Abstract: Unless the material composition field in functionally graded materials (FGM) is assumed a priori, an explicit relation between the objective function and the design variables is almost hard to derive. This implicitness naturally leads to the use of finite difference scheme for the sensitivity analysis in the numerical optimization, but which requires the remarkably long CPU time when the objective function is computed directly by the finite element analysis. In connection with this situation, this paper is concerned with the application of artificial neural network (ANN) to the material composition optimization of heat-resisting FGMs. The objective function is approximated by a back-propagation ANN model learned according to the orthogonal array DOE (design of experiments) table. For our constrained optimization problem, interior penalty-function method and golden section method are adopted as optimization techniques. Through the numerical experiments, the design accuracy and the CPU-time efficiency of the material optimization by ANN are investigated.

Abstract: We examine the combinatorial requirements of topology-transparent transmission schedules in a mobile ad hoc network (MANET). Specifically, if each of the N nodes has at most D active neighbors, we require the schedule to guarantee a collision-free transmission to each neighbor. This requirement is met by a cover-free family. We show that existing constructions for topology-transparent schedules correspond to an orthogonal array. Moreover, we show that Steiner systems support the largest number of nodes for a given schedule length. Both of these combinatorial objects are special cases of cover-free families. Analytically and numerically, we examine slot guarantees, expected throughput, and normalized expected throughput for systems of small strength, exploring the sensitivity of the response to D. Expected throughput provides a better performance metric than the minimum throughput results obtained earlier. The impact of a more realistic model of acknowledgments is also examined. The extension of the schedule to multiple frames returns us to the orthogonal arrays. The very density of Steiner systems that afforded an improvement over orthogonal arrays in one frame impedes the best extension to more frames.

Abstract: A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Abstract: Regular designs for a large number of factors require many more treatment combinations than there are lower order effects to be estimated. For example, 29−2 = 128 treatment combinations are require...

Abstract: The paper gives an example of using 4 factors and 3 dimensions orthogonal test designs,in order to show how to use this orthogonal test table and orthogonal test method′s applications on testing designs. At the same time, the example shows the details of principle, advantages, dealing with testing data of orthogonal test designs.

Abstract: The paper presents the application of the Taguchi method to develop an optimised electron-beam surface hardening of cast iron for high wear resistance. The experiments were conducted on both the ductile and grey cast iron. The factors investigated during the surface-hardened process included the material matrix, the accelerating voltage, the electrical current, the travel velocity, the melted width, the beam oscillation, and the post-heat treatment temperature. In this study, the L18 and L9 orthogonal arrays were introduced through the two-stage experimental designs and trials. Smaller-is-better was used as a quality characteristic to evaluate the experimental results by computing their signal-to-noise (S/N) ratios of the wear volume after wear tests. It was found that using the Taguchi method coupled with a two-round experimental design strategy is simple, effective and efficient in developing an optimised EB surface hardening process. The experimental results show that the most important process parameters identified are the accelerating voltage, the travel speed, the electrical current and post-heat treatment, respectively. The best wear resistance result obtained through the best combination of process parameters is 8.845×108 kg-mm/mm3.

Abstract: We consider the problem of switching off unwanted interactions in a given multi-partite Hamiltonian. This is known to be an important primitive in quantum information processing and several schemes have been presented in the literature to achieve this task. A method to construct decoupling schemes for quantum systems of pairwise interacting qubits was introduced by M. Stollsteimer and G. Mahler and is based on orthogonal arrays. Another approach based on triples of Hadamard matrices that are closed under pointwise multiplication was proposed by D. Leung. In this paper, we show that both methods lead to the same class of decoupling schemes. Moreover, we establish a characterization of orthogonal arrays by showing that they are equivalent to decoupling schemes which allow a refinement into equidistant time-slots. Furthermore, we show that decoupling schemes for networks of higher-dimensional quantum systems with t-local Hamiltonians can be constructed from classical error-correcting codes.

Abstract: Crystallization has become one of the most important unit operation in the chemical industries The need to reduce the time from product discovery to market introduction is an inherent concern In order to achieve the prescribedproduct quality characteristics, the process of engineering experimentation has to be optimized Therefore, an experimental design method for crystallization processes is presented in this paper Initially, the standardized Taguchi method was used to plan a minimum number of experiments After identifying the working levels of the design factors and the main performance characteristics of the product under study, the method can be successfully applied to the crystallization processes The simultaneous variations of the main crystallization parameters and their interactions were investigated using orthogonal array technique A statistical analysis of 'signal-to-noise' ratio was followed by performing a variance analysis After developing some special criteria, which depend on performance objectives, the optimal levels of the design factors were determined Crystallization of $KNO_3$ with desirable particle size as a performance characteristic was used to illustrate the design procedure The effects of rotational frequency of the stirrer, linear cooling rate and added admixture on final particle size were studied In order to keep the selected parameters constant during the experiment and to ensure reproduction of entire experiment the automated reaction calorimeter RC1 was used

Abstract: In this paper, we list some new orthogonal main effects plans for three- level designs for 4, 5 and 6 factors in 18 runs and compare them with designs obtained from the existing L18 orthogonal array. We show that these new designs have better projection properties and can provide better parameter estimates for a range of possible models. Additionally, we study designs in other smaller run- sizes when there are insufficient resources to perform an 18-run experiment. Plans for three-level designs for 4, 5 and 6 factors in 13 to 17 runs are given. We show that the best designs here are efficient and deserve strong consideration in many practical situations.

