Conservative quadratic RSM combined with incomplete small composite design and conservative least squares fitting
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A new quadratic response surface modeling method is presented. In this method, the incomplete small composite design (ISCD) is newly proposed to reduce the number of experimental runs than that of the SCD. Unlike the SCD, the proposed ISCD always gives a unique design assessed on the number of factors, although it may induce the rank-deficiency in the normal equation. Thus, the singular value decomposition (SVD) is employed to solve the normal equation. Then, the duality theory is used to newly develop the conservative least squares fitting (CONFIT) method. This can directly control the over- or the under-estimation behavior of the approximate functions. Finally, the performance of CONFIT is numerically shown by comparing its’ conservativeness with that of conventional fitting method. Also, optimizing one practical design problem numerically shows the effectiveness of the sequential approximate optimization (SAO) combined with the proposed ISCD and CONFIT.
Key WordsResponse Surface Model Sequential Approximate Optimization Incomplete Small Composite Design Conservative Least Squares Fitting
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