Non-iterative Solution Research Articles

Damped Multistep Formulas for Solving Stiff Dynamic Problems

A novel series of damped multistep formulas of matrix coefficients are developed to find the solutions of dynamic problems with negligible stiff components or eigenmodes. They are derived from the concept of eigenmode and the development details are presented. A total of six multistep formulas is developed and they have an order of accuracy from 1 to 6 corresponding to the 1-step to 6-step multistep formula. Each formula has damping to suppress or remove the stiff components or eigenmodes that are of no importance or of no interest while the slow eigenmode solutions can be still accurately calculated. The 1-step and 2-step formulas of the series are L-stable. Besides, each formula can have a non-iterative solution procedure and hence it is of high computational efficiency in contrast to the corresponding conventional backward differentiation method. This series can give a better quality of numerical solutions for dynamic problems with negligible stiff components or eigenmodes when compared to the methods with no damping. Numerical tests reveal that this series performs well like the backward differentiation method and it can save many efforts in computing if a non-iterative solution procedure is used when compared to the backward differentiation method.

Performance of Simplified Damage-Based Concrete Models in Seismic Applications

Significant progress in the finite-element (FE) modeling at the member-level of reinforced-concrete (RC) structures under seismic excitation has been achieved in the past decades; however, reliable and accurate analysis models for full-scale 3D system-level RC structures validated with experimental data are scarce. As the development of a complete nonlinear model is expensive and time consuming, simpler models, typically elastic or lumped-plastic in nature, are employed in practice with additional provisions prescribed to account for nonlinear behavior. Depending on the assumptions made by the analyst, there may be substantial uncertainties related to the response of a complete structure. Capturing global failure modes is challenging, and the assessment of strength and ductility capacities may be inaccurate, resulting in potentially unsafe designs. The objective of this research is to assess the performance of simplified damage-based concrete biaxial models in analyzing and capturing the structural behavior of full-scale RC systems. Damage-based models for concrete require minor input from the analyst, facilitating their use in a design setting, while their explicit, non-conditional convergence formulations allow for non-iterative solutions. This results in damage-based models featuring efficient computational analysis while accounting for complex phenomena such as the capacity to account for stiffness recovery in reversal loading (crack closing) and permanent strains in the concrete. A comparison between analytical and experimental data at both the element- and system-levels is conducted, and a viable damage-based model is proposed for a full-scale structure analysis. The results of the study show that damage-based models are a viable alternative to developing efficient analysis models for elements and whole structures.

Pulse pile-up correction by auto-regression on linear operations (ARLO) method: A comparison with integration-based algorithms

Radiation detection at high count rate suffers from pulse pile-up, where the counting data and energy information of the system are affected by the overlapping of the system output pulses. There exist various pile-up correction strategies to recover the true information of the pulses, among which pulse-tail extrapolation is a well-known method focused on in this study.Present work aims to use a mono-exponential model for extrapolating the pileup-distorted trailing edge of a pulse, to provide a reference line for calculating the true amplitude of its subsequent overlapping pulse. To this goal, the auto-regression on linear operations (ARLO) method is examined and compared with two integration-based methods (the Foss and the Matheson methods), as well as the non-linear least squares (NLS) method.Despite a higher sensitivity to noise, the ARLO method was able to provide a simple, non-iterative solution with a performance over 400 times faster than the NLS algorithm, according to the analysis of a high count rate set of experimental pulses from a NaI(Tl) detection system. Foss and Matheson methods also provided solutions reasonably faster than NLS (but not surpassing ARLO), performing exactly the same as each other with results very close to NLS, benefiting from their non-iterative nature.

Non-Iterative Solution for Coordinated Optimal Dispatch via Equivalent Projection—Part I: Theory

Coordinated optimal dispatch is of utmost importance for the efficient and secure operation of hierarchically structured power systems. Conventional coordinated optimization methods, such as the Lagrangian relaxation and Benders decomposition, require iterative information exchange among subsystems. Iterative coordination methods have drawbacks including slow convergence, risk of oscillation and divergence, and incapability of multi-level optimization problems. To this end, this paper aims at the non-iterative coordinated optimization method for hierarchical power systems. The theory of the equivalent projection (EP) is proposed, which makes external equivalence of the optimal dispatch model of the subsystem. Based on the EP theory, a coordinated optimization framework is developed, where each subsystem submits the EP model as a substitute for its original model to participate in the cross-system coordination. The proposed coordination framework is proven to guarantee the same optimality as the joint optimization, with additional benefits of avoiding iterative information exchange, protecting privacy, compatibility with practical dispatch scheme, and capability of multi-level problems.

