A Note on Construction of Orthogonal Arrays with Unequal Strength from Error-Correcting Codes

ABSTRACTOrthogonal arrays (OAs) are a key research focus in combinatorial design theory and experimental design theory. They play a very important role in an increasing number of interdisciplinary fields, such as computer science, cryptography, multipartite quantum states and quantum information. And the open problems in many fields are closely related to the construction of orthogonal arrays with high strength and large size. At present, some open problems have been solved by using orthogonal arrays. There is an urgent need for developing such orthogonal arrays. This article introduces a general method for obtaining asymmetric orthogonal arrays with high strength. The proposed method is straightforward and constructive. The constructed OAs can be utilized to generate more OAs. Some selective OAs are tabulated for practical applications.

In this chapter we present some of the most important families of codes and the orthogonal arrays that are derived from them.KeywordsGenerator MatrixOrthogonal ArrayLinear CodeCyclic CodeGenerator PolynomialThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The purpose of this paper is to survey the construction of orthogonal arrays of strength two by using difference sets. Some methods for constructing difference setD(2p,2p,p,2), wherep is a prime or a prime power, are given. It is shown that the Kronecker sum of a difference setD(λ1 p,k 1,p,2) and an orthogonal array (λ2 p 2,k 2,p,2) leads to another orthogonal array (λ1λ2 p 3,k 1 k 2+1,p,2). This enables us to construct orthogonal arrays [2p n+1, 1+2(p+p 2+...+p n ,p),2], [4p n+2, 1+2p+4(p 2+p 3+...+p n+1),p,2], and [8p n+3, 1+2p+4p 2+8(p 3+p 4+...+p n+2),p,2] wherep is a prime or a prime power.

우리는 직교배열로서 직교계획, 즉 강도(strength)가 2인 직교배열을 주로 이용한다. 그러나, 강도 3인 직교배열은 주효과들과 2인자교호작용이 포함되는 가법모형 하에서 전체최적화(universal optimality)하다는 것이 밝혀져 있다. 그러므로 임의의 배열이 강도 3인 직교배열인가를 평가하는 측도가 필요하다. 이를 확장하면 임의의 배열이 강도 t(<TEX>$\ge$</TEX> 2)인 직교배열인가를 평가하는 측도를 제안할 수 있다. We usually use orthogonal designs-orthogonal array of strength 2 as orthogonal arrays. It was shown that fractional factorial plaits represented by orthogonal arrays of strength 3 are universally optimal under the additive motels that includes the mean, all main effects and all two-factor interactions. Therefore, we need the measure for evaluating the orthogonal array of strength 3. We can extend this measure as the measure for evaluating the orthogonal array of strength t(<TEX>$\ge$</TEX> 2).

The purpose of this study is to experimentally design the drying, calcination, and sintering processes of artificial lightweight aggregates through the orthogonal array, to expand the data using the results, and to model the manufacturing process of lightweight aggregates through machine-learning techniques. The experimental design of the process consisted of L18(3661), which means that 36 × 61 data can be obtained in 18 experiments using an orthogonal array design. After the experiment, the data were expanded to 486 instances and trained by several machine-learning techniques such as linear regression, random forest, and support vector regression (SVR). We evaluated the predictive performance of machine-learning models by comparing predicted and actual values. As a result, the SVR showed the best performance for predicting measured values. This model also worked well for predictions of untested cases.

This book on experimental design is somewhat similar in flavor to the classic book by G.E

Optimization techniques to optimize the milling operation with different parameters for composite of AA 3105

We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1 ≤ k ≤ n. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes.

We develop a method for construction of arrays which are nearly orthogonal, in the sense that each column is orthogonal to a large proportion of the other columns, and which are convertible to fully orthogonal arrays via a mapping of the symbols in each column to a possibly smaller set of symbols. These arrays can be useful in computer experiments as designs which accommodate a large number of factors and enjoy attractive space-filling properties. Our construction allows both the mappable nearly orthogonal array and the consequent fully orthogonal array to be either symmetric or asymmetric. Resolvable orthogonal arrays play a key role in the construction.

