Nonlinear Iterative Process Research Articles

Simulating Fuel Assembly Bowing: A Neutron-Diffusion Method Based on Arbitrary Quadrilateral Node and Conformal Mapping Technique

Fuel assembly bowing, widely observed in a pressurized water reactor (PWR), often results in an asymmetrical power distribution. This paper proposes a neutron-diffusion method that integrates the arbitrary quadrilateral node with the conformal mapping technique to characterize the impact of fuel assembly bowing on power distribution. The proposed method involves a nonlinear iteration process to solve the neutron-diffusion equation. The global coarse-mesh finite difference equation is established on the arbitrary quadrilateral nodes, which are redivided in response to fuel assembly bowing. The local two-node nodal expansion method equation is established on the rectangular nodes, which are mapped from the original arbitrary quadrilateral nodes using the conformal mapping technique. The proposed method has improved our self-developed core code, named SPARK, for PWRs. To verify this novel method, two distinct types of fuel assembly bowing are modeled based on the mini core. The reference results for these models were obtained using the Monte Carlo code NECP-MCX. The numerical results suggest a robust agreement between the biases of keff and power distributions and their corresponding reference results.

Delve deep: Seismic revolution in acquisition and model building for exploration

Sparse-node acquisition is the latest approach to improve the earth model through the inclusion of ultra-long offsets and low-frequency generating sources. The new designs of node data collections with simultaneous shooting can be deployed on a regional basis, covering thousands of square miles in a cost-effective manner. In complex geologic settings such as salt environments, salt interpretation has a direct impact on subsalt imaging. However, salt interpretation can be quite time intensive and challenging. Full-waveform inversion (FWI), as a data-driven optimization algorithm with full-wavefield modeling, has become an essential tool for earth model building. However, its use in salt tectonic contexts, especially with streamer data collection, is limited because the frequencies acquired are not sufficiently low and the offsets are not sufficiently long. The recent advancement of the objective function enables the application of an FWI workflow, coupled with sparse-node acquisition in the deepwater settings of the Gulf of Mexico, to refine the salt geometry, correct the background velocity error in subsalt, and uncover a basin's structural framework. The increased frequency content of the FWI-updated fields enables us to extract the FWI-derived reflectivity (FDR), which is an image created by the FWI nonlinear iterative process with the full wavefield. Additionally, the classic extraction of amplitude-versus-angle/amplitude-variation-with-offset parameters employs the elastic Zoeppritz formulation to obtain rock-physics volumes and explain the amplitude on the prestack image gathers, which are typically generated by Kirchhoff or reverse time migration (RTM) depth migration. The next step is to substitute these migrations with FWI and output not only the poststack FDR but use it in a prestack mode to aid amplitude analysis at an early stage of model building.

Low-complexity clustered polynomial nonlinear filter-based electrical dispersion pre-compensation scheme in IM/DD transmission systems.

A polynomial nonlinear filter (PNLF)-based electrical dispersion pre-compensation (pre-EDC) scheme assisted with Gerchberg-Saxton (GS) algorithm is proposed to compensate the chromatic dispersion (CD) for intensity-modulation and direct-detection (IM/DD) optical transmission systems, where PNLF is utilized to fit the nonlinear transfer function of the iterative GS algorithm-based pre-EDC scheme to realize a low-complexity non-iterative CD pre-compensation. The capability of PNLF to fit the nonlinear iterative process enables the PNLF-based pre-EDC scheme to compensate for CD-induced linear distortions and address CD-induced nonlinear distortions, which are typically captured through iterative approaches. Additionally, to further reduce the computational complexity, we also introduce the k-means clustering algorithm to eliminate the weight redundancy and propose a lower-complexity clustered PNLF-based pre-EDC scheme. Simulation results show that PNLF-based and clustered PNLF-based pre-EDC schemes save 76.0% and 97.5% complexity with only 0.3 dB receiver sensitivity penalty at 20% forward error correction (FEC) threshold, compared with GS-based pre-EDC scheme in C-band 56 GBaud 80-km on-off keying (OOK) system. Furthermore, the effectiveness of PNLF-based and clustered PNLF-based pre-EDC schemes is also evaluated through the experimental demonstration. Experimental results show that under C-band 32 GBaud 80-km OOK system, bit error ratio (BER) satisfying 20% FEC threshold is achieved by applying PNLF-based and clustered PNLF-based pre-EDC schemes, which save 78.3% and 94.2% complexity with only 0.4 dB receiver sensitivity penalty compared with GS-based pre-EDC scheme, respectively. The research results indicate that the (clustered) PNLF-based pre-EDC scheme has the great application potential for CD compensation in high-performance and low-cost IM/DD optical transmission systems.

