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.

Response surface methodology-based hybrid robust design optimization for complex product under mixed uncertainties

Minimizing the impact of the mixed uncertainties(i.e.,the aleatory uncertainty and the epistemic uncertainty) for a complex product of compliant mechanism(CPCM) quality improvement signifies a fascinating research topic to enhance the robustness.However, most of the existing works in the CPCM robust design optimization neglect the mixed uncertainties, which might result in an unstable design or even an infeasible design. To solve this issue, a response surface methodology-based hybrid robust design optimization(RSM-based HRDO) approach is proposed to improve the robustness of the quality characteristic for the CPCM via considering the mixed uncertainties in the robust design optimization. A bridge-type amplification mechanism is used to manifest the effectiveness of the proposed approach. The comparison results prove that the proposed approach can not only keep its superiority in the robustness, but also provide a robust scheme for optimizing the design parameters.

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.

Engineering Design Optimization Based on Intelligent Response Surface Methodology

An intelligent response surface methodology (IRSM) was proposed to achieve the most competitive metal forming products, in which artificial intelligence technologies are introduced into the optimization process. It is used as simple and inexpensive replacement for computationally expensive simulation model. In IRSM, the optimal design space can be reduced greatly without any prior information about function distribution. Also, by identifying the approximation error region, new design points can be supplemented correspondingly to improve the response surface model effectively. The procedure is iterated until the accuracy reaches the desired threshold value. Thus, the global optimization can be performed based on this substitute model. Finally, we present an optimization design example about roll forming of a "U" channel product.

Optimization for Microbial Degumming of Ramie with Bacillus subtilis DZ_(5) in Submerged Fermentation by Orthogonal Array Design and Response Surface Methodology

As a kind of natural fiber,ramie fiber has distinctive advantages in textile application,but the application is limited due to the traditional degumming mode.Compared with the traditional degumming process,the microbial degumming process has many advantages.To obtain the optimal conditions for degumming ramie with Bacillus subtilis DZ_(5)(BS DZ_(5)),a combined statistical approach of orthogonal array design(OAD)and response surface methodology(RSM)was used.The influences of initial pH of the bacteria medium,culture temperature,shaking speed,degumming time and inoculum size on submerged fermentation degumming were evaluated by using fractional factorial design.The main factors in the analysis were culture temperature,shaking speed and initial pH.The residual gum mass fraction was used as the optimization index,and the optimal conditions for degumming were determined by central composite design and RSM.Thus with only a limited number of experiments,an optimal ramie microbial degumming condition was found as the culture temperature of 40℃,the initial pH in the culture medium of 8.5,the shaking speed of 205 r/min,the degumming time of 96 h and the inoculum size of 5%.After microbial degumming of ramie under the optimal conditions,there was only 10.6%residual gum by mass in the fiber.In addition,the effective degumming of BS DZ_(5)was also confirmed by a scanning electron microscope(SEM).

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 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.

Prediction and optimization of process parameter of friction stir welded AA5083-H111 aluminum alloy using response surface methodology

A systematic approach was presented to develop the empirical model for predicting the ultimate tensile strength of AA5083-H111 aluminum alloy which is widely used in ship building industry by incorporating friction stir welding(FSW) process parameters such as tool rotational speed,welding speed,and axial force.FSW was carried out considering three-factor five-level central composite rotatable design with full replications technique.Response surface methodology(RSM) was applied to developing linear regression model for establishing the relationship between the FSW process parameters and ultimate tensile strength.Analysis of variance(ANOVA) technique was used to check the adequacy of the developed model.The FSW process parameters were also optimized using response surface methodology(RSM) to maximize the ultimate tensile strength.The joint welded at a tool rotational speed of 1 000 r/min,a welding speed of 69 mm/min and an axial force of 1.33 t exhibits higher tensile strength compared with other joints.

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.

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.