Non-Iterative Solution for Coordinated Optimal Dispatch via Equivalent Projection—Part II: Method and Applications

This two-part paper develops a non-iterative coordinated optimal dispatch framework, i.e., free of iterative information exchange, via the innovation of the equivalent projection (EP) theory. The EP eliminates internal variables from technical and economic operation constraints of the subsystem and obtains an equivalent model with reduced scale, which is the key to the non-iterative coordinated optimization. In Part II of this paper, a novel projection algorithm with the explicit error guarantee measured by the Hausdorff distance is proposed, which characterizes the EP model by the convex hull of its vertices. This algorithm is proven to yield a conservative approximation within the prespecified error tolerance and can obtain the exact EP model if the error tolerance is set to zero, which provides flexibility to balance the computation accuracy and effort. Applications of the EP-based coordinated dispatch are demonstrated based on the multi-area coordination and transmission-distribution coordination. Case studies with a wide range of system scales verify the superiority of the proposed projection algorithm in terms of computational efficiency and scalability, and validate the effectiveness of the EP-based coordinated dispatch in comparison with the joint optimization.

Suboptimal consensus protocol design for a class of multiagent systems

This article presents a new technique for suboptimal consensus protocol design for a class of multiagent systems. The proposed technique is based upon the extension of newly developed sufficient conditions for suboptimal linear–quadratic optimal control design, which are derived in this paper by an explication of a noniterative solution technique of the infinite-horizon linear quadratic regulation problem in Krotov framework. For suboptimal consensus protocol design, the structural requirements on the overall feedback gain matrix, which are inherently imposed by agents dynamics and their interaction topology, are recast on a specific matrix introduced in a suitably formulated convex optimization problem. As a result, preassigning the identical feedback gain matrices to a network of homogeneous agents, which act on the relative state variables with respect to their neighbors is not required. The suboptimality of the computed control laws is quantified by implicitly deriving an upper bound on the cost in terms of the solution of a convex optimization problem and initial conditions of the agents instead of specifying it a priori. Numerical examples are provided to demonstrate the implementation of proposed approaches and their comparison with existing methods in the literature.

Modified Local Linear Estimators in Partially Linear Additive Models with Right-Censored Data Based on Different Censorship Solution Techniques.

This paper introduces a modified local linear estimator (LLR) for partially linear additive models (PLAM) when the response variable is subject to random right-censoring. In the case of modeling right-censored data, PLAM offers a more flexible and realistic approach to the estimation procedure by involving multiple parametric and nonparametric components. This differs from the widely used partially linear models that feature a univariate nonparametric function. The LLR method is employed to estimate unknown smooth functions using a modified backfitting algorithm, delivering a non-iterative solution for the right-censored PLAM. To address the censorship issue, three approaches are employed: synthetic data transformation (ST), Kaplan-Meier weights (KMW), and the kNN imputation technique (kNNI). Asymptotic properties of the modified backfitting estimators are detailed for both ST and KMW solutions. The advantages and disadvantages of these methods are discussed both theoretically and practically. Comprehensive simulation studies and real-world data examples are conducted to assess the performance of the introduced estimators. The results indicate that LLR performs well with both KMW and kNNI in the majority of scenarios, along with a real data example.

A non-iterative solution for frost growth on flat surfaces

An algebraic, first-principles solution for frost growth on horizontal flat surfaces is derived. To avoid dependence on the frost surface temperature, the proposed solution uses a generic, power-law frost density expression. This yields a new class of non-iterative, fully-algebraic solutions to the problem of frost growth and densification on flat surfaces that are based explicitly on time and heat transfer characteristics. Closure of the derived solution is reached via semi-empirical frost property expressions. With three frost density expressions selected from literature, the predictive accuracy of the proposed frost thickness solution for each density expression is compared to flat plate and parallel plate frost thickness databases. The proposed solution is shown to accurately predict frost thickness, with 73.2% and 81.5% of the predictions falling within ±20% proportional error bands for the flat and parallel plate geometries respectively. Moreover, the proposed solution is shown to be comparably accurate to other predictive methods. The proposed approach is particularly useful in applications that require a non-iterative implementation, or those interested in decreasing computational effort in frost predictions.

