Nonlinear Iterative Method Research Articles

The impact of innovation on intra-city economic disparity: a technological complexity perspective

ABSTRACT As innovation progresses, the overall complexity of technological inventions also grows, impacting the spatial effects of innovation. This study, utilizing data from 281 Chinese cities from 2005 to 2020 and employing panel threshold regression, re-evaluates the impact of innovation on regional disparities from the perspective of technological complexity. Initially, the paper introduces a nonlinear iteration method to generate two metrics: innovation complexity for assessing regional innovation and technological complexity for assessing patent quality. Subsequently, the study incorporates technological complexity into the theoretical framework of spillover and siphoning effects, exploring its impact on intra-city economic disparity. The results reveal: (1) Overall, innovation in Chinese cities contributes to alleviating intra-city economic disparity. However, this effect is nonlinear, gradually diminishing as innovation increases. (2) The study empirically supports the statement innovation in high-complexity technologies plays a smaller role in reducing regional disparities than innovation in low-complexity technologies. (3) We also examine how geographic factors moderate the effects of innovation of varying complexities on economic disparity, finding that increasing geographic barriers can result in opposite moderating effects on high-complexity and low-complexity innovation. Our research implies that the ongoing evolution of innovation towards domains with higher technological complexity potentially threatens balanced regional development.

Experimental study on flexural behavior and bending capacity prediction of Q550E steel beams within corroded shear span

An experimental study is carried out to investigate the degradation behavior of Q550E HPS steel beams with corroded shear span. At first, tensile tests of 15 pieces of steel are undertaken to obtain the degradation law of mechanical property parameters. Four steel beams with different corrosion damage levels in shear span are designed by electrochemical accelerated corrosion. The flexural loading tests of corroded steel beams are conducted, and the mechanical response of local corrosion to steel beams behavior is discussed. The necessity of lateral bracing is discussed theoretically. Considering the constitutive model affected by corrosion and the role of stiffeners, a predictive model of bending bearing capacity is proposed. The results show that the increasing corrosion damage will cause the failure position to move from mid-span to shear span, and the failure mode will shift from mid-span compressive flange buckling to bending-shear buckling, and finally appear web buckling. Corrosion damage level higher than 10% will lead to insufficient strain development. The proposed model can predict the flexural capacity and deflection well. Compared with the test results, the bearing capacity and deflection of corroded HPS beams are predicted by the nonlinear iterative method with high accuracy.

Application of improved Picard iteration method to simulate unsaturated flow and deformation in deformable porous media

In this paper, we investigate the effectiveness of the cascadic multigrid method applied to improved Picard iteration method for nonlinear problems arising in deforming variably saturated porous media. The finite element method with 6-node triangular elements is applied to discretize the space and obtain nonlinear algebraic equations. Then the nonlinear iterative method is used for iterative solution. Since the classical nonlinear Picard iteration method (PI) can be slow to converge, two improved Picard iteration methods are proposed. One is the improved Picard method with iterations k on the coarse grid and number of multiple grids m (PI-MG(m, k)), and the other is the improved Picard method based on the cascadic multigrid method without parameter k (PI-NMG(m)). Three numerical examples are given to verify the effectiveness of the improved method. Results indicate that the convergence rate of PI is the slowest (10–25 nonlinear iterations per time step), followed by PI-MG(m, k) (3–5 nonlinear iterations), and PI-NMG(m) is the fastest (stable 2 nonlinear iterations). The computational efficiency of PI-NMG(m) is improved by about 90% relative to PI and by about 70% relative to AR-PI. This method can be applied to large-scale numerical calculation of seepage and deformation in unsaturated deforming porous media.

Forest Aboveground Biomass Estimation in Subtropical Mountain Areas Based on Improved Water Cloud Model and PolSAR Decomposition Using L-Band PolSAR Data

