Abstract: We describe a new global electromagnetic optimization technique using Taguchi's method and apply it to linear antenna array design. Taguchi's method was developed on the basis of the orthogonal array (OA) concept, which offers systematic and efficient characteristics. This paper illustrates the implementation procedure of Taguchi's method in electromagnetic optimization problems. The optimization procedure is then used to design two linear antenna arrays with specific array factor requirements. Obtained results show that the desired null controlled pattern and sector beam pattern are successfully achieved. Compared to traditional optimization techniques, Taguchi's method is easy to implement and efficient to reach the optimum solutions

Abstract: Greedy algorithms are often used to solve under- determined inverse problems when the solution is constrained to be sparse, i.e. the solution is only expected to have a relati vely small number of non-zero elements. Two different algorithms have been suggested to solve such problems in the signal pro- cessing and control community, orthogonal Matching Pursuit and orthogonal Least Squares respectively. In the current literature, there exist a great deal of confusion between the two strategies. For example, the later strategy has often be called orthogonal Matching Pursuit and has repeatedly been "re-discovered" in several papers. In this communication we try to pull together some of the literature and clarify the difference between the methods. x and a matrix � ∈ R N x×Ns , find a vector s such that the squared error is small, while s has only a small number of non-zero elements. For the discussion here, we use the term algorithm to mean any computational procedure that gives a particular result, i.e. we here discuss two different algor ithms, which can be implemented using different computational steps.

Abstract: A methodology for the design of an experiment is proposed in order to find asmany schemes as possible with the maximum number of factors with different levels for thesmallest number of experimental runs. An algorithm was developed and homemadesoftware was implemented. The abilities in generation of the largest groups of orthogonalarrays were analyzed for experimental runs of 4, 6, 8, 9, 10, 12, 14, 15, and 16. The resultsshow that the proposed method permits the construction of the largest groups of orthogonalarrays with the maximum number of factors.

Abstract: In this paper, a grey relational analysis is applied to a set of two-stage experiments designed to determine the cutting parameters for optimizing the side milling process with multiple performance characteristics. The cutting parameters to be considered are cutting speed, feed per tooth, axial depth of cut, radial depth of cut, overhang length and flank wear of peripheral cutting edge. L36 and L9 orthogonal arrays are used in the experiments and lower-the-better is used as a qualitative characteristic to evaluate the results. It is found that using the grey relational analysis coupled with a deliberate design of the two-stage experiments is simple and efficient in determining an optimal combination of the cutting parameters. The results of the confirmation test also show that this new approach can greatly improve the cutting performance of side milling process.

Abstract: In this work we solve the problem of architecting a conceptual, near-term, cost-effective system of systems (SoS) to respond to small boats used by terrorists to attack maritime commerce traffic and critical shore infrastructures in the United States, by formulating the architecting problem as an assignment problem which is then solved using the orthogonal array experiment. Also known as the Taguchi method in quality control, the orthogonal array experiment is efficient for this class of problems. The optimality of the resulting architecture, called optimal cost-effective architecture, is validated against a heuristically developed architecture and an optimal effective architecture; the latter is obtained also with the orthogonal array experiment approach. The main purpose of this paper is an exploratory application of the Taguchi method to architecting a system of systems. The principal results of the orthogonal array experiment method reported herein underline this successful exploratory work in architecting a system of systems. This method can be extended to architecting other systems of systems. © 2007 Wiley Periodicals, Inc. Syst Eng 10: 241–259, 2007

Abstract: This book presents a new global optimization technique using Taguchi’s method and its applications in electromagnetics and antenna engineering. Compared with traditional optimization techniques, Taguchi’s optimization method is easy to implement and very efficient in reaching optimum solutions. Taguchi’s optimization method is developed based on the orthogonal array (OA) concept, which offers a systematic and efficient way to select design parameters. The book illustrates the basic implementation procedure of Taguchi’s optimization method and discusses various advanced techniques for performance improvement. In addition, the integration of Taguchi’s optimization method with commercial electromagnetics software is introduced in the book. The proposed optimization method is used in various linear antenna arrays, microstrip filters, and ultra-wideband antenna designs. Successful examples include linear antenna array with a null controlled pattern, inear antenna array with a sector beam, linear antenna array with reduced side lobe levels, microstrip band stop filter, microstrip band pass filter, coplanar waveguide band stop filter, coplanar ultra-wide band antenna, and ultra-wide band antenna with band notch feature. Satisfactory results obtained from the design process demonstrate the validity and efficiency of the proposed Taguchi’s optimization method. Contents: Introduction / Orthagonal Arrays / Taguchi's Optimization Method / Linear Antenna Array Designs / Planar Filter Designs / Ultra-wide Band (UWB) Antenna Designs / OA-PSO Method / Conclusions

Abstract: Ultrasonic consolidation, an emerging additive manufacturing technology, is one of the most recent technologies considered for fabrication of metal matrix composites (MMCs). This study was performed to identify the optimum combination of processing parameters, including oscillation amplitude, welding speed, normal force, operating temperature, and fiber orientation, for manufacture of long-fiber-reinforced MMCs. A design of experiments approach (Taguchi L25 orthogonal array) was adopted to statistically determine the influences of individual process parameters. SiC fibers of 0.1 mm diameter were successfully embedded into an Al 3003 metal matrix. Push-out testing was employed to evaluate the bond strength between the fiber and the matrix. Data from push-out tests and microstructural studies were analyzed and an optimum combination of parameters was achieved. The effects of process parameters on bond formation and fiber/matrix bond strength are discussed.