Design Thinking Skills for Senior Managers From Business and Technology Perspectives

Abstract
 Introduction: Design thinking is regarded as a non-linear iterative process that is applied in a bid to understand users, identify problems and develop innovative solutions to problems. The concept of design thinking has attracted interest from professionals across sectors. Although design thinking has been traditionally applied by design professionals the tool has proved effective in managing organizations. Several leading businesses have reported having applied design thinking to achieve organizational success. The strategy is emerging as a critical tool for businesses seeking to advance their competitive strategy.
 Purpose: The paper seeks to create an understanding of the concept of design thinking and how it is applied in business management. Consequently, the paper seeks to analyze the advantages and disadvantages of design thinking in relation to enhancing business performance.
 Methodology: This section outlines the techniques that will be used in collecting information. The study will make use of interviews from business leaders and professionals in the field. Questionnaire is used as a guide for undertaking the interviews. Qualitative and quantitative analysis is be used in analyzing the data obtained.
 Discussion: Design thinking has been an instrumental strategy in promoting business success. Business leaders are benefiting from the application of this strategy in realizing success for their organizations. However, the strategy has not received much appreciation from small organizations and hence suggested as a turnaround concept in business performance.
 Conclusion: The findings successfully answer the question regarding the pros and cons of applying design thinking strategy in business. The study finds that design thinking is a contributing factor to business success and hence a concept that should be applied in facilitating business operations.
 Key words: Design thinking, design-led professional, Technology perspective, Business perspective

Adaptive Timestepping, Linearization, and A Posteriori Error Control for Multiphase Flow of Immiscible Fluids in Porous Media with Wells

Summary This work focuses on the development of adaptive timesteps, stopping criteria, and error control strategies for reservoir simulations with fully implicit (FIM) solvers. Using a rigorous error control framework, an adaptive time selector combined with nonlinear stopping criteria is used to control nonlinear iterations as well as to balance accuracy and robustness for challenging nonlinear simulations. In reservoir simulation, efficiently solving a system of nonlinear equations arising from the FIM method can be computationally burdensome for complex recovery processes. Theoretically, an FIM reservoir simulator has no stability limit on the timestep size. In practice, standard Newton’s method often fails to converge for large timestep sizes and must therefore cut the timestep multiple times to achieve convergence, resulting in a large number of unnecessary iterations. Another cause of nonlinear convergence issues is the presence of wells, which are often presented as singular point/line sources strongly coupled to the reservoir model, posing additional restrictions on the timestep choice. Here, we use a posteriori error estimators to avoid unnecessary nonlinear iterations and timestep cuts when solving immiscible multiphase flow. First, we estimate error components (e.g., spatial, temporal, and nonlinear) and then apply these to balancing criteria, providing us with dynamic and adaptive strategies to control timestep and nonlinear iterations. The error estimators are fully and locally computable, inexpensive to use, and target the various error components, including well singularities. The method provides an adaptive criterion for stopping the nonlinear iteration process whenever the linearization error does not significantly affect the overall error. Simultaneously, timesteps are adapted to maintain a constant size of the temporal discretization error with respect to the total error. Altogether, this avoids using unnecessary linearization iterations, wasteful timestep cuts, and too small timesteps. To demonstrate the effectiveness of these adaptive features, we present results for a suite of cases, covering both standard benchmarks and conceptual problems incorporating highly heterogeneous media with multiple wells. The proposed timestep selector cooperates with the new stopping criteria to improve nonlinear solver performance and increases robustness for cases with high nonlinearity. Perhaps most important, the adaptive features ensure balanced temporal and spatial errors while maintaining sufficiently small nonlinear errors, which ensures solution accuracy by accurately reproducing saturation fronts, production plateau, and breakthrough times.

