Orthogonalization Process Research Articles

Multivariate fuzzy transform of complex-valued functions determined by monomial basis

In this paper, we introduce the multivariate fuzzy transform of higher degree of complex-valued functions. Apart from the orthogonal bases of multivariate complex polynomials of weighted Hilbert spaces that are derived by the Gram---Schmidt orthogonalization process, which can be problematic and imprecise in certain cases, we propose to compute the multivariate fuzzy transform components using a simple matrix calculus with the help of the monomial bases. By this novel approach, we derive two types of upper bound of the approximation error both of multivariate complex-valued functions and of their partial derivatives (the latter by the multivariate higher degree fuzzy transform). The results are demonstrated on examples.

Orthogonal PSO algorithm for economic dispatch of thermal generating units under various power constraints in smart power grid

Particle swarm optimization (PSO) algorithm has been successfully applied to solve various optimization problems in science and engineering. One such popular one is called global PSO (GPSO) algorithm. One of major drawback of GPSO algorithm is the phenomenon of “zigzagging”, that leads to premature convergence by falling into local minima. In addition, the performance of GPSO algorithm deteriorates for high-dimensional problems, especially in presence of nonlinear constraints. In this paper we propose a novel algorithm called, orthogonal PSO (OPSO) that alleviates the shortcomings of the GPSO algorithm. In OPSO algorithm, the m particles of the swarm are divided into two groups: active group and passive group. The d particles of the active group undergo an orthogonal diagonalization process and are updated in such way that their position vectors become orthogonally diagonalized. In the OPSO algorithm, the particles are updated using only one guide, thus avoiding the conflict between the two guides that occurs in the GPSO algorithm. We applied the OPSO algorithm for solving economic dispatch (ED) problem by taking three power systems under several power constraints imposed by thermal generating units (TGUs) and smart power grid (SPG), for example, ramp rate limits, and prohibited operating zones. In addition, the OPSO algorithm is also applied for ten selected shifted and rotated CEC 2015 benchmark functions. With extensive simulation studies, we have shown superior performance of OPSO algorithm over GPSO algorithm and several existing evolutional computation techniques in terms of several performance measures, e.g., minimum cost, convergence rate, consistency, and stability. In addition, using unpaired t-Test, we have shown the statistical significance of the OPSO algorithm against several contending algorithms including top-ranked CEC 2015 algorithms.

Preliminary results for interval feeding the orthogonal pressurized planar electrochromatography system with sample solution for its preparative separation

The orthogonal pressurized planar electrochromatography (OPPEC) is an example of 2-D separation technique, in which two simultaneous and orthogonal processes of electrophoresis and chromatography are involved in the separation mechanism. In the case of preparative separation of substances characterized by different electrophoretic mobility, such separation system can be constantly fed with the sample solution and the separated components can be constantly collected at its outlet.In the paper, as opposed to the previous studies, we discuss the capabilities of OPPEC technique for preparative separation of substances characterized by the same electrophoretic mobility. According to the proposed solution, the separation system can be periodically fed with the sample solution and separated components can be collected alternately at its outlet. The advantages of this new approach over the column chromatography with regard to the separation of complex mixtures have been signaled.

Contribution to the FEM simulation of Ti6Al4V Machining

The paper briefly reviews current scientific publications related to machining of difficult to cut materials and finite element modelling methods (FEM) applied in various chip making processes. Simulations of the orthogonal machining process with regard to define optimal cutting parameters as well as cutting wedge geometry in hole making TiAlN alloy was performed according to test plan based on design of experiment (DoE) methodology. The numerical simulations were performed using commercial finite element software (AdvantEgde), which is suitable to solve complex thermo-mechanical problems occurring in cutting zone during chip making process. A Lagrangian finite element-based model is applied within simulation procedure. Results from experimental simulation were evaluated by main effect and surface response plots.