Robust Design Optimization Method for Centrifugal Impellers under Surface Roughness Uncertainties Due to Blade Fouling

Blade fouling has been proved to be a great threat to compressor performance in operating stage. The current researches on fouling-induced performance degradations of centrifugal compressors are based mainly on simplified roughness models without taking into account the realistic factors such as spatial non-uniformity and randomness of the fouling-induced surface roughness. Moreover, little attention has been paid to the robust design optimization of centrifugal compressor impellers with considerations of blade fouling. In this paper, a multi-objective robust design optimization method is developed for centrifugal impellers under surface roughness uncertainties due to blade fouling. A three-dimensional surface roughness map is proposed to describe the nonuniformity and randomness of realistic fouling accumulations on blades. To lower computational cost in robust design optimization, the support vector regression（SVR） metamodel is combined with the Monte Carlo simulation（MCS） method to conduct the uncertainty analysis of fouled impeller performance. The analyzed results show that the critical fouled region associated with impeller performance degradations lies at the leading edge of blade tip. The SVR metamodel has been proved to be an efficient and accurate means in the detection of impeller performance variations caused by roughness uncertainties. After design optimization, the robust optimal design is found to be more efficient and less sensitive to fouling uncertainties while maintaining good impeller performance in the clean condition. This research proposes a systematic design optimization method for centrifugal compressors with considerations of blade fouling, providing a practical guidance to the design of advanced centrifugal compressors.

Optimization of Rooting Medium for Tissue Culture Seedlings of Dendrobium officinale by Response Surface Methodology

[Objectives] To increase the survival rate of tissue culture seedlings of Dendrobium officinale,and optimize the conditions of rooting medium by the response surface methodology( RSM). [Methods]The effects of 6-BA concentration,NAA concentration,potato amount and the amount of mashed banana on the growth of seedlings were determined by single factor experiment and were analyzed by Box-Behnken design and response surface methodology. [Results]The optimal culture conditions: rooting medium 1/2 MS + 6-BA 0. 24 mg/L + mashed banana 87. 63 g/L + potato 89. 30 g/L + NAA 0. 52 mg/L + sucrose 20. 0 g/L + activated carbon 4. 0 g/L + agar 7. 0 g/L,p H 5. 8,and light intensity 2 000 Lx. [Conclusions]The model established by response surface methodology has a good predictability and could be used to optimize the conditions of tissue culture and rooting medium of D. officinale.

Optimization of the Ultrasonic-assisted Extraction Process for Protocatechuic Acid from Emilia sonchifolia DC by Response Surface Methodology

[Objectives] This study was conducted to optimize the extraction process of protocatechuic acid from Emilia sonchifolia DC. [Methods] The optimal extraction conditions were determined by single factor,response surface analysis and variance analysis,and the content of protocatechuic acid was determined by HPLC. [Results] The protocatechuic acid standard curve equation was: y = 1 435 x + 8 403,R^2= 0. 999 8,indicating a good linear relationship. The optimal extraction conditions were as follows: a temperature at 80 ℃,an extraction time of 1 h,a material-to-liquid ratio at 1:10 and an ultrasonic power of 600 W,and the content of protocatechuic acid extracted was 1. 93 mg/g. The method showed a RSD of 0. 41%,less than 2%,and the detection limit was 0. 0000047261 g/ml.The experimental sample X1 was the low-level 0. 1 mg/ml standard solution,which showed recovery of protocatechuic acid between 100.8% and 105.2%,with a RSD of 0. 013%;and the sample X2 was the high-level 1. 0 mg/ml standard solution,which exhibited recovery between 100. 6% and 102. 2%,with a RSD of 0.076%. Thus,the recovery was high,and the requirements of the performance index were met. [Conclusions] The detection method is stable and reliable and can produce satisfactory results.