Forest aboveground biomass (AGB) retrieval using synthetic aperture radar (SAR) backscatter has received extensive attention. The water cloud model (WCM), because of its simplicity and physical significance, has been one of the most commonly used models for estimating forest AGB using SAR backscatter. Nevertheless, forest AGB estimation using the WCM is usually based on simplified assumptions and empirical fitting, leading to results that tend to overestimate or underestimate. Moreover, the physical connection between the model and the polarimetric synthetic aperture radar (PolSAR) is not established, which leads to the limitation of the inversion scale. In this paper, based on the fully polarimetric SAR data from the Advanced Land Observing Satellite-2 (ALOS-2) Phased Array-type L-band Synthetic Aperture Radar (PALSAR-2), the relative contributions of the three major scattering mechanisms were first analyzed in a hilly area of southern China. On this basis, the traditional WCM was extended by considering the secondary scattering mechanism. Then, to establish the direct relationship between the vegetation scattering mechanism and forest AGB, a new relationship equation between the PolSAR decomposition model and the improved water cloud model (I-WCM) was constructed without the help of external data. Finally, a nonlinear iterative method was used to estimate the forest AGB. The results show that volume scattering is the dominant mechanism, accounting for more than 60%. Double-bounce scattering accounts for the smallest fraction, but still about 10%, which means that the contribution of the double-bounce scattering component is not negligible in forested areas because of the strong penetration capability of the long-wave SAR. The modified method provides a correlation coefficient R2 of 0.665 and a root mean square error (RMSE) of 21.902, which is an improvement of 36.42% compared to the traditional fitting method. Moreover, it enables the extraction of forest parameters at the pix scale using PolSAR data without the need for low-resolution external data and is thus helpful for high-resolution mapping of forest AGB.

A Partitioned Rigid-Element and Interface-Element Method for Rock-Slope-Stability Analysis

The stability analysis of rock slopes has been a prominent topic in the field of rock mechanics, primarily due to the widespread occurrence of discontinuous structural planes in rock masses. Based on this complex characteristic of rock slopes, this paper proposes a novel numerical method, the Partitioned-Rigid-Element and Interface-Element (PRE-IE) method. In the PRE-IE method, the structure is modeled as several rigid bodies and discontinuous structural planes, which are, respectively, divided into partitioned rigid elements and interface elements. Taking the contact force of node pairs and the displacement of the rigid body centroid as mixed variables, according to the principle of minimum potential energy, the governing equations of PRE-IE can be established using the Lagrange multiplier method and then solved using the nonlinear contact iterative method and the incremental method. A classic case study demonstrates that using the failure of all contact node pairs as the criterion for slope failure is appropriate. This criterion is objective and avoids the potential impact of personal bias on safety factor calculations. Two numerical examples of differently shaped slopes are provided to verify the correctness and validity of the PRE-IE method. By comparing the safety factor calculated using the PRE-IE method with those obtained from other different methods, as well as comparing the computational time, it is shown that the PRE-IE method, in combination with the SRM, can accurately and efficiently analyze the stability problems of rock slopes.

A Fast Algorithm of Cross-Correlated Contrast Source Inversion in Homogeneous Background Media

Nonlinear iterative inversion methods are computationally expensive, which leads to limited applications. In this paper, a fast algorithm of the cross-correlated contrast source inversion (CC-CSI) method is proposed. By assuming a homogeneous background medium, the task of solving systems of linear equations, the most time-consuming part of the CC-CSI method, has been efficiently implemented with several FFTs and IFFTs for transverse magnetic (TM), transverse electric (TE), and 3-D inversion, respectively. Theoretical analysis and real experiments demonstrate that the inversion efficiency of CC-CSI has been improved dramatically in comparison to the strategies of LU decomposition and the Biconjugate gradient algorithm. Specifically, the inversion speed of the proposed fast CC-CSI algorithm is at least one order of magnitude higher than using the latter two approaches in 3-D inversion, while the memory requirement of the proposed algorithm is intermediary and acceptable. Furthermore, the proposed fast scheme is also applicable to all the inversion methods which are related to computing of the electric fields directly from the contrast sources in homogeneous background media.

Application of linear iterative methods for the proximity effect correction in electron beam lithography

The Jacobi linear iterative method and weight Jacobi method (WJM) are introduced for solving the large-scale linear problem in the proximity effect correction (PEC) of electron beam lithography. Based on the discussion of PEC physics, a symmetrical and positive defined proximity interaction matrix is constructed to ensure the convergence of the methods. It shows that zeroing the center exposure fraction in the point spread function matrix is equal to the operation of splitting the proximity interaction matrix. Then, the Jacobi method is ready for the PEC calculation. The iterative can be performed in the Fourier domain due to the inherent parallelization of the Jacobi method. The convergent property of the Jacobi method is discussed and then testified by the PEC simulation. Compared with the classical Jacobi method, an improvement of 100% in convergence efficiency can be achieved by introducing the optimized relaxation parameter quasi-ωopt in the WJM. By combining the WJM and Gold nonlinear iteration method, a new method that shows an order of magnitude superior in accuracy to the WJM is proposed. Results indicate the methods introduced here could be used to calculate the PEC problem efficiently.