An advanced phase retrieval algorithm in N-step phase-shifting interferometry with unknown phase shifts

In phase-shifting interferometry with unknown phase shifts, a normalization and orthogonalization phase-shifting algorithm (NOPSA) is proposed to achieve phase retrieval. The background of interferogram is eliminated through using the orthogonality of complex sinusoidal function; and the influence of phase shifts deviation on accuracy of phase retrieval is avoided through both normalization and orthogonalization processing. Compared with the current algorithms with unknown phase shifts, the proposed algorithm reveals significantly faster computation speed, higher accuracy, better stability and non-sensitivity of phase shifts deviation.

Segmentation of White Blood Cell using K-Means and Gram-Schmidt Orthogonalization

Testing of blood is a very important examination process, counting of cells is an important laboratory process for identifying blood related diseases. Microscopic evaluation by experts is a slow process and result is depends on skill and experience of technician, also the process is tedious and time consuming. Therefore automatic medical diagnosis system is necessary way to identifying the diseases in short time. For providing information about blood related diseases like leukemia it is necessary to identify and inspect white blood cell in a peripheral blood smear. So Segmentation is an important step in classifying the constituents of blood. This paper represents efficient segmentation of blood image by using K-means clustering method followed by Gram-Schmidt Orthogonal process to detect automatic blood cell nuclei.

Orthogonal decomposition of left ventricular remodeling in myocardial infarction

Left ventricular size and shape are important for quantifying cardiac remodeling in response to cardiovascular disease. Geometric remodeling indices have been shown to have prognostic value in predicting adverse events in the clinical literature, but these often describe interrelated shape changes. We developed a novel method for deriving orthogonal remodeling components directly from any (moderately independent) set of clinical remodeling indices. Results: Six clinical remodeling indices (end-diastolic volume index, sphericity, relative wall thickness, ejection fraction, apical conicity, and longitudinal shortening) were evaluated using cardiac magnetic resonance images of 300 patients with myocardial infarction, and 1991 asymptomatic subjects, obtained from the Cardiac Atlas Project. Partial least squares (PLS) regression of left ventricular shape models resulted in remodeling components that were optimally associated with each remodeling index. A Gram–Schmidt orthogonalization process, by which remodeling components were successively removed from the shape space in the order of shape variance explained, resulted in a set of orthonormal remodeling components. Remodeling scores could then be calculated that quantify the amount of each remodeling component present in each case. A one-factor PLS regression led to more decoupling between scores from the different remodeling components across the entire cohort, and zero correlation between clinical indices and subsequent scores. Conclusions: The PLS orthogonal remodeling components had similar power to describe differences between myocardial infarction patients and asymptomatic subjects as principal component analysis, but were better associated with well-understood clinical indices of cardiac remodeling. The data and analyses are available from www.cardiacatlas.org.

Vibration Characteristics Research of Finite Cylindrical Shells Semi-Submerged

A significant amount of research on the vibration and sound radiation of the cylindrical shell has been carried out and reported. The cylindrical shell was usually assumed to be submerged in an infinite fluid. However, the fluid region surrounding the cylindrical shell is bounded. Free vibration and forced vibration characteristics of finite cylindrical shells semi-submerged are studied in this paper, based on energy functional variational principle. The combined form of the triangular series and the Fourier series is used for the displacement of the cylindrical shell, then the orthogonality can be used to eliminate the other two directions after the variation, and only the radial displacement is kept. The relationships between the amplitudes of fluid load and the amplitudes of the radial displacement are established by the orthogonal processing of the continuous conditions of the solid-liquid coupling contact surface and the boundary conditions of the free liquid surface. Finally, the fluid structure coupling control equation is obtained. The results show that the method is correct and effective, in addition, providing a new thought for solving similar problem.