Open-circuit field prediction of IPM machine using multiple flux source network model

Accurate modeling of motor magnetic fields facilitates all aspects of motor analysis, design, and optimization. Existing methods are difficult to balance the speed and accuracy of modeling, among which the widely popular finite element method is relatively time-consuming and the accuracy of magnetic circuit modeling is difficult to guarantee. In this regard, this paper presents a magnetic equivalent circuit model based on the multiple flux source network for interior permanent magnet (IPM) machines. The model considers the magnetic saturation effect through a non-linear iterative process. The accuracy improvement of the proposed model has been verified by comparison with the traditional single-flux-source model. Furthermore, the proposed model greatly saves the calculation time while bringing fairly good accuracy compared to the finite-element method, which is beneficial for the design optimization of the IPM machines.

Rayleigh Wave Dispersion Curve Inversion with the Artificial Bee Colony Algorithm

Rayleigh wave dispersion curve inversion is a non-linear iterative optimization process with multi-parameter and multi-extrema. It is difficult to carry out inversion and reconstruction of stratigraphic parameters quickly and accurately with a single linear or non-linear inversion for the data processing of Rayleigh waves with complex seismic geological conditions. We proposed a new method that combines artificial bee colony algorithm (ABC) and damped least squares algorithm (DLS) to invert Rayleigh wave dispersion curve. First, food sources are initialized in a large scale of the model based on the prior geological information. Then, after three kinds of bee operators (employed bees, onlooker bees and scout bees) transform each other and perform search optimization with several iterations, the targets are converged near the optimal solution to obtain an initial S-wave velocity model. Finally, the final S-wave velocity model is obtained by local optimization of DLS inversion with fast convergence and strong stability. The correctness of the method has been verified by one high-velocity interlayer model, and it was further applied to a real Rayleigh wave dataset. The results show that our method not only absorbs the advantages of ABC global search optimization and strong adaptability, but also makes full use of the advantages of DLS inversion, such as high accuracy and fast convergence speed. The inversion strategy can effectively suppress the inversion falling into local extrema, get rid of the dependence on an initial model, enhance the inversion stability, further improve the convergence speed and inversion accuracy, while has good anti-noise ability.

Elementary teachers’ cognitive processes and metacognitive strategies during self-directed online learning

ABSTRACT This study involves an in-depth examination of Canadian elementary teachers’ cognitive processes and metacognitive strategies they used during a self-directed online learning experience. The virtual revisit think aloud, a methodology that combines a retrospective procedure with screen recording technology, was used to capture verbalisations from 13 elementary teachers as they used an online database. Resulting think aloud protocols and post-task interviews were analysed using qualitative methods. An inductive approach to analysis led to six themes related to the types of cognitive processes and metacognitive strategies teachers use during self-directed online learning: connecting to practice, tweaking and adapting, narrowing the focus, skimming through, reading for depth, and source credibility. The teachers in this study demonstrated a non-linear iterative process in which they continuously planned, monitored, and evaluated their learning during the self-directed online learning experience. Implications for teacher learning and research are discussed.

Towards Highly Efficient State Estimation With Nonlinear Measurements in Distribution Systems

This letter proposes a novel and highly efficient distribution system state estimation (DSSE) algorithm with nonlinear measurements from supervisory control and data acquisition (SCADA) systems. Conventional DSSE, i.e., a weighted least square (WLS)-based method, requires multiple Monte Carlo simulations for overall accuracy evaluation and has high calculation cost due to the nonlinear iterative process. The proposed method uses the Taylor series of voltages for constructing a linear DSSE model in the interval form and then solve this model by interval arithmetic. Compared with the nonlinear WLS-based method, the proposed method obtains accurate and robust estimates via a single random sampling of measurements and is computationally efficient. The comparative analysis of the IEEE 34-bus distribution system points to improved estimation results relative to the WLS-based method.

Numerical Resolution of a Three Temperature Plasma Model

This paper is devoted to the numerical approximation of a three temperature plasma model: one for the ions, one for the electrons and one for the radiation (photons). A reformulation of the model is proposed that allows to build a convex combination-based scheme that unconditionally satisfies a maximum principle, at each sub-iteration of the non-linear iterative process. This yields a very robust scheme that can handle stiff source terms. In addition, the methodology is extended to include the contribution of a radiative flux (Rosseland diffusion approximation) and electronic and ionic conductivities (Spitzer–Harm diffusion approximation). Several numerical results are carried out to demonstrate the interest of the numerical approach.

Optimal contrast analysis with heterogeneous variances and budget concerns.