Short-Arc Horizon-Based Optical Navigation by Total Least-Squares Estimation

Horizon-based optical navigation (OPNAV) is an attractive solution for deep space exploration missions, with strong autonomy and high accuracy. In some scenarios, especially those with large variations in spacecraft distance from celestial bodies, the visible horizon arc could be very short. In this case, the traditional Christian–Robinson algorithm with least-squares (LS) estimation is inappropriate and would introduce a large mean residual that can be even larger than the standard deviation (STD). To solve this problem, a simplified measurement covariance model was proposed by analyzing the propagation of measurement errors. Then, an unbiased solution with the element-wise total least-squares (EW-TLS) algorithm was developed in which the measurement equation and the covariance of each measurement are fully considered. To further simplify this problem, an approximate generalized total least-squares algorithm (AG-TLS) was then proposed, which achieves a non-iterative solution by using approximate measurement covariances. The covariance analysis and numerical simulations show that the proposed algorithms have impressive advantages in the short-arc horizon scenario, for the mean residuals are always close to zero. Compared with the EW-TLS algorithm, the AG-TLS algorithm trades a negligible accuracy loss for a huge reduction in execution time and achieves a computing speed comparable to the traditional algorithm. Furthermore, a simulated navigation scenario reveals that a short-arc horizon can provide reliable position estimates for planetary exploration missions.

Gerchberg-Saxton Based FIR Filter for Electronic Dispersion Compensation in IM/DD Transmission Part I: Theory and Simulation

Intensity-modulation and direct-detection (IM/DD) transmission over short-reach optical fiber links, require electronic dispersion compensation (EDC) at the transmitter and/or electronic equalization at the receiver. Recently, the iterative Gerchberg-Saxton (GS) algorithm was demonstrated for EDC in IM/DD systems, through treating the amplitude at the transmitter and the phase prior-to the direct detection receiver as a degree of freedom. In Part I of this work, three GS approaches using finite impulse response (FIR) filters for EDC in IM/DD systems are demonstrated. The first two are closely related and rely on a cascaded FIR structure, while the third offers a novel non-iterative EDC solution using a single GS optimized static FIR filter. This is achieved through decoupling pattern dependent aspects of transmission from the GS iterations by targeting a single impulse at the DD receiver. With every successive iteration an impulse response for the GS filter emerges and sets the FIR tap weights. It is also demonstrated that closed-form analytical expressions for the GS filter impulse response can be obtained through small-signal frequency-domain analysis. The FIR filter is simulated using 8-bit finite-precision arithmetic. An adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> -spaced post feed-forward equalizer (FFE) is utilized for mitigating residual chromatic dispersion. It is shown, that a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T/2$</tex-math></inline-formula> -spaced pre-EDC FIR filter with 417 taps can support 56 Gb/s non-return-to-zero (NRZ) on-off keying (OOK) transmission over 80 km of single mode fiber (SMF) with a chirp-free Mach-Zehnder modulator (MZM). Part II, presents experimental demonstration of the non-iterative GS FIR filter proposed and simulated in this article.

A Non-iterative Optimal Power Flow Calculation Method in Power System

The optimal power flow is very important in the study of power system, and it is of great significance for the economic operation of the power system to solve the active power output of the generator through the optimal power flow. In order to solve the problem that the traditional method is sensitive to the initial state and the large iteration times, this paper applies the holomorphic embedding method to solve the optimal power flow. By embedding holomorphic variables, the holomorphic embedding forms of constraints and KKT conditions are obtained. The power series coefficients of node voltage and generator active power output are calculated by non-iterative solution. Finally, the active power output of the generator is obtained by the method proposed in this paper, and then the lowest power generation cost of the system is calculated. Simulation results on IEEE study Case 3, Case 4, Case 30 and Case 39 verify the feasibility and accuracy of the proposed method.

Quadratic Regression Model-Based Indirect Model Predictive Control of AC Drives

Model predictive control is a promising technique for electric drives as it enables optimization for multiple parameters and offers reliable operation with nonlinear systems. In this article, a novel approach is presented that aims to harness the advantages of both finite and continuous set model predictive methods in converter-fed ac drive control. The proposed method requires the calculation of only seven predicted states. These states are then assigned cost function values. Using a quadratic regression model, the cost function is mapped to the entire modulation region. After solving a constrained optimization problem on this cost function mapping, the optimal voltage vector is obtained, which is then applied via pulsewidth modulation. The presented method can also be applied to multilevel converter structures without the need to calculate predictions for additional voltage vectors. Therefore, the proposed method does not increase in complexity with the utilized converter topology. Furthermore, the method offers a fixed switching frequency operation and an exact noniterative solution to the optimization problem due to the formulation of the regression model. As a case study, simulation and experimental results verify the operation of the predictive torque control for permanent magnet synchronous machines with the proposed method.