Research on Fast Evaluation Algorithm Based on Hopfield Neural Network

The fast evaluation algorithm based on Hopfield neural network (HNN) was presented to solve problems of multiple influencing factors, complex evaluation mechanism, inaccurate evaluation results and slow evaluation process in water quality evaluation. In storage of evaluation criteria information, this algorithm performed orthogonal and symmetric processing of information to guarantee accurate storage of information and steady operation of the network. After storage of the evaluation criteria, the connection weights of the network were determined and the actual measured data input into the HNN model, where such data were evaluated in a fast manner. In addition, the stability of this algorithm was verified, proving that this fast learning algorithm could ensure steady operation of HNN, which converged to the minimum. The fast learning algorithm avoided modular calculations currently applied in the existing algorithms, to greatly reduce the computation. As a result, only one iterative calculation would be needed to obtain the correct water quality evaluation results, which significantly enhanced the speed of water quality evaluation. At the same time, this algorithm accurately saved the evaluation criteria to ensure correctness of the final evaluation results. Finally, this algorithm was applied in surface water environmental quality evaluation and eutrophic water quality evaluation and compared with other algorithms, leading to the conclusion that this algorithm could evaluate water quality of different kinds in a fast and accurate manner.

Optimization of cryogenic milling parameters for AFRP

This paper is aimed to restrain the defects such as fluff and ablation, which were often found in machining of the aramid fiber-reinforced composites (AFRP). The cooling method of spray liquid nitrogen was adopted in the orthogonal milling process. The processing parameters including cutting depth, cutting speed, cooling temperature, feed speed, and liquid nitrogen flow were considered in details, and their effects on the processing quality were researched and analyzed. The analysis optimization methods of processing parameter were employed for the influence on the machining surface quality. Meanwhile, the optimal machining surface quality was predicted and verified. The results show that the cryogenic way realizes a bigger improved role on machining quality than the conventional one for AFRP. As well as the influence order of processing parameters on the roughness is cutting depth, cutting speed, cooling temperature, feed speed, and liquid nitrogen flow. And the predicted result Ra = 0.557 μm of minimum surface roughness value is similar with the actual one Ra = 0.572 μm and verifies the feasibility of optimization method. For processing of AFRP, the cooling way of spray liquid nitrogen has a positive role with high quality and efficiency.

On the spectra of hypermatrix direct sum and Kronecker products constructions

We extend to hypermatrices definitions and theorem from matrix theory. Our main result is an elementary derivation of the spectral decomposition of hypermatrices generated by arbitrary combinations of Kronecker products and direct sums of cubic side length 2 hypermatrices. The method is based on a generalization of Parseval's identity. We use this general formulation of Parseval's identity to introduce hypermatrix Fourier transforms and discrete Fourier hypermatrices. We extend to hypermatrices a variant of the Gram–Schmidt orthogonalization process as well as Sylvester's classical Hadamard matrix construction. We conclude the paper with illustrations of spectral decompositions of adjacency hypermatrices of finite groups and a short proof of the hypermatrix formulation of the Rayleigh quotient inequality.

Cutting Forces during Orthogonal Machining Process of AISI 1018 Steel: Numerical and Experimental Modeling

This paper deals with the plain strain 2D finite element modeling of AISI 1018 Cold Rolled Steel under orthogonal machining process. In this study the causes of machining parameters like cutting speed, depth of cut (DOC) and feed on the cutting forces are analyzed using numerical model in the Finite Element code ABAQUS/Explicit. Explicit Dynamics Time Integration with adaptive meshing Finite Element Method is employed to simulate the 2D model. The Johnson-Cook plasticity model has been considered to describe the material behavior during the process. The experimental study is carried out on CNC machine with the lathe tool dynamometer arrangement. In general purpose of this study is to investigate the effect of machining parameters on the cutting force. Consequently, the numerical and experimental results are compared and found good agreement.

Parallelization of the Rational Arnoldi Algorithm

Rational Krylov methods are applicable to a wide range of scientific computing problems, and the rational Arnoldi algorithm is a commonly used procedure for computing an orthonormal basis of a rational Krylov space. Typically, the computationally most expensive component of this algorithm is the solution of a large linear system of equations at each iteration. We explore the option of solving several linear systems simultaneously, thus constructing the rational Krylov basis in parallel. If this is not done carefully, the basis being orthogonalized may become badly conditioned, leading to numerical instabilities in the orthogonalization process. We introduce the new concept of continuation pairs, which gives rise to a near-optimal parallelization strategy that allows us to control the growth of the condition number of this nonorthogonal basis. As a consequence we obtain a significantly more accurate and reliable parallel rational Arnoldi algorithm. The computational benefits are illustrated using several numerical examples from different application areas.