The omnibus test is commonly applied to evaluate the overall disparity between group means in ANOVA. Alternatively, linear contrasts are more informative in detecting specific pattern of mean differences that cannot be obtained via the omnibus test. This article concerns power and sample size calculations for contrast analysis with heterogeneous variances and budget concerns. Optimal allocation procedures for the Welch-Satterthwaite tests of standardized and unstandardized contrasts are presented to minimize the total sample size with the designated ratios, to meet a desirable power level for the least cost, and to attain the maximum power performance under a fixed cost. Currently available methods rely exclusively on simple allocation formula and direct rounding rule. The proposed allocation strategies combine the computing techniques of nonlinear optimization search and iterative screening process. Numerical assessments of a randomized control trial for the overcoming depression on the Internet are conducted to demonstrate and confirm that the approximate procedures do not guarantee optimal solution. The suggested approaches extend and outperform the existing findings in methodological soundness and overall performance. The corresponding computer algorithms are developed to implement the recommended power and sample size calculations for optimal contrast analysis.

Sliding mode based fractional-order iterative learning control for a nonlinear robot manipulator with bounded disturbance

In this paper a new type of sliding mode based fractional-order iterative learning control (ILC) is proposed for nonlinear systems in the presence of uncertainties. For the first time, a sliding mode controller is combined with fractional-order ILC. This sliding mode based [Formula: see text] and [Formula: see text]-type ILC is applied on a nonlinear robot manipulator. Convergence of the proposed method is investigated when the stability is also proved. In this method, the control signal at any iteration is generated in two parts. The first section comes from the sliding mode controller while the second part is output of the fractional-order ILC. The latter signal is assessed using its previous amount and the sliding mode error signal. The achieved control law is capable of controlling nonlinear iterative processes, perturbed by bounded disturbances with high accuracy. The same frequent disturbance is eliminated by the iterative learning part, while the effect of nonrepetitive uncertainty is improved by the sliding mode part. The sliding mode based [Formula: see text]-type ILC (as an adaptive control law) is proposed to control a single-link arm robot. The controller is then improved to sliding mode based [Formula: see text]-type ILC. The effectiveness of the proposed method is again investigated on a single-link robot manipulator through a simulation approach. It is shown that the controller for [Formula: see text] provides performance by means of faster response together with more accuracy with respect to a conventional ILC.

An efficient optimization method for structures with local non-linearity

During the operation of turbines, one of the common accidents is due to the structure failure of blades. The contact model with strong non-linearity and time variation makes it difficult to be analyzed. In this paper, firstly, the contact model is described by using fractal theory. Secondly, the new method for the optimization of turbine blade is proposed, which is a kind of structure with local nonlinearity and multi degree of freedom. The method reduces the number of degrees of freedom by forming a new super element, which makes the linear part of turbine blade without repeated calculation in the non-linear iteration process. Therefore, it can shorten the calculation time and reduce the demand for computing resources. Finally, an optimization of the turbine blade is carried out, and the maximum equivalent stress reduces by 13.19%, which proves the effectiveness of the new optimization method.

Deflection Theory for Self-Anchored Suspension Bridges under Live Load

AbstractFor self-anchored suspension bridges having the fabrication camber subjected to live loads, a new deflection theory is formulated after an optimized initial state solution is found under dead loads. Its analytical solution for three-span continuous suspension bridges is consistently derived by considering tower effects compared with that derived by the conventional deflection theory for earth-anchored bridges. On the other hand, the unstrained length method (ULM), which keeps all element lengths constant in the nonlinear iteration process, is extended and applied to the nonlinear finite-element analysis of suspension bridges under live loads. Finally, an earth-anchored and self-anchored bridge examples are analytically and numerically solved using the two methods. The numerical results are compared to verify the accuracy and effectiveness of both the proposed deflection theory and the ULM.

Implicit Damping Iterative Algorithm to Solve Elastoplastic Static and Dynamic Equations

This paper presents an implicit damping iterative algorithm to simultaneously solve equilibrium equations, yield function, and plastic flow equations, without requiring an explicit expression of elastoplastic stiffness matrices and local iteration for “return mapping” stresses to the yield surface. In addition, a damping factor is introduced to improve the stiffness matrix conformation in the nonlinear iterative process. The incremental iterative scheme and whole amount iterative scheme are derived to solve the dynamical and static and dynamical elastoplastic problems. To validate the proposed algorithms, computation procedures are designed and the numerical tests are implemented. The computational results verify the correctness and reliability of the proposed implicit iteration algorithms.