Abstract: To satisfy the volatile nature of todays markets, businesses require a significant reduction in product development lead times. Consequently, the ability to develop precise product sales forecasts is of fundamental importance to decision-makers. Over the years, many forecasting techniques of varying capabilities have been introduced. The precise extent of their influences, and the interactions between them, has never been fully clarified, although various forecasting factors have been explored in previous studies. Accordingly, this study adopts the Taguchi method to calibrate the controllable factors of a forecasting model. An L9(3 4 ) inner orthogonal array is constructed for the controllable factors of data period, horizon length, and number of observations required. An experimental design is then performed to establish the appropriate levels for each factor. At the same time, an L4(2 3 ) outer orthogonal array is used to consider the inherited parameters of forecasting method as the noise factors of Taguchi method simultaneously. An illustrated example, employing data from a power company, serves to demonstrate the thesis. The results show that the proposed model permits the construction of a highly efficient forecasting model through the suggested data collection method. � 2005 Elsevier B.V. All rights reserved.

Abstract: In many industrial applications, the experimenter is interested in estimating some of the main effects and two-factor interactions. In this article we rank two-level orthogonal designs based on the number of estimable models containing a subset of main effects and their associated two-factor interactions. By ranking designs in this way, the experimenter can directly assess the usefulness of the experimental plan for the purpose in mind. We apply the new ranking criterion to the class of all non isomorphic two-level orthogonal designs with 16 and 20 runs and introduce a computationally efficient algorithm, based on two theoretical results, which will aid in finding designs with larger run sizes. Catalogs of useful designs with 16, 20, 24, and 28 runs are presented.

Abstract: In this paper we construct all possible orthogonal arrays OA(18,q, 3,2) with 18 runs and 3 ≤ q ≤ 7 columns and present those that are nonisomorphic. A discussion on the novelty and the superiority of many of the designs found in terms of isomorphism and generalized minimum aberration has been made.

Abstract: In this research, the nonlinear, double-dynamic Taguchi method was used as design and analysis methods for a high-precision positioning device using the combined piezo-voice-coil motor (VCM) actuator. An experimental investigation into the effects of two input signals and three control factors were carried out to determine the optimum parametric configuration of the positioning device. The double-dynamic Taguchi method, which permits optimization of several control factors concurrently, is particularly suitable for optimizing the performance of a positioning device with multiple actuators. In this study, matrix experiments were conducted with L9(34) orthogonal arrays (OAs). The two most critical processes for the optimization of positioning device are the identification of the nonlinear ideal function and the combination of the double-dynamic signal factors for the ideal function's response. The driving voltage of the VCM and the waveform amplitude of the PZT actuator are combined into a single quality characteristic to evaluate the positioning response. The application of the double-dynamic Taguchi method, with dynamic signal-to-noise ratio (SNR) and L9(34) OAs, reduced the number of necessary experiments. The analysis of variance (ANOVA) was applied to set the optimum parameters based on the high-precision positioning process

Abstract: This study analyzes the wear and the tensile properties of polypropylene (PP) components, which are applied to the interior coffer of automobiles. The specimens are prepared under different injection molding conditions by changing the melting temperature, the injection speed, and the injection pressure via three computer-controlled progressive strokes. The wear and tensile properties are adopted as the quality targets. Experiments of 16 experimental runs are based on an orthogonal array table, and apply the Taguchi method and the design of experiments (DOE) approach to determine an optimal parameter setting. In addition, a side-by-side comparison of two different approaches is provided. In this study, regression models that link the controlled parameters and the targeted outputs are developed, and the identified models can be used to predict the tensile and wear properties at various injection molding conditions.

Abstract: In a general fractional factorial design, the $n$-levels of a factor are coded by the $n$-th roots of the unity. This device allows a full generalization to mixed-level designs of the theory of the polynomial indicator function which has already been introduced for two level designs by Fontana and the Authors (2000). the properties of orthogonal arrays and regular fractions are discussed.

Abstract: This paper presents a method for combining sequential neural-network approximation and orthogonal arrays (SNAOA) in the planning of large-scale passive harmonic filters. An orthogonal array is first conducted to obtain the initial solution set. The set is then treated as the initial training sample. Next, a back-propagation sequential neural network is trained to simulate the feasible domain for seeking the optimal filter design. The size of the training sample is greatly reduced due to the use of the orthogonal array. In addition, a restart strategy is also incorporated into the SNAOA so that the searching process may have a better opportunity to reach a near global optimum. To illustrate the performance of the SNAOA, a practical harmonic mitigation problem in a chemical plant is studied. The results show that the SNAOA performs better than the original scheme and satisfies the harmonic limitations with respect to the objective of minimizing the total demand distortion of harmonic currents and total harmonic distortion of voltages. Filter loss, reactive power compensation, and the constraints of individual harmonics are also considered. Additional results related to SNAOA are also reported and discussed as well.