Orthogonal Gaussian process models

Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. This paper also discusses applications to multi-fidelity simulations using data examples.

Photoluminescence and electroluminescence of cationic PtAu2 heterotrinuclear complexes with aromatic acetylides.

Cationic PtAu2 heterotrinuclear complexes [PtAu2(dpmp)2(C[triple bond, length as m-dash]CR)2]2+ (dpmp = bis(diphenylphosphinomethyl)phenylphosphine, R = aryl) of aromatic acetylides were prepared. The PtAu2 structures are supported through doubly bridging dpmp and stabilized by a significant Pt-Au interaction. They are highly phosphorescent in fluid CH2Cl2 solution (Φem = 23.5%-78.9%), the solid state (Φem = 15.4%-70.2%), the PMMA film (Φem = 39.9%-71.7%) and the doping film of 61% TCTA : 31% OXD-7 : 8% PtAu2 complex (Φem = 16.9%-67.9%). The phosphorescence arises mainly from 3[π (C[triple bond, length as m-dash]CR) → π* (dpmp)] 3LLCT and 3[π (C[triple bond, length as m-dash]CR) → s/p (PtAu2)] 3LMCT triplet excited states for carbazole-acetylide complexes, whereas other complexes display a 3LLCT character mixed with noticeable PtAu2 centered 3[d → s/p] parentage. Utilizing a mixed host composed of hole-transporting TCTA and electron-transporting OXD-7 doped with 8% PtAu2 species as a light-emitting layer and CuSCN as a hole-transporting layer through an orthogonal solution process, the devices exhibit highly efficient electrophosphorescence with the highest current efficiency (CEmax) of 51.7 cd A-1 and external quantum efficiency (EQEmax) of 14.5%. The efficiency roll-off is small in the practical brightness range of 500-5000 cd m-2. The PtAu2 complexes with carbazole-acetylides display a higher electroluminescence efficiency ascribed to their better hole-transporting character as well as more facile energy transfer from mixed host materials.

Enhancing the Performance of Biogeography-Based Optimization Using Multitopology and Quantitative Orthogonal Learning

Two defects of biogeography-based optimization (BBO) are found out by analyzing the characteristics of its dominant migration operator. One is that, due to global topology and direct-copying migration strategy, information in several good-quality habitats tends to be copied to the whole habitats rapidly, which would lead to premature convergence. The other is that the generated solutions by migration process are distributed only in some specific regions so that many other areas where competitive solutions may exist cannot be investigated. To remedy the former, a new migration operator precisely developed by modifying topology and copy mode is introduced to BBO. Additionally, diversity mechanism is proposed. To remedy the latter defect, quantitative orthogonal learning process accomplished based on space quantizing and orthogonal design is proposed. It aims to investigate the feasible region thoroughly so that more competitive solutions can be obtained. The effectiveness of the proposed approaches is verified on a set of benchmark functions with diverse characteristics. The experimental results reveal that the proposed method has merits regarding solution quality, convergence performance, and so on, compared with basic BBO, five BBO variant algorithms, seven orthogonal learning-based algorithms, and other non-OL-based evolutionary algorithms. The effects of each improved component are also analyzed.