Abstract: This paper proposes an optimal design scheme to improve an intake's capacity of noise reduction of the exhaust system by combining the Taguchi and Kriging method. As a measuring tool for the performance of the intake system, the performance prediction software which is developed by Oh, Lee and Lee (1996) is used. In the first stage, the length and radius of each component of the current intake system are selected as control factors. Then, the L18 table of orthogonal arrays is adapted to extract the effective main factors. In the second stage, we use the Kriging method with the robust design to solve the non-linear problem and find the optimal levels of the significant factors in intake system. The L18 table of orthogonal arrays with main effects is proposed and the Kriging method is adapted for more efficient results. We notice that the Kriging method gives noticeable results and another way to analyze the intake system. Therefore, an optimal design of the intake system by reducing the noise of its system is proposed.

Abstract: Optimization of electrostatic separation processes demands the control of a multitude of factors, including the characteristics of the granular mixtures to be sorted, the feed rate, the configuration of the electrode system, the applied high-voltage and the environmental conditions. The Taguchi's experimental designs presented in this article clearly prove that the linear-interaction models of the electrostatic separation processes can reflect the effects of the main factors in a manner that is satisfactory to most case of the practical interest. The Taguchi's experimental designs are based on special matrices called orthogonal arrays.

Abstract: This paper presents a study of the cutting parameters (cutting velocity and feed) on dimensional precision and surface roughness in turning tubes of fibre reinforced plastics (FRP). A plan of experiments, based on the techniques of Taguchi, was performed machining with cutting parameters prefixed in composite workpiece. An orthogonal array and the analysis of variance (ANOVA) are employed to investigate the cutting characteristics of FRP (glass fibre-reinforced filament-wound tubes) using cemented carbide (K15) cutting tools. The objective was to establish a correlation between cutting velocity and feed with the surface roughness and the international dimensional precision (IT) in composite workpiece. The correlation was obtained by multiple linear regression. Finally, confirmation tests were performed to make a comparison between the experimental results foreseen from the mentioned correlation.

Abstract: When factorial designs or orthogonal arrays are used in an experiment, the number of runs required may be larger than that can be accommodated in practice, even for moderate numbers of factors and levels of actors. In such a case, the choice of uniform designs is a feasible alternative. A uniform design is a design in which the design points distribute uniformly over the entire design space. Uniform designs can be constructed by minimising a discrepancy over the design space. This article reports a successful application of uniform design in the manufacture of liquid crystal dsplays, in which the information obtained from the experiment resulted in a significant improvement of the percentage yield of the process.

Abstract: This abstract is based on the authors' abstract.] For experiments dealing with complex processes involving large numbers of factors, the use of traditional designs such as factorial designs or orthogonal arrays is impractical because of the large number..

Abstract: 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.

Abstract: In this paper, a novel multi-objective orthogonal simulated annealing algorithm MOOSA using a generalized Pareto-based scale-independent fitness function and multi-objective intelligent generation mechanism (MOIGM) is proposed to efficiently solve multi-objective optimization problems with large parameters. Instead of generate-and-test methods, MOIGM makes use of a systematic reasoning ability of orthogonal experimental design to efficiently search for a set of Pareto solutions. It is shown empirically that MOOSA is comparable to some existing population-based algorithms in solving some multi-objective test functions with a large number of parameters.

Abstract: A method for generating 2D orthogonal variable spectrum spreading coefficient code in multi-carrier direct sequence CDMA communication system is disclosed. The code division tree of said coefficient code array is generated by two 2X2 orthogonal arrays. The first array is used to repeat a relation equation in the code division tree to generate a pair of mother nodes, which are used to generate the subnodes containing MXN array for any of both mother nodes. Said array is generated by a relation equation.

Abstract: We establish the non-existence of a maximal set of four mols (mutually orthogonal Latin squares) of order 8 and the non-existence of (8, 5) projective Hjelmslev planes. We present a maximal set of four mols of order 9.

Abstract: The invention provides an apparatus and method for generating overspread orthogonal codes. Overspread orthogonal codes are generated code-multiplying orthogonal codes generated by any method and the overspread orthogonal code length is the product of the code lengths of the orthogonal codes that were code-multiplied. In a telecommunication application, for example, a communication signal is first spread by a first orthogonal code and then overspread by a second orthogonal code. The output of the overspreading process may be further overspread by a third orthogonal code and so on until a desired code length is obtained. Thus, orthogonal code lengths unobtainable by any of the known orthogonal code generators may be generated by overspreading using codes generated by any orthogonal code generator(s) to obtain a desired code length.