Abstract: Liquid crystal display (LCD) light-guide plate injection molding has always had the unexpected deformation issue which results in variations in the quality of the resulting products. The main cause for this lies in the setting of the processing parameters. The objective of this paper is to combine grey relational analysis (GRA) with the Taguchi method to optimize multiple-quality injection molding processing parameter combination. First, a L18(21 × 37) orthogonal array was used to plan out the processing parameters that would affect the injection molding process. Then GRA was applied to resolve the drawback of single quality characteristics in the Taguchi method, and then the optimized processing parameter combination was obtained for multiple quality characteristics from the response table and the response graph from GRA. The quality characteristics of this experiment were the depth and angle of the light-guide plate V-cut microstructure. Signal-to-noise ratio (SN ratio) calculation and analysis of variance (ANOVA) would be performed to look into the results obtained from the experiment. From ANOVA the significant factors could be obtained which had the greatest effect on the light-guide plate quality characteristics, in other words, by controlling these factors, the quality characteristics of the LCD light-guide plate could be effectively controlled. Finally, the reliability and reproducibility of the experiment was verified by confirming a confidence interval (CI) of 95%.

Abstract: Summary. Consider the problem of selecting a two-level factorial design. It is well known that two-level orthogonal arrays of strength 4 or more with e extra runs have various optimality properties including generalized Cheng (type 1) optimality when e=1, restricted Cheng (type 1) optimality when e=2 and E-optimality when 3e5. More general Schur optimality results are derived for more general values of e within the more restricted class of augmented two-level orthogonal arrays. Similar results are derived for the class of orthogonal arrays with deletions. Examples are used to illustrate the results and in many cases the designs are confirmed to be optimal across all two-level designs.

Abstract: Three-level factorial designs can be used to perform factor screening and subsequently response surface exploration on its projections in a single stage experiment. Here we select optimal designs for this approach from 18-run and 27-run orthogonal designs. Our choices are based on two types of design criteria. Besides commonly used model estimation criteria, we also consider model discrimination criteria.

Abstract: Consider a maximum-length binary shift-register sequence generated by a primitive polynomial f of degree m. Let $$C_n^f$$ denote the set of all subintervals of this sequence with length n, where m < n ? 2m, together with the zero vector of length n. Munemasa (Finite fields Appl, 4(3): 252---260, 1998) considered the case in which the polynomial f generating the sequence is a trinomial satisfying certain conditions. He proved that, in this case, $$C_n^f$$ corresponds to an orthogonal array of strength 2 that has a property very close to being an orthogonal array of strength 3. Munemasa's result was based on his proof that very few trinomials of degree at most 2m are divisible by the given trinomial f. In this paper, we consider the case in which the sequence is generated by a pentanomial f satisfying certain conditions. Our main result is that no trinomial of degree at most 2m is divisible by the given pentanomial f, provided that f is not in a finite list of exceptions we give. As a corollary, we get that, in this case, $$C_n^f$$ corresponds to an orthogonal array of strength 3. This effectively minimizes the skew of the Hamming weight distribution of subsequences in the shift-register sequence.

Abstract: We show how one can use polynomial techniques to compute all possible distance distributions of binary orthogonal arrays (OAs) of relatively small lengths and strengths. Then we exploit certain connections between OAs and their derived OAs. Having all distance distributions of OAs under consideration, we are able to test them aimed at classification results.

Abstract: Let $f:[0,1)^d \to {\mathbb R}$ be an integrable function. An objective of many computer experiments is to estimate $\int_{[0,1)^d} f(x) dx$ by evaluating f at a finite number of points in [0,1)^d. There is a design issue in the choice of these points and a popular choice is via the use of randomized orthogonal arrays. This article proves a multivariate central limit theorem for a class of randomized orthogonal array sampling designs [Owen (1992a)] as well as for a class of OA-based Latin hypercubes [Tang (1993)].

Abstract: A method for generating reliability tests for a telephone system is based upon sampling an orthogonal array which covers various combinations of test parameters. Field data is collected of actual telephone activity on a telephone system. The field data is evaluated so as to determine call-mix characteristics. Probabilistic weights for the different call-mix characteristics are obtained, and then the probabilistic weights are used to sample the test case scenarios generated in the orthogonal array which have the same call-mix characteristics. These test case scenarios are used to run tests on the telephone system. These tests are preferably performed using automated test scripts. After the test data is collected, reliability metrics are calculated from the test data.

Abstract: Compound orthogonal arrays (COAs) and single arrays are alternatives to the inner–outer arrays advocated by Taguchi for robust parameter design experiments. A criterion based on the word type pattern and strength of COAs is proposed to select optimal COAs. Single arrays are classified into prodigal single arrays (PSAs) and economical single arrays (ESAs) according to their relative estimation capacities, and various optimality criteria, again based on the word type pattern, are proposed for selecting optimal single arrays. Useful optimal COAs, PSAs, and ESAs are constructed and tabulated as convenient references for experimenters in practice.