飞秒激光正交线扫描诱导表面微纳结构

飞秒激光正交线扫描诱导表面微纳结构

Energy consumption characteristics of turn-mill machining

Reducing the energy consumption of manufacturing processes and machine tools can considerably affect the environmental and economic impact of industrial activities. Since the 2008 global financial crisis, many scholars have focused on modeling the energy consumption of basic machining processes such as turning, milling or grinding, etc., and investigated the consumption characteristics of related machine tools. At the same time, various industries have increased their use of more complex and hybrid machine tool systems such as turn-mill machines; these advanced systems have part and operation flexibility and can be set up in a relatively short amount of time. As the complexity of these typically high-precision machining systems increases, understanding their energy consumption characteristics becomes more difficult. This study aimed to develop a generic energy model for turn-mill machine tools and related processes in order to predict the energy consumption of complex parts with both turn and mill features. The generic prediction model is adapted to a high precision, high-end turn-mill machine tool and further verified by two case studies. The results of the first case study revealed that the energy estimation model developed in this study had a 95% accuracy in estimating the energy consumption of a workpiece with both milling and turning features. The second case study investigated energy consumption of orthogonal turn-milling process with a high material removal rate (MRR), first time in literature. The results of this second case study indicate that even though the power requirements of turn-milling are higher than conventional rough cut turning, the high MRR results in a lower total energy consumed per feature.

Experimental Investigation and FE Simulation of the Effect of Variable Control on Temperature Distribution in Orthogonal Metal Cutting Process

The study aimed at building a 3-Dimensional finite element simulation to monitor orthogonal machining process under a dry machining environment. The study was conducted in two stages of experimentation and finite element modelling and simulation (FEMS). The purpose of the experimentation was to obtain data which will be used to validate the FEMS result. The FEMS was carried out with a commercially available solver. The workpiece material employed for the study was mild steel in the form of round bar of solid shaft having 45mm diameter and length of 500mm. Mild steel was selected due to its wide range of applications in the fields of manufacturing tools and mould industry. The tool material used was tungsten carbide of DIN4980R 20 mm x 20 mm, with cutting angle of 80-degree tool steel, which was modelled in the FEMS as a rigid body. Various cutting conditions such as speed, feed rate and depth of cut were considered to obtain the tool chip temperature. Different values of temperature were recorded at interval of 10 seconds and ranged from 10 to 100 seconds. The FEMS was carried out by making one of the conditions vary while the others were constant. The temperature values measured with a digital thermocouple were used to validate the FEMS data obtained. The result show that the cutting temperature predicted by the FEMS is within 20% of the real experimental value and followed the same trend. It was discovered that the values of temperature obtained from simulation were also much higher than that of experimentation. Therefore, the experimental value might not be accurate, due to some experimental errors and environmental effects like partial contact between the measuring device and the cutting tools, fluctuation in the magnitude of air flow around the surrounding which may affect the cutting temperature, room temperature and pressure effect. Generally, with an increase in the cutting speed, feed rate and depth of cut, the tool temperature also increased and the cutting speed was found to be the most effective parameter when consideration is given to temperature effects, especially in high range of cutting conditions.

An Optimization Algorithm for the Design of an Irregularly-Shaped Bridge Based on the Orthogonal Test and Analytic Hierarchy Process

Irregularly-shaped bridges are usually adopted to connect the main bridge and ramps in urban overpasses, which are under significant flexion-torsion coupling effects and in complicated stress states. In irregular-shaped bridge design, the parameters such as ramp radius, bifurcation diaphragm stiffness, box girder height, and supporting condition could affect structural performance in different manners. In this paper, the influence of various parameters on three indices, including maximum stress, the stress variation coefficient, and the fundamental frequency of torsional vibration, is investigated and analyzed based on orthogonal test method. Through orthogonal analysis, the major influence parameters and corresponding optimal values for these indices are achieved. Combining with the analytic hierarchy process (AHP), the hierarchical structure model of the multi-indices orthogonal test is established and a comprehensive weight analysis method is proposed to reflect the parameter influence on overall mechanical properties of an irregularly-shaped bridge. Influence order and optimal values of parameters for overall mechanical properties are determined based on the weight of factors and levels calculated by the comprehensive weight analysis method. The results indicate that the comprehensive weight analysis method is superior to the overall balance method, which verifies the effectiveness and accuracy of the comprehensive weight analysis in the parameter optimization of the multi-indices orthogonal test for an irregularly-shaped bridge. Optimal parameters obtained in this paper can provide reference and guidance for parameter control in irregularly-shaped bridge design.