Algorithm for Retrieval of Temperature in Mesosphere and Lower Thermosphere from O2 A-Band Night Glow

The O2 A-band night glow can be used to retrieve the temperature in the range of 80–120 km in the mesosphere and lower thermosphere (MLT). From the full spectrum of A-band night glow, the band used to retrieve temperature is selected based on the sensitivity of the emission line on temperature, taking into account the compromise relationship between the spectral band and resolution, inversion efficiency, and inversion accuracy. The non-linear iterative inversion method based on optimization theory is adopted for the retrieval of temperature. Meanwhile, considering the stability of inversion, Tikhonov regularization matrix is added as a constraint, and the optimal estimation inversion algorithm is optimized to suppress the influence of measurement noise on results. Through the recovering simulated noisy spectra from an interferometer, the temperature profile with vertical resolution better than 2 km and an average accuracy better than 2 K is obtained by the optimized inversion method in this paper. In addition, the influence of a priori constraints on the inversion accuracy is studied, and a priori accuracy limits the inversion accuracy. When a priori accuracy is controlled within ±5 K, the average temperature inversion accuracy can be optimized to 1.35 K, which is better than the accuracy of OSIRIS on Odin at 90–105 km.

A Single-Pixel High-Precision Imaging Technique Based on a Discrete Zernike Transform for High-Efficiency Image Reconstructions

Single-pixel imaging (SPI) has attracted increasing attention in recent years because of its advantages in imaging systems. However, a low reconstruction quality and a long reconstruction time have hindered the development of SPI. Hence, in this study, we propose a Zernike SPI (ZSPI) technique to reduce the number of illumination patterns and reconstruction time whilst retaining robustness. First, the ZSPI technique was theoretically demonstrated. Phase-shifting Zernike moment projections were used to illuminate the target and an inverse Zernike transform was used to reconstruct the desired image. In order to prove the feasibility, numerical simulations were carried out with different sample ratios (SRs) ranging from 0.1 to 0.3; an acceptable reconstruction appeared at approximately 0.1. This result indicated that ZSPI could obtain satisfactory reconstruction results at low SRs. Further simulation and physical experiments were compared with different reconstruction algorithms, including noniterative, linear iterative, and nonlinear iterative methods under speckle modulation patterns at a sample of 0.1 in terms of different targets. The results revealed that ZSPI had a higher imaging quality and required less imaging time, particularly for low-frequency targets. The method presented in this study has advantages for the high-efficiency imaging of low-frequency targets, which can provide a new solution for the SPI method.

An Adaptive Nonlinear Iterative Method for Predicting Seafloor Topography From Altimetry‐Derived Gravity Data

AbstractThe ocean covers 71% of the Earth's surface. At present, only about 20% of the seafloor topography (ST) has been directly measured by ships, and most areas are predicted from satellite altimetry‐derived gravity products. In this study, an adaptive nonlinear iterative (ANI) method is proposed to address two major problems in gravity ST inversion: linear approximation and empirical seafloor density contrast (SDC). In ANI, the SDC is adaptively estimated as an output, while higher‐order Parker expansion and modified Bott's iteration are combined to recover nonlinear topography. We apply our new method using the DTU21GRA altimetric gravity model and single‐beam bathymetry to predict the ST in a part of the South China Sea. Results reveal that the average SDC in the study area is 1.24 g/cm3, which compares well to CRUST1.0. The root‐mean‐square (RMS) error between the nonlinear model and single‐beam checkpoints is 102.1 m, which is improved by 34.5%, 29.2%, and 18.3% compared with the non‐gravity model, topo_24.1, and linear model, respectively. The RMS error between the nonlinear model and multibeam bathymetry is 91.0 m, which is better than the linear model. Analysis of two‐dimensional profiles shows that the nonlinear model reveals more terrain details than the linear model.