This study proposes an approach for the quality improvement of feature extraction in unmanned aerial vehicle (UAV)-based images through object-based image analysis (OBIA). A fixed-wing UAV system equipped with an optical (red–green–blue) camera was used to capture very high spatial resolution images over urban and agricultural areas in an arid environment. A self-adaptive image segmentation optimization aided by an orthogonal array from the experimental design was used to optimize and systematically evaluate how OBIA classification results are affected by different settings of image segmentation parameters, feature selection, and single and multiscale feature extraction approaches. The first phase encompassed data acquisition and preparation, which included the planning of the flight mission, data capturing, orthorectification, mosaicking, and derivation of a digital surface model. In the second phase, 25 settings of multiresolution image segmentation (MRS) parameters, namely, scale, shape, and compactness, were suggested through the adoption of an L25 orthogonal array. In the third phase, the correlation-based feature selection technique was used in each experiment to select the most significant features from a set of computed spectral, geometrical, and textural features. In the fourth phase, the ensemble adaptive boosting algorithm (AdaBoost) was used to classify the image objects of segmentation levels in the orthogonal array. The overall accuracy measure (OA) and kappa coefficient (K) were computed to represent a quality indicator of each experiment. The OA and K values ranged from 89% to 95%, whereas the K values ranged from 0.75 to 0.95. The MRS parameter settings that provided the highest classification results (>94%) were analyzed, and class-specific accuracy measures and F-measure were computed. Multiscale AdaBoost classification was conducted on the basis of the computed F-measure values. Results of the multiscale AdaBoost classification demonstrated an improvement in OA, K, and F-measure.

Optimizing two-level orthogonal arrays for simultaneously estimating main effects and pre-specified two-factor interactions

Laccase production by Pleurotusostreatus 1804: Optimization of submerged culture conditions by Taguchi DOE methodology

Mechanical properties of bioceramics are poor and need to be improved for biomedical applications. In order to do this, bioceramics may be strengthened by bioresorbable polymers. In this study, the mechanical properties of poly(ε-caprolactone), PCL, coated dense bioceramic pellets made of silica-contained calcium phosphates were studied and analyzed using a statistical experimental design in conjunction with Taguchi methods for optimization. The aim of this experimental work was to maximize the pellet flexural strength and minimize the amount of deposited PCL. The most important factors affecting the strengthening of the ceramic pellets were evaluated. Four independent processing variables (a removal technique of an excess polymer solution, concentration of PCL in the solution, a heat treatment temperature and the number of dipping) with three levels of variability were tested using an L9 (34) orthogonal array. A statistical experimental design using the analysis of means and orthogonal array was applied to optimize the responses of these variables. The optimal conditions for achieving the maximal flexural strength of the coated pellets at the minimal amount of the deposited PCL were determined. A high quality dense bioceramic pellets with ~ 10.5 MPa flexural strength and ~ 80 μm thickness (~ 21 mg weight) of the deposited PCL coating were manufactured as a result.

The objective of this work was to increase laccase production by Pleurotus ostreatus PLAB through culture medium optimization using solid state culture conditions. Increased laccase activity was obtained through design of experiments (DOE) using the Taguchi orthogonal array (OA). Seven factors, viz. lignocellulose, glucose, yeast extract, peptone, KH(2)PO(4), MgSO(4) 7H(2)O and MnSO(4) H(2)O at three levels and pH at two levels. OA layout of L18 (2(1) x 3(7)) was selected for the proposed experimental design using Minitab 17 software. Data analysis showed that lignocellulose (20 %) and glucose (10 g L1) had positive effect, whereas KH(2)PO(4), MgSO(4)∙7H(2)O and MnSO(4)∙H(2)O did not have significant effect on laccase production. Taguchi OA analysis showed that pH 6, lignocellulose 20 %, glucose 10 g L(-1), yeast extract 6 g L(-1), peptone 15 g L(-1), KH(2)PO(4) 3 g L1, MgSO(4)∙7H(2)O 0.5 g L(-1) and MnSO(4)∙H(2)O 0.1 g L-1 were the optimal conditions to maximize laccase production. The model predicted a 30.37 U g(-1) dry wt., which agreed with the experimentally obtained laccase activity 29.15 U g(-1) dry wt. at optimal conditions.

Micro metal injection molding which is a new develop technology has attract most researcher where it becomes among the promising method in powder metallurgy research to produce small-scale intricate part at an effective process and competitive cost for mass production. Due to highly stringent characteristics of micro MIM feedstock,the study has been emphasized in investigating the optimization of highest green strength which plays an important characteristic in determining the successful of micro MIM. Stainless steel SS 316L with D50 = 5.96μm was used with composite binder, which consists of PEG, PMMA and Stearic Acid. From rheological characteristic and highly significant parameter through screening experiment, feedstock with 61.5% with several injection parameters were optimized such as injection pressure(A), injection temperature(B), mold temperature(C), injection time(D) and holding time(E). Besides that, interaction effects between injection pressure, injection temperature and mold temperature were also considered to optimize in the Taguchi’s orthogonal array. Analysis of variance (ANOVA) in terms of signal-to-noise ratio (S/N-larger is better) for green strength was also presented in this paper. Result shows that interaction between injection temperature and mold temperature(BxC) give highest significant factor followed by interaction between injection pressure and injection temperature(AxB). Single factor that also contributes to significant optimization are mold temperature(C), injection time(D) and injection pressure(A). This study shows that Taguchi method would be among the best method to solve the problem with minimum number of trials.