Rapid stability analysis of variable pitch and helix end mills using a non-iterative multi-frequency solution

Variable pitch and helix end mills disturb the regeneration mechanism that causes chatter vibrations, and as such, they enable stable, high-performance, and high material removal rate milling processes. The regeneration mechanism is altered by the non-uniform tool geometry that results in multiple or distributed delays between vibrations imprinted on the machined surface. The design procedure for these cutters needs characterization of the stability diagrams to decide the non-uniform geometry that improves the absolute minimum stable depth of cut as well as the changes in the size and location of stability pockets. This paper presents a unified method to rapidly analyze the stability of variable helix and pitch cutters with multiple or distributed delays using a non-iterative multi-frequency domain approach that uses the Nyquist criterion to check stability at every spindle speed and depth of cut tuple. Predictions are benchmarked with the established and widely used semi-discretization method and verified with previously published experimental data, which are further validated by our own experiments. The proposed method is as accurate as of the established one while offering computational savings of up to 94%. Since explorations of alternate and better designs were potentially precluded by the computational inefficiency of previous methods, and since the method proposed herein is fast and accurate, it can help to accelerate the design of improved variable helix and pitch end mills for their use in industrial settings.

Continuity corrected score confidence interval for the difference in proportions in paired data

For paired binary data, the hybrid method and the score method are often recommended for use to calculate the confidence interval for risk difference. These asymptotic intervals do not control the coverage probability. We propose to develop a new score interval with continuity correction to further improve the performance of the existing intervals. The traditional correction value may be too large which leads to a wide interval. For that reason, we propose three different correction values to identify the optimal correction interval with balanced coverage probability and interval width. From simulation studies, we find that a small correction value for the score interval has good performance. In addition, we derive the non-iterative solutions for the developed continuity correction score intervals.

Methods for the Accurate Real-Time Simulation of High-Frequency Power Converters

This article presents general modeling approaches to achieve an accurate real-time simulation (RTS) of high switching frequency converters.The proposed methods are based on the direct mapped method (DMM) and make use of decoupling techniques when appropriate. The DMM links state variables to diode statuses and provides an exact and noniterative solution to network equations. An electric vehicle battery charger test case comprised of a full-bridge rectifier, an interleaved boost, and a three-phase <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> is used to demonstrate the high accuracy achieved by the proposed methods compared to a conventional approach. Field-programmable gate array (FPGA) implementations are proposed and shown to achieve from 75- to 175-ns RTS time steps for this test case circuit, allowing its accurate simulation while switched at 200 kHz. To further validate the effectiveness of the FPGA-based simulator, a resonant boost converter is also implemented and simulated in real time.

An Improved Noniterative Parameter-Free Fault Location Method on Untransposed Transmission Lines Using Multi-Section Models

This paper proposes an improved noniterative fault location method on untransposed transmission lines without utilizing line parameters. Two-end three phase voltage and current phasor measurements before and during the fault are typically required. First, the parameter-free fault location problem is formulated through multi-section transmission line models, and the necessary condition of noniterative solutions is carefully investigated to determine the maximum possible section number of the multi-section line model. Afterwards, with the determined section number, the analytical solution of the fault location is derived with full utilization of the inherent characteristics of the line parameter matrices. Instead of solving all the parameters, two key variables inside the parameter matrices are extracted and the fault location is obtained by analytically solving a polynomial equation. The method provides a closed-form analytical solution, and therefore avoids convergence issues of iterative algorithms. In addition, line asymmetry of untransposed transmission lines are fully considered to minimize fault location errors. Extensive numerical experiments show that the proposed method has improved fault location accuracy compared to the existing method, with different fault types, locations and impedances.