Finite Element and Neural Network Models to Forecast Gas Well Inflow Performance of Shale Reservoirs

Shale gas reservoirs are one of the most rapidly growing forms of natural gas worldwide. Gas production from such reservoirs is possible by using extensive and deep well fracturing to contact bulky fractions of the shale formation. In addition, the main mechanisms of the shale gas production process are the gas desorption that takes place by diffusion of gas in the shale matrix and by Darcy’s type through the fractures. This study presents a finite element model to simulate the gas flow including desorption and diffusion in shale gas reservoirs. A finite element model is used incorporated with a quadrilateral element mesh for gas pressure solution. In the presented model, the absorbed gas content is described by Langmuir’s isotherm equation. The non-linear iterative method is incorporated with the finite element technique to solve for gas property changes and pressure distribution. The model is verified against an analytical solution for methane depletion and the results show the robustness of the developed finite element model in this study. Further application of the model on the Barnett Shale field is performed. The results of this study show that the gas desorption in Barnett Shale field affects the gas flow close to the wellbore. In addition, an artificial neural network model is designed in this study based on the results of the validated finite element model and a back propagation learning algorithm to predict the well gas rates in shale reservoirs. The data created are divided into 70% for training and 30% for the testing process. The results show that the forecasting of gas rates can be achieved with an R2 of 0.98 and an MSE = 0.028 using gas density, matrix permeability, fracture length, porosity, PL (Langmuir’s pressure), VL (maximum amount of the adsorbed gas (Langmuir’s volume)) and reservoir pressure as inputs.

Iterative learning model predictive control for multivariable nonlinear batch processes based on dynamic fuzzy PLS model

This paper proposes a latent variable nonlinear iterative learning model predictive control method (LV-NILMPC) based on the dynamic fuzzy partial least squares (DFPLS) model to achieve trajectory tracking and process disturbance suppression in multivariable nonlinear batch processes. The dynamic and nonlinear characteristics of the physical system are constructed by integrating the T-S fuzzy model into the regression framework of the dynamic partial least squares (PLS) inner model. The decoupling and dimensionality reduction characteristics of the DFPLS model automatically decompose a multivariable nonlinear system into multiple univariate subsystems operating independently in the latent variable space. Based on the DFPLS model, we design LV-NILMPC controllers corresponding to each latent variable subspace to track the projection of the reference trajectories. Compared with the previous control method, the method proposed in this paper has a faster convergence rate and smaller tracking error. The method is suitable for nonlinear, multivariable and strong coupling batch processes. Finally, the application of two cases shows that the method is effective.

Global trade of South Korea in competitive products and their impact on regional dependence.

The economic growth of a nation under the competition among countries can result from the interaction of the diversity and complexity of product export and import relations on the globe. This research aims to evaluate the competitiveness of South Korea’s trading products and its partner countries’ dependency by implementing a product and partner-based analysis. This research raises questions about the transactional positions of products and trading partners based on the diversification of import-export relations of South Korea. This study utilizes the matrix of products and trading partners from the Korean product export and import data from 1995 to 2015. The research analyzes Korea’s product competitiveness and dependency of trading countries on Korea using the Revealed Comparative Advantage (RCA) and a nonlinear iterative method (NIM). The study finds that the products of several manufacturing industries showed a large production scale. From the global perspective, the trade dependency on Korea was high in Asia and in Africa and South America where the portion of underdeveloped or developing countries is relatively large. This research suggests that Korea may face difficulties of continuing growth if it maintains or intensifies its trade relation pattern under the environment of rapidly changing technology and economy. Therefore, diversification and mutual complementarity could be important for the export of promising products and industrial development policy.

A finite volume scheme preserving the invariant region property for the coupled system of FitzHugh-Nagumo equations on distorted meshes

In this paper, we propose and analyze a finite volume scheme preserving the invariant region property (IRP) for the coupled system of equations of FitzHugh-Nagumo type on distorted meshes. We employ a nonlinear cell-centered finite volume scheme to approximate the flux and implicit Euler scheme to approximate the time derivative. The IRP and existence of solutions are proved for the nonlinear finite volume scheme. We also propose a nonlinear iteration method which adds a specifically designed penalization term to ensure the IRP on each iteration step. Numerical experiments and the comparison with the nine-point finite volume scheme are presented to verify the IRP of our scheme.

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.

