Non-iterative Method Research Articles

An isogeometric boundary element method for transient heat transfer problems in inhomogeneous materials and the non-iterative inversion of loads

In this paper, the transient thermal analysis theory of isogeometric dual reciprocity boundary element method (IG-DRBEM) of the multi-patch inhomogeneous complex model is established and the non-iterative inversion method of load identification is proposed based on the IG-DRBEM. The establishment of the multi-patch analysis theory framework extended the ability of IG-DRBEM to analyze complex geometry to some extent. The multi-patch analysis method adopted herein is simple and operable, and still retains the advantages of seamless connection between CAD generated geometry and response analysis of isogeometric boundary element method (IGBEM), which is very beneficial to expand IG-DRBEM to practical engineering application fields in the future. The inversion method based on IG-DRBEM makes full use of the good geometrical and field representation ability of NURBS, and further expands the application scope of IG-DRBEM. Furthermore, the introduction of the precision integration method for both forward and inverse problems improves the accuracy and stability of calculation to a certain extent. The numerical results show that the proposed method has good stability and accuracy even when solving complex geometric problems such as a fighter model. Moreover, the implementation of basis function expansion and regularization scheme further improves the accuracy and noise resistance of boundary condition inversion.

A Holomorphic Embedding Power Flow Algorithm for Islanded Hybrid AC/DC Microgrids

This paper proposes a novel power flow algorithm for islanded hybrid AC/DC microgrids. The algorithm is based on a recursive (non-iterative) method called the holomorphic embedding load flow method. The convergence properties of this method are more favorable than other iterative-based techniques such as Newton Raphson. The proposed power flow algorithm accounts for the special characteristics of hybrid microgrids by developing new holomorphically embedded versions for the DG droop characteristics on both the AC and DC microgrid as well as the interlinking AC/DC converter droop characteristics. The proposed approach is tested on two systems and in the presence of multiple interlinking systems. For each case, the results from the proposed algorithm are compared to detailed time-domain simulations performed using PSCAD/EMTDC to validate the accuracy of the proposed algorithm.

On the flow characteristics of a four square-cylinder array at a 45° incidence angle and low Re

The four-cylinder model is widely applied in many engineering projects immersed in unsteady flow. However, its flow hydrodynamic characteristics are not fully understood. In the present work, the finite volume method is adopted in spatial discretization, while the SIMPLE algorithm in association with the non-iterative fractional step method is utilized to address the governing Navier–Stokes equation. Four equilaterally arranged cylinders at a flow incidence angle of 45° (α = 45°) are numerically simulated, and the corresponding Reynolds number ranges from 40 to 160. The accuracy and applicability of the numerical method employed in this investigation are verified by flow over a single cylinder. In the current work, the hydrodynamic characteristics, flow field characteristics, and structural vibration characteristics of cylinders are systematically investigated by changing the spacing ratio L/D (L/D = 1.2–4.0) and the Reynolds number. Numerical results show that the four cylinders have respective features and interaction effects. There are approximately eight wake flow patterns influenced by the spacing ratio. In addition, the numerical results also indicate that fluid dynamics are determined by flow patterns. These results can be a reference in engineering design, such as for ocean platforms with four cylindrical columns.

F$$_3$$ORNITS : a flexible variable step size non-iterative co-simulation method handling subsystems with hybrid advanced capabilities

This paper introduces the F $$_3$$ ORNITS non-iterative co-simulation algorithm in which F $$_3$$ stands for the 3 flexible aspects of the method: flexible polynomial order representation of coupling variables, flexible time-stepper applying variable co-simulation step size rules on subsystems allowing it, and flexible scheduler orchestrating the meeting times among the subsystems and capable of asynchronousness when subsystems’ constraints require it. The motivation of the F $$_3$$ ORNITS method is to accept any kind of co-simulation model as far as they represent circuits (0D models, such as ODE or DAE), including any kind of subsystem (open circuits), regardless on their available capabilities. Indeed, one of the major problems in industry is that the subsystems usually have constraints or lack of advanced capabilities making it impossible to implement most of the advanced co-simulation algorithms on them. The method makes it possible to preserve the dynamics of the coupling constraints when necessary as well as to avoid breaking $$C^1$$ smoothness at communication times, and also to adapt the co-simulation step size in a way that is robust both to zero-crossing variables (contrary to classical relative error-based criteria) and to jumps. Five test cases are presented to illustrate the robustness of the F $$_3$$ ORNITS method as well as its higher accuracy than the non-iterative Jacobi coupling algorithm (the most commonly used method in industry) for a smaller number of co-simulation steps.