Robust Collaborative Optimization Method Based on Dual-response Surface

A novel method for robust collaborative design of complex products based on dual-response surface （DRS-RCO） is proposed to solve multidisciplinary design optimization （MDO） problems under uncertainty. Collaborative optimization （CO） which decomposes the whole system into a double-level nonlinear optimization problem is widely accepted as an efficient method to solve MDO problems. In order to improve the quality of complex product in design process, robust collaborative optimization （RCO） is developed to solve those problems under uncertain conditions. RCO does optimization on the linear sum of mean and standard deviation of objective function and gets an optimal solution with high robustness. Response surfaces method is an important way to do approximation in robust design. DRS-RCO is an improved RCO method in which dual-response surface replaces system uncertainty analysis module of CO. The dual-response surface is the approximate model of mean and standard deviation of objective function respectively. In DRS-RCO, All the information of subsystems is included in dual-response surfaces. As an additional item, the standard deviation of objective function is added to the subsystem optimization. This item guarantee both the mean and standard deviation of this subsystem is reaching the minima at the same time. Finally, a test problem with two coupled subsystems is conducted to verify the feasibility and effectiveness of DRS-RCO.

High-Speed,High-Power Motor Design for a Four-Legged Robot Actuator Optimized using the Weighted Sum and Response Surface Methods

In this paper,a design is presented for a high-speed,high-power motor for a four-legged robot actuator that was optimized using the weighted sum method(WSM)based on the Taguchi method,and the response surface method(RSM).First,output torque,torque constant,torque ripple,and efficiency were selected as objective functions for the optimized design.The sampling method was implemented to use a mixed orthogonal array and the single response characteristics of each objective function were compared using the Taguchi method.Moreover,to consider the multi-response characteristic of the objective functions,WSM was applied.Second,the 2D finite element analysis result of the RSM was compared with that using the WSM.Finally,an experiment was carried out on the manufactured motor and the optimized model is presented here.

Optimization of Culture Components for Laccase Activity from Pleurotus Ostreatus P40 Using Response Surface Methodology

High enzymatic activity is required for laccase applications.Central composite design （CCD）-based response surface methodology （RSM） can effectively increase the enzymatic activity of Pleurotus ostreatus P40 in liquid substrate fermentation.Initial screening of the nutritional components was performed using a Plackett-Burman design.The variables,namely,bran,bagasse,Tween 80,and yeast extract,were found to have statistically significant effects on laccase activity.These variables were further optimized using CCD-based RSM.Optimal concentrations for the maximum laccase activity were 8.144 2 g/L bran,50 g/L bagasse,0.424 1 mL/L Tween 80,and 2.832 5 g/L yeast extract.Under optimized conditions,the maximum measured laccase activity reached 96 480 U/L,which was close to the predicted value （104 830 U/L） by RSM.Therefore,RSM can be used to optimize culture components for laccase activity from Pieurotus ostreatus P40.

Optimization of the Impeller Geometry for an Automotive Torque Converter Using Response Surface Methodology and Desirability Function

Response surface methodology (RSM) based on desirability function approach (DFA) is applied to obtain an optimal design of the impeller geometry for an automotive torque converter. The relative importance of six design parameters including impeller blade number, blade thickness, bias angle, scroll angle, inlet angle and exit angle is investigated using orthogonal design approach. The impeller inlet angle, exit angle and bias angle are found to exert the greatest influence on the overall performance of a torque converter, with two flow area factors being considered, namely 17% and 20%. Then, RSM together with central composite design (CCD) method is used to in-depth evaluate the interaction effect of the three key parameters on converter performance. The results demonstrate that impeller exit angle has the strongest impact on peak efficiency, with larger angles yielding the most favorable results. The stall torque ratio maximization is attainable with the increase of impeller bias angle and inlet angle together with smaller exit angle. In the end, an optimized design for the impeller geometry is obtained with stall torque ratio and peak efficiency increased by 1.62% and 1.1%, respectively. The new optimization method can be used as a reference for performance enhancement in the design process of impeller geometry for an automotive torque converter.