Phase-Noise Compensation for OFDM Systems Exploiting Coherence Bandwidth: Modeling, Algorithms, and Analysis

Phase-noise (PN) estimation and compensation are crucial in millimeter-wave (mmWave) communication systems to achieve high reliability. The PN estimation, however, suffers from high computational complexity due to its fundamental characteristics, such as spectral spreading and fast-varying fluctuations. In this paper, we propose a new framework for low-complexity PN compensation in orthogonal frequency-division multiplexing systems. The proposed framework also includes a pilot allocation strategy to minimize its overhead. The key ideas are to exploit the coherence bandwidth of mmWave systems and to approximate the actual PN spectrum with its dominant components, resulting in a non-iterative solution by using linear minimum mean squared-error estimation. The proposed method obtains a reduction of more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.5 \times $ </tex-math></inline-formula> in total complexity, as compared to the existing methods. Furthermore, we derive closed-form expressions for normalized mean squared-errors (NMSEs) as a function of critical system parameters, which help in understanding the NMSE behavior in low and high signal-to-noise ratio regimes. Lastly, we study a trade-off between performance and pilot-overhead to provide insight into an appropriate approximation of the PN spectrum.

Representation learning using deep random vector functional link networks for clustering

Random Vector Functional Link (RVFL) Networks have received a lot of attention due to the fast training speed as the non-iterative solution characteristic. Currently, the main research direction of RVFLs has supervised learning, including semi-supervised and multi-label. There are hardly any unsupervised research results for RVFLs. In this paper, we propose the unsupervised RVFL (usRVFL), and the unsupervised framework is generic that can be used with other RVFL variants, thus we extend it to an ensemble deep variant, unsupervised deep RVFL (usdRVFL). The unsupervised method is based on the manifold regularization while the deep variant is related to the consensus clustering method, which can increase the capability and diversity of RVFLs. Our unsupervised approaches also benefit from fast training speed, even the deep variant offers a very competitive computation efficiency. Empirical experiments on several benchmark datasets demonstrated the effectiveness of the proposed algorithms.

Application to Differential Transform Method for MHD Fluid Flow and Heat Transfer

Present study reveals the flow of a classical non-Newtonian fluid based on the Williamson model through a vertical flat plate. The free convective flow is generated because of the effect of buoyancy relating to the temperature. In addition to that, the influence of thermal radiation and heat source/sink in conjunction with the dissipative heat enhances the efficiency of transport phenomenon within the bounding surface. Well-proposed similarity transformation is used to transform the governing equation into ordinary. However, due to the dissipation, the nonlinear coupled problems are complex. For the solution, a semi-analytical approach such as differential transformation method (DTM) in association with the Padé approximant method is used instead of traditional numerical technique. Pade-approximant is useful to get a non-iterative solution without imposing the missing boundary conditions. It is a simple and effective way to determine the solutions of complex nonlinear problems with assumed boundary conditions at infinity. The physical significance of all the contributing parameters distinguished the flow properties are achieved and accessible graphically. Moreover, the validation of the present methodology with the traditional numerical technique is obtained, showing an excellent correlation in particular cases.

A Non-Iteration Solution for Solving the Backward-in-Time Two-Dimensional Burgers’ equation with a Large Reynolds Number

This article proposes a noniteration solution based on the Lie-group shooting method (LGSM) to solve the backward-in-time two-dimensional Burgers’ equation with a large Reynolds number. The backward problem is famous for seriously ill-posed cases because the solution is generally unstable and highly dependent on the input data. Small perturbations in the input data, such as random errors inherent to the measurements in the analysis, can cause large oscillations in the solution. To handle a large Reynolds number under long time spans, it is very difficult to integrate towards the time direction. To avoid time integration and numerical iteration, the noniteration vector solution based on a two-point equation of the LGSM, including the initial and final conditions and boundary conditions (BCs) at the initial and terminal times, can be constructed. When the vector solution can be obtained from the ratios of the wave fronts on the BCs at the initial and terminal times, this solver can avoid the numerical iteration and numerical divergence of the conventional LGSM. Two benchmark examples in one and two variables are examined to illustrate the performance of the proposed method. The numerical results of this research are very consistent with the exact solutions when considering disturbances from noisy data. Even when the Reynolds number reaches 10E12, from the noisy final and boundary data, the noniteration solution can efficiently address the nonlinear Burgers’ problem with or without disturbances. This method does not use any transformation techniques, iterative processes, or regularization processes to avoid numerical instability. Hence, a noniterative solution is more stable and accurate for the unsteady nonlinear Burgers’ equation than currently used methods.