Finite‐difference P wave travel time seismic tomography of the crust and uppermost mantle in the Italian region

We present a 3‐D P wave velocity model of the crust and shallowest mantle under the Italian region, that includes a revised Moho depth map, obtained by regional seismic travel time tomography. We invert 191,850 Pn and Pg wave arrival times from 6850 earthquakes that occurred within the region from 1988 to 2007, recorded by 264 permanent seismic stations. We adopt a high‐resolution linear B‐spline model representation, with 0.1° horizontal and 2 km vertical grid spacing, and an accurate finite‐difference forward calculation scheme. Our nonlinear iterative inversion process uses the recent European reference 3‐D crustal model EPcrust as a priori information. Our resulting model shows two arcs of relatively low velocity in the crust running along both the Alps and the Apennines, underlying the collision belts between plates. Beneath the Western Alps we detect the presence of the Ivrea body, denoted by a strong high P wave velocity anomaly. We also map the Moho discontinuity resulting from the inversion, imaged as the relatively sharp transition between crust and mantle, where P wave velocity steps up to values larger than 8 km/s. This simple condition yields an image quite in agreement with previous studies that use explicit representations for the discontinuity. We find a complex lithospheric structure characterized by shallower Moho close by the Tyrrhenian Sea, intermediate depth along the Adriatic coast, and deepest Moho under the two mountain belts.

Mixed Finite Element Method for Static and Dynamic Contact Problems with Friction and Initial Gaps

A novel mixed finite element method is proposed for static and dynamic contact problems with friction and initial gaps. Based on the characteristic of local nonlinearity for the problem, the system of forces acting on the contactor is divided into two parts: external forces and contact forces. The displacement of structure is chosen as the basic variable and the nodal contact force in contact region under local coordinate system is selected as the iteration variable to confine the nonlinear iteration process in the potential contact surface which is more numerically efficient. In this way, the sophisticated contact nonlinearity is revealed by the variety of the contact forces which are determined by the external load and the contact state stick, slip, or separation. Moreover, in the case of multibody contact problem, the flexibility matrix is symmetric and sparse; thus, the iterative procedure becomes easily carried out and much more economical. In the paper, both the finite element formulations and the iteration process are given in detail for static and dynamic contact problems. Four examples are included to demonstrate the accuracy and applicability of the presented method.

Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field

An inner seepage face phenomenon is given and a numerical simulation procedure has been developed. It may appear at the interface of two materials when an unconfined seepage flows from a porous media to a coarser porous media with a higher permeability. Inaccuracy and divergent problems may arise both in a saturated-only and in a variably saturated analysis while an inner seepage face is not simulated with a special procedure. The position of the seepage face is determined during the nonlinear iteration process and the flux of the inner seepage face nodes is transferred to the downstream side nodes. Validity and efficiency of the procedure are illustrated by the simulation of two dimensional steady state seepage examples of heterogeneous zoned dams which is usually used to validate algorithms. An analysis of a three-dimensional earth core rockfill dam is also presented here. The procedure can also be applied to general transient seepage problems.

Implementation of Fictitious Crack Model Using Contact Finite Element Method for the Crack Propagation in Concrete under Cyclic Load

The mixed freedom finite element method proposed for contact problems was extended to simulate the fracture mechanics of concrete using the fictitious crack model. Pairs of contact points were set along the potential developing path of the crack. The displacement of structure was chosen as the basic variable, and the nodal contact force in contact region under local coordinate system was selected as the iteration variable to confine the nonlinear iteration process in the potential contact surface which is more numerically efficient. The contact forces and the opening of the crack were obtained explicitly enabling the softening constitutive relation for the concrete to be introduced conveniently by the fictitious crack model. According to the states of the load and the crack, the constitutive relation of concrete under cyclic load is characterized by six contact states with each contact state denoting its own displacement-stress relation. In this paper, the basic idea of the mixed freedom finite element method as well as the constitutive relation of concrete under cyclic load is presented. A numerical method was proposed to simulate crack propagation process in concrete. The accuracy and capability of the proposed method were verified by a numerical example against experiment data.

Analysis on Error Bounds of Heat Transfer Problems Using the Fast Residual Correction Method

In this article, the concept of improved fast residual correction is proposed to simplify traditional methods for residual correction. As verified by four heat transfer problems, integrating residual correction into nonlinear iterative processes makes it easier and faster to obtain upper and lower approximate solutions in combination with the finite-difference method, and can even define the maximum error bounds of approximate solutions clearly, without more iteration, solutions to nonlinear problems.