An Adaptive Interpolating MLS Based Response Surface Model Applied to Design Optimizations of Electromagnetic Devices
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A response surface model (RSM) based on a combination of interpolating moving least squares and multistep method is proposed. The proposed RSM can automatically adjust the supports of its weight functions according to the distribution of the sampling points when it is used to reconstruct a computationally heavy design problem. Numerical examples are given to demonstrate the feasibility and efficiency of the proposed method for solving inverse problemsKeywords:
Moving least squares
Adaptive sampling
A response surface model (RSM) based on a combination of interpolating moving least squares (IMLS) and multi-step method is proposed. The proposed RSM can automatically adjust the supports of its weight functions according to the distribution of the sampling points when it is used to reconstruct a computationally heavy design problem. The TEAM Workshop Problem 22 is solved to demonstrate the feasibility of the proposed method for solving inverse problems
Moving least squares
Adaptive sampling
Least-squares function approximation
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A new theorem of inverse formula is introduced for a kind of infinite series. Thus some new results for important inverse problems in physics are presented in this paper. These are the inverse problems for obtaining the phonon density of states, the inverse blackbody radiation problem for remote sensing, and the solution for inverse Ewald summation. Of more importance, it shows the possibility of the application of number theory to physical problems.
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Abstract The biodiesel production from alkali-catalyzed transesterification of karanja oil was investigated. In this study, the effect of three parameters, i.e., reaction temperature, catalyst concentration, and molar ratio of methanol to oil on biodiesel yield was studied. Central composite design (CCD) along with response surface methodology (RSM) was used for designing experiments and estimating the quadratic response surface. Catalyst concentration was found to have a negative effect on biodiesel yield, whereas molar ratio showed positive effect. Temperature and molar ratio showed significant interaction effect. The reaction conditions were optimized for maximum response, i.e., biodiesel yield from RSM. The program for the RSM model, coupled with genetic algorithm (GA), was developed for predicting the optimized process parameters for maximum biodiesel yield to obtain a global optimal solution. The results were found to be similar from both of the methods.
Central composite design
Quadratic model
Molar ratio
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It is difficult to obtain the optimal conditions on treating disperse azo dye wastewater,although biodegradation is very effective.Optimization of microbial degradation and decolorization was conducted using the Response Surface Methodology.One strain,identified as Streptomyces sp.FX649,had high potency in the degradation and decolorization of azo dye Red 30(AR30).After obtaining the single-factor experiment results,AR30 concentration,culture time,pH and culture temperature were selected for Box-Benhnken composite designing.Response Surface Methodology(RSM) was employed to study the effect of these factors on the yield of decolorization.Combined with the actual tests,the results showed that the yield of decolorization of AR30 reached 95.1% under the optimal parameters with 110 mg · L-1 AR30 cultivating for 36 h under pH 7.3 at 31.3 ℃.
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Central composite design
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Central composite design
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This paper deals with the problem of uncertainties evaluation when the procedure of inverse problems is used for processing the eddy current testing data. First the general inverse problem algorithm is described. Next the influence of different types of errors to the results of this algorithm is theoretically analyzed and some results are shown. These results show that the proper choice of the eddy current testing probe is important for achievement of accurate results of the inverse problem solution.
Inverse method
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Central composite design
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Quadratic model
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Some examples of inverse problem approach of the phenomena related to materials are introduced. What is the inverse problem?, what could be obtained, identified or estimated by an inverse approach? are discussed based on the inverse processing of elastic waves. Some problems and uncectainities involved in inverse processing are also discussed.
Inverse method
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