system level in order to find the best result. Application of the first developed multidisciplinary design optimization procedure increased accessible altitude （performance index） of the referred sounding rocket by twenty five percents and the second one twenty nine.