SPI-CGAN: Single-pixel imaging based on conditional generative adversarial network

Imaging quality at extremely sampling ratios is a key research topic in the field of single-pixel imaging (SPI). Although conventional methods can be used to reconstruct the object images at low sampling ratios, the reconstructed image is still visually unclear. To solve this problem, an SPI model based on a conditional generative adversarial network (SPI-CGAN) is proposed to achieve an end-to-end reconstruction of the object images and improve the image quality of the reconstruction at extremely low sampling ratios. To improve the stability of the training model, the objective function is composed of multiple loss functions. The validity of the model is verified through simulation data, which do not require a long time to collect. The optimized SPI-CGAN can reconstruct a sharp image edge at extremely low sampling ratios. Compared with a linear iterative method and a nonlinear iterative method, the proposed method performs better in terms of the quantitative indicators used.

Exponential integrator method for solving the nonlinear Helmholtz equation

<abstract><p>In this paper, we study the exponential integrator method (EIM) for solving the nonlinear Helmholtz equation (NLHE). As the wave number or the characteristic coefficient in the nonlinear term is large, the NLHE becomes a highly oscillatory and indefinite nonlinear problem, which makes most of numerical methods lose their expected computational effects. Based on the shooting method, the NLHE is firstly transformed into an initial-value-type problem. Then, the EIM is utilized for solving the deduced problem, by which we not only can capture the oscillation very well, but also avoid to search the nonlinear iteration method and to solve indefinite linear equations at each iteration step. Therefore, the high accuracy simulations with relative large physical parameters in the NLHE become possible and lots of computational costs can be saved. Some numerical examples, including the extension to the nonlinear Helmholtz system, are shown to verify the accuracy and efficiency of the proposed method.</p></abstract>

On stress in abdominal aortic aneurysm: Linear versus non-linear analysis and aneurysm rupture risk.

We present comprehensive biomechanical analyses of abdominal aortic aneurysms (AAA) for 43 patients. We compare stress magnitudes and stress distributions within arterial walls of abdominal aortic aneurysms (AAA) obtained using two simulation and modelling methods: (a) Fully automated and computationally very efficient linear method embedded in the software platform Biomechanics based Prediction of Aneurysm Rupture Risk (BioPARR), freely available from https://bioparr.mech.uwa.edu.au/; (b) More complex and much more computationally demanding Non-Linear Iterative Stress Analysis (Non-LISA) that uses a non-linear inverse iterative approach and strongly non-linear material model. Both methods predicted localised high stress zones with over 90% of AAA model volume fraction subjected to stress below 20% of the 99th percentile maximum principal stress. However, for the non-linear iterative method, the peak maximum principal stress (and 99th percentile maximum principal stress) was higher and the stress magnitude in the low stress area lower than for the automated linear method embedded in BioPARR. Differences between the stress distributions obtained using the two methods tended to be particularly pronounced in the areas where the AAA curvature was large. Performance of the selected characteristic features of the stress fields (we used 99th percentile maximum principal stress) obtained using BioPARR and Non-LISA in distinguishing between the AAAs that would rupture and remain intact was for practical purposes the same for both methods.

A Convolutional Sparsity Regularization for Solving Inverse Scattering Problems

In this letter, a convolutional sparsity regularization (CSR) is introduced into the framework of nonlinear iterative methods for solving inverse scattering problems (ISPs). The permittivity image of scatterers is sparsely represented in a convolutional form with prelearned dictionary filters. The CSR is then incorporated with the subspace-based optimization method (SOM), termed as (SOM-CSR), to reconstruct the target image as a sparse coding by dictionary filters. The whole optimization function of SOM-CSR is solved using an alternative iteration method. Both synthetic and experimental data are employed to validate the effectiveness of the proposed SOM-CSR method. The results demonstrate that the CSR, as a structural constraint, is beneficial to nonlinear iterative reconstruction methods for solving ISP in contrast to pixel-based inversion.

Verification and Scalability of Mixed-Element USM3D for Benchmark Three-Dimensional Flows

The unstructured-grid mixed-element cell-centered finite-volume flow solver USM3D is enhanced for massively parallel computations. The paper describes modifications to the flow solver and parallelization strategy. The new parallel implementation is verified through comparison of residuals and force coefficients computed on a given grid using varying number of partitions. The accuracy of the parallel USM3D is verified through grid convergence studies and comparison with available reference solutions for two benchmark turbulent flows, namely, a subsonic separated flow around a three-dimensional hemisphere-cylinder configuration and a supersonic flow through a square duct. The strong and weak scalability assessments are conducted using two different nonlinear iteration methods.