Noniterative method for frequency estimation based on interpolated DFT with low-order harmonics elimination

The paper describes a new interpolated discrete Fourier transform (IpDFT) method for the frequency estimation of the real sine wave distorted by harmonics. The method complements recent work on the direct-formula IpDFT methods by expanding the model of the signal included in the interpolation. Spectral superposition for a total of four frequency components is accounted for in a one-step formula. Alongside the positive and negative components of the fundamental frequency, the influence from the closest low-order real harmonic is eliminated. By using the generalized maximum sidelobe decay (GMSD) window family, the interference from more distant harmonics and interharmonics is suppressed. This approach allows us to perform the measurement with a shortened data record compared to previous methods and improves accuracy in the case that a second-order harmonic is present in the signal. The study provides a five-point analytical, one-step formula that is verified by simulations and experiments in terms of accuracy and complexity. The experimental results are presented featuring straightforward C implementation on the system with an affordable microcontroller.

Performance analysis of parameter estimator on non-linear iterative methods for ultra-wideband positioning

ABSTRACT Ultra-wideband is a promising technology in indoor positioning due to its accurate time resolution and good penetration. Since the positioning model is non-linear, iterative methods are often considered for solving the localisation problem. However, the positioning system is prone to become ill-posed. The iterative methods cannot easily converge to a global optimal solution. In this paper, the convergence property of four non-linear iterative methods is analytically reviewed under ill-conditioned configuration. For the iteration, three types of initial values are selected. Experimental results are given to demonstrate that although the barycentre method can converge correctly, it is inefficient with too many iterations. In addition, with a good initial value, the Gauss–Newton method can converge effectively, and it sometimes converges to a false local optimisation solution when selecting a bad initial value. Moreover, both the regularised Gauss–Newton method and closed-form Newton method can converge to the global optimum effectively with fewer iterations. This study shows that the closed-form Newton method has higher efficiency of convergence than the other methods. Meanwhile, to make complete use of measurements available to improve the accuracy, the result of non-iterative method is generally used as the initial value of the iterative method.

Non-iterative multifold strip segmentation phase method for six-dimensional optical field modulation.

In this Letter, we propose a non-iterative multifold strip segmentation phase method for a spatial light modulator (SLM) to generate multifocal spots of diverse beams (Airy, spiral, perfect vortex, and Bessel-Gaussian beams) in a high-numerical-aperture system, with up to 6D controllability. The method is further validated by an inverted fluorescence microscope. By adjusting the bright and dark voltage parameters of the SLM, zero-order light caused by the pixelation effect of the SLM has been successfully eliminated. We hope this research provides a more flexible and powerful approach for the rapid modulation of multi-focus light fields in the development of biomedicine and lithography.

A new discrete element modelling approach to simulate the behaviour of dense assemblies of true polyhedra

A new molecular dynamics-like modelling approach aimed at simulating the mechanical behaviour of true polyhedra dense assemblies is presented. Thanks to an improved version of the Gilbert-Johnson-Keerthi contact detection algorithm called GJK − TD, this approach involves no edge or corner rounding and accounts for multipoint face − face or edge − face contacts between any set of two particles. Furthermore, torques equations are simply and efficiently solved using an improved leap-frog Verlet non-iterative method suggested by Omelyan [I.P. Omelyan, Molecular Simulation, 22 : 3, 213–236 (1999)], in which no periodic renormalization of the quaternions is necessary. The potential of this new discrete element approach is then highlighted by simulating the gravity packing of frictionless polyhedra and the gavity flow of frictional polyhedra down an incline, and comparing the results with those reported in the literature. Of particular interest in the stationary flow regime, a linear decrease of the bulk solid fraction and a power law decrease of the bulk coordination number with increasing inertial number are observed, thus generalizing to polyhedra these observations initially made with disks in plane shear flow by da Cruz and co-workers [F.da Cruz, S. Emam, M. Prochnow, J.N. Roux and F. Chevoir, Phys. Rev. E 72, 021309, (2005)]. Beyond this regime, in the collisional regime, the granular temperature was found to achieve its maximum a few particle diameter above the rough bottom, suggesting the localization of significant particle agitation close to the flowing bed.