Catalytic Hydrothermal Liquefaction of Water Hyacinth Using Fe3O4/NiO Nanocomposite: Optimization of Reaction Conditions by Response Surface Methodology

This research aimed at optimizing the reaction conditions for the catalytic hydrothermal liquefaction (HTL) of water hyacinth using iron oxide/nickel oxide nanocomposite as catalysts. The iron oxide/nickel oxide nanocomposite was synthesized by the co-precipitation method and used in the hydrothermal liquefaction of water hyacinth. The composition and structural morphology of the synthesized catalysts were determined using X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), and atomic absorption spectroscopy (AAS). The particle size distribution of the catalyst nanoparticles was determined by the Image J software. Three reaction parameters were optimized using the response surface methodology (RSM). These were: temperature, residence time, and catalyst dosage. A maximum bio-oil yield of 59.4 wt% was obtained using iron oxide/nickel oxide nanocomposite compared to 50.7 wt% obtained in absence of the catalyst. The maximum bio-oil yield was obtained at a temperature of 320°C, 1.5 g of catalyst dosage, and 60 min of residence time. The composition of bio-oil was analyzed using gas chromatography-mass spectroscopy (GC-MS) and elemental analysis. The GC-MS results showed an increase of hydrocarbons from 58.3% for uncatalyzed hydrothermal liquefaction to 88.66% using iron oxide/nickel oxide nanocomposite. Elemental analysis results revealed an increase in the hydrogen and carbon content and a reduction in the Nitrogen, Oxygen, and Sulphur content of the bio-oil during catalytic HTL compared to HTL in absence of catalyst nanoparticles. The high heating value increased from 33.5 MJ/Kg for uncatalyzed hydrothermal liquefaction to 38.6 MJ/Kg during the catalytic HTL. The catalyst nanoparticles were recovered from the solid residue by sonication and magnetic separation and recycled. The recycled catalyst nanoparticles were still efficient as hydrothermal liquefaction (HTL) catalysts and were recycled four times. The application of iron oxide/ nickel oxide nanocomposites in the HTL of water hyacinth increases the yield of bio-oil and improves its quality by reducing hetero atoms thus increasing its energy performance as fuel. Iron oxide/nickel oxide nanocomposites used in this study are widely available and can be easily recovered magnetically and recycled. This will potentially lead to an economical, environmentally friendly, and sustainable way of converting biomass into biofuel.

Response Surface Methodology as an Approach for Optimization of Vinegar Fermentation Conditions Using Three Different Thermotolerant Acetic Acid Bacteria

This study aimed to investigate optimal fermentation conditions of biological acetic acid fermentation for vinegar production. Optimization was performed on 3 acetic acid bacteria strains namely VMA1, VMA7 and VMAO using Response Surface Methodology (RSM). A Box-Behnken-Design (BBD) was achieved with three different independent process parameters involving: fermentation temperature, original alcohol concentration and original acetic acid concentration and one dependent variable (acetic acid yield). The results showed that the mathematical models describe correctly the relationship between responses and factors (F values of the models (p R2 (coefficient of correlation) respectively 0.96, 0.94, 0.98, and adjusted R2 0.95, 0.92, 0.98). The maximum acidity was obtained respectively at fermentation temperatures, original alcohol concentrations and original acetic acid concentrations ranging from [37.5°C - 45°C], [16% - 20% (v/v)], [1.5% - 2% (w/v)] for VMA1, [40°C - 45°C], [14.5% - 20% (v/v)], [1.7% - 2% (w/v)] for VMA7 and [42°C - 45°C], [17% - 20% (v/v)], [1.5% - 2% (w/v)] for VMAO. The use of these acetic strains in the production of vinegar may seriously lead to a decrease or even an ablation of the costs related to the cooling of bioreactors especially in warm and hot countries, in the context of global warming.

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.