A Non-Iterative Method for the Difference of Means on the Lie Group of Symmetric Positive-Definite Matrices

A non-iterative method for the difference of means is presented to calculate the log-Euclidean distance between a symmetric positive-definite matrix and the mean matrix on the Lie group of symmetric positive-definite matrices. Although affine-invariant Riemannian metrics have a perfect theoretical framework and avoid the drawbacks of the Euclidean inner product, their complex formulas also lead to sophisticated and time-consuming algorithms. To make up for this limitation, log-Euclidean metrics with simpler formulas and faster calculations are employed in this manuscript. Our new approach is to transform a symmetric positive-definite matrix into a symmetric matrix via logarithmic maps, and then to transform the results back to the Lie group through exponential maps. Moreover, the present method does not need to compute the mean matrix and retains the usual Euclidean operations in the domain of matrix logarithms. In addition, for some randomly generated positive-definite matrices, the method is compared using experiments with that induced by the classical affine-invariant Riemannian metric. Finally, our proposed method is applied to denoise the point clouds with high density noise via the K-means clustering algorithm.

A non-iterative vapor-liquid split calculation in isothermal flash problem

A synergistic union is presented between a non-iterative method for calculating the vapor-liquid split in the isothermal flash problem and an extrapolation technique based on a third-order Taylor series, which is used as numerical refinement. This synergistic union results in an efficient and robust numerical procedure with a low numerical cost in the solution of the Rachford-Rice equation. After an extensive numerical experimentation, using as convergence criterion the sum of the mole fractions of liquid phase with respect to the unit, a convergence is achieved in 98.66% of the studied cases with 4 significant digits and 87.35% for 6 significant digits. With a second application of the numerical refinement, it is obtained a 99.89% of the cases with 8 significant digits. Likewise, the use of proposed numerical refinement is shown in the implicit solution of the Rachford-Rice system of equations in the isothermal vapor-liquid-liquid flash separation problem.

Non-iterative equivalent linearization method for generating seismic fragility curve of equipment

In the seismic PRA, tremendous computational and human resources are required to evaluate the seismic fragility curves of facilities in a nuclear building, so the development of a simple evaluation method has been desired. In this study, we propose and apply a non-iterative equivalent linearization method for evaluating the real capacity (median value of fragility curve) and propose a method that can easily evaluation seismic fragility curves. Then, the method was tested using 6 equivalent linearization models for equipment installed on the ground surface and comparing the results with those obtained using nonlinear analysis. The validation was done by using 37 ground motion records observed by Japan Meteorological Agency. As a result, the equivalent linearization method proposed by Liu et al. (2015) and Watabe et al (1985) can obtain relatively stable results. In particular, the equivalent linearization method of Liu et al. was found to be independent of parameter changes.

A non-iterative sampling method for inverse elastic wave scattering by rough surfaces

<p style='text-indent:20px;'>Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-iterative sampling method is proposed for detecting the rough surface by taking elastic field measurements on a bounded line segment above the surface, based on reconstructing a modified near-field equation associated with a special surface, which generalized our previous work for the Helmholtz equation (SIAM J. Imag. Sci. 10(3) (2017), 1579-1602) to the Navier equation. Several numerical examples are carried out to illustrate the effectiveness of the inversion algorithm.</p>

A Randles Circuit Parameter Estimation of Li-Ion Batteries With Embedded Hardware

Accurate modelling of electrochemical sources is very important to predict how a source will perform in specific applications related to the load or environmental parameters. A Randles circuit is considered as a reliable equivalent electrical circuit in studying and modelling various electrochemical systems and processes. The classical parameter estimation approach based on use of software packages (ZSim, MEISP, LEVMW, etc.) requires for the high computational performance processing units, decreasing the reliability as proper maintenance actions can be delayed because of offline analysis. Advancing the state of the art, we propose a low-complexity approach for embedded hardware-based parameter estimation of the Randles circuit. Our non-iterative method uses only the measured real and imaginary part of impedance, with numerical approximation of the first derivative of real/imaginary part quotient, to create closed-form expressions with a unique solution. The initial estimated values are available from partial dataset (after measurement at only 3 frequencies). Moreover, it is not software platform-specific, which enables a high level of portability. The presented method is verified with theoretical, numerical and experimental analysis, with more than 1000 datasets. We also demonstrated the applicability in parameter estimation of the Randles circuit of a Li-ion battery. Finally, we verified suitability for embedded hardware platforms, with deployment on a microcontroller-based platform with a clock speed of 16 MHz and 8 kB of SRAM. Reliable parameter estimation processing of a 100-points dataset was performed in just 106 milliseconds with 1% relative error, requiring less than 53 mJ of energy.

Deep Mode Decomposition: Real-time Mode Decomposition of Multimode Fibers Based on Unsupervised Learning

Mode decomposition (MD), detecting the mode content of a laser beam, is an important technique that has wide applications in research and industry areas. This paper demonstrated a novel non-iterative mode decomposition method, called deep mode decomposition (DeepMD), which relies on a deep neural network with unsupervised learning for the first time. A trained network can directly compute the accurate modal coefficients of the eigenmodes propagating in the fibers, including the modal amplitudes and relative phases with only one near-field intensity image. Regardless of the number of modes, the decomposing rate is similar in simulations, around 571.4 Hz, benefiting real-time applications. The quantitative results of both simulation and real-time experiments show the superiority of our method

A fast, non-iterative ray-intersection approach for three-dimensional microscale particle tracking.

We propose a non-iterative ray tracing method with robust post-capture microlens array sensor alignment to reconstruct sparse particle concentration in light field particle image velocimetry and particle tracking velocimetry nearly instantaneously. Voxels traversed by various rays are stored by a kd-tree to reduce memory load and computational time. A cloud point classification algorithm is employed for particle identification and spatial reconstruction. The approach is tested with a physically-based realistic model of a light field camera. Also, an optical system is assembled in a microscope to directly obtain the 3D laminar velocity field in the fully-developed region, which exhibits good agreement with the theoretical solution.

Data-driven Control of Temporally and Spatially Redundant Systems

The present study proposes a data-driven design method for redundant systems where temporal and spatial redundancy are achieved by multi-rate design and multiple actuators, respectively. In the proposed method, the noniterative correlation-based tuning method for non-redundant systems is extended to temporally and spatially redundant systems. The effectiveness of the proposed method is demonstrated through experimental results.

Fast Noniterative Data Analysis Method for Frequency-Domain Near-Infrared Spectroscopy with the Microscopic Beer-Lambert Law

Fast Noniterative Data Analysis Method for Frequency-Domain Near-Infrared Spectroscopy with the Microscopic Beer-Lambert Law

Non-Iterative Method for Extracting Complex Permittivity and Thickness of Materials From Reflection-Only Measurements

Non-Iterative Method for Extracting Complex Permittivity and Thickness of Materials From Reflection-Only Measurements

On recovering space or time-dependent source functions for a parabolic equation with nonlocal conditions

The paper studies inverse source problems for a parabolic equation with nonlocal initial and boundary conditions. The specificity of these problems is that the identifiable coefficients depend on only space or time variable. A numerical method for solution to problems is proposed based on reducing the initial problems to the parametric inverse problems with respect to ordinary differential equations using the method of lines. Then, we propose a non-iterative method based on using a special representation of the solutions to the obtained problems. We prove the existence and uniqueness of their solutions, and substantiate the existence of special representation of the solutions to these problems. Computation schemes, formulae, and the results of numerical experiments on test problems are provided.

Two three-phase linear power flow models for distribution power system under polar coordinates

PurposeThe purpose of this study is to provide a non-iterative linear method to solve the power flow equations of alternating current (AC) power grid. Traditional iterative power flow calculation is limited in speed and reliability, and it is unsuitable for the real-time and online applications of the modern distribution power system (DPS). Thus, it would be of great significance if a fast and flexible linear power flow (LPF) solution could be introduced particularly necessary for the robust and fast control of DPS, especially when the system consists of star and delta connections ZIP load (a constant impedance, Z, load, a constant current, I, load and a constant power, P, load) and the high penetration of distributed solar and wind power generators.Design/methodology/approachBased on the features of DPS and considering the approximate balance of three-phase DPS, several approximations corresponding to the three-phase power flow equations have been discussed and analyzed. Then, based on those approximations, two three-phase LPF models have been developed under the polar coordinates. One model has been formulated with the voltage magnitudes [referred to the voltage magniudes based linear power flow method (VMLPF)], and another model has been formulated with the logarithmic transform of voltage magnitudes [referred to the logarithmic transform of voltage based linear power flow method LGLPF)].FindingsThe institute of electrical and electronic engineers (IEEE) 13-bus, 37-bus, 123-bus and an improved 615-bus unbalanced DPSs are used to test the performances of the methods considering star and delta connections ZIP load and PV buses (voltage-controlled buses). The test results validate the effectiveness and accuracy of the proposed two models. Especially when considering the PV buses and delta connection ZIP load, the proposed two models perform much well. Moreover, the results show that VMLPF performs a bit better than LGLPF.Research limitations/implicationsExcept for the transformer with Yg–Yg connection winding can be dealt with directly, the transformers with other connections are not discussed in this proposed paper and need to be further studied.Originality/valueThese proposed two models can deal with ZIP load with star and delta connections as well as multi slack buses and PV buses. The single-phase, two-phase and three-phase hybrid networks can be directly included too. The proposed two models are capable of offering enough accuracy level, and they are therefore suitable for online applications that require a large number of repeated power flow calculations.